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A theoretical study of normal alkane combustion
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A theoretical study of normal alkane combustion
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A THEORETICAL STUDY OF NORMAL ALKANE COMBUSTION by Xiaoqing You A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MECHANICAL ENGINEERING) August 2008 Copyright 2008 Xiaoqing You ii Acknowledgments During my Ph.D. study, I am indebted to many people in many ways. First and foremost, I would like to acknowledge and extend my heartfelt gratitude to my advisor Professor Hai Wang for his guidance, patience, support, and encouragement over the past five years. Prof. Wang has been a great mentor, and impressed me deeply with his enthusiasm and dedication to science. I thank him for providing me many collaboration opportunities with other research groups. I would also like to express my sincere gratitude to my dissertation committee members, Professors Fokion Egolfopoulos, Anna Krylov, Denis Phares, and Paul Ronney, for their invaluable insights and careful reviews on my dissertation work. I have learnt so much from taking their courses and discussing scientific problems with them. I am grateful to Dr. Tim Barckholtz for his guidance and friendship. Tim has been generously sharing me with his knowledge and experience, and has inspired my interests in exploring chemical reaction pathways through quantum chemistry calculations. I would also like to thank Dr. John Farrell for giving me the opportunity to gain skills on developing chemical kinetic models. Thanks should be given to other collaborators as well. I am thankful to Dr. Stephen Klippenstein for his theoretical insights, which enlightened my iii understandings in chemical kinetics. I appreciate Professor C. J. Sung, Dr. Elke Goos, Professor C. K. Law, Dr. Andrew Smallbone, and Wei Liu for their inputs and collaborative altitudes. I wish to thank Adam Holley and Chunsheng Ji for providing their experimental data that are useful to my research work. My group members have made my graduate study so much fun. My previous group members Drs. Ameya Joshi, Zhigang Li, Zhiwei Yang, and Bin Zhao have helped me on the way to do independent research. I would also like to thank my current group members. I am grateful that Dr. Baptiste Sirjean has shared his experience in quantum chemistry calculations with me. I have enjoyed the discussions with David Sheen on model optimization and uncertainty propagation. Thanks to Enoch Dames for his contributions to estimating the transport properties. I thank Aamir Abid, Jeremy Cain, Sonya Collier, Nick Heinz, Dr. Jianrong Qiu, Angela Shibata, Tsutomu Shimizu, and Erik Tolmachoff for sharing ideas and discussions. Last but not least, I would like to express my special thanks to my parents and brothers for their unconditional love, support, and encouragement. My life has been so blessed because of my husband, Fulin Lei, who is always there helping me when I am in need. Not enough words that I can use to express my thanks to him. There will never be enough time or space to thank all of the people who have helped me reach this point in my life. For those I have missed in specific, I thank in general; I hope I have or will contribute something of worth to all of you. iv Table of Contents Acknowledgments ii List of Tables vii List of Figures ix Abstract xvi Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Review of previous studies 4 1.3 Structure of this dissertation 6 Chapter 2. Computational Methodologies 9 2.1 Introduction 9 2.2 Thermodynamic properties 9 2.3 Reaction rate parameters 13 2.3.1 Transition state and RRKM theories 14 2.3.2 Master equation modeling 17 2.3.3 Monte Carlo simulation 18 2.4 Validation of the reaction model 23 2.4.1 Laminar flame speed 24 2.4.2 Nonpremixed counterflow ignition 25 2.4.3 Ignition delay time 25 2.4.4 Turbulent flow reactor 26 2.5.5 Jet-stirred reactor 26 Chapter 3. Reaction Kinetics of CO + HO 2 • → Products: Ab Initio Transition State Theory Study with Master Equation Modeling 28 3.1 Introduction 28 3.2 Computational details 34 3.2.1 Potential energy surface 34 3.2.2 Reaction rate coefficients 37 3.2.3 Hindered internal rotation 38 3.3 Results and discussion 44 3.4 Conclusion 64 v Chapter 4. Reaction Kinetics of •OH + HO 2 • → products 66 4.1 Motivation 66 4.2 Computational details 70 4.2.1 Potential energy surface 70 4.2.2 Reaction rate coefficients 71 4.3 Results and discussion 75 4.3.1 Potential energy surface 75 4.3.2 Reaction rate coefficients 85 4.4 Conclusion 89 Chapter 5. High-Temperature Combustion Reaction Model of H 2 /CO/C 1 -C 4 Compounds 91 5.1 Introduction 91 5.2 Thermodynamic database for C 1 to C 4 species 92 5.2.1 Calculation methods 93 5.2.2 Error and accuracy of G3//B3LYP calculated values 96 5.2.3 Thermodynamic property results 98 5.3 Validation of H 2 /CO/C 1 -C 4 model 105 5.3.1 H 2 and CO 105 5.3.2 C 1 -C 4 n-alkanes 109 5.3.3 C 2 -C 4 alkenes 113 5.3.4 C 2 -C 4 alkynes and 1, 3-butadiene 119 5.4 Summary 121 Chapter 6. Detailed Kinetic Reaction Mechanism for n-Alkane Combustion 122 6.1 Introduction 122 6.2 Detailed reaction mechanism 124 6.2.1 Reaction mechanism for C 1 -C 4 n-alkanes 124 6.2.2 Reaction mechanism for C 5 -C 12 n-alkanes 126 6.2.3 Thermodynamic database for C 5 -C 12 n-alkanes 130 6.2.4 Transport data for C 5 -C 12 n-alkanes 130 6.3 Kinetic modeling 136 6.3.1 Pyrolysis of n-dodecane 136 6.3.2 Laminar flame speeds of higher n-alkanes 141 6.3.3 Ignition delay times of higher n-alkanes 146 6.4 Summary 149 Chapter 7. Simplification and Analysis of n-Alkane Combustion Mechanism 150 7.1 Introduction 150 7.2 Simplified n-dodecane reaction mechanism 151 7.3 Kinetic modeling results and discussions 155 7.3.1 n-dodecane 155 vi 7.3.2 n-decane 163 7.3.3 n-heptane 165 7.4 Summary 172 Chapter 8. Conclusions and Future Work 174 8.1 Conclusions 174 8.2 Future work 176 Bibliography 179 Appendix A. Master Equation Code 206 A.1 Input files for master equation code 206 A.2 Source code for master equation solution 208 Appendix B. The Reaction Mechanism 239 B.1 List of species 239 B.2 Reactions and rate coefficients 244 vii List of Tables Table 3.1 Energies (Hartrees) computed at selected levels of theory. 48 Table 3.2 Energies (kcal/mol) at 0 K relative to CO + HO 2 •. 48 Table 3.3 Literature values of enthalpy of formation (kcal/mol). 49 Table 3.4 Multireference energies 50 Table 3.5 Molecular properties used for computing the rate coefficient of CO + HO 2 • → CO 2 + •OH 58 Table 3.6 Effect of internal rotor treatments on k 1 (cm 3 /mol·s). 60 Table 4.1 Energies (kcal/mol) at 0 K relative to OH• + HO 2 •. 80 Table 4.2 Literature values of enthalpy of formation (kcal/mol). 80 Table 4.3 Electron density ρ and its Laplacian Δ at critical points for intermediates and transition states of •OH + HO 2 • → products. Structures are optimized at BHandHLYP/6-311++G(d,p) level of theory. 84 Table 4.4 Molecular properties for computing the rate coefficient of •OH + HO 2 • → products. 85 Table 5.1 Average absolute deviation of enthalpy (kcal/mol) from experiment for G3 and G3B3 composite methods for several series of compounds (Baboul et al. 1999). 97 Table 5.2 Comparison of average and maximum errors of enthalpy (kcal/mol) of formation predicted by G3B3 atomisation energy and isodesmic reaction. 98 Table 5.3 Isodesmic reactions for 15 target species. 100 Table 5.4 Enthalpies of formations for reference species in isodesmic reactions. 101 viii Table 5.5 Comparison of enthalpies of formation at 298.15 K ( ∆ f H ◦ 298.15 ) from present work, Imperial College, previous database, and other sources (unit: kcal/mol). 102 Table 5.6 Molecular properties used for computing the thermodynamic properties. 104 Table 6.1 Lennard-Jones 12-6 potential parameters for selected alkanes and alkene compounds. 133 Table 7.1 Rate parameters of reactions employed in the simplified model a . 153 ix List of Figures Figure 2.1 Flow chart of the stochastic algorithm for solutions of the master equation (A and B denote different species, i, j, k are different energy states, and n A indicates the number of A). 22 Figure 3.1 Arrhenius plot of k 1 . Symbols: experimental data. Arrows indicate that the rate values are upper limits. Lines: selected compilations and theoretical studies. 30 Figure 3.2 Schematic illustration of the potential energy function for the asymmetric, hindered internal rotation. 41 Figure 3.3 Relaxed potential energy scan for (CO + HO 2 •) → TS1 → trans- HOOC•O → TS2 → (CO 2 + •OH) at the B3LYP/6-31G(d) level of theory without zero point correction. 45 Figure 3.4 Relaxed potential energy scan at the B3LYP/6-31G(d) level of theory without zero point correction, showing the reaction (CO + HO 2 •) → TS3 → CO 2 + •OH. cis-HOOC•O is represented by a local inflection point without a pronounced energy well. 46 Figure 3.5 Potential energy diagram for CO + HO 2 • → products. For CO + HO 2 • → CO 2 + •OH, the energy values are determined using the CCSD(T)/CBS method, and include zero-point energy corrections. For CO + HO 2 • → HC•O + O 2 , the energy values are taken from Martinez-Avila et al. (2003) at QCISD(T)/6- 311G(2df,2p)//QCISD/6-311G(d,p) level of theory. 50 Figure 3.6 Geometry parameters determined at the CCSD(T)/cc-pVTZ level of theory. The bond lengths are in Å; and the bond and dihedral angles are in degrees. 52 x Figure 3.7 Energy scans for internal rotation in HOOC•O (top panels) and TS1 (bottom panels), computed at the CCSD(T)/cc-pVTZ (symbols and solid lines) and B3LYP/6-31G(d) (dotted lines) levels of theory. Except for the dihedral angle, geometries are frozen at those of trans-HOOC•O and TS1, respectively. Species/critical geometries given in quotes designate structures close to the respective optimized geometries. 54 Figure 3.8 Energy scans for internal rotation in TS3, computed at the CCSD(T)/cc-pVTZ (symbols and solid lines) and B3LYP/6- 31G(d) (dotted lines) levels of theory. Except for the dihedral angle, geometries are frozen at those of TS3. Critical geometry given in quotes designates a structure close to the optimized geometry. 55 Figure 3.9 Experimental and theoretical rate coefficient for reaction R3.1. See the caption of Figure 3.1 for source of experimental data. The thick, dashed lines indicate the uncertainty bound of the current theoretical expression (see text). 62 Figure 4.1 Arrhenius plot of k 4.1 . Symbols: selected experimental data. Lines: selected rate coefficient compilations and theoretical studies. 67 Figure 4.2 Potential energy diagram for OH• + HO 2 • → products on the triplet surface (unit: kcal/mol). The energy values are determined using at CBS-QBH level of theory with zero-point energy corrections. 76 Figure 4.3 Potential energy diagram for OH• + HO 2 • → products on the singlet surface (unit: kcal/mol). Grey lines: closed-shell singlet surface; Black lines: open-shell singlet surface. The energy values are determined using at CBS-QBH level of theory with zero-point energy corrections. 77 Figure 4.4 Geometry parameters determined at BHandHLYP/6-311++G(d,p) level of theory. The bond lengths are in Å; and the bond and dihedral angles are in degrees. 79 Figure 4.5 Number of states ( ) EJ NR as a function of separation distance R on triplet potential energy surface with excess energy of 800 cm -1 at two angular momentum number J. 86 xi Figure 4.6 Arrhenius plot of k for •OH + HO 2 • → HOOOH occurring on the closed shell singlet surface. 87 Figure 4.7 Comparison of experimentally and theoretically obtained rate coefficients for R4.1. Symbols: selected experimental data. Lines: selected rate coefficient compilations and theoretical studies. 88 Figure 5.1 Energy scans for internal rotation in the 15 species studied by isodesmic reaction approach, computed at the B3LYP/6-31G(d) level of theory. Except for the dihedral angle, geometries are frozen. 103 Figure 5.2 Experimental (symbols, (Kalitan et al. 2007)) and computed (lines) ignition delay times of H 2 -CO-air mixtures behind reflected shock waves. 106 Figure 5.3 Experimental (symbols, (Kalitan et al. 2007)) and computed (lines) ignition delay times of H 2 -CO-air mixtures behind reflected shock waves. 107 Figure 5.4 Experimental (symbols, (Kalitan et al. 2007)) and computed (lines) ignition delay times of H 2 -CO-air mixtures behind reflected shock waves. 108 Figure 5.5 Experimental (symbols) and computed (lines) laminar flame speeds of methane, ethane, propane, and n-butane-air mixture at atmospheric pressure and unburned gas temperature 298 K. The methane and propane data are taken from Vagelopoulos et al. (1994), and ethane data are taken from Egolfopoulos et al. (1991), n-butane data are taken from Davis and Law (1998). 110 Figure 5.6 Experimental (symbols (Burcat et al. 1971)) and computed (line) ignition delay times for a 3.22% propane, 16.1% oxygen, and 80.68% argon mixture at temperature range from 1240-1690 K and pressure range 7.82-15.39 atm. All calculations were made with an average molar density of 9.39×10 -5 mol/cm 3 . 111 Figure 5.7 Experimental (symbols (Qin 1998)) and computed (lines) ignition delay times for mixture of propane, oxygen, and argon mixture at temperature range from 1300-1900 K and pressure range 3-4 atm, equivalence ratio from 0.75-1.0 in reflected shock waves. Ignition delay times were derived from OH absorption profiles. 112 xii Figure 5.8 Experimental (symbols) and computed (lines) laminar flame speeds of ethylene-air mixtures at 1, 2, and 5 atm at unburned gas temperature 298 K. 114 Figure 5.9 Experimental (symbols) and computed (lines) of ignition delay time of ethylene-oxygen-argon mixtures behind reflected shock waves. Ignition delay times were determined by (a) the onset of CH emission (Brown and Thomas 1999), (b through e) the onset of CO 2 emission (Hidaka et al. 1999), and (f) 10% of maximum [CO]+[CO 2 ] (Homer and Kistiako 1967). 115 Figure 5.10 Experimental (symbols (Davis and Law 1998)) and computed (lines) laminar flame speeds of propene and 1-butene-air mixture at p = 1 atm, T = 300 K. 116 Figure 5.11 Experimental (symbols (Qin 1998)) and computed (lines) ignition delay times for mixture of propene, oxygen, and argon mixture at temperature range from 1250-1900 K and pressure range 1-4 atm in reflected shock waves. Ignition delay times were derived from OH absorption profiles. 118 Figure 5.12 Experimental (symbols) and computed laminar flame speeds of acetylene, propyne, and 1,3-butadiene-air mixture at the atmospheric pressure. The acetylene data are taken from Egolfopoulos et al. (1991). The propyne and 1,3-butadiene data are taken from Davis and Law (1998). 119 Figure 5.13 Experimental (symbols (Curran et al. 1996)) and computed (lines) ignition delay times for propyne and allene oxidation behind reflected shock waves. The experimental ignition delay was determined by the appearance of chemiluminescence from the CO+O reaction and by the onset of pressure rise, and the computational ignition delay was determined by the maximum pressure gradient. 120 Figure 6.1 Lennard-Jones self-collision diameter (σ) and well depth (ε/k B ) of n-alkanes plotted against molecular weight (MW). 134 Figure 6.2 Binary diffusion coefficient estimated for n-C 12 H 26 and N 2 at the atmospheric pressure. 135 xiii Figure 6.3 Experimentally (symbols (Dahm et al. 2004)) and numerically (solid lines: detailed model) determined conversion of n-C 12 H 26 during its pyrolysis in a plug flow reactor (0.336% n-C 12 H 26 -N 2 , p = 1 atm). 137 Figure 6.4 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid lines: detailed model) determined conversion of n-C 12 H 26 as a function of the residence time for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor (p = 1 atm). 138 Figure 6.5 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid lines: detailed model) determined conversion of n-C 12 H 26 as a function of temperature for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor (p = 1 atm). 139 Figure 6.6 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid lines: detailed model) determined product mole fractions as a function of the residence time for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor at 973 K (p = 1 atm). 140 Figure 6.7 Experimentally (symbols) and numerically (solid lines: detailed model) determined laminar flame speeds of n-C 12 H 26 /air mixtures. 142 Figure 6.8 Experimentally (symbols) and numerically (solid lines: detailed model) determined laminar flame speeds of n-C 10 H 22 /air mixtures. 143 Figure 6.9 Experimentally (symbols (Davis and Law 1998; Smallbone et al. 2008)) and numerically (solid lines: detailed model) determined laminar flame speeds of n-C 7 H 16 /air mixtures. The 2-atm experiment and computation were carried out in nitrogen-diluted air (18%O 2 -82% N 2 ). 144 Figure 6.10 Logarithmic sensitivity coefficient of laminar flame speed with respect to reaction rate parameters, computed for n-C 12 H 26 /air mixtures at φ = 1.0, T 0 = 403 K, using the detailed model. 145 Figure 6.11 Experimentally (symbols) and numerically (solid lines: detailed model) determined ignition delay times for n-C 12 H 26 oxidation behind reflected shock waves. 147 Figure 6.12 Experimentally (symbols) and numerically (solid lines: detailed model) determined ignition delay times for n-C 10 H 22 oxidation behind reflected shock waves. 148 xiv Figure 7.1 Experimentally (symbols (Dahm et al. 2004)) and numerically (solid lines: detailed model; dashed lines: simplified model) determined conversion of n-C 12 H 26 during its pyrolysis in a plug flow reactor (0.336% n-C 12 H 26 -N 2 , p = 1 atm). 156 Figure 7.2 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid lines: detailed model; dashed lines: simplified model) determined conversion of n-C 12 H 26 as a function of the residence time for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor (p = 1 atm). 157 Figure 7.3 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid line: detailed model; dashed line: simplified model) determined conversion of n-C 12 H 26 as a function of temperature for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor (p = 1 atm). 158 Figure 7.4 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid lines: detailed model; dashed lines: simplified model) determined product mole fractions as a function of the residence time for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor at 973 K (p = 1 atm). 159 Figure 7.5 Experimentally (symbols) and numerically (solid lines: detailed model; dashed lines: simplified model) determined laminar flame speeds of n-C 12 H 26 /air mixtures. 160 Figure 7.6 Experimentally (symbols) and numerically (solid lines: detailed model; dashed line: simplified model) determined ignition delay times for n-C 12 H 26 oxidation behind reflected shock waves. 161 Figure 7.7 Logarithmic sensitivity coefficient of laminar flame speed with respect to reaction rate parameters, computed for n-C 12 H 26 /air mixtures at φ = 1.0, T 0 = 403 K, using both the detailed model and the simplified model. 162 Figure 7.8 Experimentally (symbols) and numerically (solid lines: detailed model; dashed lines: simplified model not shown here) determined laminar flame speeds of n-C 10 H 22 /air mixtures. 164 Figure 7.9 Experimentally (symbols) and numerically (solid lines: detailed model; dashed lines: simplified model not shown here) determined ignition delay times for n-C 10 H 22 oxidation behind reflected shock waves. 165 xv Figure 7.10 Experimental (symbols (Davis and Law 1998; Smallbone et al. 2008)) and computed (solid lines: detailed model; dashed lines: skeletal model) laminar flame speeds of n-heptane–air mixtures. The 2-atm experiment and computation were carried out in nitrogen-diluted air (18%O 2 -82% N 2 ). 166 Figure 7.11 Ignition temperatures of 4.5% n-heptane in nitrogen at 298 K versus air as a function of strain rates (p = 1atm). Symbols: experimental data (Smallbone et al. 2008); solid line: prediction of the detailed model; dashed line: prediction with the binary diffusivity of n-heptane increased by 50%. 167 Figure 7.12 Ignition temperatures of 2.5% n-heptane in nitrogen at 298 K versus air as a function of pressure with density-weighted strain rate K = 325 s -1 . Symbols: experimental data (Smallbone et al. 2008); solid line: prediction of the detailed model; dashed line: prediction with the binary diffusivity of n-heptane increased by 50%. 168 Figure 7.13 Ranked logarithmic sensitivity coefficients of rate coefficients and diffusion coefficients (D ij ) to the turning point, computed for the turning point with 4.5% n-heptane in nitrogen versus air at p = 1 atm and strain rate K = 150 s -1 . 170 xvi Abstract Basic understanding of the combustion kinetics of jet fuels is critical to optimal design of gas-turbine engines. Because jet fuels contain a large number of compounds, a current approach to their combustion kinetics is to use a surrogate, containing several compounds, to mimic jet-fuel behaviors. Towards the goal of developing a combustion kinetic model for jet-fuel surrogates, a theoretical study was undertook here, focusing largely on a particular class of surrogate component, namely, the normal alkanes. To develop a combustion reaction model for fuel surrogates requires a reliable H 2 /CO/C 1 -C 4 combustion sub-model as its foundation. Therefore, a significant portion of the current work is to improve H 2 /CO/C 1 -C 4 high-temperature combustion model through a critical evaluation of rate parameters, theoretical studies for several key reactions, ab initio calculations of thermochemical properties, and validation tests against a wide range of experimental data. Notably, the kinetics of reactions CO+HO 2 • → CO 2 +•OH and •OH+HO 2 • → H 2 O+O 2 were studied using a combination of ab initio electronic structure methods, transition state and RRKM theories, and master equation modeling. New mathematical formulations and numerical algorithms for treating asymmetric hindered xvii internal rotation were developed. Rate parameters were recommended along with their uncertainty factors. On the basis of the updated H 2 /CO/ C 1 -C 4 kinetic model, a detailed kinetic model was proposed for the combustion of normal alkanes up to n-dodecane. The model is valid for fuel oxidation and pyrolysis above 850 K, and was validated against a wide range of experimental data, including fuel pyrolysis in plug flow and jet-stirred reactors, laminar flame speeds, and ignition delay times behind reflected shock waves, with n-heptane, n-decane, and n-dodecane being the emphasis. Analyses revealed that for a wide range of combustion conditions, the kinetics of fuel cracking to form smaller molecular fragments is fast and may be decoupled from the oxidation kinetics of the fragments. Subsequently, a simplified reaction model containing 4 species and 20 reaction steps was proposed to predict the fuel pyrolysis rate and product distribution. Combined with the base H 2 /CO/C 1 -C 4 model, the simplified model was shown to predict fuel pyrolysis, laminar flame speeds, and ignition delays as closely as the detailed model. 1 Chapter 1 Introduction 1.1 Motivation Fossil fuel combustion remains to be an important part of our daily life and world’s economy; most of the world’s electricity is generated from it. On one hand, combustion is desirable in providing energy and power for transportation, propulsion, electric power generation, heating, light, and in producing useful materials; on the other hand, it is undesirable in causing wild fires, polluting our living environment, and causing damage from explosions. To better take advantage of combustion, and reduce its hazard effect, it is necessary to acquire a fundamental understanding of combustion phenomena. A basic understanding of combustion chemistry and physics is critical to a large range of practical applications, including engine and other combustor designs. The challenge lies in the complexity of exothermic, autocatalytic chemical reactions accompanied by the rapid production of heat. Turbulence is often involved that enhances mixing. To understand the underlying complexity and highly nonlinear behavior of combustion processes, a fundamental approach of first-principle modeling is often necessary. For instance, quantum mechanical electronic structure calculations are useful tools for exploring elementary reaction pathways. Other theories such as 2 statistical mechanics and reaction rate theories can be applied to determine rate parameters of elementary reactions relevant to fuel combustion. Detailed kinetic modeling uses a large number of elementary reaction steps to describe the conversion of reactants into products at the molecular level. Coupled with solutions of mass, momentum, and energy conservation equations, detailed kinetic modeling has been and will remain to be instrumental in advances of combustion science. A detailed reaction model is a compilation of relevant reaction pathways with kinetic data for each elementary reaction and thermodynamic and transport properties for each species. This dissertation work centers on the development of a predictive reaction model for high-temperature oxidation of normal alkanes up to n- dodecane. The model contains three submodels: H 2 /CO, C 1 -C 4 , and C n H 2n+2 (5 ≤n≤12). The H 2 /CO reaction model was based on a previous study, but was improved here through a comprehensive theoretical study of two key reactions. The C 1 -C 4 submodel was also derived from previous studies, but it was updated here to improve its fundamental validity and predictiveness. The normal C n H 2n+2 (5≤n≤12) model was the product of this dissertation work. Below, each component of the current work will be briefly discussed. Reactions involved in H 2 /CO combustion play an essential role in the hierarchical structure of oxidation models of hydrocarbon fuels. The H 2 /CO system itself has attracted significant attention in recent years, owing to its applications in advanced combustion technologies, such as Integrated Gasification Combined Cycle (IGCC) power generation systems involving the gasification of fossil fuels or biomass 3 to a hydrogen rich mixture, known as syngas. The reaction kinetics of syngas has relevance not only in its combustion and power conversion, but also in the production of chemical feedstocks, fuels, and solvents. In addition, a predictive H 2 /CO model is critical to a number of technologies in which the burnout of CO is important. The reaction kinetics of H 2 /CO mixture is also of relevance to risk and hazard assessments since such mixtures present significant safety problems. To improve the existing H 2 /CO combustion models, a key portion of this dissertation work focuses on theoretical analyses of two key reactions with notable uncertainties in their rate parameters. These are CO+HO 2 • →CO 2 +•OH and HO 2 •+•OH →H 2 O+O 2 . The rate parameters of both reactions were subject to recent debates. The issues underlying these debates were examined in detail and the controversies were resolved through this dissertation work. Combustion reaction models are hierarchical in nature. A kinetic model, developed for higher hydrocarbons, should be predictive for small hydrocarbons as they are intermediates formed during the combustion of higher hydrocarbons. Moreover, the oxidation of small hydrocarbon species or combustion intermediates is usually rate-limiting. For this reason, the validity and accuracy of a base model of C 1 - C 4 hydrocarbon combustion is critical to any combustion model of higher hydrocarbons. A previous C 1 -C 4 hydrocarbon combustion model was updated and 4 revised in this work. The revisions were based on critical review of recent literature, on relevant reaction kinetics, thermodynamics, and transport properties. Recent interests in normal alkane combustion kinetics stem from the need to better design gas turbine and other internal combustion engines. Practical fuels such as jet fuels contain a large number of compounds. It is not feasible to perform a direct numerical simulation of the combustion behavior of these fuels. Rather, a viable option is to use surrogates, containing several pure compounds, to mimic real fuel behavior. By examining kinetic features unique to a particular component, it will be possible to make simplifications at the component level before a joint model may be assembled for all surrogate components. The combustion kinetics of normal alkanes, a major component of jet fuels (Colket et al. 2007), was chosen to be studied here with a specific goal to address the question concerning the level of kinetic details required for describing high-temperature oxidation of normal alkanes. 1.2 Review of previous studies Over the past thirty years, tremendous progresses have been made in chemical kinetic mechanism development and kinetic modeling of hydrocarbon fuel combustion, e.g., (Westbrook and Dryer 1984; Miller et al. 1990; Westbrook 2000; Ranzi et al. 2001; Battin-Leclerc 2002; Simmie 2003). These kinetic models have enabled the understanding of various combustion phenomena and are now essential to engine design and optimization. However, existing models have much room for improvement. 5 This dissertation work started from a previously available, high- temperature H 2 /CO/C 1 -C 4 hydrocarbon combustion model. This model was proposed, expanded, and revised in a series of publications (Davis et al. 1999a; Laskin and Wang 1999; Laskin 2000; Wang et al. 2000; Davis et al. 2005; Joshi 2005). The H 2 /CO oxidation sub-model (Davis et al. 2005), though generally accurate, was found to underpredict or overpredict combustion responses under extreme conditions. A recent shock tube study (Sivaramakrishnan et al. 2007) for H 2 and CO mixture oxidation at extremely high pressures suggested that the rate parameters for HO 2 •+•OH →H 2 O+O 2 might have to be revised. In another study, the rate coefficient of CO+HO 2 • →CO 2 +•OH had to be notably reduced from the previous understanding to reproduce the autoignition data of H 2 /CO mixture in the temperature range of 950- 1100 K and pressures from 15-50 bar in a rapid compression machine (Mittal et al. 2007). In addition, compared to a few other thermodynamic databases, discrepancies in thermodynamic properties were found for several species of the previous H 2 /CO/C 1 -C 4 model. As mentioned earlier, combustion kinetics of normal alkanes is the focus of this study. Although several comprehensive kinetic models have been proposed for normal alkane combustion, e.g., (Lindstedt and Maurice 1995; Curran et al. 1998; Doute et al. 1999; Battin-Leclerc et al. 2000; Zeppieri et al. 2000; Bikas and Peters 2001; Fournet et al. 2001; Westbrook et al. 2001; Dahm et al. 2004; Herbinet et al. 2007), no single model can predict the combustion properties for all normal alkanes. The origin of this problem is clearly our limitation of fundamental knowledge 6 necessary to achieve a self-consistent explanation for the combustion behaviors of a wide range of hydrocarbons. Other problems of existing kinetic models are that some focused on a specific fuel or one specific aspect of the fuel, while others were constructed on the basis of kinetic sub-mechanisms of certain smaller hydrocarbons that lacked validation. The consequence is that many of the existing models are expected to be unreliable or contain internal thermodynamic and chemical kinetic inconsistency. The objectives of this dissertation are to improve the H 2 /CO/C 1 -C 4 model, develop a detailed, comprehensive, predictive kinetic combustion mechanism for normal alkanes up to n-dodecane, and discuss the possible simplification of the mechanism. The model is comprehensive in that it incorporates the recent thermodynamic, kinetic, and species transport updates relevant to fuel oxidation; and it must be validated against a wide variety of combustion data, from global combustion properties such as laminar flame speeds, shock-tube ignition delay times, and extinction strain rates, to detailed species profiles during fuel combustion in flow- reactors and laminar premixed flames. 1.3 Structure of this dissertation In Chapter 2, the general methodology of kinetic model development and kinetic modeling were introduced, including several theoretical approaches to obtain kinetic parameters and thermodynamic data, the types of combustion data for simulation and the corresponding mathematical formulae. 7 Because global combustion properties are not determined by a single elementary reaction, and all reactions are coupled, the validity of a rate constant must be verified by a direct study of that reaction. To provide kinetic evidence for the above mentioned H 2 /CO reactions, in Chapter 3, the kinetics of the reaction CO+HO 2 • →CO 2 +•OH was studied using a combination of ab initio electronic structure theory, transition state theory, and master equation modeling. The potential energy surface was examined with the CCSD(T) and CASPT2 methods. Because CO+HO 2 addition can follow two separate conformer paths, the rate coefficient calculation considered the contributions from both of them. Special attention was paid to the hindered internal rotations of the HOOC•O adduct and the critical geometries on the potential energy surface. The pressure and temperature dependence of the rate constant was proposed. In Chapter 4, to investigate the temperature and possible pressure dependence of the rate coefficient for HO 2 •+•OH →H 2 O+O 2 , the potential energy surfaces on both the singlet and triplet surfaces were studied by quantum mechanical electronic structure methods at the CBS-QBH level of theory, and the rate coefficient was calculated by microcanonical variational transition state theory and master equation modeling. The C 1 -C 4 thermodynamic database was updated and improved as will be discussed in Chapter 5. The revised H 2 /CO/C 1 -C 4 model, incorporating the updated thermodynamic database and several new kinetic parameters, was subject to validation tests against a wide range of combustion properties for a series fuels, including 8 hydrogen, carbon monoxide, methane, acetylene, ethylene, ethane, propyne, propene, propane, 1,3-butadiene, 1-butene, and n-butane. In Chapter 6, a detailed kinetic model was proposed for the combustion of normal alkanes up to n-dodecane above 850 K. The model was validated against a variety of experimental data. The role of fuel cracking in the combustion process was also analyzed. Chapter 7 explored the question of the simplification of the kinetic model for fuel cracking. A simplified model was proposed to predict the fuel pyrolysis rate and product distribution. Combined with the base C 1 -C 4 model, the performance of simplified model was compared with that of the detailed model. To understand the effect of transport properties on the flame ignition and propagation, the nonpremixed ignition temperature responses for n-heptane/air mixtures were analyzed by numerical sensitivity analysis on reaction kinetics and fuel diffusion rate. The influence of uncertainties in the molecular transport on the model prediction of diffusive ignition was discussed. Finally, the last chapter summarizes the contributions and findings of this dissertation work. Future work to improve the current model is also proposed. 9 Chapter 2 Computational Methodologies 2.1 Introduction The validity of a reaction model is determined by how well it describes the underlying physics and chemistry of combustion phenomenon. The physical parameters of reaction models include the reaction rate parameters, and thermodynamic and transport properties of relevant species. Clearly, the more accurate these parameters are, the closer the kinetic model prediction is to physical reality. The general methodologies to estimate thermodynamic and rate parameters are introduced in this Chapter. Kinetic modeling provides a way to explore underlying reaction pathways and to validate the reaction model by comparing predictions against available experimental data. The fundamentals of kinetic modeling and the numerical procedures will be presented. 2.2 Thermodynamic properties Generally, thermodynamic properties are either taken from experimental measurements or calculated from computational methods. While thermodynamic properties may be measured from experiments directly, for most species produced in combustion, being free radicals or having a very short life time, it is almost impossible 10 to carry out such experiments. Instead, theoretical approaches may be employed to estimate those properties with good accuracy. These approaches range from the empirical group additivity method, the use of active thermochemical tables, to ab initio calculations. Benson’s group additivity method (Benson 1976) assumes the contributions of individual molecular groups in a compound to the thermodynamic properties are additive. While this method gives reasonably accurate estimations for molecules composed of well-known molecular groups, it often fails for molecules with complex structures. The method of active thermochemical tables predicts enthalpies of formation from tables where experimental or calculated information has been stored for a large number of species on the relationships of enthalpy of formation (Ruscic 2004). The ab initio method relies on the accuracy of quantum mechanical calculations and the knowledge of statistical mechanics. In this work, the group additivity method is used to estimate the straight-chain molecules and radicals in Chapter 6, and ab initio method is applied to study several C 3 -C 4 species in Chapter 5. The thermodynamic properties of most species in the kinetic model can be determined with high accuracy by the ab initio method. According to the knowledge of statistical thermodynamics, the macroscopic properties can be calculated from the properties of the individual molecules making up the system (McQuarrie 1973), which may be computed accurately at a high level theory from ab initio calculations. The quantum mechanical energy levels for an N-body system are related to thermodynamic properties through the partition function. The internal energy E <> at temperature T may be calculated from partition function Q as below, 11 2 ln B Q EkT T ∂ <>= ∂ , (2.1) where k B is Boltzmann’s constant. The entropy S can be derived from ln B B E SNk Q kT ⎛⎞ <> =+ ⎜⎟ ⎝⎠ . (2.2) Other thermodynamic properties such as heat capacity p C , sensible enthalpy H , and equilibrium constant can be determined from thermodynamic relations. For example, equilibrium constant can be derived from () ( ) ( ) exp / exp / exp / PRu Ru Ru KGRT SR HRT =−Δ = Δ −Δ , (2.3) where R G Δ , R S Δ , and R H Δ are Gibbs function of reaction, entropy of reaction and enthalpy of reaction at the reference pressure of 1 atm, respectively. u R is the universal gas constant. Equilibrium constant can be calculated directly from partition functions of the products and reactants, and enthalpy of reaction R H Δ at 0 K, () ,0 exp / prod PRK reac Q KHRT Q =−Δ . (2.4) The canonical ( ) ,, NV T ensemble defines an N -body system with fixed volume V and temperature T . For this ensemble the partition function is () , (, , ) !! N NN N N tran rot vib elec qVT qq q q QN V T NN == , (2.5) where tran q , rot q , vib q , and elec q are molecular translational, rotational, vibrational, and electronic partition functions. A molecular partition function measures the total 12 number of possible energy states that a molecule can take at the equilibrium temperature T . It is given by / (, ) jB EkT j qV T e − = ∑ , (2.6) where j E is the energy at the th j state. As j E is obtained from solving the time- independent Schr ӧdinger equation jjj HE ψ ψ =, (2.7) these molecular partition functions may be calculated. The translational partition function is 3/2 2 2 (, ) B tran mk T qVT V h π⎛⎞ = ⎜⎟ ⎝⎠ , (2.8) where h is Planck’s constant, and m is the molecular mass. The rotational partition function for a polyatomic molecule is 1/ 2 1/ 2 1/ 2 1/ 2 BBB rot XY Z kT kT kT q BB B π σ ⎛⎞⎛⎞⎛⎞ = ⎜⎟⎜⎟⎜⎟ ⎝⎠⎝⎠⎝⎠ , (2.9) where σ is symmetry number, B is the rotational constant, and subscripts ,, X YZ denote the three principal axes of rotation. For internal torsional motions, it is usually inappropriate to treat them as harmonic oscillators, but they may be better treated as hindered internal rotors. The classical partition function of a one-dimensional hindered rotor is (Knyazev et al. 1994; Knyazev and Tsang 1998) 0 1/ 2 1/ 2 2 0 0 2 B V kT B h B V kT qe B kT π σ − ⎛⎞ ⎛⎞ = ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ I , (2.10) 13 where 0 I is the modified Bessel function, and 0 V is the barrier height of the sinusoidal potential function for the corresponding rotor. Details about the special treatment of hindered internal rotation are discussed in Chapter 3. The vibrational partition function for a nonlinear N -atom molecule is /2 36 / 1 (, ) 1 B B hkT N vib hkT i e qVT e ν ν − − = = − ∏ , (2.11) where ν are vibrational frequencies. Finally, the electronic partition function is 2 / 12 (, ) B EkT elec qVT g ge − =++, (2.12) where i g is the degeneracy of the i th electronic state. The electronic partition function quantifies the electronic degeneracy for molecules at the ground and electronically excited states. 2.3 Reaction rate parameters Reaction rate parameters in a kinetic model are usually derived from three sources: experimental studies, estimations, and theoretical studies. A theoretical study of rate parameters may be necessary when they are not well known, yet exert a notable effect on model prediction. Empirically, the relationship between the rate coefficient of a reaction and temperature T is expressed by the modified Arrhenius equation, ( ) exp / n au kAT E RT =−, (2.13) where A is a coefficient, n is the temperature exponent, a E is the activation energy. Theoretically, reaction rate coefficients may be determined if the potential energy 14 surface of a reaction process, molecular properties of the reactants and transition states are known. 2.3.1 Transition state and RRKM theories For most bimolecular reactions, the rate coefficient k is only a function of the temperature. The canonical transition state theory may be applied to reactions with a pronounced saddle point on the potential surface along the reaction coordinate. The canonical transition state theory states that the rate coefficient k is () * 0 exp / TS B u reac Q kT kERT hQ =−. (2.14) where 0 E is the critical energy, reac Q is the partition function of the reactants, * TS Q is the partition function of the transition state in the remaining degrees of freedom excluding the one along the reaction coordinate. Rate coefficients of many unimolecular reactions and several bimolecular reactions are found to depend on the total species molar concentration or pressure. A unimolecular reaction requires collision to proceed to the products. Any gas molecule M in the system may be capable of collisionally activating or deactivating the reactant molecule A . This process may be represented as * AMA M + ↔+, (2.15) where * A is the reactant with excess internal energy capable of overcoming the potential energy barrier to form products. For * A to react, its rate coefficient ( ) kE , known as the microcanonical rate constant, is energy-dependent. To derive ( ) kE , 15 RRKM (Rice-Ramsperger-Kassel-Marcus) theory uses two principal assumptions (Gilbert and Smith 1990; Holbrook et al. 1996). The first assumption is that the energy throughout vibrationally degrees of freedom randomizes rapidly. The second one is the existence of a critical geometry ( ) AE + for the transition from a vibrationally excited molecule * () AE to the products, i.e., † () * () () kE k A E A E products + ⎯⎯⎯→⎯⎯ → . (2.16) The microcanonical rate constants () kE can be derived as ( ) () () r a r QW E kE l Qh E ρ + + = , (2.17) where a l is the reaction path degeneracy; ( ) WE + is the sum of rovibrational energy states of the transition state at energy level E + ; ( ) E ρ is the density of energy states of the reactant species at energy level † 0 EE E = + ; 0 E is the critical energy. To account for the effect of adiabatic rotations, the above expression contains the factor † rr QQ , where † r Q and r Q are the partition functions for inactive rotational degrees of freedom of the transition state and the reactant molecule, respectively. In its discrete form the density of energy states ( ) i E ρ or the Maxwell- Boltzmann distribution of energy is / / () iB jB EkT i EkT j e E e ρ − − = ∑ . (2.18) 16 The sum of states is simply the integration of density of states, i.e. 0 () () E WE E dE ρ = ∫ . The direct-count algorithm of Beyer and Swinehart (1973) may be used to calculate the sum of energy states and density of states. Active rotations may be accommodated using the method of Astholz et al. (1979). The thermal rate coefficients as a function of T and pressure P may be obtained by two models. One is the modified strong collision model (Gilbert et al. 1983; Troe 1983; Gilbert and Smith 1990), which assumes a steady state for the energized species and implements weak collision stabilization. For unimolecular dissociation/elimination reactions, the thermal rate coefficient can be expressed as () ( ) ( ) () 0 , 1/ uni E kE P E dE kTP kE βω ∞ = + ∫ , (2.19) where β is the collision efficiency factor with 01 β < ≤ , ω is the collision rate constant, () PE is the probability of finding a molecule in the energy range of E to E dE + in a Boltzmann distribution of energy. At the high-pressure limit, () () ( ) () ( ) 0 , 0 0 exp / exp / exp( / ) B E uni B rot vib B au rot vib kE E E kT dE k EEkTdE qq kT lERT hq q ρ ρ ∞ ∞ ∞ ++ − = − =− ∫ ∫ . (2.20) The modified strong collision model is for single-channel unimolecular reactions with large energies barriers. The second method, master equation modeling, is more rigorous and can be applied to single or multi-channel thermally and chemically activated reaction systems. 17 2.3.2 Master equation modeling For a reacting system, the rovibrationally excited molecules are subject to competitive processes of collisional activation/deactivation and unimolecular isomerization, or dissociation, () ( ) () ( ) () ij ji m k ji k ij k i AE M A E M AE M A E M A E products + ⎯⎯→+ + ⎯⎯→+ ⎯⎯ → . (2.21) The time evolution of such a system shown in (2.21) can be described by the master equation of collision energy transfer in [( )] [][( )] [][( )] ( )[( )] i ij j ji i m i i jj m dA E k M AE k M AE k E AE dt =− − ∑∑ ∑ , (2.22) where A is the reactant molecule or an isomer; [ ] denotes the number concentration, M is a bath-gas molecule, ij k is the second-order rate constant for the collisional energy transfer of a molecule from state j E to state i E and () mi kE denotes the microcanonical rate constant of a particular isomerization or dissociation channel m . The first and second terms on the right hand side of the equation represent the rates of collisional energy transfer into and out of a particular energy range, while the last term represents the microcanonical rate for all possible reaction channels. The master equation may be solved using a stochastic approach, as implemented in Multiwell (Barker 2001; Barker and Ortiz 2001; Barker et al. 2001). The method of solution is based on Gillespie’s exact stochastic method (Gillespie 1976, 1978). 18 The rate constant for the collisional energy transfer is related to the energy transition probability P ij by ij ij kPZ = , (2.23) where Z is the collision frequency. The energy transition probability can be calculated using an exponential-down model, which states that the probability of energy transfer varies exponentially and inversely with the amount of energy transferred, ( ) ()() 1/ for , for ji Bi j EE j kT E E ij i i j Ce j i P Ce j i α α ρ ρ −− −+ − ⎧ ≥ ⎪ = ⎨ < ⎪ ⎩ (2.24) where j C are the normalization constants calculated based on the condition 1 ij i P = ∑ , () E ρ is the energy specific density of states of the energized molecule, 1 d E α − =< Δ > , and d E <Δ > is the average energy transferred upon collisions in the downward transition. 2.3.3 Monte Carlo simulation The first step in the stochastic algorithm is to determine the initial energy distribution of the thermally excited species for a thermally activated system or the adduct for a chemically activated system, where the activated species is formed from the association of two reactants. The fundamental cause for this pressure dependence is identical to that of the unimolecular reactions. 19 Consider a chemically activated system () * () () recom decom kE kE A B AB E products AB +→ ↓ , (2.25) where A and B are the two reactants; * () AB E is the adduct at energy E ; AB denotes the stabilized adduct; ( ) recom kE and ( ) decom kE indicate the microcanonical rate constants for recombination of the reactants to form * AB and dissociation of * AB to regenerate reactants, respectively. The probability density function of * () AB E , () gE , may be related to the rate of * AB formation ( ) r vE as , ( ) ( ) [][] rrecom vEdE gEk A BdE ∞ = , (2.26) where , recom k ∞ is the recombination rate coefficient at the high pressure limit. ( ) gE can be calculated by the principle of detailed balancing, for the situation where the dissociation process can be ignored in calculating * AB ⎡ ⎤ ⎣ ⎦ and in which the equilibrium is established between the reactants and AB. The rate of dissociation () d vE from the energized molecule * AB in the range of E to E dE + is given by () ()[*] ()[]() ddecom decom v E dE k E AB dE k E AB f E dE == , (2.27) where ( ) f EdE is the equilibrium fraction of AB molecules in the energy range of E to E dE + , 0 ( )exp( / ) () ( )exp( / ) B B EEkT fE EEkTdE ρ ρ ∞ − = − ∫ . (2.28) 20 At equilibrium, the microcanonical rates of dissociation and recombination are equal, i.e. () () rd vE v E = . Hence, 0 ( ) ( )exp( / ) () () ()exp( / ) aB aB E kE E E kT gE kE E E kTdE ρ ρ ∞ − = − ∫ . (2.29) The stochastic solution of the master equation implemented here (Joshi and Wang 2006) starts by selecting a random number 1 R (0 ≤ 1 R ≤ 1) is chosen from the unit interval uniform distribution and the initial energy E is selected such that 1 0 () E R gE dE ′ ′ = ∫ . (2.30) The second step is to determine the outcome of the state change of this hot molecule, i.e., the isomerization or collisional energization/de-energization, until the molecule stabilizes or decomposes to form final products. According to Gillespie’s algorithm, the time intervals τ between stochastic steps are chosen randomly as, 2 ln( ) n n R a τ − = ∑ , (2.31) where 2 R (0 ≤ 2 R ≤ 1) is a random number similar to 1 R and n a is probability rate for the transition to the accessible state n . Here, n a is replaced by the microcanonical rate constants and the collision frequency. Another random number 3 R (0 ≤ 3 R ≤ 1) is chosen from unit interval uniform distribution and the state n is chosen such that 21 1 3 11 nn nn n nn n aR a a − ′ ′ ′′ == <≤ ∑ ∑∑ . (2.32) If the molecule undergoes isomerization, the event and the resulting isomer is updated accordingly and the above process is repeated at the same energy. If the molecule undergoes dissociation, the crossing into the dissociated products is assumed to be irreversible, i.e., no re-crossing is possible, in agreement with the classical transition state story. Another stochastic trial will follow. If the collisional energy transfer process is chosen, another random number 4 R ( ) 4 01 R ≤≤ is selected and if 4 act R P ≤ , it is an activation process, and if 4 deact R P ≤ , it is a deactivation process, where act P and deact P are probabilities for activation and deactivation, respectively. For a molecule in a given energy state i, , act i ji ji PP ≥ = ∑ and , deact i ji ji PP < = ∑ . (2.33) The amount of energy transferred is then calculated using yet another random number 5 R () 5 01 R ≤≤ and the transition probabilities previously calculated. The final energy state n upon collision is given by random number 5 R : 5 n ji ji R P ≥ = ∑ for activating collisions and 5 n ji ji R P ≤ = ∑ for deactivating collisions. The final energy is determined by interpolation of the discrete probabilities. When the probability for activation is equal to that for deactivation, i.e., ,, act i deact i PP = (Joshi 2005), the molecule may be 22 considered to be stabilized, and another stochastic trial will start. A diagram for the above stochastic process is shown in Figure 2.1. Figure 2.1 Flow chart of the stochastic algorithm for solutions of the master equation (A and B denote different species, i, j, k are different energy states, and n A indicates the number of A). While the above procedure can be applied ideally to a system composed of many molecules, the memory requirement is prohibitive and instead the random Isomerize? Ready to change? Activate? A(E i ) Yes No Stabilize? No Yes B(E i ) Yes A(E j ) Yes A(E k ) No A(E k ) No n A = n A + 1 23 walk for one molecule at a time is simulated and the results for an ensemble of stochastic trials are averaged. More specifically, counters are initiated for reactants, isomers and products in the reaction system. The stochastic process is repeated for hundreds of thousand molecules, with the accuracy of results improved with the increase in the number of trials. The rate constant for the q th channel is given by , , d qqr q c k kFk F K ∞ ∞ ==, (2.34) where q F denotes the fraction of molecules and c K is the equilibrium constant for the entrance channel AB AB + . 2.4 Validation of the reaction model The quality of a reaction model can be ascertained only upon validation against existing experimental data. Moreover, validation tests may be used to uncover the discrepancy between simulation results and experimental observations, and thus help to improve the reaction model and guide additional experimental measurements. The availability of newer and more accurate data can then pave the way to a better and deepened understanding of the underlying physics and chemistry, and thus reduce the uncertainty of the various parameters associated with the reaction model. The experimental validation targets considered here include laminar flame speeds, ignition delay times behind reflected shock wave, species profiles in flow reactors and jet-stirred reactors. Simulations of these targets are performed in conjunction with Sandia CHEMKIN-II (Kee et al. 1990), which reads a symbolic 24 description of a user-specified chemical reaction mechanism from an Interpreter and outputs a link to the Gas-Phase Subroutine Library, which may then be accessed by other application programs. 2.4.1 Laminar flame speed The ability to model chemical kinetics and transport processes in the premixed flame is critical to interpreting flame experiments and to understanding the combustion process itself. The laminar flame speed is defined as the velocity of steady, laminar, isobaric, quasi-one-dimensional propagation of a planar, adiabatic combusting wave propagating into a uniform fuel-air mixture. As the laminar flame speed is closely related to the heat release rate (Glassman 1996), it provides important information in the global response of a reaction kinetic model. Simulations of laminar flame speeds were performed using the Sandia PREMIX code (Kee et al. 1985) with multicomponent transport formula and including thermal diffusion. PREMIX program computes species and temperature profiles in freely propagating premixed laminar flames. The finite-difference discretization is used and the Newton method is employed in solving the two-point boundary-value problem. Steady-state convergence of the premixed-flame solution is aided by invoking time integration procedures when the Newton method has convergence difficulties. The PREMIX program runs in conjunction with the Sandia CHEMKIN-II (Kee et al. 1990) and TRANSPORT software packages (Kee et al. 1986) for processing the chemical reaction mechanism and for calculating the transport 25 properties. Simulations of laminar flame speeds in this dissertation work were carried out over a domain of 12 cm with 600 mesh points. 2.4.2 Nonpremixed counterflow ignition Simulations for nonpremixed counterflow ignition are described in Blouch and Law (2000), using a numerical code developed by Kreutz and Law (1996) on the basis of the steady-state stagnation flow code of Smooke et al. (1986). The computation involves obtaining a response S-curve, characterized by the variation of the peak concentration of a free radical versus the boundary temperature of the heated air. The turning point on the lower branch of the S-curve identifies the ignition state. Multicomponent transport formulae are used and thermal diffusion is included. For nonpremixed counterflow ignition, S-curve sensitivity analyses, defined through - ∂lnT ign / ∂ln Ai for reaction rate coefficients and - ∂lnT ign / ∂lnD jk for binary diffusion coefficients jk D , are performed at a point very close to the ignition turning point (less than 1K). 2.4.3 Ignition delay time Shock tubes have the advantage of studying chemical kinetics because the transport time scale is usually longer than a few milliseconds, and the reaction inside a shock tube is adiabatic and homogeneous without interference of fluid transport and heat loss. A typical definition of ignition delay time behind the reflected shock wave is the time from the arrival of the reflected shock wave to onset of the pressure rise in a shock tube. Experiments may be simulated purely as an initial value problem. In 26 general, shock tube experiments without significant heat release during the course of reaction may be simulated as a constant-pressure process, whereas those with significant heat release should be simulated as a constant volume/density process. Numerically, to solve ordinary differential equations (ODEs) in the system, time integration is performed using DVODE solver (Brown et al. 1989). Sensitivity analyses were conducted for ignition delay with the brute force method. 2.4.4 Turbulent flow reactor Turbulent flow reactor can be used to validate kinetic model because it provides a homogenous reaction zone. If a control volume is considered with flow velocity equal to that of the reacting flow, the fluid inside in the control volume does not exchange mass with fluid outside. In flow reactor simulations, constant pressure and adiabatic condition or constant temperature is usually assumed according to experimental conditions. A system of differential equations is solved numerically similarly as for the previously described ignition problem. An in-house kinetic solver similar to shock tube simulation was used. 2.5.5 Jet-stirred reactor Jet-stirred reactors are characterized by a reactor volume, mass flow rate, heat loss or temperature, inlet composition and temperature. The governing equations are a system of nonlinear algebraic relations that balance mass and energy in the system, which describe the time-dependent or steady-state properties in a well-mixed 27 or perfectly-stirred reactor. For steady-state problems, these equations are solved using the hybrid Newton/time-integration. The Sandia PSR code (Glarborg et al. 1986) was used for simulation in this work. 28 Chapter 3 Reaction Kinetics of CO + HO 2 • → Products: Ab Initio Transition State Theory Study with Master Equation Modeling 3.1 Introduction Recent interests in the reaction kinetics of CO + HO 2 • → CO 2 + •OH (R3.1) stem from its influence on the oxidation rate of CO and H 2 mixtures at high pressures. (Mittal et al. 2006; Mittal et al. 2007; Sivaramakrishnan et al. 2007) Although extensive experimental studies have been reported, there exist large discrepancies among literature rate values over the temperature range of interest to combustion kinetics, as seen in Figure 3.1. Above the temperature of 500 K, all measurements are either indirect, or the rate coefficient values were inferred from kinetic measurements on reaction processes in which reaction R3.1 is of secondary importance. Below 500 K, a few direct measurements are available; all of them yield only an upper limit for the rate coefficient. Hence, these studies provide little to no quantitative guidance for the rate coefficient above 500 K. Among measurements made above 500 K, Baldwin and coworkers (Baldwin et al. 1965; Baldwin et al. 1970; Atri et al. 1977) studied the rate coefficient of R3.1, denoted as k 1, relative to the reaction HO 2 • + HO 2 • → H 2 O 2 + O 2 (R3.2) 29 30 Figure 3.1 Arrhenius plot of k 1 . Symbols: experimental data. Arrows indicate that the rate values are upper limits. Lines: selected compilations and theoretical studies. : (Baldwin et al. 1965), based on 1 ref kk measurements relative to HO 2 • + HO 2 • = H 2 O 2 + O 2 (R3.2) (k ref taken from Kappel et al. (2002)) and HO 2 • + H 2 = H 2 O 2 + H• (k ref taken from Baulch et al. (2005)); : (Hoare and Patel 1969), based on measurements relative to C 2 H 6 + HO 2 • → C 2 H 5 • + H 2 O 2 (k ref based on Baldwin et al. (1986) and also from Kappel et al. (2002)) and to C 2 H 4 + HO 2 • → products (k ref taken from Baulch et al. (2005)); : (Baulch et al. 2005), based on 1 ref kk measurements relative to reaction R3.2 (k ref taken from Kappel et al. (2002)); –: (Azatyan 1971); : (Volman and Gorse 1972), based on measurements relative to CO + •OH → CO 2 + H• (k ref taken from Joshi and Wang (2006)); : (Khachatrian et al. 1972); : (Davis et al. 1973), based on 1 ref kk measurements relative to reaction R3.2 (k ref taken from Atkinson et al. (2004)); : (Simonaitis and Heicklen 1973), based on 1 ref kk measurements relative to reaction R3.2 (k ref taken from Atkinson et al. (2004)); : (Wyrsch et al. 1974); : (Hastie 1974), based on measurements relative to CO + •OH → CO 2 + H• (k ref taken from Joshi and Wang (2006)); : (Vardanyan et al. 1975); : (Atri et al. 1977), based on 1 ref kk measurements relative to reaction R3.2 (k ref taken from Kappel et al. (2002)); : (Colket et al. 1977); : (Graham et al. 1979); : (Burrows et al. 1979); : (Howard 1979); : (Arustamyan et al. 1980), re- evaluated in the present work, using the rate coefficient values of •OH + H 2 → H 2 O + H• and CO + •OH → CO 2 + H• from Baulch et al. (2005) and Joshi and Wang (2006), respectively; : (Vandooren et al. 1986); : (Bohn and Zetzsch 1998); : (Mittal et al. 2006). Lines are selected compilations and theoretical studies (Lloyd 1974; Tsang and Hampson 1986; Mueller et al. 1999; Sun et al. 2007). in a static reactor. They obtained 12 kk = 13.4±0.05 (cm 3 /mol-s) 1/2 , and based on an obsolete k 2 value of R3.2, they recommended k 1 = 1.9×10 7 cm 3 /mol-s at 773 K (Atri et al. 1977). Mueller et al. (1999) reinterpreted the rate data by taking k 2 from Hippler et 31 al. (1990) and obtained k 1 = 1×10 7 cm 3 /mol-s. Based on this rate value, Mueller et al. (1999) recommended () 3 13 11575 1 cm mol s 3 10 T ke − ⋅= × for 750 ≤ T ≤ 1100 K. The rate expression has been used extensively in subsequent combustion kinetics studies. Other rate expressions that have been frequently used include that of Tsang and Hampson (1986), () 3 14 11900 1 cm mol s 1.5 10 T ke − ⋅= × for 700 ≤ T ≤ 1000 K. The above rate expression is based on a wider range of experimental data and is about a factor of 3 larger than that of Mueller et al. (1999). The discrepancies of the two rate expressions given above are, however, well within the uncertainties of each other. Very recently, Mittal et al. (2006) carried out an autoignition study of H 2 /CO mixtures in the temperature range of 950-1100 K and pressures from 15-50 bar in a rapid compression machine (RCM). They noted that the reproduction of their experimental data requires k 1 values that are notably smaller than previously understood. Based on the prediction of onset of ignition and sensitivity analyses, Mittal et al. (2006) recommended that ( ) 3 12 11575 1 cm mol s 7.5 10 T ke − ⋅= × At 1000 K, the above expression gives k 1 = 7×10 7 cm 3 /mol-s, as much as a factor of 4 smaller than that of Mueller et al. (1999). The rate coefficient given in Mittal et al. (2006) is also outside of the uncertainties of previously reported values (see, Figure 3.1). A follow-up study by Mittal et al. (2007) used “Morris-one-at-a-time” and 32 Monte Carlo uncertainty analyses. The results again pointed to a much lower value for k 1 than those from previous experimental studies and evaluations. Around 1000 K, there have been several experimental studies reported for reaction R3.1, all of which were based on indirect measurements. In all cases, the k 1 values reported are substantially larger than what was needed to explain the RCM data. Colket et al. (1977) estimated the value of k 1 from the rate of CO 2 formation in acetaldehyde oxidation for temperatures between 1030 and 1150 K, obtaining a k 1 value that is over an order of magnitude larger than that of Mittal et al. (2006). These experiments might have been influenced by impurities present in the acetaldehyde (Mueller et al. 1999). Vardanyan et al. (1975) measured the CO 2 production in a CH 2 O flame in the temperature range of 878-952 K. The concentration of HO 2 • radicals was estimated by freezing out the free radicals and analyzing them with electron spin resonance. Based on these measurements, a k 1 value of 7×10 8 cm 3 /mol-s was reported for T = 952 K. Using a similar approach, Arustamyan et al. (1980) studied the slow oxidation of CO in the presence of H 2 in a flow system for temperatures of 803-843 K and pressures of 300-530 Torr. By following the CO 2 production rate, a k 1 value of 1.1×10 8 cm 3 /mol-s may be obtained from the modeling of the overall reaction process. The only experiment that produced a rate value close to that of Mittal et al. (2006) was that of Hoare and Patel (1969), who measured k 1 relative to C 2 H 6 + HO 2 • → C 2 H 5 • + H 2 O 2 (R3.3) C 2 H 4 + HO 2 • → products (R3.4) 33 at temperatures 734 and 773 K. Unfortunately neither k 3 of R3.3 nor k 4 of R3.4 is accurately known, and the resulting k 1 value is still highly uncertain. Reaction R3.1 has also been the subject of a few theoretical studies. Allen et al. (1996) carried out single-point CISD calculations at geometries optimized at the HF/6-31G (d) level of theory. Based on the resulting potential energy surface, they proposed that the reaction proceeds through a chemically activated path via the trans- HOOC•O adduct: [ ] * 22 CO HO -HOOCO CO OH trans +→ → + ii i (R3.1’) The ground-state of the adduct was predicted to be a shallow well, lying 11.6 kcal/mol above the entrance channel, and with critical energies of only 11 and 7 kcal/mol for dissociation into CO + HO 2 • and CO 2 + •OH, respectively. The shallowness of the well suggests that the discrepancy in k 1 between Mittal et al. (2006) and earlier measurements cannot be attributed to its pressure dependency, since collision stabilization of the adduct is expected to be inefficient for pressures up to several hundred atmospheres. Very recently, Sun et al. (2007) computed k 1 using canonical transition state theory based on G3MP2 energies and optimized MP2 (full)/6-31G (d, p) geometries. They considered only the trans-conformer pathway, as did Hsu et al. (1996), and presented a theoretical expression for k 1 of () 3 5 2.28 8830 1 cm mol s 1.15 10 T kTe − ⋅= × for 300 ≤ T ≤ 2500 K. Within the temperature range of 950 to 1100 K, this theoretical rate coefficient is well within a factor of 2 from the rate coefficient obtained from the RCM experiment. 34 Unfortunately, these prior theoretical efforts are insufficient to ensure an accurate rate coefficient. In all cases, the hindered internal rotations in the HOOC•O adduct and the critical geometries were inadequately treated; and the complexity of the potential energy surface due to the trans- and cis-conformers and their mutual isomerization was not considered. In addition, the calculations of the potential energy barriers may not be sufficiently reliable to obtain accurate k 1 values. The purpose of the present study is to provide an improved theoretical treatment of reaction R3.1. This treatment includes a more detailed analysis of the potential energy surface of reaction R3.1 using several high-level quantum chemistry methods. The best estimates for the saddle point energies are then incorporated in transition state theory simulations that consider the full complexity of the hindered rotational motions. Furthermore, the possibility of collisional stabilization and the dissociation of the adduct back to CO + HO 2 • along the trans pathway is examined via master equation simulations. 3.2 Computational details 3.2.1 Potential energy surface The geometries and vibrational frequencies for all the stationary points considered here were obtained from coupled cluster theory with single and double excitations, including perturbational estimates of the effects of the connected triple excitations, CCSD(T), and employing Dunning’s correlation consistent cc-pVTZ basis sets. Additional single-point calculations were performed at the CCSD (T)/cc-pVQZ 35 level of theory and the CCSD (T)/cc-pVTZ geometries. The results of G3B3 calculations are also reported here for comparison. All the CCSD (T) and G3B3 ab initio calculations were carried out using the Gaussian 03 program package (Frisch et al. 2004). Basis set extrapolation was carried out following the method (Halkier et al. 1998), 3 CCSD(T) CCSD(T) () ( ) EX E aX − ≈∞+. (3.1) where CCSD(T) () EX and CCSD(T) () E ∞ are the CCSD(T) energies with the cc-pVXZ basis set and at the CBS limit, respectively. The basis sets cc-pVDZ, cc-pVTZ, and cc- pVQZ have X =2, 3, and 4, respectively. The resulting CCSD(T)/CBS energy is CCSD(T)/CBS CCSD(T)/cc-pVQZ CCSD(T)/cc-pVQZ CCSD(T)/cc-pVTZ 27 37 EE E E ⎡ ⎤ ≈+× − ⎣ ⎦ , (3.2) where CCSD(T)/cc-pVQZ E is the single-point energy at the CCSD(T)/cc-pVTZ geometry. In addition to basis set extrapolation, an approximate correction was also made for the CI truncation error using the somewhat empirical scaling method proposed by He et al. (2000). The same method was adopted by Yu et al. (2001) in their study of CO + •OH = CO 2 + H•. Let CCSD(T)/cc-pVTZ T E be the perturbation energy of the connected triple excitations at the CCSD(T)/cc-pVTZ level of theory. The CI truncation error may be estimated to be 20~25% of CCSD(T)/cc-pVTZ CCSD(T)/cc-pVTZ CCSD/cc-pVTZ T EE E =− (He et al. 2000). Therefore, the full coupled cluster/complete basis set (FCC/CBS) energy may be estimated to be 36 FCC/CBS CCSD(T)/cc-pVQZ CCSD(T)/cc-pVQZ CCSD(T)/cc-pVTZ T CCSD(T)/cc-pVTZ 27 37 1 5 EE E E E ⎡ ⎤ ≈+× − ⎣ ⎦ + . (3.3) During the course of the study, it was found that the T1 diagnostic of our CCSD(T) calculation is modestly larger than 0.02 for the two key transition states (TS1 following the trans pathway and TS3 following the cis pathway of CO + HO 2 • addition, as described below). This finding casts some doubt on the reliability of single-reference based CCSD(T) correlation treatments for these transition states (Lee et al. 1990). For this reason, multireference CASPT2 (Werner 1996; Celani and Werner 2000) and configuration interaction (MRCI) calculations were also carried out, with the goal of delineating the uncertainty of the energy barriers for such cases. These calculations focused on TS1, since similar results are expected for the closely related TS3. For these calculations, the geometry was optimized with a 5 electron 5 orbital (5e,5o) CASPT2 calculation employing Dunning’s correlation consistent aug- cc-pVTZ basis set. The 5 active orbitals in this calculation correlate with the π and π* orbitals of CO, and the radical orbital of HO 2 • (i.e., the O 2 π* orbital). Single-point calculations at these geometries were performed with 9 electron 8 orbital (9e,8o), and 11 electron 10 orbital active spaces (11e,10o). The (9e,8o) active space included the O 2 π, pσ and pσ* orbitals. The (11e,10o) space added the CO pσ and pσ* orbitals to the (9e,8o) active space. These CASPT2 and MRCI calculations were performed with the MOLPRO software package (Werner et al. 2006). 37 3.2.2 Reaction rate coefficients Rate coefficients were calculated using a Monte Carlo code for the solution of the master equation of the collision energy transfer, as reported previously (Joshi and Wang 2006). Briefly, for the reaction path through the trans-HOOC•O adduct, the time evolution of a rovibrationally excited molecule is described by the master equation in discrete form, [ ] [] () [] () () () A( ) MA MA A i ij j ji i m i i ji m dE kE k E kE E dt ⎡⎤ =− − ⎡⎤⎡⎤ ⎣⎦⎣⎦ ⎣⎦ ∑∑ ∑ (3.4) where () A i E ⎡⎤ ⎣⎦ denotes the concentration of species A at the energy state i E ; [ ] M is the concentration of bath-gas molecules; ij k is the rate constant for the collision energy transfer from energy state j to state i, and ( ) mi kE is the microcanonical rate constant for the m th channel, which also accounts for the dissociation of the adduct back to CO + HO 2 •. In this formulation, the bimolecular rate coefficient of CO + HO 2 • is handled by the equilibrium constant of CO + HO 2 • addition. The collisional energy transfer probability was described by the exponential down model, with down E Δ = 260 cm –1 . Because of the shallow potential energy well, the stabilization of the adduct is minimal and the computed k 1 value was insensitive to the down E Δ value. Monte Carlo simulations used an energy grain size equal to 10 cm –1 , as in a previous study (Joshi and Wang 2006). 38 For the cis-pathway, it will be shown that a potential energy minimum does not exist along the reaction path, and, as such, its contribution to the overall rate is calculated with conventional transition state theory: 0 / u ERT TS B reac Q kT ke hQ − = (3.5) where k B is Boltzmann’s constant, h is Planck’s constant, Q is the total partition function, E 0 is the energy barrier, and u R is the universal gas constant. 3.2.3 Hindered internal rotation There are two hindered rotors in the HOOC•O adduct and in the transition states associated with the adduct: about the HOO—C•O bond and the HO—OC•O bond. The HOO—C•O internal rotation is responsible for the mutual isomerization of the trans- and cis- conformers along the reaction path. Both hindered rotors are expected to influence the partition functions of the internal degrees of freedom. Here the energy barriers for these hindered internal rotors were examined at the B3LYP/6- 31G(d) and CCSD(T)/cc-pVTZ levels of theory. Moment of inertia were estimated using several approaches, following East and Radom (1997). Here the various approximations are denoted as I (m,n) for moment of inertia or B (m,n) for the rotational constant, where n denotes the level of approximation for a rotor attached to a fixed frame due to coupling with external or other internal rotation; while the m indicates the level of approximation of the coupling reduction. At a lower level of approximation, the moment of inertia may be given as 39 (1, ) (1, ) (2, ) (1, ) (1, ) nn n LR nn LR II I II = + (3.6) where subscript L and R indicate the “left” and “right” rotating group of the twisting bond, respectively. For n = 1, the moment of inertia is calculated by assuming the rotational axis to be the twisting bond; and for n = 2, the axis is assumed to be parallel to the twisting bond but passing through the center of mass of the rotating group. For n = 3, the axis passes through the centers of mass of both the rotating groups and the remainder of the molecule. These approximations have been extensively used in previous theoretical rate studies (see, e.g., (Gilbert and Smith 1990)). During the course of this study, the theoretical k 1 value was found to be quite sensitive to the approximations made for the moments of inertia of the hindered internal rotors. For this reason, they were treated with some care, by considering fully the coupling with external rotation (Pitzer 1946; East and Radom 1997). In this approach, two coordinate systems are defined. The first (x, y, z) is attached to one of the two rotating moieties; and the second is associated with the principal axes of external rotation (1, 2, 3). It may be shown that the moment of inertia is independent of the choice of the moiety (“left” or “right”) selected for the (x, y, z) coordinates (East and Radom 1997). The z axis is the twisting bond, and the x axis passes through the center of mass of a rotating moiety. The axes of the rotating moiety (x, y, z) and the axes of the parent molecule are both right-handed with α ix , α iy , and α iz being the direction cosines between the two sets of coordinate, where i = 1, 2, and 3 for principal axes 1, 2, and 3, respectively. The moment of inertia is given by 40 ( ) 2 2 3 (3, 4) (1,1) 1 iy i i LR i U II mm I α β = ⎡ ⎤ ⎢ ⎥ =− + ⎢ ⎥ + ⎣ ⎦ ∑ (3.7) where (1,1) I is the moment of inertia about the z axis, ( ) (1,1) 2 2 jj j jLorR I mx y ∈ =+ ∑ . (3.8) m j is the mass of the j th atom, and x j and y j are the position of the j th atom in the (x, y, z) coordinates. In eq. (3.7), U is the off-balance factor, given by jj jLorR Umx ∈ = ∑ ; (3.9) β i is given by ( ) (1,1) 1, 1 1, 1 iiz ix iy iyi iyi I CDU r r βα α α α α − ++ − =− − + − , (3.10) where the subscripts i–1 and i+1 refer to cyclic shifts of axes so that i–1 = 3 if i = 1, and i+1=1 if i=3, r i is the distance along the i th coordinate from the center of mass of the parent molecule to the origin of coordinates of the rotating moiety; and C and D are the cross products, which are given respectively by jj j jLorR Cmxz ∈ = ∑ , (3.11) jj j jLorR Dmyz ∈ = ∑ . (3.12) For the current calculation, the non-symmetric nature of the hindered internal rotations in HOOC•O and its transition states was considered. Specifically, the two potential energy wells following a full internal rotation are assumed to be 41 asymmetric about the minima (see, Figure 3.2). The potential energy can be expressed in four separate parts: V 02 V 03 0 π/2 π 3π/2 2π Potential Energy Rotation Angle, φ V 01 V 04 Figure 3.2 Schematic illustration of the potential energy function for the asymmetric, hindered internal rotation. 42 () () () ( ) () ( ) () 01 02 01 02 03 01 02 04 1 cos 2 0 / 2 2 1 cos 2 / 2 2 1 cos 2 3 / 2 2 1 cos 2 3 /2 2 2 V V VV V V VV V φφπ φ πφπ φ φπφπ φ πφ π ⎧⎛⎞ −≤< ⎡⎤ ⎜⎟ ⎪ ⎣⎦ ⎝⎠ ⎪ ⎪ ⎛⎞ −+− ≤< ⎡⎤ ⎪⎜⎟⎣⎦ ⎪⎝ ⎠ = ⎨ ⎛⎞ ⎪ −+− ≤< ⎡⎤ ⎜⎟⎣⎦ ⎪ ⎝⎠ ⎪ ⎛⎞ ⎪ −≤< ⎡⎤ ⎜⎟⎣⎦ ⎪ ⎝⎠ ⎩ (3.13) where φ is the rotation angle. Obviously, the four potential energy barriers are bound by the relation V 03 = V 04 – (V 01 – V 02 ). The classical partition function of a one- dimensional hindered rotor for the above potential function may be written as () () () 12 4 /2 12 1 4 00102 0 0 1 1 () 2 2 exp 42 2 B i Vk T B h i i f ii i i BB kT QT e d B QT VVV V kT kT π π π φ π δ − − = = ⎛⎞ = ⎜⎟ ⎝⎠ +− ⎡⎤⎛⎞ =− ⎜⎟ ⎢⎥ ⎝⎠ ⎣⎦ ∑ ∫ ∑ I , (3.14) where δ i = 0 for i = 1 and 4, and δ i = 1 for i = 2 and 3, B is the rotational constant, Q f is the partition function in the limit of a free rotor, and I 0 () is the modified Bessel function. The density of energy states for a full 2π internal rotation is a sum of contributions from the four parts of the potential function, () ( ) ( ) ( ) ( ) 1 234 hh h h h E EE EE ρρ ρ ρ ρ =+ + + (3.15) where 43 () 01 01 01 1 01 01 for 0 2 for 2 h E V EV BV E V E EV BE π ρ π ⎧⎛⎞ ⎪⎜⎟ ⎪⎝⎠ << ⎪ ⎪ = ⎨ ⎛⎞ ⎪ ⎜⎟ ⎪ ⎝⎠ ⎪ > ⎪ ⎩ Κ Κ () () () () () () 01 02 02 01 02 02 02 2 02 01 02 01 02 02 01 02 for 0 2 for 2 h EV V V EV V V BV E V EV V EV V V BE V V π ρ π ⎧⎛⎞ −− ⎪⎜⎟ ⎜⎟ ⎪ ⎝⎠ < −− < ⎪ ⎪ = ⎨ ⎛⎞ ⎪ ⎜⎟ ⎪ ⎜⎟ −− ⎝⎠ ⎪ −− > ⎪ −− ⎡⎤ ⎣⎦ ⎩ Κ Κ () () () () () () 01 02 03 01 02 03 03 3 03 01 02 01 02 03 01 02 for 0 2 for 2 h EV V V EV V V BV E V EV V EV V V BE V V π ρ π ⎧⎛⎞ −− ⎪⎜⎟ ⎜⎟ ⎪ ⎝⎠ <− − < ⎪ ⎪ = ⎨ ⎛⎞ ⎪ ⎜⎟ ⎪ ⎜⎟ −− ⎝⎠ ⎪ −− > ⎪ −− ⎡⎤ ⎣⎦ ⎩ Κ Κ () 04 04 04 4 04 04 , for 0 2 , for 2 h E V EV BV E V E EV BE π ρ π ⎧⎛⎞ ⎪⎜⎟ ⎪⎝⎠ << ⎪ ⎪ = ⎨ ⎛⎞ ⎪ ⎜⎟ ⎪ ⎝⎠ ⎪ > ⎪ ⎩ Κ Κ where E is the energy relative to the lower one of the two potential energy wells, and K() is the complete elliptic integral of the first kind. In eq. (3.15), the four terms 44 correspond to rotations with 0 < φ < π/2, π/2 < φ < π, π < φ < 3π/2, and 3π/2 < φ < 2π, respectively. Because of the unique potential energy surface to be discussed later, there is a need to treat the trans- and cis-conformers separately along the reaction coordinates. Since each of the two potential energy wells illustrated in Figure 3.2 corresponds to a particular conformer, eq. (3.15) may be reduced to only two terms to give the hindered rotation contribution from a particular conformer, as will be discussed later. The total density of states can be obtained by the convolution procedure (Knyazev et al. 1994; Knyazev and Tsang 1998), () ( ) 0 () E hnh EE Eede ρρ ρ =− ∫ (3.16) where nh ρ is the density of states for degrees of freedom other than the hindered rotors. The sum of states is calculated by integrating ρ(E) 0 () () E WE ede ρ = ∫ (3.17) The integration employed an energy spacing value equal to 1 cm −1 , which is sufficiently small to accurately compute ρ(E) and W(E) around the singularity point of E = V 0 (Knyazev et al. 1994). 3.3 Results and discussion The potential energy surface (PES) of reaction R3.1 is somewhat complicated by the existence of trans- and cis-conformers. At the B3LYP/6-31G(d) 45 level of theory, a relaxed potential energy scan shows that trans-HOOC•O is a local minimum with two exit channels, one leading to CO + HO 2 • (TS1) and the other leading to CO 2 + •OH (TS2), as seen in Figure 3.3. For cis-HOOC•O, a local minimum either does not exist or the potential energy well is too shallow to be of any importance. Figure 3.3 Relaxed potential energy scan for (CO + HO 2 •) → TS1 → trans- HOOC•O → TS2 → (CO 2 + •OH) at the B3LYP/6-31G(d) level of theory without zero point correction. 46 Figure 3.4 presents the companion potential energy scan for the cis- configuration. Here the only saddle point corresponds to the direct CO + HO 2 • → CO 2 + •OH reaction through TS3. The qualitative PES feature observed at the B3LYP/6-31G(d) level of theory is consistent with calculations carried out using the CCSD(T)/cc-pVTZ method, though in the latter case only a limited PES scan is performed. Figure 3.4 Relaxed potential energy scan at the B3LYP/6-31G(d) level of theory without zero point correction, showing the reaction (CO + HO 2 •) → TS3 → CO 2 + •OH. cis-HOOC•O is represented by a local inflection point without a pronounced energy well. 47 A schematic diagram illustrating the various stationary points along the trans and cis reaction pathways is provided in Figure 3.5. The corresponding CCSD(T)/cc-pVTZ geometry parameters are provided in Figure 3.6. These geometries are qualitatively similar to those obtained previously at the HF/6-31G(d) level of theory (Allen et al. 1996) for the trans-conformer and its transition states. Quantitatively, however, there are significant differences, with the CCSD(T)/cc-pVTZ O–O and O–C bond lengths being larger than the HF/6-31G(d) ones by as much as 0.1Å. Table 3.1 lists the absolute energies for the stationary points along these reaction pathways as computed using the semi-empirical G3B3 method and for selected levels of single-reference theories. Here the CCSD(T)/cc-pVTZ energies were obtained from geometries optimized using the same method. The CCSD(T)/cc- PVQZ energies are the results of single-point calculations at the CCSD(T)/cc-pVTZ geometries. Energies extrapolated to the complete basis set (eq. 3.2) are denoted as CCSD(T)/CBS and those including the correction for the CI truncation error (eq. 3.3) are denoted as FCC/CBS. The reaction enthalpies and energy barriers are presented in Table 3.2, where the literature values for the enthalpy of reaction are based on the heats of formation given in Table 3.3. Notably, both the CCSD(T)/CBS and FCC/CBS methods yield calculated reaction enthalpies within 0.5 kcal/mol of the literature value. 48 Table 3.1 Energies (Hartrees) computed at selected levels of theory. G3B3 CCSD(T)/cc-pVTZ CCSD(T) /cc-pVQZ c CCSD(T) /CBS d FCC/CBS e Species E 0 E 0 T1 Diag. ZPE a E T b E 0 E 0 E 0 O2 -150.25273 -150.12904 0.003795 -0.01796 -150.17386 -150.20658 -150.21017 •OH -75.69637 -75.63772 0.008531 -0.00510 -75.66163 -75.67908 -75.68010 CO -113.26997 -113.15558 0.004907 -0.01714 -113.18787 -113.21143 -113.21485 CO2 -188.50435 -188.32722 0.011831 -0.02875 -188.38452 -188.42633 -188.43208 HO2• -150.82995 -150.71272 0.014231 -0.01715 -150.75988 -150.79429 -150.79773 HC•O -113.79409 -113.68411 0.013000 -0.01712 -113.71782 -113.74242 -113.74584 HOOC•O -264.08981 -263.86006 0.020 0.023732 -0.03862 -263.94091 -263.99991 -264.00764 TS1 -264.07072 -263.84072 0.028 0.021468 -0.03904 -263.92096 -263.97951 -263.98732 TS2 -264.08075 -263.84751 0.021308 -0.04115 -263.92858 -263.98773 -263.99596 TS3 -264.06920 -263.83881 0.028 0.021287 -0.03984 -263.91913 -263.97774 -263.98571 TS4 -264.07527 -263.84451 0.022808 -0.03857 -263.92525 -263.98416 -263.99187 a Zero-point energy using the vibrational frequencies as calculated. For CO, CO 2 and •OH the average deviation of the vibrational frequencies from the experimental values is < 1%, whereas for HO 2 • the deviation is 4.5%. b The triple excitation CCSD(T)/cc-pVTZ T E . c Single point calculation at CCSD(T)/cc- pVTZ geometry. d See text and eq. 3.2. e See text and eq. 3.3. Table 3.2 Energies (kcal/mol) at 0 K relative to CO + HO 2 •. Products/ transition state G3B3 CCSD(T)/ cc-pVTZ CCSD(T)/ cc-pVQZ a CCSD(T)/ CBS FCC/CBS Literature value CO 2 + •OH -63.3 -59.9 -61.0 -61.8 -61.7 -61.6±0.1 HOOC•O 6.3 8.1 7.2 6.5 6.0 TS1 18.3 18.8 18.3 17.9 17.3 TS2 12.0 14.4 13.4 12.7 11.8 TS3 19.3 19.9 19.3 18.9 18.2 TS4 15.5 17.2 16.4 15.8 15.3 HC•O + O 2 33.3 33.1 33.7 34.1 34.0 33.6±0.1 a With CCSD(T)/cc-pVTZ zero-point energies. 49 Table 3.3 Literature values of enthalpy of formation (kcal/mol). a Δ f H 0 values are obtained from Δ f H 298 and the sensible enthalpy values taken from Chase (1998). The CCSD(T)/CBS and FCC/CBS energy barriers are 17-18 kcal/mol for the addition of CO and HO 2 • following the trans path (TS1) and around 18-19 kcal/mol following the cis path (TS3). Without basis set extrapolation, these energy barriers are generally 0.5-1.0 kcal/mol larger than with basis set extrapolation. Interestingly, energy barriers predicted by the G3B3 method are within ~1 kcal/mol of to the CCSD(T)/CBS results, but this agreement may be fortuitous, since the G3B3 enthalpy of reaction R3.1 is ~2 kcal/mol too low compared to the literature value (see, Table 3.2). There are two pathways for trans-HOOC•O dissociation into CO 2 and •OH, as shown in Figure 3.5. The first path is a single O–O fission (TS2), and it requires only 6.2 kcal/mol of energy barrier. The second path involves trans → cis isomerization or internal rotation about HOO–C•O bond. Because cis-HOOC•O does not have a pronounced local energy minimum, the reaction path upon this isomerization collapses onto the cis-pathway, as shown in Figure 3.5. Species Δ f H 298 Δ f H 0 Reference •OH 8.9 ±0.07 8.8 (Ruscic et al. 2002) HO 2 • 2.9±0.1 3.6 (Ruscic et al. 2006) a CO -26.4 ±0.04 -27.2 (Burcat and Ruscic 2005) a CO 2 -94.1 ±0.003 -94.0 (Burcat and Ruscic 2005) a HC•O 10.1 ±0.07 10.0 (Marenich and Boggs 2003) 50 0 CO+HO 2 • TS1 (trans) 17.9 trans-HOOC•O TS2 (trans) 12.7 –61.8 TS3 (cis) 18.9 TS4 Internal rotation (trans →cis) 15.8 cis-HOOC•O (no stationery geometry found) 6.5 CO 2 +•OH TS5 22.8 HCO 3 • 32.8 HC•O+O 2 TS6 35.1 TS7 35.7 -1.1 0 CO+HO 2 • TS1 (trans) 17.9 trans-HOOC•O TS2 (trans) 12.7 –61.8 TS3 (cis) 18.9 TS4 Internal rotation (trans →cis) 15.8 cis-HOOC•O (no stationery geometry found) 6.5 CO 2 +•OH TS5 22.8 HCO 3 • 32.8 HC•O+O 2 TS6 35.1 TS7 35.7 -1.1 Figure 3.5 Potential energy diagram for CO + HO 2 • → products. For CO + HO 2 • → CO 2 + •OH, the energy values are determined using the CCSD(T)/CBS method, and include zero-point energy corrections. For CO + HO 2 • → HC•O + O 2 , the energy values are taken from Martinez-Avila et al. (2003) at QCISD(T)/6-311G(2df,2p)//QCISD/6- 311G(d,p) level of theory. Table 3.4 Multireference energies a With 1.38 kcal/mol zero-point energy correction from PT2(5e,5o)/atz. Electronic energy (Hartree) Critical energy (kcal/mol) Geom. Opt. (Active Space) Species PT2/CBS CI/CBS CI+QC/CBS PT2/CBS a CI/CBS a CI+QC/CBS a PT2(5e,5o) CO+HO 2 • -263.95871 -263.86127 -263.96559 TS1 -263.93363 -263.82223 -263.93379 17.1 25.9 21.3 PT2(9e,8o) CO+HO 2 • -263.96020 -263.88270 -263.97633 TS1 -263.93333 -263.84389 -263.94445 18.2 25.7 21.4 PT2(11e,10o) CO+HO 2 • -263.96211 TS1 -263.93497 18.4 51 The T1 diagnostic computed for TS1 and TS3 casts some minor doubt on the reliability of the single-reference based CCSD(T) correlation energies. For this reason, the energetics of TS1 with CASPT2 and MRCI calculations was also explored, as reported in Table 3.4. The CASPT2 predictions of 18.2 and 18.4 kcal/mol for the TS1 barrier with the (9e,8o) and (11e,10o) active spaces are in good agreement with the CCSD(T)/CBS barrier of 17.9 kcal/mol, but are larger than the FCC/CBS barrier by about 1 kcal/mol. The somewhat lower value of 17.1 for the (5e,5o) active space is likely due to the importance of including the O-O π orbital in the active space. It has been found to be of similar importance in other related studies of radical + O 2 reactions. The MRCI calculations yield a much higher TS1 barrier of about 26 kcal/mol. The Davidson corrected (CI+QC) TS1 barrier of about 21 kcal/mol is much closer to the CCSD(T) and CASPT2 values. It appears that the Davidson correction is qualitatively correct, but not quantitatively so. In related calculations for C 2 H 4 + •OH and for radical-radical abstraction reactions, it is similarly found that CASPT2 appears to provide a more consistent set of barriers (Klippenstein and Harding 2007) and that the Davidson correction is not quite as large as it needs to be. Thus, it appears reasonable to assume that the TS1 barrier is 17.9 kcal/mol, i.e., an average among the barrier values from CCSD(T)/CBS, FCC/CBS, and CASPT2 with the (9e,8o) and (11e,10o) active spaces. The error bar on the energy barrier is expected to be ± 1 kcal/mol, which corresponds to our experience for the typical uncertainty in CCSD(T) calculations of transition state energies and is also supported by the CASPT2 results. 52 The CI and CI+QC calculations suggest that the upper error bar may be larger, but, importantly, there is no indication that the lower error bar should be any larger. 1.391 1.742 1.150 0.968 θ (O 5 CO 3 )=122.5, θ (CO 3 O 2 )=108.1 θ (O 3 O 2 H)=102.2, τ (O 5 CO 3 O 2 )=–4.7 τ (HO 2 O 3 C)=90.9 θ (O 5 CO 3 )=127.9, θ (CO 3 O 2 )=103.9 θ (O 3 O 2 H)=99.6, τ (O 5 CO 3 O 2 )=89.6 τ (HO 2 O 3 C)=107.2 1.456 1.354 1.184 0.967 1.615 1.267 1.190 0.971 1.400 1.758 1.149 0.969 1.460 1.412 1.175 0.967 TS1 trans-HOOC•O TS2 TS3 TS4 θ (O 5 CO 3 )=118.2, θ (CO 3 O 2 )=112.0 θ (O 3 O 2 H)=102.0, τ (O 5 CO 3 O 2 )=172.7 τ (HO 2 O 3 C)=92.3 θ (O 5 CO 3 )=124.6, θ (CO 3 O 2 )=108.1 θ (O 3 O 2 H)=99.1, τ (O 5 CO 3 O 2 )=177.2 θ (HO 2 O 3 C)=113.9 θ (O 5 CO 3 )=137.4, θ (CO 3 O 2 )=106.0 θ (O 3 O 2 H)=95.3, τ (O 5 CO 3 O 2 )=180.0 τ (HO 2 O 3 C)=180.0 Figure 3.6 Geometry parameters determined at the CCSD(T)/cc-pVTZ level of theory. The bond lengths are in Å; and the bond and dihedral angles are in degrees. For comparison, the potential energies for the reaction CO + HO 2 • → HC•O + O 2 , (R3.5) are also presented in Figure 3.5, based on QCISD(T)/6-311G(2df,2p)//QCISD/6- 311G(d,p) results of Martinez-Avila et al. (2003). The formation of the HCO 3 • adduct has an energy barrier around 23 kcal/mol, and the exit HC•O + O 2 channel has energy barriers around 35 kcal/mol. These barrier heights essentially rule out any importance of reaction R3.5 towards the total rate constant of CO + HO 2 • → products. 53 The treatment of hindered internal rotation requires special consideration. The two rotors in question are those for rotating about the O–O and O–C bonds. The rotation about the O–C bond is responsible for the key trans-to-cis mutual isomerization. Figure 3.7 presents the potential energies for these two hindered internal rotations in HOOC•O and TS1. These potential energies were computed at the B3LYP/6-31G(d) and CCSD(T)/cc-pVTZ levels of theory. Except for the dihedral angle, the geometries are frozen during potential energy scans. Thus, the relative energies are expected to be somewhat larger than the true values. For example, the CCSD(T)/cc-pVTZ energy difference between TS3 and TS1 is 1.3 kcal/mol, whereas the rotation scan based on frozen geometries gives 1.8 kcal/mol (see, the lower-right panel of Figure 3.7). These differences are considered in our assessment of the accuracy of the theoretical rate coefficient, as will be discussed later. In the adduct, the rotational energy barrier for the HO–OC•O torsion is highly asymmetric, with barrier heights of roughly 0.6 and 3 kcal/mol. For the HOO– C•O torsion, the energy barrier is notably higher, being about 12 kcal/mol. In TS1, the HO–OC•O rotational barrier increases to about 9 kcal/mol, while the rotation about the HOO–C•O bond decreases to about 4 kcal/mol. The barrier heights calculated for TS3 are of a similar magnitude, as illustrated in Figure 3.8. 54 0 1 2 3 4 0 100 200 300 400 500 600 Relative Energy (kcal/mol) Rotation about HO-OC . O trans-HOOC . O trans-HOOC . O 0 4 8 12 100 200 300 400 500 600 Rotation about HOO-C . O trans-HOOC . O"cis-HOOC . O" trans-HOOC . O "TS4" 0 2 4 6 8 10 12 100 200 300 400 500 Relative Energy (kcal/mol) Dihedral Angle, degree Rotation about HO-OC . O (TS1) TS1 TS1 0 1 2 3 4 5 6 150 200 250 300 350 400 450 500 550 Dihedral Angle, degree Rotation about HOO-C . O (TS1) TS1 TS1 "TS3" Figure 3.7 Energy scans for internal rotation in HOOC•O (top panels) and TS1 (bottom panels), computed at the CCSD(T)/cc-pVTZ (symbols and solid lines) and B3LYP/6-31G(d) (dotted lines) levels of theory. Except for the dihedral angle, geometries are frozen at those of trans-HOOC•O and TS1, respectively. Species/critical geometries given in quotes designate structures close to the respective optimized geometries. 55 0 5 10 15 -100 0 100 200 300 Relative Energy (kcal/mol) Dihedral Angle, degree Rotation about HO-OC . O (TS3) TS3 TS3 -1 0 1 2 3 0 100 200 300 400 Relative Energy (kcal/mol) Dihedral Angle, degree Rotation about HOO-C . O (TS3) "TS1" TS3 TS3 Figure 3.8 Energy scans for internal rotation in TS3, computed at the CCSD(T)/cc-pVTZ (symbols and solid lines) and B3LYP/6-31G(d) (dotted lines) levels of theory. Except for the dihedral angle, geometries are frozen at those of TS3. Critical geometry given in quotes designates a structure close to the optimized geometry. The absence of a potential minimum along the cis-pathway suggests that it is best to treat the cis and trans reaction pathways separately. This separation is 56 accomplished by excluding the contribution of the cis-configuration to the partition function of the HOO–C•O hindered rotor for the trans-pathway and vice versa for the trans-configuration in the cis-pathway. Specifically, the partition functions of HOO– C•O and TS1 were obtained by integrating over a rotation angle of φ = –π/2 to π/2, or equivalently 0 < φ ≤ π/2 and 3π/2 < φ ≤ 2π. In other words, for these species the partition function given by eq. (3.15) is truncated to only two terms, ( ) ( ) ( ) 14 hh h EEE ρρ ρ =+ (3.18) Likewise, TS3, the transition state of CO + HO 2 • on the cis-pathway, is treated by neglecting contributions from the trans-part of the partition function. For the internal rotation about the HO–OC•O bond, the partition function is given by eq. (3.15), where the asymmetric nature of the potential function is closely accounted for. The internal rotational constants vary widely, depending on the level of approximation. For example, the B values for rotation about the HOO–C•O bond of trans-HOOC•O are 1.6, 14, and 4.1 cm –1 for B (2,1) , B (2,3) , and B (3,4) , respectively. It is worth noting that the rotational constant is expected to be related to the force constant through the relation () 2 22 2 B dV d ν φ = , (3.19) where ν is the vibrational frequency. Using the CCSD(T)/cc-pVTZ frequency value of 249 cm –1 , and the potential energy shown in the upper-right panel of Figure 3.7, B is equal to 3.8 cm –1 , which is in reasonably good agreement with the B (3,4) value. 57 Furthermore, the B (3,4) value is the fundamentally most appropriate value and was thus adopted for all hindered internal rotations. Table 3.5 lists the molecular parameters used in the rate calculation. Master equation modeling shows that, due to the shallow trans-HOOC•O potential energy well, there is no appreciable collisional stabilization of the rovibrationally excited trans-HOOC•O adduct for pressures up to 500 atm. Hence, for combustion applications the overall rate constant may be modeled as being independent of pressure. On the other hand, the trans-HOOC•O adduct has a finite, albeit short lifetime. At high temperatures, the overall rate constant through the trans-pathway is influenced by the back dissociation to CO + HO 2 •. The contribution of the trans- pathway to the total rate coefficient is calculated to be ( ) 3 5 1.87 8950 1, cm mol s 6.8 10 T trans kTe − ⋅= × over the temperature range of 300 to 2500 K. Conventional transition state theory calculations yield a cis-pathway contribution to the total rate coefficient of ( ) 3 4 2.39 9260 1, cm mol s 2.2 10 T cis kTe − ⋅= × over the same temperature range. The trans-pathway contributes 83, 55, and 42% of the total rate constant for T = 300, 1000, and 2000 K, respectively. As mentioned before, the decrease of the trans contribution with an increase in temperature is caused by the increasingly competitive dissociation of the rovibrationally excited trans- HOOC•O back to CO + HO 2 • at higher temperatures. 58 Table 3.5 Molecular properties used for computing the rate coefficient of CO + HO 2 • → CO 2 + •OH Species E 0 a B(cm –1 ) Hindered internal rotors d (kcal/ mol) inactive b active c mode B(cm –1 ) range V 0 e (kcal /mol) v (cm −1 ) h CO 1.91 2154 HO 2 • 20.5& 1.1(2) 1135, 1437, 3674 trans- HOOC•O 6.5 0.155 2.24 HO-OC•O20.5 0<φ ≤π/2 0.6 3π/2<φ ≤2π 3.0 π/2<φ ≤π 0.5 π<φ ≤3π/2 2.9 HOO-C•O4.1 0<φ ≤π/2 11.4 3π/2<φ ≤2π 12.0 189 f , 249 f , 352, 592, 931, 1047, 1414, 1861, 3781 TS1 17.9 0.133 1.89 HO-OC•O20.8 0<φ ≤π/2 8.8 3π/2<φ ≤2π 9.0 π/2<φ ≤π 8.6 π<φ ≤3π/2 8.8 HOO-C•O3.6 0<φ ≤π/2 3.1 3π/2<φ ≤2π 3.8 661.1i, 129.6 f , 265, 417 f , 446, 972, 1429, 2016, 3748 TS2 12.7 0.149 2.02 HO-OC•O 19.6 0<φ ≤2π 2.8 g 1535i, 77 f, 322, 343, 784, 928, 1233, 1916, 3749 TS4 15.8 0.179 1.04 HO-OC•O19.6 0<φ ≤π/2 2.5 g 3π/2<φ ≤2π 7.8 g π/2<φ ≤π 1.9 g π<φ ≤3π/2 7.3 g 290i, 290 f , 325, 617, 852, 877, 1380, 1894, 3776 TS3 18.9 0.172 0.77 HO-OC•O19.5 0<φ ≤π/2 9.6 3π/2<φ ≤2 10.0 π/2<φ ≤π 9.7 π<φ ≤3π/2 10.1 HOO-C•O6.5 π/2<φ ≤π 2.1 π<φ ≤3π/2 2.8 705i, 103 f , 224, 467 f , 473, 929, 1400, 2013, 3736 a Relative to the energy of CO+HO 2 • at 0 K. b With the exception of HO 2 •, these are two-dimensional external inactive rotors (symmetry number σ=1). c One-dimensional external rotors (symmetry number σ=1). d One- dimensional hindered rotors (symmetry number σ=1). e Unless otherwise indicated, the energy barriers of hindered rotor V 0 (kcal/mol) are estimated from CCSD(T)/cc-pVTZ potential energy scan. f Vibrational mode replaced by hindered internal rotation. g The energy barriers of hindered rotor V 0 (kcal/mol) are estimated from B3LYP/6- 31G(d) potential energy scan. These barrier values may be slightly over estimated. h From CCSD(T)/cc-pVTZ calculation (fully optimized geometry and numerical secondary derivatives). 59 The total pressure independent rate coefficient, given as the sum of those for the two “channels”, is () 3 5 2.18 9030 1 cm mol s 1.57 10 T kTe − ⋅= × for 300 ≤ T ≤ 2500 K, (3.20) where the fitting error is less than 5% over the entire range of temperature. Figure 3.1 shows a comparison of the current theoretical predictions for the rate coefficient with previous studies and evaluations. The same Arrhenius plot is shown over a narrower temperature region in Figure 3.9. Clearly the current analysis supports the lower k 1 values based on the RCM analysis (Mittal et al. 2006; 2007). Quantitatively, our k 1 expression is within 10% of the expression of Mittal et al. over the temperature range of 950 to 1100 K. Although this close agreement may be fortuitous, the current results, obtained from very high level quantum chemistry calculation and master equation modelling with a careful treatment of internal rotor, clearly supports the notion advanced in these RCM studies that the literature rate values for k 1 are too large. To illustrate the need to properly treat the hindered internal rotors and their reduced moments of inertia, Table 3.6 presents k 1 values obtained at several levels of theoretical approximations. As expected, the limiting case of the free-rotor treatment (with I (3,4) ) yields k 1 values substantially larger than those of the harmonic oscillator treatment, by approximately by a factor of 10. The different treatments for the reduced moment inertia can lead to an uncertainty of a factor of ~2. In particular, rate constants from I (2,1) are a factor of ~2 larger than those from I (3,4) . Thus the 60 combined uncertainty is expected to be of a factor of 20, which underscores the need for an accurate treatment of the hindered internal rotor. The hindered rotor approach gives k 1 values much closer to the harmonic oscillator than to free rotor, but the close agreement between hindered rotor and harmonic oscillator treatments is fortuitous at best, since the relevant vibrational frequencies are generally < 150 cm -1 , and thus the harmonic approximation for these otherwise anharmonic oscillators are dubious at best. An important point here is that without a careful treatment of the hindered rotors, the uncertainty in the theoretical rate constant is as large as the scatter in the experimental data shown in Figure 3.1, and even more importantly the true uncertainty in the theoretical k 1 cannot be quantified. Table 3.6 Effect of internal rotor treatments on k 1 (cm 3 /mol·s). Hindered rotor T(K) Harmonic oscillator Free rotor with I (3,4) I (2,1) I (2,3) I (3,4)* 500 2.1×10 3 3.8×10 4 2.9×10 3 1.5×10 3 1.7×10 3 1000 5.6×10 7 6.1×10 8 1.1×10 8 6.3×10 7 6.5×10 7 1500 2.6×10 9 2.1×10 10 5.5×10 9 3.4×10 9 3.2×10 9 2000 2.2×10 10 1.4×10 11 4.7×10 10 2.9×10 10 2.7×10 10 2500 8.8×10 10 4.6×10 11 1.9×10 11 1.2×10 11 1.1×10 11 * Theory with which the final theoretical rate constant was computed. Our earlier discussion placed an uncertainty bar of ±1 kcal/mol on the reaction energy barriers. Sensitivity tests showed that k 1 is the most sensitive to the 61 energy values of TS1 and TS3, and the energy barriers of internal rotation between TS1 and TS3. Assuming that all of these barrier values are accurate to within ±1 kcal/mol, plus an additional, temperature-independent uncertainty of 50% in state counting, the theoretical upper and lower limits for k 1 were obtained, as shown by the thick, dashed lines in Figure 3.9. The corresponding uncertainty factors are about 8, 2 and 1.7 for temperatures at 300, 1000 and 2000 K. Almost all earlier experimental rate values may now be rejected in light of the current analysis. An inspection of Figure 3.9 shows that the measurements reported by Baldwin and coworkers (Baldwin et al. 1965; Baldwin et al. 1970; Atri et al. 1977) fall above the upper bound of the current theoretical results. In addition, the k 1 expression of Mueller et al. (1999) is close, but above our upper limit, whereas the rate values of Sun et al. (2007) are within our uncertainty bounds, despite the fact that only the trans-configuration was considered in their analysis. It is worth noting that the rate coefficient for the second channel (reaction R3.5) is substantially smaller than the current theoretical k 1 value. The k 5 values of R3.5 may be estimated from the rate coefficient of the back reaction (Hsu et al. 1996) to be 3×10 5 and 2×10 9 cm 3 /mol-s at 1000 and 2000 K, respectively, which are no larger than 10% of k 1 , as expected from the potential energy differences of reaction R3.1 and R3.5, as seen in Figure 3.5. 62 10 6 10 7 10 8 10 9 10 10 10 11 0.6 0.8 1.0 1.2 1.4 k 1 (cm 3 /mol-s) 1000K/T Mueller et al. Sun et al. This work Tsang and Hampson Upperlimit (this work) Lowerlimit (this work) Figure 3.9 Experimental and theoretical rate coefficient for reaction R3.1. See the caption of Figure 3.1 for source of experimental data. The thick, dashed lines indicate the uncertainty bound of the current theoretical expression (see text). Since this work was completed, another study of the PES and rate constant of reaction R3.1 was presented at a recent conference (Asatryan et al. 2006). The 63 present study supersedes this unpublished study in a number of ways. The study of Asatryan et al. (2006) includes a broader analysis of the potential energy surface, but employs considerably lower level quantum chemical methods (CBS/QB3, CCSD(T)/6-311+G(d,p)//B3LYP/6-311G(d,p), and CBS-APNO) and appears to focus on only the trans-pathway. The resulting predictions for the energy barrier for the CO + HO 2 • addition ranged from 15.4 to 19 kcal/mol and no conclusion could be drawn as to what is the correct value. Furthermore, the QRRK and modified strong collision assumptions employed in their kinetic analysis are generally believed to be of, at best, questionable accuracy. The net result is that the predicted k 1 value of Asatryan et al. (2006) is substantially larger, by an order of magnitude, than the k 1 value reported here. This difference is attributable, to a small extent, to the difference in the energy barrier of the two studies. A larger part of the difference likely arises from the QRRK treatments of vibrational frequencies from the B3LYP basis of that vibrational analysis and a lack of the treatment of hindered internal rotation. The above discussion applies equally to the theoretical studies of Sun et al. (2007). The authors considered only the trans-pathway, and employed considerably lower-level quantum chemical and reaction rate theory methods than the present study. Lastly, despite the arguments made above, the validity of the theoretical results is yet to be proved by well-defined kinetic measurement. In comparison to other theoretical studies, however, the unique contribution of the present work is that it provides a test case for the highest levels of quantum chemistry methods and rate theory suitable for this type of reactions. 64 3.4 Conclusion The reaction kinetics of CO + HO 2 • → CO 2 + •OH (R3.1) is studied using the single-reference CCSD(T) method with Dunning’s cc-pVTZ and cc-pVQZ basis sets and multireference CASPT2 methods. The classical energy barriers are found to be about 18 and 19 kcal/mol for CO + HO 2 • addition following the trans and cis paths. The HOOC•O adduct has a well defined local energy minimum in the trans- configuration, but the cis-conformer is either a very shallow minimum or an inflection point on the potential energy surface. Therefore, the cis-pathway is treated with conventional transition state theory and the trans-pathway with a master equation analysis. The computation shows that the overall rate is independent of pressure up to 500 atm. Upon a careful treatment of the hindered internal rotations in the HOOC•O adduct and relevant transition states, a rate coefficient expression () 3 5 2.18 9030 1 cm mol s 1.57 10 T kTe − ⋅= × is obtained for 300 ≤ T ≤ 2500 K. This rate expression is within 10% of that of Mittal et al. (2006), obtained on the basis of an analysis of rapid compression machine experiments of H 2 /CO oxidation in the temperature range of 950 and 1100 K. Considering the underlying uncertainties in the theoretical energy barriers, a parameter sensitivity analysis is carried out for k 1 and the uncertainty factor for the theoretical expression is estimated to be 8, 2, and 1.7 at temperatures of 300, 1000, and 2000 K, respectively. These error bars reject almost 65 all rate values reported in earlier studies, with the exception of Mittal et al. (2006; 2007). 66 Chapter 4 Reaction Kinetics of •OH + HO 2 • → products 4.1 Motivation A quantitative understnding of the H 2 /CO combustion kinetics is a prerequisite to achieve clean syngas combustion and utilization. Reactions involved in H 2 /CO combustion also play critical roles in the hierarchical structure of oxidation models of hydrocarbon fuels. In current models of H 2 /CO combustion, a key uncertainty stems from the reaction •OH + HO 2 • → H 2 O + O 2 . (R4.1) Although the reaction kinetics of R4.1 was extensively studied, the rate coefficient remains uncertain. As seen from Figure 4.1, early observations at room temperatures (Hochanadel et al. 1980; Lii et al. 1980; Cox et al. 1981; Kaufman 1981; Thrush and Wilkinson 1981; Rozenshtein et al. 1984; Sridharan et al. 1984; Temps and Wagner 1984; Dransfeld and Wagner 1987; Keyser 1988; Schwab et al. 1989) show that the rate coefficient k 4.1 scatter in the range (2~6) ×10 13 cm 3 /mol-s. Around room temperatures, several studies suggested that k 4.1 has negative activation energy. Sridharan et al. (1984) reported that at a pressure of 2.5 Torr k 4.1 (cm 3 /mol-s) = 10 13 exp (416/T) for 252 ≤T ≤420 K. Keyser (1988) reported that at 1 Torr, over the temperature range from 254 to 382 K, k 4.1 (cm 3 /mol-s) = 1.1×10 13 exp (250/T). 67 10 13 10 14 0 1234 Gonzalez et al. (1992) Davis et al. (2005) Sridharan et al. (1984) Keyser et al. (1988) Kim et al. (1994) Temps and Wagner (1982) Hochanadel et al. (1980) Schwab et al. (1989) Dransfeld and Wagner (1987) Thrush and Wilkinson (1981) Kaufman (1981) Baulch et al. (1994) Rozenshtein et al. (1984) Cox et al. (1981) Lii et al. (1980) Srinivasan et al. (2006) Goodings and Hayhurst (1988) Kappel et al. (2002) Hippler et al. (1995) Sivaramakrishnan et al. (2007) k 4.1 (cm 3 /mol-s) 1000K /T Figure 4.1 Arrhenius plot of k 4.1 . Symbols: selected experimental data. Lines: selected rate coefficient compilations and theoretical studies. A series of studies reported by Troe and co-workers (Kijewski and Troe 1971; Hippler and Troe 1992; Hippler et al. 1995; Kappel et al. 2002) suggested that over the temperature range of 970 to 1220 K the rate coefficient reaches a minimum at 68 T=~1000 K, and it increases rapidly towards higher temperatures. These measurements were made by following the kinetics of H 2 O 2 thermal decomposition behind reflected shock waves, in which R4.1 was only a secondary reaction. The recommendation by Kim et al. (1994) over the temperature range of 254 K to 1050 K was based on the results of Keyser (1988) and Hippler and Troe (1992). In a recent high-pressure shock tube H 2 /CO oxidation study (Sivaramakrishnan et al. 2007), R4.1 was identified as critical to model the CO oxidation rates over the pressure range of 25 to 450 atm and the temperature from 1000 to 1500 K. The peculiar temperature dependence reported by Troe and coworkers was found to provide a better agreement between model and experiment. Unfortunately, no experimental data are available in the intermediate temperature range 420~950 K to confirm the peculiar behavior in k 4.1 . Contrary to the findings of Troe and co-workers, Srinivasan et al. (2006) found little to no temperature dependency in k 4.1 between 1237 and 1554 K. In their experiments, they followed the disappearance of •OH in C 2 H 5 I/NO 2 mixtures behind reflected shock waves, employing a multipass optical system which detects the •OH radical electronic absorption. The time-dependent decay profile of •OH was fitted with a 23-step mechanism by varying the rate constants of •OH + NO 2 ↔ HO 2 • + NO and •OH + HO 2 • ↔ H 2 O + O 2 . The recommended rate constant for R4.1 over the temperature range of 1200~1700 K is 3×10 13 cm 3 /mol-s, which is a compromise of 4×10 13 cm 3 /mol-s over the temperature 69 range of 1237~1554 K and previous high-temperature data in the range of (1~6)×10 13 cm 3 /mol-s (Goodings and Hayhurst 1988; Hippler et al. 1990; Hippler and Troe 1992; Hippler et al. 1995; Kappel et al. 2002). Among available theoretical studies (Cremer 1978; Jackels and Phillips 1986; Mozurkewich 1986; Toohey and Anderson 1989; Gonzalez et al. 1991; Gonzalez et al. 1992), Gonzalez et al. carried out HF/6-31G(d,p) and MP2/6-31G(d,p) calculations for R4.1 on both singlet (Gonzalez et al. 1991) and triplet surfaces (Gonzalez et al. 1992). The singlet pathway through the adduct hydrogen trioxide was considered to be unimportant because the critical geometry was found to be 15.2 kcal/mole higher than that of the entrance channel. The critical geometry identified on the triplet surface corresponds to an H-abstraction pathway. Using the transition state theory, they calculated a rate constant which is too small to be realistic. For this reason, they estimated the rate constant using a vibrationally/rotationally adiabatic capture dipole-dipole model. After scaling the resulting rate constant by a factor of 0.61, they found that the results are well within the range of low-temperature values reported earlier (Sridharan et al. 1984; Temps and Wagner 1984; Dransfeld and Wagner 1987; Keyser 1988; Schwab et al. 1989). The computed results do not show the peculiar temperature dependency as reported by Troe and coworkers. Considering that the theoretical studies of Gonzalez et al. (1991) employed methods that do not consider electron correlation and with a relative small basis set, additional studies are warranted, as will be reported here. 70 In the present work, the temperature and possible pressure dependence of the rate coefficient for R4.1 was examined by ab initio electronic structure calculations. Both singlet and triplet potential energy surfaces for R4.1 were investigated at the CBS-QBH level of theory and the rate coefficient was calculated by microcanonical variational transition state theory and master equation modeling. 4.2 Computational details 4.2.1 Potential energy surface For all the stationary points, geometry optimization and vibrational frequency calculations are obtained from the density functional theory BHandHLYP/6-311++G(d,p). BHandHLYP denotes Becke’s half-and-half nonlocal exchange with the Lee–Yang–Parr (LYP) correlation functionals (Lee et al. 1988). BHandLYP is preferred over B3LYP because geometry optimization of species involving a hydrogen bond often fails at B3LYP level, as expected. In addition, a recent study (Anderson and Tschumper 2006) reveals that among 10 popular density functionals, BHandHLYP hybrid functional is the only one that correctly reproduces the number of imaginary frequencies for all stationary points of water dimmers. To account for the electronic correlation energy and the major source of error in molecular energies caused by truncation of the one-electron basis set, an energy correction procedure, hereafter called CBS-QBH similar to CBS-QB3 reported in Montgomery et al. (1999; 2000) is employed. First, geometry optimization and frequencies calculations are carried out at BHandLYP/6-311++G(d,p) instead of 71 B3LYP/CBS7 level; and single-point calculations are performed at CCSD(T)/6- 31+G(d’) and MP4SDQ/CBSB4 levels. The total energy is extrapolated to the infinite basis set limit using pair natural-orbital energies at the MP3/CBSB3 level of theory and an additive correction to the CCSD(T) energy. Finally, a correction for spin contamination is incorporated for open-shell species. Calculations at other levels of theory, including density functional theory B3LYP/6-31G(d), Møller-Plesset correlation energy methods MPn(n=2,3,4)/6- 311++G(d,p), CCSD(T)/cc-pVTZ, CCSD(T)/CBS, G3B3, CBS-QB3, CBS- QBMP4DQ are also used to explore the potential energy surface. Except for the composite methods, all energies were obtained for geometries optimized using the same methods. All electronic structure calculations were carried out using the Gaussian 03 program package (Frisch et al. 2004). In addition, to examine the characteristics of the bonding and interactions in the most relevant structures, an analysis of the electronic charge density was performed within the framework of the topological theory of atom in molecules using the AIM2000 software (Biegler-König et al. 2001). The first-order electron density matrix obtained from the BHandHLYP/6-311++G(d,p) wavefunction was used in this analysis. 4.2.2 Reaction rate coefficients RRKM theory and master equation analysis are adopted here to calculate the rate coefficients. For critical geometries with a pronounced energy barrier, the 72 canonical transition state theory is used as described in Chapter 2. For the addition reaction, which is barrierless, the variable reaction coordinate-transition state theory (VRC-TST) (Klippenstein and Marcus 1988; Klippenstein 1990, 1991) is employed. For reactions involving little or no potential energy barrier, the location of the transition state is dependent on quantities such as the excess kinetic energy and total angular momentum. The transition state is determined by a delicate balance between entropic and enthalpy effects. Therefore variational implementations are particularly important (Klippenstein 1992). Both tight transition state theory and VRC-TST have been implemented in the open-source program package VariFlex (Klippenstein et al. 1999), which is used to calculate reaction rate coefficients in this study. The VRC- TST and VariFlex are briefly summarized below. In RRKM theory, the unimolecular dissociation rate constant EJ k at a given energy E and angular momentum J is given by (Klippenstein and Marcus 1988; Klippenstein 1991) † / ρ = EJ EJ EJ kN h (4.1) where ρ EJ is the rovibrational density of states for the reactant, and † EJ N is the number of available energy states of the transition state. In the variation approach, which † EJ N is given by the minimum in ( ) EJ NR along the reaction coordinate R . The value of ρ EJ is evaluated via application of the Beyer-Swinehart direct counting algorithm. The fragment modes are separated into the conserved modes, typically including the vibrational modes in the fragmenting moieties, and the transitional 73 modes, which are typically rotational in nature and undergoes considerable change during the reaction process. Here, the number of states ( ) EJ NR is given by the convolution (Klippenstein 1994) ()( ) 0 () , d ε ρε ε =− ∫ E EJ c t NR N E J (4.2) where () c NE is the number of quantum states for the conserved modes with energies ≤ E, and ( , ) ρ ε t J is the density of states for the transitional modes at the given energy ε and total angular momentum quantum number J for a given reaction coordinate R . Within this convolution the vibrational modes of the fragments may be treated quantum mechanically with direct counting algorithms while the relative and overall rotational motions may be treated in terms of classical phase space integrals evaluated via Monte Carlo integration (Klippenstein 1994). The first step in implementing a method for calculating ( ) EJ NR is the choice of reaction coordinate, which implicitly defines the transition state surface and is subsequently varied in the minimization of the rate constant. A natural choice of reaction coordinate is the center-of-mass separation distance; however, the bond length reaction coordinate, defined by the separation distance between the two atoms whose bond is being broken, is a better choice when the transition state evolves into small separation distances (Klippenstein 1990). Formulations and algorithms for evaluating the number of states ( ) EJ NR , for using a bond length reaction coordinate in the variational implementation of RRKM theory, were presented by Klippenstein 74 (1990; 1991), and the approach may be generalized to include a more general definition of the reaction coordinate in terms of the distance between two fixed points; one in each of the two fragments (Klippenstein 1992). In the present investigation, the bond length is chosen as the reaction coordinate. In the loose transition state calculation, the potential energy surface is approximated using an approach similar to those of Klippenstein et al. (1988). Specifically, the potential is separated into three parts: (a) the potential for the conserved modes orthogonal to the reaction coordinate; (b) the bonding potential along the reaction coordinate; (c) the nonbonding potential for other inter-fragment interactions. For the conserved modes the potential energy of interactions is assumed to be harmonic and identified as normal-mode vibrations in the separated fragments. The vibrational frequencies of the conserved modes are assumed to be independent of reaction coordinate. The nonbonding potential is assumed to be a sum of the 12-6 Lennard-Jones potentials for the van der Waals interactions between the nonbonded atoms. The bonding potential is approximated by a Varshni potential, multiplied by a cylindrically symmetric angular dependence function (see VariFlex Manual). The Varshni potential is chosen here over the traditionally used Morse function, because the Varshni potential is believed to be a more accurate representation of true bonding potential (Miller and Klippenstein 2000). In its standard form, the potential is given by (Varshni 1957; Klippenstein et al. 1988; Miller and Klippenstein 2000) 75 () () 22 0 0 1 RR ee R VR D e D R β−− ⎡⎤ =−− ⎢⎥ ⎣⎦ , (4.3) where e D is the electronic bond energy without zero-point energy correction, 0 R is the equilibrium bond distance. The parameter β is related to the second derivative of () VR at 0 R as () 0 2 00 2 11 42 RR e VR R DR β=−. (4.4) () 0 RR VR is readily obtained from electronic structure theory. Tunnelling effect involving the H-atom transfer is accounted for by Eckart tunnelling (Eckart 1930). To account for the pressure dependence, rate coefficients are calculated from the solution of the master equation of the collision energy transfer. The rate coefficients of the two reaction pathways (singlet and triplet surfaces) are calculated separately. Convergences of the VariFlex calculations are carefully tested, with the errors of Monte Carlo integrations smaller than 10% for the considered temperature ranges. 4.3 Results and discussion 4.3.1 Potential energy surface Reaction R4.1 can occur on both triplet and singlet surfaces. The schematic potential energy diagrams illustrating the various stationary points along the reaction coordinates on the two surfaces are provided in Figure 4.2 and Figure 4.3 76 separately. The results are obtained at the CBS-QBH level of theory. The BHandHLYP/6-311++G(d,p) geometry parameters are presented in Figure 4.4. Figure 4.2 Potential energy diagram for OH• + HO 2 • → products on the triplet surface (unit: kcal/mol). The energy values are determined using at CBS-QBH level of theory with zero-point energy corrections. On the triplet surface, the reaction follows an H-abstraction pathway (Figure 4.2). A hydrogen-bonded complex HO … HOO is formed from the barrierless recombination of the reactants •OH and HO 2 •. Its energy lies 5 kcal/mol below the potential energy of the entrance channel. For the complex to dissociate into the products H 2 O and the ground state 3 O 2 , it requires only 1 kcal/mol of energy barrier. •OH+HO 2 • 3 HO ... HOO complex -5.0 0 H 2 O+ 3 O 2 -69.5 3 TS2 (-3.8) 77 OH+HO 2 1 HO ... OOH complex 1 TS4 (-0.6) 1 HOHOO -4.5 0 H 2 O+ 1 O 2 -40.3 1 HOOOH -32.4 1 TS1 (13.9) OH+HO 2 1 HO ... OOH complex 1 TS4 (-0.6) 1 HOHOO -4.5 0 H 2 O+ 1 O 2 -40.3 1 HOOOH -32.4 1 TS1 (13.9) Figure 4.3 Potential energy diagram for OH• + HO 2 • → products on the singlet surface (unit: kcal/mol). Grey lines: closed-shell singlet surface; Black lines: open-shell singlet surface. The energy values are determined using at CBS-QBH level of theory with zero-point energy corrections. To be noted, the open-shell singlet 1 HOHOO, similar in structure to the triplet complex 3 HO … HOO, is only 1 kcal/mol higher in energy. Unfortunately, no results from other methods are available to provide theoretical confirmation for the above findings because the geometry optimization fails routinely with these methods. Compared to previous studies for the triplet surface at the MP4/6-31G**//MP2/6- 31G** level of theory (Gonzalez et al. 1992), the complex and the critical geometry obtained here are similar in their structures, but their energy for the critical geometry 3 TS 2 is as much as 6 kcal/mol larger than the present results. To be noted, the complex and critical geometry reported by Gonzalez et al. are not a true local 78 minimum or a saddle point as one of the out-of-plane torsional frequencies for both the complex and critical geometry are imaginary. In the present work, 3 TS 2 was calculated to have only one imaginary frequency, as expected for a true critical geometry. Meanwhile, the triplet PES was explored also at several levels of the MPn theory. While MP2 and MP4(STQ) failed to provide the transition state, and B3LYP and MP4(SDTQ) failed for both the complex and transition state, at the MP3 and MP4(DQ) level of theory stationary points were successfully computed; and this was accomplished only when a tight optimization convergence criteria are used. Although similar results can be seen with all methods when applied to the triplet hydrogen-bonded complex HO … HOO, the results for the energy barrier 3 TS2 are quite different (Table 4.1). MPn methods produce 3 TS2 with energies from 6.4 to 6.9 kcal/mol above the entrance channel. In comparison, a procedure similar to the CBS- QBH method but with geometry optimization at MP4(DQ)/6-311++G(d,p) level (CBS-QMP4DQ) gives a quite low value for 3 TS2, about 7.5 kcal/mol below the entrance channel. The CBS-QBH energy is consistent with the results from BHandHLYP/6-6-311++G(d,p) and CBS-QMP4DQ and is probably more reliable than other methods employed here. The reaction enthalpies and energy barriers are presented in Table 4.1, where the literature values for the enthalpy of reaction are based on the heats of formation given in Table 4.2. As seen, the CBS-QB3, CBS- QBH, and CBS-AMP4DQ methods yield reaction enthalpies within 0.5 kcal/mol of the literature values. 79 0.958 θ(H 2 O 1 O 5 )=103.2, θ(O 1 O 5 O 4 )=107.7, θ(O 5 O 4 H 3 )=103.2, τ(H 2 O 1 O 5 O 4 )=-82.7, τ(O 1 O 5 O 4 H 3 )=-82.7 1.389 1.389 0.958 1 HOOOH θ(H 2 O 1 O 5 )=104.9, θ(O 1 O 5 O 4 )=93.0, θ(O 5 O 4 H 3 )=74.8, τ(H 2 O 1 O 5 O 4 )=-105.3, τ(O 1 O 5 O 4 H 3 )=1.4 θ(H 2 O 1 H 3 )=92.4, θ(O 1 H 3 O 4 )=143.2, θ(H 3 O 4 O 5 )=105.2, τ(H 2 O 1 H 3 O 4 )=-0.0, τ(O 1 H 3 O 4 O 5 )=0.0 1 TS1 0.963 1.565 1.359 1.389 3 HOHOO 3 TS2 0.967 1.956 0.970 1.301 0.962 1.433 1.024 1.273 θ(H 2 O 1 H 3 )=111.6, θ(O 1 H 3 O 4 )=168.0, θ(H 3 O 4 O 5 )=107.7, τ(H 2 O 1 H 3 O 4 )=-17.0, τ(O 1 H 3 O 4 O 5 )=92.0 1.102 θ(H 2 O 1 O 5 )=78.1, θ(O 1 O 5 O 4 )=110.2, θ(O 5 O 4 H 3 )=106.1, τ(H 2 O 1 O 5 O 4 )=-106.6, τ(O 1 O 5 O 4 H 3 )=91.7 θ(H 2 O 1 O 5 )=92.7, θ(O 1 O 5 O 4 )=108.0, θ(O 5 O 4 H 3 )=105.4, τ(H 2 O 1 O 5 O 4 )=100.8, τ(O 1 O 5 O 4 H 3 )=87.4 1 TS3 1 HO-OOH θ(H 2 O 1 O 5 )=77.6, θ(O 1 O 5 O 4 )=104.4, θ(O 5 O 4 H 3 )=106.1, τ(H 2 O 1 O 5 O 4 )=126.1, τ(O 1 O 5 O 4 H 3 )=65.0 0.962 2.361 1.302 0.962 0.96 1.849 1.317 0.961 0.962 2.48 1.300 0.963 0.966 1.951 0.970 1.301 θ(H 2 O 1 H 3 )=94.5, θ(O 1 H 3 O 4 )=144.3, θ(H 3 O 4 O 5 )=105.1, τ(H 2 O 1 H 3 O 4 )=-11.8, τ(O 1 H 3 O 4 O 5 )=8.4 1 TS4 1 HOHOO Figure 4.4 Geometry parameters determined at BHandHLYP/6-311++G(d,p) level of theory. The bond lengths are in Å; and the bond and dihedral angles are in degrees. 80 Table 4.1 Energies (kcal/mol) at 0 K relative to OH• + HO 2 •. H 2 O+ 1 O 2 1 HOOOH 1 HO- OOH TS1 TS3 TS4 H 2 O + 3 O 2 3 HOHO 2 1 HOHO 2 TS2 Literature value -69.5 B3LYP/6-31g(d) -25.9 -30 14.7 -65.2 BHandHLYP/6- 311++g(d,p) -39.2 -14.0 -1.2 39.21.4 -1.4 -61.6 -4.9 -4.9 -2.0 MP2/6-311++g(d,p) -50.8 -32.6 15 -81.1 -4.7 MP3/6-311++g(d,p) -32.8 -21.9 34 -67.5 -4.3 6.4 MP4(DQ)/6- 311++g(d,p) -35.7 -22.1 33.9 -68.8 -4.2 -4.1 6.9 MP4(SDQ)/6- 311++g(d,p) -36.9 -22.9 28.1 -69.6 -4.3 MP4(SDTQ)/6- 311++g(d,p) -44.1 -28.9 -73.7 CCSD(T)/cc-pVTZ -38.3 -68 G3B3 -40.2 -31.3 16.2 -69.1 CBS-QBH -40.3 -32.4 13.9 -69.5 -5.0 -4.0 -3.8 CBS-QMP4DQ -41.5 -33.2 13.1 -70.0 -4.8 -3.9 -7.5 CBS-QB3 -41.2 -33.4 -0.6 11.7-6.1 -0.6 -69.8 CCSD(T)/CBS -69.4 Table 4.2 Literature values of enthalpy of formation (kcal/mol). a Δ f H 0 values are obtained from Δ f H 298 and the sensible enthalpy values taken from Chase (1998). Species Δ f H 298 Δ f H 0 Reference •OH 8.9 ±0.07 8.8 (Ruscic et al. 2002) HO 2 • 2.9±0.1 3.6 (Ruscic et al. 2006) a H 2 O -57.8 -57.1 (Chase 1998) 81 On the closed-shell singlet surface, the barrierless combination of •OH and HO 2 • forms a stable intermediate hydrogen trioxide (HOOOH), which lies 32.4 kcal/mol below the entrance channel. The complex can undergo dissociation to form H 2 O + 1 O 2 through a four-center transition state, but the critical energy for dissociation is rather higher, requiring 46.3 kcal/mol, as determined by the CBS-QBH method. This value is consistent with the CBS-QB3 result, which gives a critical dissociation energy about 1 kcal/mol lower. The optimized geometries and energetics obtained at CBS-QBH level agree quite well with those reported by Gonzalez et al. (1991). In addition to the aforementioned calculations, the pathways involving the open-shell singlet diradicals (OSDs) were investigated also. Although the triplet and closed-shell singlet potential energy surfaces have been studied previously, no study has been conducted which takes into account the possible reaction pathways occurring on the open-shell singlet potential energy surface. As shown by Anglada et al. (2007) for a similar system (HO 2 • + HO 2 •) forming a hydrogen-bonded adduct, intersystem crossing between the singlet and triplet surfaces can occur. The rigorous description of an open-shell singlet requires a multi-determinantal description of the wavefunction by describing the system with advanced methods such as the Complete Active Space SCF (CASSCF) calculations. Such calculations are however not trivial for the current reaction system. For this reason, an alternative method based on a combination of CBS-QBH and spin broken symmetry approach was used to study the role of open- shell singlets (OSDs). 82 The ability of the CBS-QBH method to describe OSDs remains questionable, but there are ample evidences that the method may be adequate. For example, geometries obtained with the unrestricted density functional theory (UDFT) approach for OSDs with separated radical centers were found to compare well with those obtained at more refined levels of theory (Grafenstein et al. 2000; Grafenstein et al. 2002). The UDFT method allows spin symmetry to be broken. That is, the α and β orbitals are permitted to have different spatial functions. Another problem for OSDs using UDFT is the spin-contamination. Because of an almost equivalent mixture of singlet and triplet states, one- determinantal wave functions cause <S 2 > values to be close to 1. Such a strong spin contamination is not correctly handled in the CBS-QB3 method because of the correction implemented in it. In a recent study (Sirjean et al. 2007), a term is added to correct the total energy of a singlet diradical in CBS-QB3 calculations due to spin- contamination. The correction is applied here for the CBS-QBH method. The validity of this approach is examined by applying to the reaction HO 2 • + HO 2 • ↔ H 2 O 2 + O 2 . For both the triplet and open-shell singlet hydrogen- bonded complexes formed from barrierless self-reaction of the HO 2 • radical, the geometries are found to be close to those reported by Anglada et al. (2007) at CASPT2/6-311+G(3df,2p)//CASSCF/6-311+(G,3df,2p) level of theory. In addition, the energies are also within 1 kcal/mol of those of Anglada et al. (2007). The open shell-singlet surface the hydrogen-bonded complex 1 HOHOO is only 1 kcal/mol above its triplet state (cf. Figures 4.2 and 4.3). Since this open-shell 83 singlet surface is very close to the triplet surface, crossing between the two surfaces may occur. Unfortunately, the critical geometry between 1 HOHOO and products H 2 O + 1 O 2 are yet to be determined. For this reason, the current rate coefficient calculation does not consider the open-shell singlet surface. If the reaction can proceed on this open-shell singlet surface without a notable energy barrier, the current theoretical rate constant is probably still within a factor of 2, if such a channel is considered. Regardless, further studies may be needed at the CASSCF level of calculation to verify the results and characterize possible conical intersection and spin-state crossing. Table 4.3 presents the results from the AIM topological analysis. The electron density and its Laplacian are indicative of the bond-breaking potential. Interestingly, the analysis of the electron charge density in 3 HO … HOO revealed the presence of bond critical points between atoms O (2) and H (3) and between atoms H (1) and O (5) , indicating that bonding interactions exist between these atom pairs. The small and positive electron charge densities and the negative Laplacians of the electron densities calculated at these bond-critical points are typical for hydrogen- bond-like interactions. In addition, a ring critical point with a small electron charge density is located in the middle of the ring. 84 Table 4.3 Electron density ρ and its Laplacian Δ at critical points for intermediates and transition states of •OH + HO 2 • → products. Structures are optimized at BHandHLYP/6-311++G(d,p) level of theory. Name Critical Points # ρ Δ 1 0.378 0.691 1 HOOOH 2 0.334 0.038 1 0.366 0.662 2 0.019 -0.021 3 0.368 0.674 4 0.420 0.109 5 0.011 -0.010 3 HOHOO 6 0.010 -0.012 1 0.366 0.632 2 0.027 -0.020 3 0.353 0.689 1 HOHOO 4 0.421 0.096 1 0.366 0.678 2 0.200 -0.079 3 0.357 0.035 4 0.106 -0.032 5 0.228 0.300 1 TS1 6 0.076 -0.128 1 0.369 0.663 2 0.085 -0.040 3 0.303 0.468 3 TS2 4 0.453 0.136 1 2 2 1 1 4 5 6 2 3 1 2 3 4 2 3 1 4 5 6 1 2 3 4 85 4.3.2 Reaction rate coefficients Table 4.4 lists the molecular parameters used in the rate coefficient calculation. Two chemically activated systems corresponding to the triplet and open- shell singlet surfaces are investigated separately. For the association of the reactants, being barrierless, the transition state locates at the minimum of the number of energy states. As an example, Figure 4.5 shows the number of states EJ N as a function of separation distance R on the triplet potential energy surface with excess energy of 800 cm -1 at two angular momentum number J. The minimum point of EJ N represents the transition state at a given angular momentum number J. Table 4.4 Molecular properties for computing the rate coefficient of •OH + HO 2 • → products. E 0 a B (cm –1 ) Vibrational frequencies v d Species (kcal/mol) inactive b active c (cm −1 ) •OH 19.2 3881.6 HO 2 • 21.6& 1.1(2) 1253, 1505.3, 3823.5 1 HOOOH -32.4 0.351 1.821 373.1, 419.6, 585.3, 980.7, 1036.0, 1469.4, 1479.7, 3904, 3908 1 TS1 13.9 0.378 1.376 1758.8i, 436.4, 554.4, 860.1, 1037.8, 1058.3, 1462.5, 2173.9, 3871.2 3 HOHOO -5.0 0.186 1.125 120.5, 216.1, 219.7, 415.1, 444.4, 1278.1, 1574.9, 3689.9, 3839.5 3 TS2 -3.8 0.185 1.656 1527.9i, 94.3, 190.2, 426.9, 628.4, 1109.8, 1414.5, 1848.7, 3897.6 a Relative to the energy of •OH + HO 2 • at 0 K. b With the exception of HO 2 •, these are two- dimensional external inactive rotors (symmetry number σ=1). c One-dimensional external rotors (symmetry number σ=1). d From BHandHLYP/6-6-311++G(d,p) calculation (fully optimized geometry). 86 0 2 10 5 4 10 5 6 10 5 8 10 5 2 468 10 J=3 J=33 N EJ (R) R (Angstrom) Figure 4.5 Number of states () EJ NR as a function of separation distance R on triplet potential energy surface with excess energy of 800 cm -1 at two angular momentum number J . On the closed-shell singlet potential surface, the rate coefficient of forming the adduct HOOOH is pressure dependent. As expected, the activated adduct is more likely to stabilize towards low temperatures. However, the rate coefficient is too small to be of any importance even up to 100 atm, as shown in Figure 4.6. Moreover, the rate coefficient for the adduct to dissociate back to the reactant is orders of magnitude faster than that for it to proceed to the products. Therefore, the chemically activated adduct HOOOH neither stabilizes nor decomposes into products. 87 For this reason, the close-shell singlet channel contributes little to the total rate constant. 10 4 10 6 10 8 10 10 10 12 10 14 0.511.5 2 2.5 33.5 k (cm 3 /mol-s) 1000K /T OH+HO 2 HOOOH high-P limit 100 atm 1 atm 0.01 atm Figure 4.6 Arrhenius plot of k for •OH + HO 2 • → HOOOH occurring on the closed shell singlet surface. On the triplet potential energy surface, the rate to form stabilized complex HO … HOO is negligible, but since the well depth is shallow, the rate constant for R4.1 is the result of two competing channels, one is the decomposition of the adduct to form products, the other is the dissociation of the adduct back to the reactants. 88 10 13 10 14 01234 Gonzalez et al. (1992) Davis et al. (2005) Sridharan et al. (1984) Keyser et al. (1988) Kim et al. (1994) Temps and Wagner (1982) Hochanadel et al. (1980) Schwab et al. (1989) Dransfeld and Wagner (1987) Thrush and Wilkinson (1981) Kaufman (1981) Baulch et al. (1994) Rozenshtein et al. (1984) Cox et al. (1981) Lii et al. (1980) Srinivasan et al. (2006) Goodings and Hayhurst (1988) Kappel et al. (2002) Hippler et al. (1995) this work k 4.1 (cm 3 /mol-s) 1000K /T TS2 - 0.5 kcal/mol TS2 + 0.5 kcal/mol this work Figure 4.7 Comparison of experimentally and theoretically obtained rate coefficients for R4.1. Symbols: selected experimental data. Lines: selected rate coefficient compilations and theoretical studies. Both channels are at their high-pressure limit. The rate coefficient 4.1 k computed for the triplet surface is plotted in Figure 4.7. It shows a negative activation energy in the 89 temperature range of 300 to 1000 K. Above 1000 K, 4.1 k slightly increases as temperature is increased. The calculated 4.1 k seems to be larger than most experimental values at room temperatures, which is probably caused by the uncertainty in 3 TS2. An increase or decrease of the energy barrier of 3 TS2 by 0.5 kcal/mol would cause 4.1 k to decrease or increase by as much as ~50%. The final rate coefficient for R4.1, which is pressure independent, can be fitted by the sum of two modified Arrhenius expressions as () 3 21 2.19 190 6 1.94 1581 4.1 cm mol s 4.838 10 3.489 10 TT kTe Te − ⋅= × + × for 300 ≤ T ≤ 2500 K, where the fitting error is less than 5% over the entire range of temperature. The above rate expression is only preliminary as it does not consider the possible intersystem crossing. Furthermore, the discrepancy between the calculated and experimental rate values will require additional examination. 4.4 Conclusion The singlet and triplet potential energy surfaces of •OH + HO 2 • → H 2 O + O 2 (R4.1) were investigated using quantum-mechanical electronic structure methods at CBS-QBH level of theory. A hydrogen-bonded diradical complex (HOHOO) and a stable close-shell singlet intermediate hydrogen trioxide (HOOOH) are formed from •OH + HO 2 • addition on the triplet surface and closed-shell singlet surface, separately. The critical energies are about 1.2 and 46.3 kcal/mol for the 3 HOHOO and 1 HOOOH 90 adduct to dissociate following the triplet and singlet surface pathways. Compared to existing theoretical studies, the results obtained here for closed-shell singlet and triplet potential surface are considered to be more reliable. Reaction pathways involving the open-shell singlet diradicals (OSDs) were investigated for the first time. Although the results are preliminary, new pathways were found, and the possible intersystem crossing was discussed. 91 Chapter 5 High-Temperature Combustion Reaction Model of H 2 /CO/C 1 -C 4 Compounds 5.1 Introduction A reliable H 2 /CO/C 1 -C 4 combustion model serves as a kinetic foundation for developing a predictive reaction model for practical fuel or fuel surrogates because of the hierarchical nature of reaction models. A physically justifiable and predictive reaction model of surrogate combustion must also have the capability to predict the combustion behavior of C 1 -C 4 hydrocarbon fuels. Therefore, to establish such a reliable foundation, a previous H 2 /CO/C 1 -C 4 kinetic model is reevaluated and updated. The previous model was based on a well validated, partially optimized, detailed model documented in a number of publications over the last decade (Sun et al. 1996; Wang and Frenklach 1997; Davis et al. 1999a, b; Laskin and Wang 1999; Laskin 2000; Qin et al. 2000; Wang 2001; Hirasawa et al. 2002; Law et al. 2003; Davis et al. 2005; Joshi 2005). In the present study, the thermodynamic database is compared with several other databases and improved by ab initio studies; rate parameters are updated when new kinetics studies are made available; uncertainty factors are quantified for all rate coefficients; and finally the model is validated against a large range of experimental combustion properties. Besides the kinetic and thermodynamic 92 databases being updated, the transport database contains revisions for several H-atom diffusion coefficients of several key pairs based on the ab initio studies (Middha et al. 2003; Middha and Wang 2005). This update affects H 2 /CO flame, but has a negligible effect on hydrycarbon laminar flame speed simulations. A list of high-temperature H 2 /CO/C 1 -C 4 reaction mechanism consisting of 111 chemical species and 784 elementary reactions can be found in Appendix B. The uncertainty factors of rate constants are estimated from a comprehensive literature review of available combustion kinetic data. Each reaction in the mechanism is specified by reactants → products, the modified Arrhenius parameters, and the uncertainty factors, which denote the uncertainty for the rate constant. Key reactions are examined by quantum chemistry calculations and reaction rate theory analysis. During model compilation and development, efforts are made to ensure the model to be as complete and comprehensive as possible. The resulting model is expected to cover a wide range of combustion conditions, including homogeneous ignition, laminar flame propagation, flame ignition/extinction, and diffusive burning and ignition/extinction. 5.2 Thermodynamic database for C 1 to C 4 species A reliable thermodynamic database is of the same importance as the reaction mechanism. An error in a thermodynamic equilibrium constant can propagate into the backward reaction rate constant because it is derived from both thermodynamic equilibrium constant and the forward rate constant. Recently, 93 discrepancies in thermodynamic properties were found for some species between the previous C 1 -C 4 thermodynamic database and the one developed at Imperial College using ab initio methods. The objective of current work is to resolve the discrepancies and improve the quality of the previous thermodynamic database. Thermodynamic properties are presented as a function of temperature in the standard form of NASA polynomials, which consist of 14 polynomial coefficients, with the first 7 for calculating thermodynamic data in the range of 1000 K to 6000 K, and the rest 7 for data from 298 K to 1000 K. The two polynomials are constrained to give the same thermodynamic properties at 1000 K for continuity. In this work, the previous H 2 /CO/C 1 -C 4 thermodynamic data for 111 species are compared to the latest data available from several sources. Polynomials are updated for 15 species with new data calculated from ab initio quantum mechanical methods and isodesmic reactions. 5.2.1 Calculation methods The thermodynamic properties for each species are calculated using statistical mechanic principle (Lewis and Randall 1961; McQuarrie 1973) by considering the translational, vibrational, rotational, and electronic contributions to the energy of the molecule. The molecular properties required for the calculations are obtained from G3//B3LYP methods (Curtis et al. 1998; Baboul et al. 1999), often known as the G3B3 composite method, using the Gaussian 03 package (Frisch et al. 2004). 94 Generally, in electronic structure calculations, the level of accuracy is correlated with the computing time. Composite methods have been designed to achieve the accuracy at a reasonable computational cost. First, the molecule geometry is optimized at a relatively lower level of theory. A series of high-level single point energy calculations are then made to correct errors in electronic energy caused by the use of limited basis set and incomplete electron correlations. Since only single point calculations at high levels of theory are required, computing time is shortened notably from optimizing geometries at the same levels of theory. The current G3//B3LYP method (Curtis et al. 1998) used the Becke 3- Parameter Lee, Yang and Parr (B3LYP) density functional theory to obtain geometries and zero point energy instead of the Möller-Plesset (MP2) ab initio theory or the Hartree-Fock (HF) theory in other composite methods, such as G1 and G2. G3//B3LYP method tends to produce more accurate energies with the trade-off of a slight increase in processing time. The full procedure for G3//B3LYP method is described as follows: (a) Geometry optimization and vibrational frequency calculation are carried out at the B3LYP/6-31G(d) level. The vibrational frequencies, scaled by a correction factor of 0.96, are then used to calculate the zero point energy. (b) A series of single point energy calculations are made at higher levels of theory as follows: MP4(FC)/6-31G(d); MP4(FC)/6-31+G(d); MP4(FC)/6-31G(2df,p); QCISD(T,FC)/6-31G(d); MP2(FU)/G3Large. 95 (c) The remaining deficiencies in the energy calculation are then taken into account. The corrections can be calculated from HLC molecules = –An β – B(n α –n β ) and HLC atoms = – Cn β – D(n α –n β ), where n α and n β are the number of α and β valence electrons respectively; A = 6.760, B = 3.233, C = 6.786, and D = 1.269. (d) Finally, the total energy considers all energy corrections and zero-point energy. Molecule thermodynamic properties are calculated from partition functions through statistical mechanics. Partition function calculations require the information of molecule properties including vibrational frequencies, enthalpies of formation, moments of inertia, molecular weight, and molecular symmetry number. All these information can be extracted from G3//B3LYP calculations. Apart from getting accurate electronic energy by G3B3 method, the corrected vibrational frequencies from the B3LYP density functional theory compare quite well with experimental measurements, which ensure accurate thermodynamic data. For molecules with one or more internal torsional rotations, the contribution of the internal rotation to the thermodynamic data may be treated specially. Quantum chemical calculations were performed at the B3LYP/6-31G level to explore the internal rotations of the molecules. Spin-restricted theory was used for singlet states and spin-unrestricted for doublets and triplets. Each internal rotation underwent a scan by examining through 360º with an interval of 15º (24 steps) and the energy of molecule was calculated at each point to provide a full picture of the barrier to internal rotation. The internal rotational constants were calculated for the respective rotation using a high-level of approximation reported in You et al. (2007). 96 Its contribution to the thermodynamic properties can be calculated from solving Schödinger equation with the barrier energy profile in a fitted Fourier series function, or using Pitzer-Gwinn thermodynamics tables (Pitzer and Gwinn 1942). This process was carried out for each internal rotation in the molecule. Initial screening tests showed that the enthalpies of formation of 15 C 3 and C 4 species differed quite substantially (> 1 kcal/mol) from Imperial College database, where the enthalpies of formation were calculated from the atomization energy. Here, the enthalpies of formation of these 15 species were subject to additional scrutiny using the approach of isodesmic or homodesmic reactions. The use of this approach reduces the error in the predicted enthalpy of formation, because systematic computational errors in electronic energy calculations are expected to be cancelled in an iso-/homodesmic reaction. 5.2.2 Error and accuracy of G3//B3LYP calculated values The enthalpy of formation calculated using the G3B3 composite method is reported to have an average accuracy of 0.93 kcal/mol (Baboul et al. 1999), which is similar as previous reported value 0.94 kcal/mol for G3 (Curtis et al. 1998) composite methods. The value is the average deviation from experimental data for a sample set of 148 species from organic and inorganic molecules as well as radical species (Table 5.1). 97 Table 5.1 Average absolute deviation of enthalpy (kcal/mol) from experiment for G3 and G3B3 composite methods for several series of compounds (Baboul et al. 1999). Type No. Molecules Average Deviation G3 (kcal/mol) Average Deviation G3B3 (kcal/mol) Nonhydrogens 35 1.72 1.65 Hydrocarbons 22 0.68 0.57 Subst. Hydrocarbons 47 0.56 0.70 Inorganic Hydrides 15 0.87 0.78 Radicals 29 0.84 0.76 All 148 0.94 0.93 In some cases the computational error of G3B3 enthalpy of formation can be notably larger than the average accuracy. The accuracy may be improved by employing iso-/homodesmic reactions. Table 5.2 shows the comparison of the average and maximum deviations predicted for the enthalpies of formation of 30 C/H/O compounds and free radical species considered in the original G3B3 set (Baboul et al. 1999). As seen the average errors of the two methods are similar, but the use of isodesmic reactions reduces the maximum deviations from 2.4 to 1.4 kcal/mol. The reduction in maximum error is quite uniform for the four classes of compounds listed in Table 5.2. Excluding cyclic species the maximum error from the isodesmic reaction approach is well within 1 kcal/mol, and the average error is no larger than 0.6 kcal/mol. 98 Table 5.2 Comparison of average and maximum errors of enthalpy (kcal/mol) of formation predicted by G3B3 atomisation energy and isodesmic reaction. Number of From atomisation energy From isodesmic reaction Species Average Maximum Average Maximum Hydrocarbons 9 0.2 0.5 0.2 0.6 Oxygenates 8 0.6 1.6 0.4 0.9 Cyclic hydrocarbons 6 0.9 2.4 0.8 1.4 Free radicals 7 0.5 1.3 0.6 1.0 All 30 0.5 2.4 0.5 1.4 The uncertainty of the enthalpy of formation recommended here is assigned from the maximum deviation shown in Table 5.2. The specific assignment considers the method used as well as the class of compounds. In case a species belongs to more than one class of compounds, the largest value of the maximum deviations is chosen as the uncertainty. 5.2.3 Thermodynamic property results The discrepancies in the enthalpy of formation at 298.15 K for most of the species between present work and the previous database are within 10%. For 15 species including 4 species above 10% discrepancy, the enthalpies of formation are calculated using isodesmic reaction approach, since their absolute discrepancies in enthalpy of formation at 298.15 K between G3B3 calculation and the previous database are greater than 1 kcal/mol. The results from isodesmic reaction calculation 99 and G3B3 calculation are almost all within the uncertainty of each other. The values of the former approach are adopted and shown in Table 5.3 and Table 5.4. Table 5.3 presents the 15 species and the isodesmic reactions used for each species. The optimized geometries and vibration frequencies for all the 15 species and reference species were obtained from B3LYP/6-31G(d) calculations. Electronic energies were computed using G3B3 method. The contribution to the thermodynamic properties by the hindered internal rotation was considered using Pitzer-Gwinn’s thermodynamic tables (Pitzer and Gwinn 1942). The hindered rotation barriers were estimated from the rigid internal rotor rotation scan at B3LYP/6-31G(d) level (Figure 5.1). The moments of inertia for hindered rotors were computed by a method with a high level of approximation as described in You et al. (2007), which considered the coupling between the internal rotation and the external rotation. Comparisons of present study with several other sources are shown in Table 5.5 for species having large discrepancies in enthalpy of formation at 298.15 K among different sources. Molecular properties used to calculate the thermodynamic properties are summarized in Table 5.6. 100 Table 5.3 Isodesmic reactions for 15 target species. No. Name Structure Isodesmic reactions 1 CH 2 =CHC·=O (CH 2 CHCO) CH 2 CHCO + C 2 H 6 ↔ CH 3 CH=CH 2 + CH 3 CO 2 CH 2 =CHCH=O (C 2 H 3 CHO) C 2 H 3 CHO + C 2 H 6 ↔ CH 3 CH=CH 2 + CH 3 CHO 3 CH 3 CH 2 CH=O (CH 3 CH 2 CHO) CH 3 CH 2 CHO + CH 4 ↔ C 2 H 6 + CH 3 CHO 4 CH ≡CCH=CH 2 (C 4 H 4 ) C 4 H 4 + C 2 H 6 ↔ CH 3 C ≡CH + CH 3 CH=CH 2 5 CH ≡CCH=CH· (nC 4 H 3 ) nC 4 H 3 + C 2 H 4 ↔ C 4 H 4 + C 2 H 3 6 pC 4 H 9 pC 4 H 9 + 2CH 4 ↔ 2 C 2 H 6 + C 2 H 5 7 CH 2 =CHCH 2 CH 2 · (C 4 H 7 ) C 4 H 7 + CH 4 ↔ CH 3 CH=CH 2 + C 2 H 5 8 CH 3 CH·CH=C=O (CH 3 CHCHCO) CH 3 CHCHCO + C 2 H 6 ↔ C 2 H 5 CHCO + C 2 H 5 C 2 H 5 CHCO + CH 4 ↔ CH 3 CH=CH 2 + CH 3 CHO 9 CH 2 =C=C=C=O (H 2 C 4 O) H 2 C 4 O + C 2 H 6 ↔ C 4 H 6 + CH 2 =C=O 10 CH 2 =C·C ≡CH (iC 4 H 3 ) iC 4 H 3 + CH 4 ↔ CH 3 C ≡CH + C 2 H 3 11 CH 2 =CHCH=CH· (nC 4 H 5 ) nC 4 H 5 + C 2 H 4 ↔ C 4 H 6 + C 2 H 3 12 CH 2 =CHCH·CH=O (CH 2 CHCHCHO) CH 2 CHCHCHO + C 2 H 4 ↔ C 4 H 6 + CH 2 CHO 13 CH 2 =C(CH 3 )CH 2 · (iC 4 H 7 ) iC 4 H 7 + C 2 H 6 ↔ iC 4 H 8 + C 2 H 5 14 iC 4 H 9 iC 4 H 9 + C 2 H 6 ↔ iC4H10 + C 2 H 5 15 CH 2 =CHC·=CH 2 (iC 4 H 5 ) iC 4 H 5 + C 2 H 4 ↔ C 4 H 6 + C 2 H 3 101 Table 5.4 Enthalpies of formations for reference species in isodesmic reactions. Reference species ∆ f H ◦ 298.15 (kcal/mol) Reference CH 4 -17.89±0.07 (Chase 1998) C 2 H 3 71.5 (Wu and Carter 1990) C 2 H 4 12.55±0.1 (Chase 1998) C 2 H 5 28.4±0.5 (Tsang 1996) C 2 H 6 -20.24±0.12 (Prosen and Rossini 1945) CH 3 CO -2.9±0.7 (Kudchadker and Kudchadker 1975) CH 2 =C=O -11.85 CH 2 CHO 3.52±0.38 CH 3 CHO -39.7±0.12 (Pedley et al. 1986) CH 3 CH=CH 2 4.88±0.16 (Furuyama et al. 1969) CH 3 C ≡CH 44.32±0.21 (Wagman et al. 1945) C 4 H 6 26±0.19 iC 4 H 8 -4.1 iC 4 H 10 -32.07 102 Table 5.5 Comparison of enthalpies of formation at 298.15 K ( ∆ f H ◦ 298.15 ) from present work, Imperial College, previous database, and other sources (unit: kcal/mol). Target species Structure Imperial College Previous database this work Burcat Others CH 2 CHCO CH2=CHC·=O 21.16 a 17.30 b 22.38 21.16 a C 2 H 3 CHO CH2=CHCHO -16.27 c -17.80 -15.66 -16.27 c CH 3 CH 2 CHO CH3CH2CHO -44.24 -45.90 -45.13 -45.90 -45.09 k C 4 H 4 CH ≡CCH=CH2 68.80 c 70.41 d 69.33 68.80 c nC 4 H 3 CH ≡CCH=CH· 129.90 134.10 e 131.26 129.81 c 129.81 c , 130.8 i , 131.38 j , 125.96 j pC 4 H 9 CH3CH2CH2CH2· 19.55 c 18.38 f 18.47 19.55 c C 4 H 7 CH2=CHCH2CH2· 48.90 g 44.08 f 48.57 48.90 g CH 3 CHCHCO CH3CH·CH=C=O 16.14 9.40 h 16.33 H 2 C 4 O CH2=C=C=C=O 51.78 54.60 51.96 iC 4 H 3 CH2=C·C ≡CH 119.93 123.50 f 121.01 119.93 nC 4 H 5 CH2=CHCH=CH· 86.84 85.41 87.31 86.84 CH 2 CHCHCHO CH2=CHCH·CH=O 8.38 9.41 h 8.10 iC 4 H 7 CH2=C(CH3)CH2· 32.42 29.66 32.50 32.89 iC 4 H 9 CH3CH(CH3)CH2· 17.63 16.33 17.22 17.63 iC 4 H 5 CH2=CHC·=CH2 75.34 c 77.41 75.42 75.34 a (Burcat and Ruscic 2005), taken from Janoschek and Rossi (2004). b (Burcat 1999), taken from McMillen and Golden (1982). c (Burcat and Ruscic 2005). d (Roth et al. 1991). e (Wang et al. 2000). f (Wang and Frenklach 1994a). g (Burcat and Ruscic 2005), taken from Miller (2004). h (Burcat 1997). i (Klippenstein and Miller 2005). j (Krokidis et al. 2001). k (Wiberg et al. 1991). 103 0 2 4 6 8 10 12 0 100 200 300 400 Relative Energy (kcal/mol) C 2 H 3 CHO, rotation about C=C-CO 0 2 4 6 8 10 12 -150 -100 -50 0 50 100 150 200 250 CH 3 CH 2 CHO, rotation about CC-CO 0 2 4 6 8 10 50 100 150 200 250 300 350 400 450 CH 3 CH 2 CHO, rotation about C-CCO 0 2 4 6 8 10 150 200 250 300 350 400 450 500 550 Relative Energy (kcal/mol) nC 4 H 5 , rotation about C=C-C=C. 0 2 4 6 8 10 50 100 150 200 250 300 350 400 450 C 4 H 7 , rotation about C=CC-C. 0 2 4 6 8 10 -100 0 100 200 300 C 4 H 7 , rotation about C=C-CC. 0 2 4 6 8 10 -200 -100 0 100 200 pC 4 H 9 , rotation about C-CCC. 0 2 4 6 8 10 100 200 300 400 pC 4 H 9 , rotation about CC-CC. 0 2 4 6 8 10 200 300 400 500 Relative Energy (kcal/mol) pC 4 H 9 , rotation about CCC-C. 0 2 4 6 8 10 -200 -100 0 100 200 iC 4 H 9 , rotation about C-C(C)C. 0 2 4 6 8 10 -200 -100 0 100 200 Relative Energy (kcal/mol) Dihedral angle, degree iC 4 H 9 , rotation about CC(-C)C. 0 2 4 6 8 10 100 200 300 400 500 Dihedral angle, degree CH 3 CHCHCHO, rotation about C-C.CCO 0 0.2 0.4 0.6 0.8 0 100 200 300 400 Relative Energy (kcal/mol) iC 4 H 7 , rotation about .CC(-C)=C 0 2 4 6 8 10 0 100 200 300 400 iC 4 H 9 , rotation about CC(C)-C. 0 5 10 15 200 300 400 500 Dihedral angle, degree CH 3 CHCHCO, rotation about CC.-CCO Figure 5.1 Energy scans for internal rotation in the 15 species studied by isodesmic reaction approach, computed at the B3LYP/6-31G(d) level of theory. Except for the dihedral angle, geometries are frozen. 104 Table 5.6 Molecular properties used for computing the thermodynamic properties. ∆ f H ◦ 298 B (cm -1 ) a Hindered internal rotors b Species (kcal/ mol) value σ mode B (cm -1 ) σ V 0 c (kcal/ mol) ν (cm -1 ) e CH 2 CHO 22.7 0.3344 1 212 288 362 511 617 692 894 1064 1139 1345 1443 2102 3049 3074 3170 C 2 H 3 CHO -15.9 0.3265 1 C=C-CO 3.111 1 9.717 168 d 307 550 587 892 953 983 1003 1134 1257 1354 1416 1634 1733 2782 3036 3071 3121 CH 3 CH 2 CHO -45.0 0.2546 1CC-CO 3.711 1 2.735 C-CCO 5.643 3 2.190 129 d 224 d 249 647 651 824 871 970 1076 1110 1241 1327 1374 1390 1422 1465 1468 1762 2779 2900 2922 2945 3011 3016 C 4 H 4 69.1 0.3384 1 220 325 536 565 606 686 863 907 973 1077 1282 1405 1623 2136 3034 3053 3135 3355 nC 4 H 3 131.2 0.3787 1 220 337 516 563 611 655 784 791 988 1232 1587 2137 2927 3135 3356 pC 4 H 9 18.7 0.2316 1C-CCC 6.145 3 3.106 CC-CC 1.641 1 3.480 CCC-C 10.383 2 0.606 97 d 129 d 231 d 252 405 448 707 794 840 935 998 1042 1057 1134 1214 1276 1287 1355 1384 1427 1439 1461 1468 1477 2810 2905 2914 2920 2945 2982 2988 3034 3127 C 4 H 7 48.5 0.2552 1 C-CC=C 10.175 2 0.915 CC-C=C 2.237 1 3.133 97 d 129 d 310 402 453 631 771 869 902 992 1014 1040 1081 1204 1278 1300 1410 1425 1432 1660 2838 2907 3022 3031 3041 3105 3138 CH 3 CHCHCO 16.0 0.1856 1C-C·C=CO 6.835 3 0.612 CC·-C=CO 1.532 1 14.04 48 d 134 d 161 269 375 545 596 679 884 977 1047 1078 1162 1256 1386 1418 1441 1472 2096 2884 2915 2980 3039 3069 H 2 C 4 O 52.1 0.3650 2 101 148 409 429 504 603 704 738 951 1329 1482 2000 2265 3041 3114 iC 4 H 3 121.5 0.5683 2 71 136 242 431 556 602 847 874 957 1407 1743 1952 2971 3027 3346 105 nC 4 H 5 87.8 0.3266 1 C=C-C=C 3.083 1 7.806 176 d 288 492 542 700 777 822 892 921 994 1144 1218 1277 1406 1583 1638 2922 3037 3051 3119 3136 CH 2 CHCHCHO 8.0 0.1883 1 143 203 263 449 522 551 787 839 940 949 984 1120 1191 1246 1251 1378 1446 1490 1624 2796 3027 3047 3067 3135 iC 4 H 7 32.3 0.2493 1 ·CC(-C)=C 5.696 3 0.090 29 d 393 413 463 527 534 727 758 821 944 997 1017 1030 1297 1335 1387 1449 1463 1465 1495 2927 2984 3004 3037 3044 3125 3127 iC 4 H 9 17.0 0.2242 1C-C(C)C 5.596 3 3.565 CC(C)-C 9.882 2 0.732 CC(-C)C 5.597 3 3.571 114 d 224 d 250 d 343 357 384 495 785 876 915 937 952 1060 1143 1169 1284 1293 1367 1382 1430 1458 1461 1471 1479 2797 2918 2923 2984 2985 2987 2989 3031 3124 iC 4 H 5 76.3 0.3040 1 209 219 475 507 552 697 846 878 903 960 1058 1161 1342 1421 1457 1852 2974 3008 3028 3056 3148 a External rotors. b One-dimensional hindered rotors. c The energy barriers of hindered rotor V 0 are estimated from B3LYP/6-31G(d) potential energy scan. d Vibrational mode replaced by hindered internal rotation. e From B3LYP/6-31G(d)calculation (fully optimized geometry and numerical second derivatives, scaled by a factor of 0.96). 5.3 Validation of H 2 /CO/C 1 -C 4 model This updated, high-temperature H 2 /CO/C 1 -C 4 combustion model (111 chemical species and 784 elementary reactions) is validated against a wide range of combustion property data published over the last two decades. Selected comparisons of experiments and simulations are shown for hydrogen/carbon monoxide mixtures, several alkanes, alkenes, and alkynes. 5.3.1 H 2 and CO The H 2 /CO sub-model is kept almost the same as the optimized H 2 /CO model (Davis et al. 2005), except the rate parameters of the three reactions 106 CO+OH ↔CO 2 +H (Joshi and Wang 2006), CO+HO 2 ↔CO 2 +OH (You et al. 2007), and OH+HO 2 ↔H 2 O+O 2 (Sivaramakrishnan et al. 2007) are updated. 10 2 10 3 13.9%H 2 + 17.4%O 2 + 3.5%CO in N 2 , p 5 = 1.05 atm Ignition Delay, τ (μs) 10 2 10 3 0.8 0.9 1.0 1.1 1000K /T 7%H 2 + 17.4%O 2 + 10.4%CO in N 2 , p 5 =1.09 atm Ignition Delay, τ (μs) Figure 5.2 Experimental (symbols, (Kalitan et al. 2007)) and computed (lines) ignition delay times of H 2 -CO-air mixtures behind reflected shock waves. 107 The validation tests have been carried out using the updated H 2 /CO model for all the experimental targets reported in Davis et al. (2005). It turns out that negligible influence can be seen from the modification of the kinetic parameters for the above three reactions. 10 1 10 2 10 3 10 4 0.8 0.9 1.0 1000K /T Ignition Delay, τ (μs) 1.7%H 2 + 17.5%O 2 + 15.6%CO in N 2 p 5 = 14.3 atm p 5 = 1.1 atm p 5 = 2.4 atm Figure 5.3 Experimental (symbols, (Kalitan et al. 2007)) and computed (lines) ignition delay times of H 2 -CO-air mixtures behind reflected shock waves. 108 10 1 10 2 10 3 10 4 0.7 0.8 0.9 1.0 1000K /T Ignition Delay, τ (μs) 0.9%H 2 + 17.4%O 2 + 16.5%CO in N 2 p 5 = 14.9 atm p 5 = 1.1 atm p 5 = 2.0 atm Figure 5.4 Experimental (symbols, (Kalitan et al. 2007)) and computed (lines) ignition delay times of H 2 -CO-air mixtures behind reflected shock waves. Figures 5.2-5.4 depict the comparisons of the computed ignition delay times for H 2 /CO/air mixture with a shock-tube experimental study (Kalitan et al. 2007) at reflected-shock temperatures (890 K< T 5 < 1300 K) in three pressure regimes of approximately 1, 2.4, and 15 atm. In most cases, the kinetic model prediction is in excellent agreement with the experimental data, especially at higher temperatures and 109 lower pressures. The only exceptions are that the model tends to predict longer ignition delay times at 2~2.4 atm and lower temperatures. Sensitivity analyses are applied to identify the key reactions responsible for ignition. The results indicate that the ignition-enhancing reaction H+O 2 ↔O+OH and hydrogen oxidation kinetics in general are the most important, regardless of mixture composition, temperature, or pressure. However, at lower temperatures and higher pressures, additional influence on ignition comes from HO 2 and CO reactions, including the three body reactions H+O 2 +M ↔HO 2 +M and CO+O+M ↔CO 2 +M, and CO+HO 2 ↔CO 2 +OH. Although the observed discrepancy between predicted and experimental ignition delay times below 1000 K could be due to inaccuracy in the kinetic model, a recent study of hydrogen oxidation behind reflected shock resolved this discrepancy (Pang et al. 2008). The analyses of their low-temperature data showed that non-ideal effects associated with shock tube performance and localized pre-ignition energy release must be considered in the modeling. With the use of experimental pressure trace, the agreement between model predictions and experimental ignition delays was satisfactory. 5.3.2 C 1 -C 4 n-alkanes Figure 5.5 presents the comparisons of numerical simulations with experimental laminar flame speeds for methane, ethane, propane, and n-butane-air mixtures at atmospheric pressure and unburned gas temperature 298 K. 110 0 10 20 30 40 50 0.6 0.8 1 1.2 1.4 1.6 CH 4 C 2 H 6 n-C 3 H 8 n-C 4 H 10 Laminar Flame Speed (cm/s) Equivalence ratio, φ CH 4 C 2 H 6 n-C 3 H 8 n-C 4 H 10 Figure 5.5 Experimental (symbols) and computed (lines) laminar flame speeds of methane, ethane, propane, and n-butane-air mixture at atmospheric pressure and unburned gas temperature 298 K. The methane and propane data are taken from Vagelopoulos et al. (1994), and ethane data are taken from Egolfopoulos et al. (1991), n- butane data are taken from Davis and Law (1998). The experimental laminar flame speeds for the four mixtures are very similar at fuel-lean condition. For fuel-rich mixture, both experimental measurement and model predictions show that ethane/air flame speed is highest among the four 111 alkane flames. The reaction model predicts quite well against the experimental data over the entire range of the equivalence ratio for methane and ethane. For butane, propane/air mixtures, the model predicts the fuel-lean data well, but it underpredicts laminar flame speed at fuel-rich conditions. 10 0 10 1 10 2 10 3 0.55 0.60 0.65 0.70 0.75 0.80 0.85 Ignition Delay (μs) 1000K /T 0.0322 C 3 H 8 -0.1610 O 2 -0.8068 Ar Figure 5.6 Experimental (symbols (Burcat et al. 1971)) and computed (line) ignition delay times for a 3.22% propane, 16.1% oxygen, and 80.68% argon mixture at temperature range from 1240-1690 K and pressure range 7.82-15.39 atm. All calculations were made with an average molar density of 9.39×10 -5 mol/cm 3 . 112 10 1 10 2 10 3 5.5 6.0 6.5 7.0 7.5 0.15%C 3 H 8 -0.84%O 2 -99.01%Ar ρ 5 = 2.9x10 -5 mol/cm 3 10 1 10 2 10 3 5.0 5.5 6.0 6.5 7.0 7.5 0.20%C 3 H 8 -1.0%O 2 -98.8%Ar ρ 5 = 2.8x10 -5 mol/cm 3 Ignition Delay (μs) 10 0 10 1 10 2 10 3 5.0 5.5 6.0 6.5 7.0 7.5 0.152%C 3 H 8 -1.0%O 2 -98.848%Ar ρ 5 = 2.8x10 -5 mol/cm 3 10000K /T Figure 5.7 Experimental (symbols (Qin 1998)) and computed (lines) ignition delay times for mixture of propane, oxygen, and argon mixture at temperature range from 1300-1900 K and pressure range 3-4 atm, equivalence ratio from 0.75-1.0 in reflected shock waves. Ignition delay times were derived from OH absorption profiles. 113 To better understand the propane combustion, Figures 5.6 and 5.7 depict the comparison of numerical simulations and experimental ignition delay times of propane-oxygen-argon mixtures behind reflected shock wave. The model predicts fairly well the experimental data. All these shock-tube measurements are carried out for highly dilute propane/O 2 /Ar mixture, and only a few reactions show large sensitivity on the ignition delay times. 5.3.3 C 2 -C 4 alkenes Figure 5.8 denotes the experimental and computed laminar flame speeds of ethylene-air mixtures at unburned gas temperature T = 300 K, p = 1, 2, and 5 atm. As expected, laminar flame speeds decrease as pressure increases. It is seen that the reaction model reproduces very closely the experiment. At 1 atm, the model prediction and all three measurements by different research group agree with each other on laminar flame speeds at fuel-lean condition. At fuel-rich condition, the predictions seem to agree better with the experimental flame speeds of Hassan et al. (1998) and Jomaas et al. (2005). Figure 5.9 presents the comparison for the ignition delay of ethylene- oxygen-argon mixtures behind reflected shock waves. Again the model prediction is satisfactory. 114 0 20 40 60 80 100 120 0.5 1.0 1.5 2.0 Egolfopoulos et al. (1991), 1 atm Hassan et al. (1998), 1 atm Jomaas et al. (2005), 1 atm Hassan et al. (1998), 2 atm Jomass et al. (2005), 2 atm Jomaas et al. (2005), 5 atm Laminar Flame Speed, S u o (cm/s) Equivalence ratio, φ 1 atm 2 atm 5 atm Figure 5.8 Experimental (symbols) and computed (lines) laminar flame speeds of ethylene-air mixtures at 1, 2, and 5 atm at unburned gas temperature 298 K. 115 10 1 10 2 10 3 4 567 8 1%C 2 H 4 /3%O 2 /Ar p 5 =1.3-3 atm (a) 10 2 10 3 6.06.5 7.07.5 0.1%C 2 H 4 /0.6%O 2 /Ar p 5 =1.7-2.2 atm (b) 10 1 10 2 10 3 5.5 6 6.5 7 7.5 1%C 2 H 4 /1.5%O 2 /Ar p 5 =1.7-2.4 atm Ignition Delay (μs) (c) 10 2 10 3 66.5 77.5 8 0.5%C 2 H 4 /1.5%O 2 /Ar p 5 =1.5-2.3 atm (d) 10 1 10 2 10 3 5.5 6 6.5 7 7.5 8 8.5 0.5%C 2 H 4 /3%O 2 /Ar p 5 =1.5-2.4 atm 10000K /T (e) 10 1 10 2 10 3 45 67 0.5%C 2 H 4 /1%O 2 /Ar p 5 ~ 0.7 atm 10000K /T (f) Figure 5.9 Experimental (symbols) and computed (lines) of ignition delay time of ethylene-oxygen-argon mixtures behind reflected shock waves. Ignition delay times were determined by (a) the onset of CH emission (Brown and Thomas 1999), (b through e) the onset of CO 2 emission (Hidaka et al. 1999), and (f) 10% of maximum [CO]+[CO 2 ] (Homer and Kistiako 1967). 116 0 10 20 30 40 50 60 C 3 H 6 1-C 4 H 8 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Laminar Flame Speed, S u o (cm/s) Equivalence ratio, φ 1-C 4 H 8 C 3 H 6 Figure 5.10 Experimental (symbols (Davis and Law 1998)) and computed (lines) laminar flame speeds of propene and 1-butene-air mixture at p = 1 atm, T = 300 K. Figure 5.10 shows the comparisons between simulation results and the nonlinearly extrapolated flame speed data for propene and 1-butene/air mixtures at the atmospheric pressure. The peaks in the flame speed data are found to occur at around φ = 1.1 for both fuel molecules. The model predictions agree with the experimental observations that the laminar flame speed for 1-butene/air mixture is higher than that 117 of propene/air mixture. The present kinetic model predicts reasonably well the shape of the flame speed curve, but it underpredicts the experimental data at stoichiometric to fuel-rich conditions. Sensitivity analysis performed using the present model shows the reactions governing propene oxidation in laminar premixed flames include C 3 H 6 +H ↔aC 3 H 5 +H 2 , C 3 H 6 +OH ↔aC 3 H 5 +H 2 O, and aC 3 H 5 +H+M ↔C 3 H 6 +M. Within the uncertainty limits in the rate coefficients of these reactions and without simultaneously deteriorating other type of predictions such as ignition delays in shock waves, it is not possible to further improve flame speed predictions at fuel-rich equivalence ratios. To improve the prediction for fuel-rich mixtures, it may be necessary to take into account the formation of higher molecular weight species. Similar conclusion can be drawn for 1-butene oxidation. Figure 5.11 presents the comparison of ignition delay times of propene- oxygen-argon mixtures behind reflected shock wave over the temperature range of 1200 to 2000 K, at several pressures and reactant compositions. Generally, the model predicts fairly well the experimental data. 118 10 1 10 2 5.2 5.6 6.0 6.4 6.8 1.6%C 3 H 6 -7.2%O 2 -91.2%Ar p 5 = 1 atm 10 1 10 2 6.0 6.2 6.4 6.6 6.8 7.0 1.6%C 3 H 6 -7.2%O 2 -91.2%Ar p 5 = 4 atm 10 1 10 2 10 3 5.4 5.8 6.3 6.7 7.2 1.59%C 3 H 6 -3.58%O 2 -94.83%Ar p 5 = 4 atm Ignition Delay (μs) 10 1 10 2 10 3 6.0 6.5 7.0 7.5 8.0 1.6%C 3 H 6 -14.4%O 2 -84.0%Ar p 5 = 4 atm 10 2 10 3 6.4 6.8 7.2 7.6 3.17%C 3 H 6 -7.83%O 2 -89.0%Ar p 5 = 4 atm 10000K /T Figure 5.11 Experimental (symbols (Qin 1998)) and computed (lines) ignition delay times for mixture of propene, oxygen, and argon mixture at temperature range from 1250-1900 K and pressure range 1-4 atm in reflected shock waves. Ignition delay times were derived from OH absorption profiles. 119 5.3.4 C 2 -C 4 alkynes and 1, 3-butadiene Figure 5.12 shows the comparisons of the laminar flame speed for acetylene, propyne, and 1,3-butadiene-air mixtures at the atmospheric pressure. It is seen that the reaction model produces quite well the experimental data over a wide range of the equivalence ratio, even though the flame speeds of acetylene are somewhat underpredicted for fuel-rich mixtures. 0 40 80 120 160 0.60.8 1.0 1.2 1.41.6 1.8 Laminar Flame Speed, S u o (cm/s) Equivalence ratio, φ C 2 H 2 p-C 3 H 4 1,3-C 4 H 6 Figure 5.12 Experimental (symbols) and computed laminar flame speeds of acetylene, propyne, and 1,3-butadiene-air mixture at the atmospheric pressure. The acetylene data are taken from Egolfopoulos et al. (1991). The propyne and 1,3-butadiene data are taken from Davis and Law (1998). 120 10 2 10 3 55.5 66.5 77.5 1%pC 3 H 4 /2%O 2 /Ar p 5 =3.5 atm 10 2 10 3 5.5 6 6.5 7 7.5 8 1%pC 3 H 4 /4%O 2 /Ar p 5 =3.5 atm Ignition Delay (μs) 10 2 10 3 6 6.5 7 7.5 8 8.5 1%pC 3 H 4 /8%O 2 /Ar p 5 =3.5 atm 10000K /T 10 2 10 3 55.5 66.5 7 1%aC 3 H 4 /2%O 2 /Ar p 5 =2.1 atm 10 2 10 3 5.56 6.57 7.5 1%aC 3 H 4 /4%O 2 /Ar p 5 =2.1 atm 10 1 10 2 10 3 5.5 6 6.5 7 7.5 8 1%aC 3 H 4 /8%O 2 /Ar p 5 =2.1 atm 10000K /T Figure 5.13 Experimental (symbols (Curran et al. 1996)) and computed (lines) ignition delay times for propyne and allene oxidation behind reflected shock waves. The experimental ignition delay was determined by the appearance of chemiluminescence from the CO+O reaction and by the onset of pressure rise, and the computational ignition delay was determined by the maximum pressure gradient. Figure 5.13 presents the comparison of ignition delay times of propyne and allene-oxygen-argon mixtures behind reflected shock wave over the temperature 121 range from 1200 K to 2000 K at different pressures and composition. Generally, the model predicts fairly well the experimental data. 5.4 Summary A previous detailed H 2 /CO/C 1 -C 4 chemical kinetic model consisting of 111 species and 784 reactions is updated and used to describe the high-temperature reaction kinetics of hydrogen, carbon monoxide, methane, acetylene, ethylene, ethane, propyne, allene, propene, propane, 1,3-butadiene, 1-butene, and n-butane. It was shown that the kinetic model accurately predicts a wide range of combustion data for these fuels, including laminar premixed flame speeds and ignition in shock tubes. The model will serve as the kinetic foundation for developing reaction model of higher normal alkanes to be discussed next. 122 Chapter 6 Detailed Kinetic Reaction Mechanism for n-Alkane Combustion 6.1 Introduction Basic understanding of the combustion kinetics of jet fuels is critical to optimal design of gas-turbine engines. Because jet fuels contain a large number of compounds, a direct kinetic simulation of their combustion behavior is not feasible. A viable option is to use a surrogate, containing five to six pure compounds, to mimic jet-fuel behaviors (Colket et al. 2007). Conceptually, developing reaction models for surrogates remains challenging. The reaction kinetics of large hydrocarbon molecules and radicals are not as accurately known as those of small hydrocarbons. Additionally, surrogate components and their cracking products may couple kinetically because of mutual reactions. Considering this effect can increase the problem dimensionality and difficulty drastically. The closure of the surrogate problem will have to start from a particular surrogate component. By examining kinetic features unique to that component, it will be possible to make simplifications at the component level before a joint model is assembled for all surrogate components. Here an effort is presented in that direction by examining a major class of surrogate component, n-dodecane, with a specific goal 123 to address the question concerning the level of kinetic details required for description of high-temperature oxidation of n-alkanes. In the realm of β-scission of free radicals (Glassman 1996), normal alkanes crack rapidly above ~1100 K as compared to the subsequent reactions of cracked products. Cracking forms mostly H 2 , CH 4 , and C 2 -C 4 alkenes. Hence, a detailed description of the pyrolysis process may not be necessary as long as the major cracking product distribution is predicted well. Then the overall reaction rate may be modeled with a simplified fuel cracking model along with an accurate reaction model for the cracked products, as will be discussed in Chapter 7. Unknown effects from kinetic coupling of cracked products remain to be causes for concern, but this issue has been examined in the context of laminar flame speed of binary mixtures of ethylene, n-butane, and toluene in air (Hirasawa et al. 2002). For the equivalence ratio < 1.7, the laminar flame speed is primarily determined by the adiabatic flame temperature of the binary fuel-air mixture with negligible effects resulting from kinetic coupling between the fuel components. If this is true, an exact description of the cracking process would be unimportant to an accurate prediction of combustion properties of the parent fuel. Indeed, this principle was utilized previously for developing predictive reaction models of higher alkanes with different levels of details, for example, in these publications (Held et al. 1997; Seiser et al. 2000; Zeppieri et al. 2000; Dahm et al. 2004; Ranzi et al. 2005; Herbinet et al. 2007; Zhang et al. 2007). 124 In this chapter, a detailed kinetic model for the combustion of normal alkanes up to n-dodecane is proposed. Because of limited experimental data available for n-dodecane, and all considering straight-chain alkanes have similar combustion properties due to their structural similarity, the detailed model is validated against experimental data for several fuel molecules, including n-dodecane pyrolysis in plug flow and jet-stirred reactors (Zhou et al. 1987; Yoon et al. 1996a; Yoon et al. 1996b; Yu et al. 2001; Dahm et al. 2004; Herbinet et al. 2007), laminar flame speeds for n- dodecane (Kumar and Sung 2007; Ji et al. 2008), n-decane (Wagner and Dugger 1955; Kumar and Sung 2007), and n-heptane (Smallbone et al. 2008), and their oxidation behind reflected shock waves (Pfahl et al. 1996; Horning et al. 2002; Vasu et al. 2008). 6.2 Detailed reaction mechanism 6.2.1 Reaction mechanism for C 1 -C 4 n-alkanes Before the reaction model for higher n-alkanes is discussed, a review of reaction pathways for C 1 -C 4 n-alkanes will be useful to understand general rule of n- alkane combustion. The H 2 /CO/C 1 -C 4 model described in Chapter 5 is taken as the base model for developing higher n-alkane model. The base model considers pressure dependency for most unimolecular and bimolecular chemically activated reactions, and has been validated against experimental data ranging from laminar flame speeds, ignition delay times behind reflected shock waves to species profiles in flow reactor 125 and burner stabilized flame for hydrogen, carbon monoxide, methane, acetylene, ethylene, ethane, propyne, propene, propane, 1,3-butadiene, 1-betene, and n-butane. Generally, the first step in fuel oxidation process is chain initiation, in which free radicals such as H, O, OH, and CH 3 are generated. These free radicals, being extremely reactive, can readily attack the reactants and other intermediates. Depending on the number of radical generated, the reaction can be chain propagating, or chain branching, or chain terminating. If the number of radicals in the products is larger than that in the reactants, it is chain branching; if the same number, it is chain propagating; otherwise, it is chain terminating. For high-temperature oxidation of an n-alkane molecule RH and when free radicals are abundant, their reactions with an n-alkane are exclusively the H abstraction reactions. RH + (H, O, OH) = R + (H 2 , OH, H 2 O). Subsequently, the alkyl radicals R decompose rapidly. Taking propane as an example, we have n-C 3 H 8 + (H, O, OH) = n-C 3 H 7 + (H 2 , OH, H 2 O). The resulting n-propyl radical (n-C 3 H 7 ) will decompose following the β-scission rule, n-C 3 H 7 (+ M) = CH 3 + C 2 H 4 (+ M), where, M can be any species in the system. In the case of i-C 3 H 7 , i-C 3 H 7 (+ M) = H + C 3 H 6 (+ M). The main feature of a β-scission reaction is the scission of a bond beta connected to an adjacent atom to the atom bearing a radical. A unimolecular reaction involving β- 126 scission of a bond in a molecular entity results in the formation of a radical in one product and an unsaturation bond in the other. In the case of n-butyl radical (n-C 4 H 9 ), the preferred products are largely ethylene and ethyl radical, n-C 4 H 9 (+ M) = C 2 H 5 + C 2 H 4 (+ M), C 2 H 5 (+ M) = C 2 H 4 + H (+ M). For i-butyl radical (i-C 4 H 9 ), i-C 4 H 9 (+ M) = CH 3 + C 3 H 6 (+ M), or i-C 4 H 9 (+ M) = C 4 H 8 + H (+ M). The resulting alkene molecules would undergo dissociation, again following the H- abstraction and the β-scission rule. For example, C 4 H 8 + (H, O, OH) = CH 2 •CH 2 CHCH 2 + (H 2 , OH, H 2 O) or C 4 H 8 + (H, O, OH) = CH 3 CH•CHCH 2 + (H 2 , OH, H 2 O), CH 2 •CH 2 CHCH 2 (+ M) = C 2 H 4 + C 2 H 3 (+ M), CH 3 CH•CHCH 2 (+ M) = H + C 4 H 6 (+ M). 6.2.2 Reaction mechanism for C 5 -C 12 n-alkanes From above discussions for small n-alkanes, it is clear that upon the initial H abstraction, a straight-chain alkane molecule can decompose into small fragments following the β-scission rule. These fragments include mainly H, CH 3 , and small alkene molecules, C 2 H 4 , C 3 H 6 , and C 4 H 6 . A higher n-alkane molecule, for example, n-dodecane molecule, exhibits the similar behavior. At high temperatures, n-dodecane molecule is consumed by C-C fission reactions and H-atom abstraction by radical species, followed by β-scission of the dodecyl radicals, and radical reactions with 127 olefins. To be noted, compared to the small n-alkanes, larger n-alkanes can produce more alkyl radicals, which may generate more intermediates and have more possible pathways. As an example, the radical sites of a strain-chain dodecyl radical (C 12 H 25 ), can locate at six different C atoms. The number of reaction pathways increases rapidly as the number of intermediate species increases. Some of the reaction types, which may not apply for small n-alkanes, need to be included for large n-alkanes, for instance, mutual isomerization of the n-alkyl radicals. To describe high-temperature pyrolysis and oxidation of normal alkanes (C n H 2n+2 , 5 ≤ n ≤ 12), the base model discussed in Chapter 5 is appended with a set of reactions (60 species and 522 reactions). The final detailed kinetic model contains 1306 elementary reactions and 171 species. Efforts were made to ensure kinetic consistency among this set of reactions and those in the base model. Most of the kinetic parameters were estimated from analogous reactions in the base model. A rigorous treatment of the pressure dependence for the dissociation rate constants is not currently possible, but such a treatment is unnecessary, as will be discussed later. In this work the pressure dependency of rate parameters for higher alkanes, alkyl radicals, and alkenes was based on that of n-butane, 1-butyl radical, and 1-butene, respectively. The 522 reactions include (a) C-C fission, (b) H-atom abstraction from primary and secondary C atoms in n-alkanes by H, O, OH, O 2 , and CH 3 , (c) mutual isomerization of the alkyl radicals, (d) their β-scission to produce olefins and lower alkyl radicals, (e) H-atom abstraction from n-alkenes, and (f) reactions of n-alkenyl radicals. Details are discussed below. 128 (a) C-C fission of n-alkanes The rate constants of C-C fissions for n-alkanes are calculated from the reverse direction, that is, the recombination of two radical species to produce the stable n-alkane molecule. The decomposition rates are computed by using the equilibrium constants. There have been few studies for larger alkyl radicals, so these rates are estimated using reactions with similar characteristics. Due to the symmetry of an n-alkane molecule, for example n-dodecane, six different carbon sites are available, and six different dodecyl radicals may be formed. The recombination rate coefficient of C 11 H 23 radical with methyl is assumed to be the same as that of an n- propyl reacting with methyl. When the smaller alkyl radical is ethyl or larger, the recombination rate coefficients are assumed to be the rate coefficient of ethyl radical reacting with ethyl radical. For recombination of large alkyl radicals with atomic hydrogen, the rate coefficients are assumed to those of butyl radicals with hydrogen. (b) H-atom abstraction reactions of n-alkanes The reaction rates of H-atom abstraction from n-alkanes depend on the types of C-H bond being broken and the number of equivalent H atoms in the fuel. Usually, H-atom abstraction reactions can be subdivided into three types according to the nature of the H atom being abstracted: (1) primary hydrogen R-CH 3 ; (2) secondary hydrogen R-CH 2 -R’; and (3) tertiary hydrogen R 3 -CH. For n-alkane molecules, only the first two types are applicable. 129 H-atom abstractions can be carried out by the main chain carriers: H, O 2 , OH, HO 2 , CH 3 , etc. Similarly, the rate coefficients are taken from those of analogous reactions for n-butane. (c) Mutual isomerization of the alkyl radicals For the mutual isomerization of the alkyl radicals, all possible H-shift reactions were considered with their kinetic parameters taken from Matheu et al. (2003). The rate coefficients are assumed to be at the high-pressure limit. (d) β-scission reactions As discussed earlier, at high temperatures, the major reaction of an n-alkyl radical is thermal decomposition, primarily via β-scission. These decomposition reaction rates were determined by specifying the rate of the exothermic, reverse addition reaction of an alkyl radical or H atom to an olefin. The rate of alkyl radical addition to olefins is assumed to be 3×10 11 (cm 3 /mol-s) exp (-7300 cal/mol /R u T). All of these reactions are assumed be at their high pressure limits and the reverse reaction rate constants are computed from the forward rate constants and their corresponding equilibrium constants. (e) H-atom abstraction from n-alkenes The same H-abstractions for the n-alkanes are included for the olefins. Only the allylic C-H bonds are included. The rate coefficients of analogous reactions for 1-butene are used. 130 (f) Reactions of n-alkenyl radicals Because limited number of alkenyl species is included, only a few reactions are possible. For the same reason of consistency, the rate constants are assumed to be the same as those of C 4 H 7 radical. Additionally, a 4-species, 12-step lumped, low-temperature n-dodecane oxidation model is appended to the 1306 reaction-171 species model to capture some of the low- to intermediate-temperature chemistry. The lumped model is based on Bikas and Peters (2001). The use of this lumped, low-temperature model does not offer the possibility to closely predict the low-temperature chemistry, but it enables us to understand the impact of low- to intermediate-temperature chemistry on ignition delay times at high temperatures. The detailed reaction model, including the chemistry of n-pentane to n-dodecane, the lumped low-temperature model, and the base H 2 /CO/C 1 -C 4 model can be found in the Appendix B. 6.2.3 Thermodynamic database for C 5 -C 12 n-alkanes Efforts were made to ensure thermodynamic consistency as well. Thermochemical properties for the added 60 species were estimated from group additivity (Benson 1976; Lay et al. 1995). 6.2.4 Transport data for C 5 -C 12 n-alkanes To date, the only set of Lennard-Jones (LJ) 12-6 potential parameters available for normal alkanes is that of Mansoori et al. (1980), who employed the method of corresponding states and liquid properties, including molar volume, 131 viscosity, and thermal conductivity, to estimate the potential parameters. Considering non-spherical nature of molecules and that molecular configurations and interactions are not identical between liquid and vapor states, the validity of these LJ parameters for calculating gaseous diffusion coefficients remains questionable. For this reason, correlations of corresponding states of Tee et al. (1966), as used in an earlier study on the transport properties of aromatics (Wang and Frenklach 1994b), were employed here to estimate these parameters. In this method, LJ self-collision diameter σ and well depth ε are related to critical pressure P c (atm) and temperature T c (K), 1/3 σσ σ ω ⎛⎞ =− ⎜⎟ ⎝⎠ c c P ab T (6.1) εε ε ω =+ Bc ab kT (6.2) where ω is the acentric factor, and a’s and b’s are empirically derived coefficients. A consideration of 14 substances ranging from noble gases to benzene and n-heptane yielded 2.3511 σ = a , 0.0874 σ = b , 0.7915 ε = a , and 0.1693 ε = b (Tee et al. 1966). Recognizing that these coefficients may not be optimized for hydrocarbon compounds, alternative values of the coefficients are tested for closer predictions of n- alkanes up to n-heptane, as presented by Tee et al. (1966). These values are 2.3511 σ = a , 0.3955 σ = b , 0.8063 ε = a , and 0.6802 ε = b . The use of the first and second sets of coefficients is referred hereafter as methods 1 and 2, respectively. 132 The acentric factor ω was evaluated using the Lee-Kesler vapor-pressure relations (Lee and Kesler 1975) ( ) 16 16 ln 5.93 6.10 1.29ln 0.17 15.25 15.69 13.47ln 0.44 c P θ θθ ω θθ θ − − −− + + − = −− + (6.3) where θ = T b /T c , and T b is the boiling point at the ambient pressure. With the exceptions of 1-nonene and 1-undecene, values of T c and P c were obtained from (Lide 1990), so were the boiling points of all compounds. For 1-nonene and 1-undecene, critical constants were taken from Steele and Chirico (1993). All physical property data used herein are listed in Table 6.1. Lennard-Jones parameters of n-alkanes are shown in Figure 6.1 against molecular weight, comparing three different methods. Figure 6.2 depicts the corresponding binary diffusion coefficients of n-dodecane in nitrogen at the pressure of 1 atm. As seen, values of method 1 and Mansoori et al. (1980) differ markedly, especially for large molecules. Method 2 yields the collision diameter and diffusion coefficient values that lie between the two estimates. The results of method 2, as presented in Table 6.1, were adopted for the current work, as they represent an average of available estimates. 133 Table 6.1 Lennard-Jones 12-6 potential parameters for selected alkanes and alkene compounds. Formula Compound T b (K) a T c (K) a P c (atm) a ω ε/k B (K) σ (Å) n-C 5 H 12 n-pentane 309.2 469.7 33.3 0.249 458 5.45 n-C 6 H 14 n-hexane 341.9 507.6 29.9 0.298 512 5.74 n-C 7 H 16 n-heptane 371.6 540.2 27.0 0.350 564 6.00 n-C 8 H 18 n-octane 398.8 568.7 24.6 0.400 613 6.25 n-C 9 H 20 n-nonane 424.0 594.6 22.6 0.447 660 6.47 n-C 10 H 22 n-decane 447.3 617.7 20.8 0.492 705 6.68 n-C 11 H 24 n-undecane 469.1 639.0 19.5 0.541 750 6.83 n-C 12 H 26 n-dodecane 489.5 658.0 18.0 0.58 790 7.05 n-C 13 H 28 n-tridecane 508.6 675.0 16.6 0.621 829 7.24 n-C 14 H 30 n-tetradecane 526.7 693.0 15.5 0.643 862 7.44 1-C 5 H 10 1-pentene 303.1 464.8 35.1 0.233 449 5.34 1-C 6 H 12 1-hexene 336.6 504.0 31.7 0.287 505 5.63 1-C 7 H 14 1-heptene 366.8 537.3 28.8 0.341 558 5.88 1-C 8 H 16 1-octene 394.4 567.0 26.4 0.392 608 6.10 1-C 9 H 18 1-nonene 420.1 593.7 24.2 0.438 655 6.33 1-C 10 H 20 1-decene 443.7 617.0 21.9 0.478 698 6.58 1-C 11 H 22 1-undecene 469.1 638.0 20.4 0.575 764 6.69 1-C 12 H 24 1-dodecene 487.0 658.0 18.0 0.547 775 7.09 a All property values were taken from Lide (1990) except for the critical temperature and pressure values for 1-nonene and 1-dodecene, which were taken from Steele and Chirico (1993). 134 3 4 5 6 7 8 9 0 500 1000 1500 2000 60 80 100 120 140 160 180 200 220 Method 1 Method 2 Mansoori et al. (1980) 6 8 10 12 14 ε/k B (K) σ (Angstrom) MW (g/mol) Number of Carbon Atom Figure 6.1 Lennard-Jones self-collision diameter (σ) and well depth (ε/k B ) of n- alkanes plotted against molecular weight (MW). 135 0.0 0.2 0.4 0.6 0.8 1.0 1.2 500 1000 1500 D n-C12H26-N2 (cm 2 /s) T (K) Method 1 Method 2 Mansoori et al. (1980) Figure 6.2 Binary diffusion coefficient estimated for n-C 12 H 26 and N 2 at the atmospheric pressure. To be noted, the use of the empirical correlations of corresponding state involves an extrapolation of available data, which introduce uncertainty in the LJ parameters. Additionally, based on factors discussed in recent gas-kinetic analyses of the transport properties of nanoparticles and nano-tubular materials (Li and Wang 2003), the spherical potential may model the diffusivity of long-chain alkanes poorly at high temperatures. At the molecular level, normal alkanes are non-spherical. The 136 spherical potential function represents merely an average over molecular orientations over the temperature and pressure ranges for which the potential parameters are derived. The validity of these potential parameters for high-temperature application remains questionable. 6.3 Kinetic modeling The combined, detailed model was used to predict the laminar flame speeds for several normal alkanes over a wide range of equivalence ratio φ. In addition, computational ignition delay times of n-dodecane, n-decane, and n-heptane were compared to available data. Additional comparison includes n-decane oxidation in a burner-stabilized flame and flow reactor. 6.3.1 Pyrolysis of n-dodecane To ensure that the detailed model properly predicts the product distribution in the thermal cracking of n-dodecane, the experimental and predicted pyrolysis rates and product distributions are compared first. Figure 6.3 depicts the time evolution of n-dodecane conversion in an atmospheric-pressure flow reactor at 950, 1000 and 1050 K. The detailed model captures the conversion rate of n-dodecane closely. The same type of agreement extends to the conversion of n-dodecane pyrolysis in a jet-stirred reactor at 1 atm as a function of residence time (Figure 6.4) and temperature (Figure 6.5). 137 0 20 40 60 80 100 0.00 0.05 0.10 0.15 0.20 Conversion of n-C 12 H 26 (%) Residence Time (s) 950 K 1000 K 1050 K 1100 K 1150 K Figure 6.3 Experimentally (symbols (Dahm et al. 2004)) and numerically (solid lines: detailed model) determined conversion of n-C 12 H 26 during its pyrolysis in a plug flow reactor (0.336% n-C 12 H 26 -N 2 , p = 1 atm). Analysis shows that the relative contributions of C-C fission and H- abstraction are dictated by the large activation energy of C-C fission. In the flow reactor at 950 K and residence time of 0.05 s, 8% of the fuel molecule consumption originates from C-C fission in n-dodecane. The rest comes from H-abstraction by H and CH 3 at an approximately 2-to-1 ratio. As temperature increases, fuel consumption by C-C fission becomes more important. At 1050 K, 29% of the fuel was consumed 138 through C-C fission and 49% from hydrogen abstraction by H atom, with the remaining from H-abstraction by CH 3 radical. 0 20 40 60 80 100 012345 Conversion of n-C 12 H 26 n (%) Residence Time (s) 973 K 873 K 1073 K Figure 6.4 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid lines: detailed model) determined conversion of n-C 12 H 26 as a function of the residence time for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor (p = 1 atm). 139 0 20 40 60 80 100 850 900 950 1000 1050 Conversion of n-C 12 H 26 (%) T (K) Residence time = 1 s Figure 6.5 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid lines: detailed model) determined conversion of n-C 12 H 26 as a function of temperature for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor (p = 1 atm). As expected, the major products of n-dodecane pyrolysis include H 2 , CH 4 , C 2 H 4 , and C 3 H 6 , with C 2 H 4 being the most dominant. The detailed kinetic model reproduces this feature, as seen in Figure 6.6. It captures the evolution of C 2 H 4 well, but it underpredicts the production of H 2 , CH 4 , and C 3 H 6 . 140 0 0.02 0.04 0.06 Mole Fraction C 3 H 6 C 2 H 4 0 0.01 0.02 0 1234 5 H 2 CH 4 Mole Fraction Residence Time (s) H 2 CH 4 Figure 6.6 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid lines: detailed model) determined product mole fractions as a function of the residence time for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor at 973 K (p = 1 atm). 141 Note that since kinetic parameters of the current model were derived from either analogous C 4 reactions or literature without ad hoc parameter tuning, the agreement is considered to be good. Based on flux and sensitivity analysis, the discrepancy is likely to be a result of our estimate for pressure dependence for the unimolecular isomerization and dissociation reactions. In general, the rate parameters are expected to approach the high-pressure limit faster than those for the smaller C 4 H x species. Nonetheless, the discrepancy in product distribution does not affect the rate predicted for fuel pyrolysis. 6.3.2 Laminar flame speeds of higher n-alkanes The detailed model predicts the laminar flame speed of n-dodecane-air mixtures well over the whole range of equivalence ratio for experimental data from Ji et al. (2008) and the fuel-lean data reported in Kumar and Sung (2007), as showed in Figure 6.7. There exists an apparent disagreement between the experimental data reported in the two independent studies for stoichiometric and fuel-rich mixtures at 403 K. There is ample evidence that the flame speed data reported for φ > 1 in Kumar and Sung (2007) are too high, because the stretch-free flame speed values were derived from linear extrapolation of reference velocity measured at very large flame stretch, especially for fuel-rich flames. This problem is solved using computation- assisted non-linear extrapolations and a discussion of this issue can be found in Ji et al. (2008). 142 20 40 60 80 100 0.6 0.8 1.0 1.2 1.4 1.6 Kumar and Sung (2007) Ji et al. (2008) Laminar Flame Speed, S u (cm/s) Equivalence Ratio, φ 470 K 403 K p = 1 atm Figure 6.7 Experimentally (symbols) and numerically (solid lines: detailed model) determined laminar flame speeds of n-C 12 H 26 /air mixtures. Comparison of experimental (Wagner and Dugger 1955; Kumar and Sung 2007) and computed laminar flame speeds of n-decane-air mixtures at several unburned gas temperatures show similar discrepancy, as seen in Figure 6.8. Given the experimental challenges in measuring flame speeds for long-chain alkanes under the fuel-rich condition and the similar experimental discrepancy for n-dodecane (Figure 6.7), these modeling results are considered trustworthy. 143 0 20 40 60 80 100 0.6 0.8 1.0 1.2 1.4 1.6 Wagner and Dugger (1955) Kumar and Sung (2007) Laminar Flame Speed, S u (cm/s) Equivalence Ratio, φ p = 1 atm 470 K 400 K 360 K 298 K Figure 6.8 Experimentally (symbols) and numerically (solid lines: detailed model) determined laminar flame speeds of n-C 10 H 22 /air mixtures. The computed flame speeds for n-heptane-air mixtures are shown in Figure 6.9 together with the corresponding experimental data. These measurements at the freestream temperature of 350 K and pressures of 0.5, 1.0, 1.5, and 2 atm were carried out by Smallbone et al. (2008). The data at the freestream temperature of 298 K and ambient pressure are from Davis and Law (1998). The qualitative trends of the data are expected, namely, the laminar flame speed increases with increasing mixture temperature and decreasing pressure. 144 10 20 30 40 50 60 70 80 0.6 0.8 1.0 1.2 1.4 1.6 1 298 1 350 1.5 350 0.5 350 2 350 Laminar Flame Speed, S u o (cm/s) Equivalence Ratio, φ p (atm) T u (K) 1.5 atm, 350 K 1 atm, 350 K Figure 6.9 Experimentally (symbols (Davis and Law 1998; Smallbone et al. 2008)) and numerically (solid lines: detailed model) determined laminar flame speeds of n-C 7 H 16 /air mixtures. The 2-atm experiment and computation were carried out in nitrogen-diluted air (18%O 2 -82% N 2 ). Compared to the 1-atm data at the same mixture temperature, the flame speed data obtained at 2 atm in diluted air are reduced for all equivalence ratios because of the dilution and increased system pressure (Figure 6.9). The comparison demonstrates that the flame speeds are largely predicted well. At 1 atm and 298 K, there is reasonable agreement, with some overestimation on the lean side of up to 2 145 cm/s. For 350 K unburned gas temperature, the flame speeds computed for 1 and 1.5 atm are larger than the experimental values, typically by around 5 cm/s. For 0.5 and 2 atm, however, the agreement is considered good. -0.1 0 0.1 0.2 0.3 0.4 C 2 H 3 +O 2 =CH 2 CHO+O C 2 H 4 +OH=C 2 H 3 +H 2 O C 2 H 3 +H=C 2 H 2 +H 2 C 2 H 3 (+M)=C 2 H 2 +H(+M) CH 3 +OH=CH 2 *+H 2 O HCO+M=CO+H+M CH 3 +H(+M)=CH 4 (+M) H+OH+M=H 2 O+M HCO+H 2 O=CO+H+H 2 O HCO+H=CO+H 2 CO+OH=CO 2 +H H+O 2 =O+OH φ = 1, T 0 = 403 K Sensitivity Coefficient Figure 6.10 Logarithmic sensitivity coefficient of laminar flame speed with respect to reaction rate parameters, computed for n-C 12 H 26 /air mixtures at φ = 1.0, T 0 = 403 K, using the detailed model. 146 To illustrate the fact that the underlying heat release rate in a laminar premixed flame is sensitive neither to low-temperature chemistry nor to the fuel cracking rate, Figure 6.10 presents the ranked logarithmic sensitivity coefficients for laminar flame speed of a stoichiometric n-dodecane-air mixture at T 0 = 403 K. As seen, flame propagation is sensitive to the rates of H 2 /CO/C 1 -C 2 reactions only, indicating that the rate limiting steps in the overall heat release rate are identical to those in small-hydrocarbon flames. The same conclusion may be drawn by examining the results of sensitivity analysis over a broad range of equivalence ratio for n-dodecane and other straight- chain alkanes. Fuel cracking through H-abstraction-β-scission is generally fast, and occurs mostly in the pre-flame region prior to intense heat release. 6.3.3 Ignition delay times of higher n-alkanes The detailed model was validated against ignition delay times behind reflected shock waves during n-dodecane and n-decane oxidation. The computation was made for n-dodecane-air mixtures by including a lumped, low temperature model. As shown in Figure 6.11, the computed ignition delay times for a pressure of 20 atm and equivalence ratios 0.5 and 1.0 compare favorably to experimental data above a temperature of 850 K. The discrepancy between experiment and model is well within 50%, except for some cases around 1100 K. Below 850 K, the lumped, low-temperature chemistry model over predicts the experimental ignition delay, as 147 expected. The discrepancy is not of significant concern since our focus is the high- temperature chemistry. 10 1 10 2 10 3 10 4 0.7 0.8 0.9 1.0 1.1 φ=0.5, Vasu et al. (2008) φ=1.0, Vasu et al. (2008) Ignition Delay (μs) 1000K / T p 5 = 20 atm φ = 0.5 φ = 1 Figure 6.11 Experimentally (symbols) and numerically (solid lines: detailed model) determined ignition delay times for n-C 12 H 26 oxidation behind reflected shock waves. Figure 6.12 depicts the ignition delays computed for n-decane-oxygen- diluent mixtures behind reflected shock waves at 1.2 and 12 atm. The data were taken from Horning et al. (2002) and Pfahl et al. (1996), respectively. For these simulations 148 the detailed model includes the high-temperature chemistry only, as low- to intermediate-temperature chemistry is not expected to play a role in the temperature range of interest. Again, the comparison between model and experiment is satisfactory. 10 0 10 1 10 2 10 3 10 4 0.60.7 0.80.9 1.0 0.2%n-C 10 H 22 -3.1%O 2 in Ar, Horning et al. (2002) 1.34%n-C 10 H 22 -20.73%O 2 in N 2 , Pfahl et al. (1996) Ignition Delay (μs) 1000K / T p 5 = 1.23 atm p 5 = 12 atm Figure 6.12 Experimentally (symbols) and numerically (solid lines: detailed model) determined ignition delay times for n-C 10 H 22 oxidation behind reflected shock waves. 149 Through extensive sensitivity analysis, a similar conclusion to the laminar flame speeds can be drawn for the induction period chemistry at temperatures higher than 1100 K and pressures below 10 atm that is sensitive to the rates of H 2 /CO/C 1 -C 2 reactions only. 6.4 Summary A detailed kinetic model for straight-chain alkane compounds is proposed with an emphasis on n-dodecane, n-decane, and n-heptane oxidation at high temperatures. The model uses the updated H 2 /CO/C 1 -C 4 reaction model as the base model and an extended set of reactions and their kinetic parameters is developed in the present work to describe fuel cracking. The detailed model is validated against a fairly extensive set of experimental data for straight-chain alkanes up to n-dodecane. Computational results show that the detailed model is able to capture the fuel combustion responses over a wide range of conditions. Analysis of these results lead to the conclusion that in laminar premixed flames and for induction period chemistry above 1100 K, the kinetics of fuel cracking to form smaller molecular fragments (H 2 , CH 4 , C 2 H 4 , and C 3 H 6 ) may be decoupled from the oxidation kinetics of these fragments. The observation indeed provides the fundamental justification for model simplification. The simplification will be discussed in Chapter 7. 150 Chapter 7 Simplification and Analysis of n-Alkane Combustion Mechanism 7.1 Introduction In the previous chapter, a detailed kinetic model for straight-chain alkane compounds is proposed with an emphasis on n-dodecane, n-decane, and n-heptane oxidation at high temperatures. The model is validated against a fairly extensive set of experimental data for straight-chain alkanes up to n-dodecane. The fact that fuel cracking is fast allows its chemistry to be decoupled from the oxidation kinetics of the cracked H 2 /C 1 -C 4 products. The observation indeed provides the fundamental justification for model simplification. On the basis of this consideration, a simplified model for fuel cracking may be developed. In this chapter, the question how simple the cracking reaction model can be for normal alkane oxidation at high temperatures will be explored. For this purpose, the detailed model is used as a basis to obtain a minimal set of semi-global reactions to describe fuel pyrolysis above 850 K for n-dodecane. By combining this simplified model with a kinetic model of H 2 , CO, and C 1 -C 4 hydrocarbon combustion, the simplified model is demonstrated to work as well as the detailed model for predicting combustion properties of n-dodecane and n-decane. 151 The model simplification not only provides insights into the role of fuel cracking in the normal alkane combustion, but also facilitates the simulations to understand better the roles of chemical kinetics and molecular transport in a range of flame phenomena. The nonpremixed ignition temperature responses for n-heptane/air mixture are analyzed by numerical sensitivity analysis on reaction kinetics and fuel diffusion rate. The influence of uncertainties in the molecular transport on the model prediction of diffusive ignition is discussed. 7.2 Simplified n-dodecane reaction mechanism For a wide range of combustion properties, including laminar flame speeds and induction period chemistry above ~1100 K, n-alkanes first undergo fast thermal cracking, forming a range of H 2 , and C 1 -C 4 hydrocarbon fragments. Rate processes, including heat release, radical accumulation, and induction period chemistry, are generally sensitive to the chemistry of the cracked products, or more precisely the H 2 /CO/C 1 -C 4 chemistry. While this behavior is conceptually understood (Glassman 1996) and has been utilized to develop semi-detailed reaction models of higher hydrocarbons, for example (Held et al. 1997; Zeppieri et al. 2000), it remains unclear what constitutes the simplest set of reactions for each n-alkane, so that combining this set with the base H 2 /CO/C 1 -C 4 model would be sufficient to predict all relevant high-temperature pyrolysis and combustion properties of that alkane compound. Here, such a minimum basis-set model for n-dodecane is proposed. 152 To obtain this model, the detailed reaction model was reduced to a skeletal model using the method described in Wang and Frenklach (1991). Further simplification of the skeletal model was accomplished by flux analyses and the quasi- steady state approximation, and by combining parallel reactions, leading to non- integer product stoichiometric coefficients. This results in a semi-empirical model, shown in Table 7.1, which describes the cracking kinetics and product distribution for n-dodecane. The cracking products considered include H 2 and C 1 -C 4 species, all of which were considered in detail in the base model. Thus, the final model, featuring only 4 species (n-dodecane and three intermediates), is added to the base H 2 /CO/C 1 -C 4 model. Rate parameters of the semi-global reactions in Table 7.1 are expressed using the modified Arrhenius expression. Sensitivity analyses for n-dodecane pyrolysis in a flow reactor show that fuel conversion rate is controlled by C-C fission of n-dodecane and H-abstractions by H and CH 3 . A decrease in the rate of these reactions will obviously lead to a smaller conversion rate. The decomposition of the resulting alkyl radicals via β-scission is not rate limiting and is thus assumed to be infinitely fast. The rate parameters of reactions 1 and 2 of Table 7.1 are chosen to be those of the C-C fission of n-dodecane of the detailed model. That is, they are taken to be the reverse rate coefficients of p-C 9 H 19 +n-C 3 H 7 = n-C 12 H 26 and p-C 8 H 17 +p-C 4 H 9 = n-C 12 H 26 , both of which are dominant among all C-C fission of n-C 12 H 26 . 153 Table 7.1 Rate parameters of reactions employed in the simplified model a . No. Reaction A n E a 1 n-C 12 H 26 →3C 2 H 4 +2n-C 3 H 7 5.6×10 26 -2.7 88171 2 n-C 12 H 26 →2C 2 H 4 +2p-C 4 H 9 5.1×10 25 -2.5 88117 3 n-C 12 H 26 +H →4C 2 H 4 +p-C 4 H 9 +H 2 1.3×10 6 2.5 6756 4 n-C 12 H 26 +H →1.2C 2 H 4 +0.2C 3 H 6 +0.4n-C 3 H 7 +0.2C 4 H 8 -1+0.6 p-C 4 H 9 +0.2C 5 H 10 +0.6C 6 H 12 +H 2 1.3×10 6 2.4 4471 5 n-C 12 H 26 +O →4C 2 H 4 +p-C 4 H 9 +OH 1.9×10 5 2.7 3716 6 n-C 12 H 26 +O →1.2C 2 H 4 +0.2C 3 H 6 +0.4n-C 3 H 7 +0.2C 4 H 8 -1+0.6 p-C 4 H 9 +0.2C 5 H 10 +0.6C 6 H 12 +OH 4.8×10 4 2.7 2106 7 n-C 12 H 26 +OH →4C 2 H 4 +p-C 4 H 9 +H 2 O 1.4×10 3 2.7 527 8 n-C 12 H 26 +OH →1.2C 2 H 4 +0.2C 3 H 6 +0.4n-C 3 H 7 +0.2C 4 H 8 -1+0.6 p-C 4 H 9 +0.2C 5 H 10 +0.6C 6 H 12 + H 2 O 2.7×10 4 2.4 393 9 n-C 12 H 26 +CH 3 →4C 2 H 4 +p-C 4 H 9 +CH 4 1.8 3.7 7153 10 n-C 12 H 26 + CH 3 →1.2C 2 H 4 +0.2C 3 H 6 +0.4n-C 3 H 7 +0.2C 4 H 8 -1+0.6 p-C 4 H 9 +0.2C 5 H 10 +0.6C 6 H 12 + CH 4 3.0 3.5 5480 11 C 6 H 12 +H+(M) ↔C 3 H 6 + n-C 3 H 7 +(M) k ∞ k 0 1.3×10 13 8.7×10 42 -7.5 1560 4722 12 C 6 H 12 +H ↔C 2 H 4 + p-C 4 H 9 8.0×10 21 -2.4 11180 13 C 6 H 12 +H ↔C 6 H 11 + H 2 6.5×10 5 2.5 6756 14 C 5 H 10 +H+(M) ↔C 3 H 6 +C 2 H 5 +(M) k ∞ k 0 1.3×10 13 8.7×10 42 -7.5 1560 4722 15 C 5 H 10 +H ↔C 2 H 4 +n-C 3 H 7 8.0×10 21 -2.4 11180 16 C 5 H 10 +H ↔C 2 H 4 +a-C 3 H 5 + H 2 6.5×10 5 2.5 6756 17 C 6 H 12 +O ↔HCO+C 2 H 4 +n-C 3 H 7 3.3×10 8 1.5 -402 18 C 5 H 10 +O ↔HCO+ p-C 4 H 9 3.3×10 8 1.5 -402 19 C 6 H 11 +H ↔CH 3 +C 2 H 4 +a-C 3 H 5 2.0×10 21 -2.0 11000 20 C 6 H 11 +HO 2 →CH 2 O+OH+C 2 H 4 +a-C 3 H 5 2.4×10 13 a Units are mol, cm, sec, cal, and K. 154 Reactions 3 to 10 are combined H-abstraction and the subsequent β- scissions, leading to smaller fragments. For example, the primary H-abstraction by the H atom — a rate limiting step, and the subsequent C-C β-scission of the primary n-dodecyl radical (p-C 12 H 25 ) leads to the production of 4C 2 H 4 + p-C 4 H 9 . Hence the global reaction step is n-C 12 H 26 + H → 4C 2 H 4 + p-C 4 H 9 + H 2 (primary). Here we omitted the slower C-H β-scission and H-shift reactions and assigned the rate coefficient to be that of the corresponding H-abstraction reaction of the detailed model. Likewise, the H-abstraction reactions from the H atoms in the secondary positions and beyond are n-C 12 H 26 + H →s-C 12 H 25 + H 2 → … → C 3 H 6 + n-C 3 H 7 + C 6 H 12 + H 2 (secondary), → s2-C 12 H 25 + H 2 → … → C 4 H 8 -1 + 2C 2 H 4 + p-C 4 H 9 + H 2 (tertiary), → s3-C 12 H 25 + H 2 → … → C 5 H 10 + 2C 2 H 4 + n-C 3 H 7 + H 2 (quaternary), → s4-C 12 H 25 + H 2 → … → C 6 H 12 + C 2 H 4 + p-C 4 H 9 + H 2 (quinary), → s5-C 12 H 25 + H 2 → … → C 6 H 12 + C 2 H 4 + p-C 4 H 9 + H 2 (senary). Since the rate coefficients of the initial, H-abstraction steps are assumed to be identical, we sum the 5 reactions algebraically, leading to a global reaction with non- integer stoichiometric coefficients n-C 12 H 26 + H → 1.2C 2 H 4 + 0.2C 3 H 6 + 0.4n-C 3 H 7 + 0.2C 4 H 8 -1 + 0.6p-C 4 H 9 + 0.2C 5 H 10 + 0.6C 6 H 12 + H 2 . The rate parameters of Reaction 4 are those of the H abstraction reactions. Reactions 5 to 10 and their rate parameters were derived in a similar manner. 155 Reactions 11 to 20 describe the thermal decomposition and oxidation kinetics of intermediates, including 1-hexene, 1-pentane, and 1-hexenyl radical. The rate parameters of these reactions are based on analogous reactions of 1-butene and 1- butenyl in the base model. 7.3 Kinetic modeling results and discussions 7.3.1 n-dodecane Numerical predictions made by the simplified model are presented as dashed lines in Figures 7.1 through 7.6. Clearly the comparison is satisfactory for all experimental data considered. Compared to the detailed model, the simplified model predicts very well about the conversion of the fuel molecule in both flow reactor (Figure 7.1) and jet- stirred reactor (Figure 7.2 and Figure 7.3), but slightly more ethylene and less propene in n-dodecane pyrolysis, as shown in Figure 7.4. The agreement on the fuel conversion is mainly due to the fact that the dominant reactions C-C fission and H-abstraction reactions are well described in the simplified model, however, the discrepancy observed for the concentration of the intermediates is certainly caused by an oversimplification of the alkene chemistry, which does not however affect the ability of the simplified model to predict laminar flame speeds and ignition delays in Figures 7.5 and 7.6. 156 0 20 40 60 80 100 0.00 0.05 0.10 0.15 0.20 Conversion of n-C 12 H 26 (%) Residence Time (s) 950 K 1000 K 1050 K 1100 K 1150 K Figure 7.1 Experimentally (symbols (Dahm et al. 2004)) and numerically (solid lines: detailed model; dashed lines: simplified model) determined conversion of n-C 12 H 26 during its pyrolysis in a plug flow reactor (0.336% n-C 12 H 26 -N 2 , p = 1 atm). 157 0 20 40 60 80 100 0123 45 Conversion of n-C 12 H 26 n (%) Residence Time (s) 973 K 873 K 1073 K Figure 7.2 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid lines: detailed model; dashed lines: simplified model) determined conversion of n-C 12 H 26 as a function of the residence time for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor (p = 1 atm). 158 0 20 40 60 80 100 850 900 950 1000 1050 Conversion of n-C 12 H 26 (%) T (K) Residence time = 1 s Figure 7.3 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid line: detailed model; dashed line: simplified model) determined conversion of n-C 12 H 26 as a function of temperature for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor (p = 1 atm). 159 0 0.02 0.04 0.06 Mole Fraction C 3 H 6 C 2 H 4 0 0.01 0.02 01 23 4 5 H 2 CH 4 Mole Fraction Residence Time (s) H 2 CH 4 Figure 7.4 Experimentally (symbols (Herbinet et al. 2007)) and numerically (solid lines: detailed model; dashed lines: simplified model) determined product mole fractions as a function of the residence time for the pyrolysis of 2% n-C 12 H 26 in He in a jet-stirred reactor at 973 K (p = 1 atm). 160 20 40 60 80 100 0.6 0.8 1.0 1.2 1.4 1.6 Kumar and Sung (2007) Ji et al. (2008) Laminar Flame Speed, S u (cm/s) Equivalence Ratio, φ 470 K 403 K p = 1 atm Figure 7.5 Experimentally (symbols) and numerically (solid lines: detailed model; dashed lines: simplified model) determined laminar flame speeds of n-C 12 H 26 /air mixtures. Figure 7.5 compares the laminar flame speeds predicted for n-dodecane using the detailed model and the simplified model. The two model predictions agree with each other very well with maximum absolute deviation between them less than 2 cm/s over the whole equivalence ratio range from 0.6 to 1.6. 161 10 1 10 2 10 3 10 4 0.70.8 0.91.0 1.1 φ=0.5, Vasu et al. (2008) φ=1.0, Vasu et al. (2008) Ignition Delay (μs) 1000K /T p 5 = 20 atm φ = 0.5 φ = 1 Figure 7.6 Experimentally (symbols) and numerically (solid lines: detailed model; dashed line: simplified model) determined ignition delay times for n-C 12 H 26 oxidation behind reflected shock waves. Figure 7.6 shows the ignition delay times for n-dodecane oxidation behind reflected shock waves. Above 1100 K, the simplified model gives close results to the detailed model; below 1100 K, it starts to over predict the ignition delay times. The reason is at relatively lower temperature, the initiation chemistry becomes more complicated, which require better description for the reaction mechanism. 162 -0.1 0 0.1 0.2 0.3 0.4 HO 2 +H=2OH CH 3 +HO 2 =CH 3 O+OH 2CH 3 =H+C 2 H 5 C 2 H 3 +O 2 =CH 2 CHO+O C 2 H 4 +OH=C 2 H 3 +H 2 O C 2 H 3 +H=C 2 H 2 +H 2 C 2 H 3 (+M)=C 2 H 2 +H(+M) CH 3 +OH=CH 2 *+H 2 O CH 3 +H(+M)=CH 4 (+M) HCO+M=CO+H+M H+OH+M=H 2 O+M HCO+H 2 O=CO+H+H 2 O HCO+H=CO+H 2 CO+OH=CO 2 +H H+O 2 =O+OH φ = 1, T 0 = 403 K detailed model simplified model Sensitivity Coefficient Figure 7.7 Logarithmic sensitivity coefficient of laminar flame speed with respect to reaction rate parameters, computed for n-C 12 H 26 /air mixtures at φ = 1.0, T 0 = 403 K, using both the detailed model and the simplified model. Figure 7.7 presents the ranked logarithmic sensitivity coefficients for laminar flame speed of a stoichiometric n-dodecane-air mixture at T 0 = 403 K using the detailed and the simplified models. As seen, both model give very similar results, except the magnitude is slightly different. However, the difference does not influence the flame propagation speeds. 163 The validity of this simplified model lies in its ability to predict the product distribution of n-dodecane pyrolysis, as well as the overall pyrolysis rate with a limited number of reaction steps. The number of steps involved is the smallest set, as further simplification would lead to significant problems in predicting the distribution of the cracking products. To examine the range of its applicability, extensive numerical simulations were carried out in a perfectly stirred reactor, varying the temperature, residence time, and equivalence ratio. It was found that for n- dodecane the simplified model mimics the combustion behavior of detailed model closely for temperatures above 1100 K. Below that temperature the simplified model starts to deviate from the detailed model, not because of inaccuracy of the pyrolysis rate or product distribution, but because of lack of good low-temperature chemistry. The simplified model predicts the pyrolysis experiments down to 873 K very well (Figure 7.2). Hence, the validity of the simplified model must cover the entire range of the detailed model so long as high-temperature chemistry dominates the oxidation process. 7.3.2 n-decane The same approach may be employed for other alkanes. Figures 7.8 and 7.9 compare the laminar flame speeds and ignition delay times predicted for n-decane using the detailed model and a simplified model similar to the one presented in Table 7.1. The agreement between the two models is similar to that for n-dodecane. 164 0 20 40 60 80 100 0.60.8 1.01.2 1.41.6 Wagner and Dugger (1955) Kumar and Sung (2007) Laminar Flame Speed, S u (cm/s) Equivalence Ratio, φ p = 1 atm 470 K 400 K 360 K 298 K Figure 7.8 Experimentally (symbols) and numerically (solid lines: detailed model; dashed lines: simplified model not shown here) determined laminar flame speeds of n-C 10 H 22 /air mixtures. 165 10 0 10 1 10 2 10 3 10 4 0.6 0.7 0.8 0.9 1.0 0.2%n-C 10 H 22 -3.1%O 2 in Ar, Horning et al. (2002) 1.34%n-C 10 H 22 -20.73%O 2 in N 2 , Pfahl et al. (1996) Ignition Delay (μs) 1000K /T p 5 = 1.23 atm p 5 = 12 atm Figure 7.9 Experimentally (symbols) and numerically (solid lines: detailed model; dashed lines: simplified model not shown here) determined ignition delay times for n-C 10 H 22 oxidation behind reflected shock waves. 7.3.3 n-heptane The detailed kinetic model up to n-heptane oxidation contains 955 reactions and 130 species. A skeletal model of 65 species and 315 reactions is reduced from the detailed model using the method of Wang and Frenklach (1991). This skeletal model may be further reduced to a simplified model similar to the one 166 presented in Table 7.1, however, the goal here is not to get the minimal set of reactions but to facilitate sensitivity calculations for the opposed jet problem. 10 20 30 40 50 60 70 80 0.60.8 1.01.2 1.4 1.6 1 298 1 350 1.5 350 0.5 350 2 350 Flame Speed, S u o (cm/s) Equivalence Ratio, φ p (atm) T u (K) 1.5 atm, 350 K 1 atm, 350 K Figure 7.10 Experimental (symbols (Davis and Law 1998; Smallbone et al. 2008)) and computed (solid lines: detailed model; dashed lines: skeletal model) laminar flame speeds of n-heptane–air mixtures. The 2-atm experiment and computation were carried out in nitrogen-diluted air (18%O 2 -82% N 2 ). Figure 7.10 compares the laminar flame speeds predicted for n-heptane using the detailed model and the skeletal model. The two model predictions agree 167 with each other very well, which demonstrates that the skeletal model accurately represents the detailed model. The maximum absolute deviation between them is less than 2 cm/s over the entire range of conditions tested. 100 200 300 400 500 1150 1200 1250 1300 1350 Strain Rate, K (s -1 ) Ignition Temperature, T ign (K) Figure 7.11 Ignition temperatures of 4.5% n-heptane in nitrogen at 298 K versus air as a function of strain rates (p = 1atm). Symbols: experimental data (Smallbone et al. 2008); solid line: prediction of the detailed model; dashed line: prediction with the binary diffusivity of n-heptane increased by 50%. 168 01 23 1200 1250 1300 1350 1400 1450 Pressure, p (atm) Ignition Temperature, T ign (K) Figure 7.12 Ignition temperatures of 2.5% n-heptane in nitrogen at 298 K versus air as a function of pressure with density-weighted strain rate K = 325 s -1 . Symbols: experimental data (Smallbone et al. 2008); solid line: prediction of the detailed model; dashed line: prediction with the binary diffusivity of n-heptane increased by 50%. The results of the simulations using the detailed kinetic model against the experimental measurements (Smallbone et al. 2008) for the air temperature at ignition are shown in Figures 7.11 and 7.12. These experiments were carried out using the counterflow twin-flame technique and the simulations were performed by Dr. Andrew Smallbone and Wei Liu at Princeton University. The ignition temperature exhibits the 169 anticipated behaviors with respect to the strain rate and pressure. Namely, it increases with increase strain rate at the ambient pressure (Figure 7.11) and decreases with increasing pressure at the constant strain rate of K = 325 s -1 in Figure 7.12. The simulation results, however, are systematically higher than the measurements by about 50 K. Corresponding results obtained by using the skeletal model are about 20 K greater than those of the detailed model. The ranked sensitivity coefficients of reaction rate and binary diffusion coefficients were computed with the skeletal model and listed in Figure 7.13. For all the reported cases, the computed ignition temperature is more sensitive to the binary diffusion coefficient, especially for the n-heptane–N 2 pair, than the reaction rate coefficients, by at least one order of magnitude, as shown in Figure 7.13. Hence, while the underlying oxidation of the fuel is ultimately responsible for flame ignition, it is the molecular transport that determines the observed ignition temperature. This observation is consistent with the finding of a recent numerical study by Andac and Egolfopoulos (2007), who found the sensitivity of ignition to diffusion coefficients was of the same order or larger than that to kinetics for both laminar premixed and non-premixed conterflow ignition of n-heptane flames. The large sensitivity of the binary diffusion coefficient of n-heptane-N 2 is due to the fact that the amount of fuel accessible for the nonpremixed counterflow ignition is diffusion controlled. Specifically, ignition occurs on the oxidizer side of the stagnation plane because the oxidizer boundary has the highest temperature in the flow field. However, the fuel can reach the ignition kernel only after it crosses the 170 stagnation plane of the counterflow stream by diffusion. In other words, the binary diffusion coefficient of n-heptane–N 2 essentially dictates the quantity of fuel available for ignition. -1.6 -1.2 -0.8 -0.4 0.0 H+O 2 =O+OH HO 2 +OH=O 2 +H 2 O HCO+O 2 =CO+HO 2 HCO+M=CO+H+M C 2 H 4 +OH=C 2 H 3 +H 2 O C 2 H 3 +O 2 =CH 2 CHO+O C 2 H 3 +O 2 =HCO+CH 2 Ο CH 3 +HO 2 =CH 3 O+OH N 2 -nC 7 H 16 O 2 -nC 7 H 16 N 2 -O 2 Logarithmic Sensitivity Coefficient D ij { Figure 7.13 Ranked logarithmic sensitivity coefficients of rate coefficients and diffusion coefficients (D ij ) to the turning point, computed for the turning point with 4.5% n-heptane in nitrogen versus air at p = 1 atm and strain rate K = 150 s -1 . To gain a quantitative assessment of the sensitivity of n-heptane diffusion rates on the simulation results, the binary diffusivity between n-heptane and N 2 was 171 artificially increased by 50%. Figure 7.11 shows that this results in a systematic decrease of the ignition temperature by approximately 40K at 1 atm pressure. This decrease is even more significant for higher pressures, as seen in Figure 7.12. The increased diffusivity brings the simulation in better agreement with the experimental data. It is of interest to note that this strong sensitivity towards fuel diffusivity is not observed for the laminar flame speed. For example, an increase of the n- heptane diffusivity by 50% leads to negligible changes in the flame speeds, indicating that while the diffusivity strongly affects the ignition state, it has practically no influence on the laminar flame propagation rate. The reason is that n-heptane, as other normal alkanes, decomposes upon entering the preheat zone of the flame, hence losing its identity as a distinct species. As discussed in Chapter 6, the Lennard-Jones (LJ) parameters for n- heptane were estimated from the correlations of corresponding states (Tee et al. 1966). The underlying assumption for molecular diffusion is that the spherical potential function of molecular interactions remains valid at elevated temperatures, and that the empirical LJ parameters are independent of temperature. Since the intermolecular interactions for n-heptane are inherently non-spherical, the spherical potential function represents merely an average over molecular orientations, and as such, the potential parameters, obtained typically from low-temperature properties, are not expected to reproduce high temperature transport behaviors. In particular, the variations of molecular rotation and kinetic energy of the dilute gas as a function of temperature 172 and non-elastic collision resulting from collision-induced, hindered internal rotation in n-heptane can render the spherical assumption inaccurate. While the issues just discussed have not been addressed at a fundamental level, it may be noted that a 50% increase in the binary diffusivity for n-heptane is not beyond reason. Considering that the binary diffusivity is inversely proportional to the collision diameter, a 50% increase in the binary n-heptane–N 2 diffusivity would require the collision diameter of n-heptane to be reduced from 6 Å to 4.2 Å. This reduction is plausible, if we consider n-heptane as a stick with diameter approximately equal to that the collision diameter of methane, which is 3.7 Å (Kee et al. 1986). 7.4 Summary The model proposed here contains 4 species and 20 reaction steps, and describes accurately n-dodecane cracking above 850 K. This model represents the smallest set required to predict both the pyrolysis rate and product distribution. When this simplified model is used with the base H 2 /CO/C 1 -C 4 model, it predicts accurately the global combustion properties of n-dodecane. The method proposed here may provide an alternative approach to jet fuel surrogate. For practical fuels, such as JP-7 and JP-8, the cracking kinetics is expected to be even faster than n-dodecane. Fuel cracking should lead to the production of hydrogen, methane and C 2 -C 4 compounds. Thus, an alternative approach to understand the quantitative combustion behaviors of jet fuel may be taken, in which the initial pyrolytic process is described by a semi- empirical model, but the reaction kinetics of the cracked products is treated 173 fundamentally. This approach, though untested, is attractive since the reaction kinetics of H 2 and C 1 -C 4 hydrocarbons is relatively well understood. Comparisons with the experimental laminar flame speeds of n-heptane show that a similar simplified model predicts the experimental data reasonably well, whereas the counterflow ignition temperature are generally overpredicted by about 50 K. The study further shows that, unlike the laminar flame speed, the counterflow ignition temperature was overwhelmingly sensitive to the diffusion rate of n-heptane. The fact that a 50% increase in the binary diffusivity of n-heptane is needed to reproduce the experimental ignition temperature suggests that the gas-phase molecular transport of long-chain hydrocarbons requires further scrutiny. 174 Chapter 8 Conclusions and Future Work 8.1 Conclusions A detailed high-temperature reaction model is developed for combustion of normal alkanes up to n-dodecane by updating a previous detailed high-temperature model for H 2 /CO/C 1 -C 4 combustion, and developing an extended set of reactions for higher hydrocarbon combustion. Kinetic modeling results show that the detailed model is able to capture the fuel combustion responses over a wide range of conditions. In laminar premixed flames and for induction period chemistry above 1100 K, the kinetics of fuel cracking to form smaller molecular fragments (H 2 , CH 4 , C 2 H 4 , and C 3 H 6 ) may be decoupled from the oxidation kinetics of these fragments. The observation indeed provides the fundamental justification for model simplification. A simplified model containing 4 species and 20 reaction steps for n- dodecane cracking is found to be the smallest set required to predict both pyrolysis rate and product distribution. When this simplified model is used with the base H 2 /CO/C 1 -C 4 model, it is able to predict combustion properties as well as the detailed model. Comparisons with the experimental laminar flame speeds of n-heptane show that the model predicts the data reasonably well, whereas the counterflow 175 ignition temperature are generally over predicted by about 50 K. The study further shows that, unlike the laminar flame speed, the counterflow ignition temperature was overwhelmingly sensitive to the diffusion rate of n-heptane. The fact that a 50% increase in the binary diffusivity of n-heptane is needed to reproduce the experimental ignition temperature suggests that the gas-phase molecular transport of long-chain hydrocarbons requires further scrutiny. The nonpremixed ignition temperature responses for n-heptane/air mixture are analyzed by numerical sensitivity analysis on reaction kinetics and fuel diffusion rate. The influence of uncertainties in the molecular transport on the model prediction of diffusive ignition is discussed. The reaction kinetics of CO + HO 2 • → CO 2 + •OH is studied using the single-reference CCSD(T) method with Dunning’s cc-pVTZ and cc-pVQZ basis sets and multireference CASPT2 methods. The classical energy barriers are found to be about 18 and 19 kcal/mol for CO + HO 2 • addition following the trans and cis paths. The HOOC•O adduct has a well defined local energy minimum in the trans- configuration, but the cis-conformer is either a very shallow minimum or an inflection point on the potential energy surface. Therefore, the cis-pathway is treated with conventional transition state theory and the trans-pathway with a master equation analysis. Formulations and algorithms are developed for partition function and density of energy states of asymmetric one-dimensional hindered rotation. The computation shows that the overall rate is independent of pressure up to 500 atm. The derived rate expression is within 10% of that of Mittal et al. (2006), obtained on the basis of an analysis of rapid compression machine experiments of H 2 /CO oxidation in 176 the temperature range of 950 and 1100 K. Considering the underlying uncertainties in the theoretical energy barriers, a parameter sensitivity analysis is carried out for the rate constant and the uncertainty factor is estimated. These error bars reject almost all rate values reported in earlier studies, with the exception of (Mittal et al. 2006; 2007). The reaction kinetics of •OH + HO 2 • → H 2 O + O 2 is studied using quantum-mechanical electronic structure methods at the CBS-QBH level of theory. A hydrogen-bonded diradical complex (HOHOO) and a stable close-shell singlet intermediate hydrogen trioxide (HOOOH) lying about 5 kcal/mol and 32.4 kcal/mol below the energy of the reactants at 0 K are formed from •OH + HO 2 • barrierless addition on the triplet surface and singlet surface, respectively. The energy barriers are found to be about 1.2 and 46.3 kcal/mol for the complexes 3 HOHOO and 1 HOOOH to dissociate following their respective spin state surfaces. Both pathways are treated with microcanonical variational transition state theory and a master equation analysis. Because the decomposition of 1 HOOOH into H 2 O + 1 O 2 requires a large energy barrier, the contribution to rate constant from singlet surface is negligible and the H-atom abstraction on the triplet PES is the dominant pathway leading to H 2 O + 3 O 2 . 8.2 Future work The ultimate goal of chemical kinetic modeling is to develop an ideal set of thermodynamic data and a reaction mechanism which will describe all essential chemistry details of a combustion process. At the current stage, much progress has 177 been made, but we are still far from the ultimate goal. The future work should consider the following aspects of model development. Detailed or semi-detailed low-temperature chemistry may need to be included, as current model can only be applied to high-temperature n-alkane oxidation. Transport properties were overlooked; more attention should be drawn to deriving these parameters experimentally and theoretically and quantifying the uncertainties. Kinetic model optimization and uncertainty propagation analysis may help to improve model predication and understand better the impact of uncertainty of kinetic parameters in the model on numerical simulation results. The simplified model of n-dodecane combustion may provide an alternative approach to jet fuel surrogate. For practical fuels, such as JP-7 and JP-8, the cracking kinetics is expected to be faster than n-dodecane. Fuel cracking should lead to the production of hydrogen, methane, and C 2 -C 4 compounds. Thus, an alternative approach to understand the quantitative combustion behaviors of jet fuel may be taken, in which the initial pyrolytic process is described by a semi-empirical model, but the reaction kinetics of the cracked products is treated fundamentally. This approach, though untested, is attractive since the reaction kinetics of H 2 and C 1 -C 4 hydrocarbons is relatively well understood. While we should take the fundamental approach for model development by keeping in mind the hierarchical nature of reaction models, evaluating rate parameters for each elementary reaction, and validating the model against experiments, the question is how to make this development process more efficiently 178 and effectively. Since new kinetic data and experimental measurements are produced continuously, these data need be evaluated and incorporated in the model immediately. However, this is almost impossible to be accomplished by a single researcher, given the tremendous amount of information. Therefore, if we desire to develop a ‘real’ predictive model, it is critical to properly organize data, develop tools for analyzing and processing data, and engage the whole combustion chemistry community in the process. 179 Bibliography Adusei, G. Y., Blue, A. S. and Fontijn, A. (1996). The O( 3 P) methylacetylene reaction over wide temperature and pressure ranges. Journal of Physical Chemistry 100, 16921-16924. Allen, T. L., Fink, W. H. and Volman, D. H. (1996). Theoretical studies of the mechanism of the gas phase reaction of the hydroperoxo radical with carbon monoxide to form hydroxyl radical and carbon dioxide. Journal of Physical Chemistry 100, 5299-5302. Andac, M. G. and Egolfopoulos, F. N. (2007). Diffusion and kinetics effects on the ignition of premixed and non-premixed flames. Proceedings of the Combustion Institute 31, 1165-1172. Anderson, J. A. and Tschumper, G. S. (2006). Characterizing the potential energy surface of the water dimer with DFT: failures of some popular functionals for hydrogen bonding. Journal of Physical Chemistry A 110, 7268-7271. Anglada, J. M., Olivella, S. and Sole, A. (2007). New insight into the gas-phase bimolecular self-reaction of the HOO radical. Journal of Physical Chemistry A 111, 1695-1704. Arustamyan, A. M., Shakhnazaryan, I. K., Philipossyan, A. G. and Nalbandyan, A. B. (1980). Kinetics and the mechanism of the oxidation of carbon-monoxide in the presence of hydrogen. International Journal of Chemical Kinetics 12, 55- 75. Asatryan, R., Rutz, L., Bockhorn, H. and Bozzelli, J. W. (2006). Computational thermochemistry and kinetics for the HO 2 +CO reaction. International Workshop on Gas Kinetics, Sonderforschungsbereich SFB 606, Karlsruhe, Germany. Astholz, D. C., Troe, J. and Wieters, W. (1979). Unimolecular processes in vibrationally highly excited cycloheptatrienes 1. Thermal-isomerization in shock-waves. Journal of Chemical Physics 70, 5107-5116. 180 Atkinson, R., Baulch, D. L., Cox, R. A., Crowley, J. N., Hampson, R. F., Hynes, R. G., Jenkin, M. E., Rossi, M. J. and Troe, J. (2004). Evaluated kinetic and photochemical data for atmospheric chemistry: Volume I - gas phase reactions of O-x, HOx, NOx and SOx species. Atmospheric Chemistry and Physics 4, 1461-1738. Atri, G. M., Baldwin, R. R., Jackson, D. and Walker, R. W. (1977). Reaction of OH radicals and HO 2 radicals with carbon-monoxide. Combustion and Flame 30, 1-12. Azatyan, V. V. (1971). Mechanism of ethane inhibition of hydrogenoxygen mixture ignition. Doklady Akademii Nauk SSSR 196, 617-&. Baboul, A. G., Curtiss, L. A., Redfern, P. C. and Raghavachari, K. (1999). Gaussian-3 theory using density functional geometries and zero-point energies. Journal of Chemical Physics 110, 7650-7657. Baldwin, R. R., Dean, C. E., Honeyman, M. R. and Walker, R. W. (1986). Arrhenius parameters for the reaction HO 2 +C 2 H 6 →C 2 H 5 +H 2 O 2 over the temperature- range 400-500 ºC. Journal of the Chemical Society-Faraday Transactions I 82, 89-102. Baldwin, R. R., Hisham, M. W. M. and Walker, R. W. (1985). Elementary reactions involved in the oxidation of propene: Arrhenius parameters for the reaction HO 2 +C 3 H 6 =C 3 H 6 O+OH. Symposium (International) on Combustion 20, 743- 750. Baldwin, R. R., Jackson, D., Walker, R. W. and Webster, S. J. (1965). The use of the hydrogen-oxygen reaction in evaluating velocity constants. Symposium (International) on Combustion 10, 423-433. Baldwin, R. R., Keen, A. and Walker, R. W. (1984). Studies of the decomposition of oxirane and of its addition to slowly reacting mixtures of hydrogen and oxygen at 480 ºC. Journal of the Chemical Society-Faraday Transactions I 80, 435- 456. Baldwin, R. R., Walker, R. W. and Webster, S. J. (1970). Carbon monoxide-sensitized decomposition of hydrogen peroxide. Combustion and Flame 15, 167-&. Barker, J. R. (2001). Multiple-well, multiple-path unimolecular reaction systems. I. MultiWell computer program suite. International Journal of Chemical Kinetics 33, 232-245. 181 Barker, J. R. and Ortiz, N. F. (2001). Multiple-well, multiple-path unimolecular reaction systems. II. 2-methylhexyl free radicals. International Journal of Chemical Kinetics 33, 246-261. Barker, J. R., Yoder, L. M. and King, K. D. (2001). Vibrational energy transfer modeling of nonequilibrium polyatomic reaction systems. Journal of Physical Chemistry A 105, 796-809. Battin-Leclerc, F. (2002). Development of kinetic models for the formation and degradation of unsaturated hydrocarbons at high temperature. Physical Chemistry Chemical Physics 4, 2072-2078. Battin-Leclerc, F., Fournet, R., Glaude, P. A., Judenherc, B., Warth, V., Come, G. M. and Scacchi, G. (2000). Modeling of the gas-phase oxidation of n-decane from 550 to 1600 K. Symposium (International) on Combustion 28, 1597-1605. Baulch, D. L., Bowman, C. T., Cobos, C. J., Cox, R. A., Just, T., Kerr, J. A., Pilling, M. J., Stocker, D., Troe, J., Tsang, W., Walker, R. W. and Warnatz, J. (2005). Evaluated kinetic data for combustion modeling: Supplement II. Journal of Physical and Chemical Reference Data 34, 757-1397. Baulch, D. L., Cobos, C. J., Cox, R. A., Esser, C., Frank, P., Just, T., Kerr, J. A., Pilling, M. J., Troe, J., Walker, R. W. and Warnatz, J. (1992). Evaluated kinetic data for combustion modeling. Journal of Physical and Chemical Reference Data 21, 411-734. Baulch, D. L., Cobos, C. J., Cox, R. A., Frank, P., Hayman, G., Just, T., Kerr, J. A., Murrells, T., Pilling, M. J., Troe, J., Walker, R. W. and Warnatz, J. (1994). Evaluated kinetic data for combustion modeling: Supplement I. Journal of Physical and Chemical Reference Data 23, 847-1033. Benson, S. W. (1976). Thermochemical Kinetics: Methods for the Estimation of Thermochemical Data and Rate Parameters. John Wiley & Sons, Inc., New York. Beyer, T. and Swinehart, D. F. (1973). Number of multiply-restricted partitions. Communications of the ACM 16, 379-379. Biegler-König, F., Schönbohm, J. and Bayles, D. (2001). Software news and updates AIM2000 - A program to analyze and visualize atoms in molecules. Journal of Computational Chemistry 22, 545-559. Bikas, G. and Peters, N. (2001). Kinetic modelling of n-decane combustion and autoignition. Combustion and Flame 126, 1456-1475. 182 Blouch, J. D. and Law, C. K. (2000). Non-premixed ignition of n-heptane and iso- octane in a laminar counterflow. Symposium (International) on Combustion 28, 1679-1686. Bogan, D. J. and Hand, C. W. (1978). Absolute rate constant, kinetic isotope effect, and mechanism of reaction of ethylene-oxide with oxygen ( 3 P) atoms. Journal of Physical Chemistry 82, 2067-2073. Bohland, T., Temps, F. and Wagner, H. G. (1988). Kinetics of the reactions of CH 2 (X 3 B 1 )-radicals with C 2 H 2 and C 4 H 2 in the temperature range 296 K<=T<=700 K. Symposium (International) on Combustion 21, 841-850. Bohn, B. and Zetzsch, C. (1998). Formation of HO 2 from OH and C 2 H 2 in the presence of O 2 . Journal of the Chemical Society-Faraday Transactions 94, 1203-1210. Bozzelli, J. W. and Dean, A. M. (1990). Chemical activation analysis of the reaction of ethyl radical with oxygen. Journal of Physical Chemistry 94, 3313-3317. Bozzelli, J. W. and Dean, A. M. (1993). Hydrocarbon radical reactions with O 2 - comparison of allyl, formyl, and vinyl to ethyl. Journal of Physical Chemistry 97, 4427-4441. Brown, C. J. and Thomas, G. O. (1999). Experimental studies of shock-induced ignition and transition to detonation in ethylene and propane mixtures. Combustion and Flame 117, 861-870. Brown, P. N., Byrne, G. D. and Hindmarsh, A. C. (1989). VODE: A variable- coefficient ODE solver. SIAM Journal on Scientific and Statistical Computing 10, 1038-1051. Burcat, A. (1997). ftp://ftp.technion.ac.il/pub/supported/aetdd/thermodynamics. Burcat, A. (1999). ftp://ftp.technion.ac.il/pub/supported/aetdd/thermodynamics. Burcat, A. and Ruscic, B. (2005). Third millennium ideal gas and condensed phase thermochemical database for combustion with updates from active thermochemical tables. Technion-IIT, Aerospace Engineering, and Argonne National Laboratory. Burcat, A., Scheller, K. and Lifshitz, A. (1971). Shock-tube investigation of comparative ignition delay times for C 1 -C 5 alkanes. Combustion and Flame 16, 29. 183 Burrows, J. P., Cliff, D. I., Harris, G. W., Thrush, B. A. and Wilkinson, J. P. T. (1979). Atmospheric reactions of the HO 2 radical studied by laser magnetic-resonance spectroscopy. Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences 368, 463-481. Carl, S. A., Sun, Q. and Peeters, J. (2001). Laser-induced fluorescence of nascent CH from ultraviolet photodissociation of HCCO and the absolute rate coefficient of the HCCO+O 2 reaction over the range T=296-839 K. Journal of Chemical Physics 114, 10332-10341. Celani, P. and Werner, H. J. (2000). Multireference perturbation theory for large restricted and selected active space reference wave functions. Journal of Chemical Physics 112, 5546-5557. Chase, M. W. J. (1998). NIST–JANAF thermochemical tables. Journal of Physical and Chemical Reference Data Monograph 9. Choi, Y. M., Xia, W. S., Park, J. and Lin, M. C. (2000). Kinetics and mechanism for the reaction of phenyl radical with formaldehyde. Journal of Physical Chemistry A 104, 7030-7035. Colket, M., Edwards, T., Willians, S., Cernansky, N. P., Miller, D. L., Egolfopoulos, F. N., Lindstedt, P., Seshadri, K., Dryer, F. L., Law, C. K., Friend, D., Lenhert, D. B., Pitsch, H., Sarofim, A., Smooke, M. and Tsang, W. (2007). Development of an experimental database and kinetic models for surrogate jet juels. 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada. Colket, M. B., III, Naegeli, D. W. and Glassman, I. (1977). High temperature oxidation of acetaldehyde. Symposium (International) on Combustion 16, 1023-1039. Cox, R. A., Burrows, J. P. and Wallington, T. J. (1981). Rate coefficient for the reaction OH+HO 2 =H 2 O+O 2 at 1 atmosphere pressure and 308 K. Chemical Physics Letters 84, 217-221. Crawford, R. J., Lutener, S. B. and Cockcroft, R. D. (1976). Thermally induced rearrangements of 2-vinyloxirane. Canadian Journal of Chemistry-Revue Canadienne De Chimie 54, 3364-3376. Cremer, D. (1978). Theoretical determination of molecular-structure and conformation II. Hydrogen trioxide - model compound for studying conformational modes of geminal double rotors and 5 membered rings. Journal of Chemical Physics 69, 4456-4471. 184 Curran, H., Simmie, J. M., Dagaut, P., Voisin, D. and Cathonnet, M. (1996). The ignition and oxidation of allene and propyne: Experiments and kinetic modeling. Symposium (International) on Combustion 26, 613-620. Curran, H. J., Gaffuri, P., Pitz, W. J. and Westbrook, C. K. (1998). A comprehensive modeling study of n-heptane oxidation. Combustion and Flame 114, 149-177. Curtis, L. A., Raghavachari, K., Redfern, P. C., Rassolov, V. and Pople, J. A. (1998). Gaussian-3 (G3) theory for molecules containing the first and second-row atoms. Journal of Chemical Physics 109, 7764-7776. Dahm, K. D., Virk, P. S., Bounaceur, R., Battin-Leclerc, F., Marquaire, P. M., Fournet, R., Daniau, E. and Bouchez, M. (2004). Experimental and modelling investigation of the thermal decomposition of n-dodecane. Journal of Analytical and Applied Pyrolysis 71, 865-881. Davis, D. D., Payne, W. A. and Stief, L. J. (1973). Hydroperoxyl radical in atmospheric chemical dynamics - reaction with carbon-monoxide. Science 179, 280-281. Davis, S. G., Joshi, A. V., Wang, H. and Egolfopoulos, F. (2005). An optimized kinetic model of H 2 /CO combustion. Proceedings of the Combustion Institute 30, 1283-1292. Davis, S. G. and Law, C. K. (1998). Determination of and fuel structure effects on laminar flame speeds of C1 to C8 hydrocarbons. Combustion Science and Technology 140, 427-449. Davis, S. G., Law, C. K. and Wang, H. (1998). An experimental and kinetic modeling study of propyne oxidation. Symposium (International) on Combustion 27, 305-312. Davis, S. G., Law, C. K. and Wang, H. (1999a). Propene pyrolysis and oxidation kinetics in a flow reactor and laminar flames. Combustion and Flame 119, 375-399. Davis, S. G., Law, C. K. and Wang, H. (1999b). Propyne pyrolysis in a flow reactor: An experimental, RRKM, and detailed kinetic modeling study. Journal of Physical Chemistry A 103, 5889-5899. Dean, A. M. (1990). Detailed kinetic modeling of autocatalysis in methane pyrolysis. Journal of Physical Chemistry 94, 1432-1439. 185 Doute, C., Delfau, J. L. and Vovelle, C. (1999). Detailed reaction mechanisms for low pressure premixed n-heptane flames. Combustion Science and Technology 147, 61-109. Dransfeld, P. and Wagner, H. G. (1987). Comparative study of the reactions of 16OH and 18OH with H 16 O 2 . Z. Naturforsch. 42a, 471-476. East, A. L. L. and Radom, L. (1997). Ab initio statistical thermodynamical models for the computation of third-law entropies. Journal of Chemical Physics 106, 6655-6674. Eckart, C. (1930). The penetration of a potential barrier by electrons. Physical Review 35, 1303-1309. Egolfopoulos, F. N., Zhu, D. L. and Law, C. K. (1991). Experimental and numerical determination of laminar flame speeds: Mixtures of C2-hydrocarbons with oxygen and nitrogen. Symposium (International) on Combustion 23, 471-478. Eiteneer, B., Yu, C. L., Goldenberg, M. and Frenklach, M. (1998). Determination of rate coefficients for reactions of formaldehyde pyrolysis and oxidation in the gas phase. Journal of Physical Chemistry A 102, 5196-5205. Emdee, J. L., Brezinsky, K. and Glassman, I. (1992). A kinetic model for the oxidation of toluene near 1200 K. Journal of Physical Chemistry 96, 2151- 2161. Eng, R. A., Fittschen, C., Gebert, A., Hibomvschi, P., Hippler, H. and Unterreiner, A. N. (1998). Kinetic investigations of the reactions of toluene and of p-xylene with molecular oxygen between 1050 and 1400 K. Symposium (International) on Combustion 27, 211-218. Fahr, A. and Stein, S. E. (1989). Reactions of vinyl and phenyl radicals with ethyne, ethene and benzene. Symposium (International) on Combustion 22, 1023-1029. Farhat, S. K., Morter, C. L. and Glass, G. P. (1993). Temperature-dependence of the rate of reaction of C 2 H with H 2 . Journal of Physical Chemistry 97, 12789- 12792. Flowers, M. C. (1977). Kinetics of thermal gas-phase decomposition of 1,2- epoxypropane. Journal of the Chemical Society-Faraday Transactions I 73, 1927-1935. 186 Fournet, R., Battin-Leclerc, F., Glaude, P. A., Judenherc, B., Warth, V., Come, G. M., Scacchi, G., Ristori, A., Pengloan, G., Dagaut, P. and Cathonnet, M. (2001). The gas-phase oxidation of n-hexadecane. International Journal of Chemical Kinetics 33, 574-586. Frank, P., Bhaskaran, K. A. and Just, T. (1988). Acetylene oxidation: The reaction C 2 H 2 +O at high temperatures. Symposium (International) on Combustion 21, 885-893. Frank, P., Herzler, J., Just, T. and Wahl, C. (1994). High-temperature reactions of phenyl oxidation. Symposium (International) on Combustion 25, 833-840. Frenklach, M., Wang, H., Goldenberg, M., Smith, G. P., Golden, D. M., Bowman, C. T., Hanson, R. K., Gardiner, W. C. and Lissiansky, V. (1995). GRI-Mech: An optimized chemical reaction mechanism for methane combustion (version GRI-Mech 1.2), GRI Report No. GRI-95/0058. Gas Research Institute. Chicago. Frisch, M. J., Trucks, G. W., Schlegel, H. B., Scuseria, G. E., Robb, M. A., Cheeseman, J. R., Montgomery, J., J. A., Vreven, T., Kudin, K. N., Burant, J. C., Millam, J. M., Iyengar, S. S., Tomasi, J., Barone, V., Mennucci, B., Cossi, M., Scalmani, G., Rega, N., Petersson, G. A., Nakatsuji, H., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Klene, M., Li, X., Knox, J. E., Hratchian, H. P., Cross, J. B., Bakken, V., Adamo, C., Jaramillo, J., Gomperts, R., Stratmann, R. E., Yazyev, O., Austin, A. J., Cammi, R., Pomelli, C., Ochterski, J. W., Ayala, P. Y., Morokuma, K., Voth, G. A., Salvador, P., Dannenberg, J. J., Zakrzewski, V. G., Dapprich, S., Daniels, A. D., Strain, M. C., Farkas, O., Malick, D. K., Rabuck, A. D., Raghavachari, K., Foresman, J. B., Ortiz, J. V., Cui, Q., Baboul, A. G., Clifford, S., Cioslowski, J., Stefanov, B. B., Liu, G., Liashenko, A., Piskorz, P., Komaromi, I., Martin, R. L., Fox, D. J., Keith, T., Al-Laham, M. A., Peng, C. Y., Nanayakkara, A., Challacombe, M., Gill, P. M. W., Johnson, B., Chen, W., Wong, M. W., Gonzalez, C. and Pople, J. A. (2004). Gaussian 03. Gaussian, Inc., Wallingford CT. Furuyama, S., Golden, D. M. and Benson, S. W. (1969). Thermochemistry of the gas phase equilibria i-C3H7I = C3H6 + HI, n-C3H7I = i-C3H7I, and C3H6 + 2HI = C3H8 + I2. Journal of Chemical Thermodynamics 1, 363-375. Gilbert, R. G., Luther, K. and Troe, J. (1983). Theory of thermal unimolecular reactions in the fall-off range. II. Weak collision rate constants. Berichte Der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics 87, 169-177. 187 Gilbert, R. G. and Smith, S. C. (1990). Theory of Unimolecular and Recombination Reactions. blackwell Scientific, Oxford. Gillespie, D. T. (1976). General method for numerically simulating stochastic time evolution of coupled chemical-reactions. Journal of Computational Physics 22, 403-434. Gillespie, D. T. (1978). Monte-Carlo simulation of random-walks with residence time- dependent transition-probability rates. Journal of Computational Physics 28, 395-407. Glarborg, P., Kee, R. J., Grcar, J. F. and Miller, J. A. (1986). PSR: A Fortran program for modeling well-stirred reactors. SAND86-8209. Sandia National Laboratories. Albequerque, NM. Glassman, I. (1996). Combustion. Academic Press, San Diego, CA. Gonzalez, C., Theisen, J., Schlegel, H. B., Hase, W. L. and Kaiser, E. W. (1992). Kinetics of the reaction between oh and HO 2 on the triplet potential-energy surface. Journal of Physical Chemistry 96, 1767-1774. Gonzalez, C., Theisen, J., Zhu, L., Schlegel, H. B., Hase, W. L. and Kaiser, E. W. (1991). Kinetics of the reaction between OH and HO 2 on the singlet potential- energy surface. Journal of Physical Chemistry 95, 6784-6792. Goodings, J. M. and Hayhurst, A. N. (1988). Heat release and radical recombination in premixed fuel-lean flames of H 2 +O 2 +N 2 - rate constants for H+OH+M -> H 2 O+M and HO 2 +OH -> H 2 O+O 2 . Journal of the Chemical Society-Faraday Transactions II 84, 745-762. Grafenstein, J., Hjerpe, A. M., Kraka, E. and Cremer, D. (2000). An accurate description of the Bergman reaction using restricted and unrestricted DFT: Stability test, spin density, and on-top pair density. Journal of Physical Chemistry A 104, 1748-1761. Grafenstein, J., Kraka, E., Filatov, M. and Cremer, D. (2002). Can unrestricted density-functional theory describe open shell singlet biradicals? International Journal of Molecular Sciences 3, 360-394. Graham, R. A., Winer, A. M., Atkinson, R. and Pitts, J. N. (1979). Rate constants for the reaction of HO 2 with HO 2 , SO 2 , CO, N 2 O, trans-2-butene, and 2,3- dimethyl-2-butene at 300 K. Journal of Physical Chemistry 83, 1563-1567. 188 Grela, M. A. and Colussi, A. J. (1986). Kinetics and mechanism of the thermal- decomposition of unsaturated aldehydes - benzaldehyde, 2-butenal, and 2- furaldehyde. Journal of Physical Chemistry 90, 434-437. Halkier, A., Helgaker, T., Jorgensen, P., Klopper, W., Koch, H., Olsen, J. and Wilson, A. K. (1998). Basis-set convergence in correlated calculations on Ne, N 2 , and H 2 O. Chemical Physics Letters 286, 243-252. Hassan, M. I., Aung, K. T., Kwon, O. C. and Faeth, G. M. (1998). Properties of laminar premixed hydrocarbon/air flames at various pressures. Journal of Propulsion and Power 14, 479-488. Hastie, J. W. (1974). Mass-spectrometric evidence for HO 2 in 1 atm flames. Chemical Physics Letters 26, 338-343. He, Y., He, Z. and Cremer, D. (2000). Size-extensive quadratic CI methods including quadruple excitations: QCISDTQ and QCISDTQ(6) - On the importance of four-electron correlation effects. Chemical Physics Letters 317, 535-544. He, Y. Z., Mallard, W. G. and Tsang, W. (1988). Kinetics of hydrogen and hydroxyl radical attack on phenol at high-temperatures. Journal of Physical Chemistry 92, 2196-2201. Held, T. J., Marchese, A. J. and Dryer, F. L. (1997). A semi-empirical reaction mechanism for n-heptane oxidation and pyrolysis. Combustion Science and Technology 123, 107 - 146. Herbinet, O., Marquaire, P. M., Battin-Leclerc, F. and Fournet, R. (2007). Thermal decomposition of n-dodecane: Experiments and kinetic modeling. Journal of Analytical and Applied Pyrolysis 78, 419-429. Hidaka, Y., Higashihara, T., Ninomiya, N., Masaoka, H., Nakamura, T. and Kawano, H. (1996). Shock tube and modeling study of 1,3-butadiene pyrolysis. International Journal of Chemical Kinetics 28, 137-151. Hidaka, Y., Nishimori, T., Sato, K., Henmi, Y., Okuda, R., Inami, K. and Higashihara, T. (1999). Shock-tube and modeling study of ethylene pyrolysis and oxidation. Combustion and Flame 117, 755-776. Hippler, H., Neunaber, H. and Troe, J. (1995). Shock wave studies of the reactions HO+H 2 O 2 → H 2 O+HO 2 and HO+HO 2 → H 2 O+O 2 between 930 and 1680 K. Journal of Chemical Physics 103, 3510-3516. 189 Hippler, H., Reihs, C. and Troe, J. (1991). Shock tube UV absorption study of the oxidation of benzyl radicals. Symposium (International) on Combustion 23, 37-43. Hippler, H. and Troe, J. (1992). Rate constants of the reaction HO+H 2 O 2 → HO 2 +H 2 O at T >= 1000 K. Chemical Physics Letters 192, 333-337. Hippler, H., Troe, J. and Willner, J. (1990). Shock wave study of the reaction HO 2 +HO 2 → H 2 O 2 +O 2 : Confirmation of a rate constant minimum near 700 K. Journal of Chemical Physics 93, 1755-1760. Hirasawa, T., Sung, C. J., Joshi, A., Yang, Z., Wang, H. and Law, C. K. (2002). Determination of laminar flame speeds using digital particle image velocimetry: Binary fuel blends of ethylene, n-butane, and toluene. Proceedings of the Combustion Institute 29, 1427-1434. Hoare, D. E. and Patel, M. (1969). Role of OH and HO 2 radicals in slow combustion of mixtures of methane ethane and ethylene. Transactions of the Faraday Society 65, 1325-&. Hochanadel, C. J., Sworski, T. J. and Ogren, P. J. (1980). Rate constants for the reactions of HO 2 with OH and with HO 2 . Journal of Physical Chemistry 84, 3274-3277. Holbrook, K. A., Pilling, M. J. and Robertson, S. H. (1996). Unimolecular Reactions. Wiley, Chichester. Homann, K. H. and Wellmann, C. (1983). Kinetics and mechanism of hydrocarbon formation in the system C 2 H 2 /O/H at temperatures up to 1300 K. Berichte Der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics 87, 609-616. Homer, J. B. and Kistiako, G. B. (1967). Oxidation and pyrolysis of ethylene in shock waves. Journal of Chemical Physics 47, 5290-5295. Horn, C., Roy, K., Frank, P. and Just, T. (1998). Shock-tube study on the high- temperature pyrolysis of phenol. Symposium (International) on Combustion 27, 321-328. Horning, D. C., Davidson, D. F. and Hanson, R. K. (2002). Study of the high- temperature autoignition of n-alkane/O 2 /Ar mixtures. Journal of Propulsion and Power 18, 363-371. Howard, C. J. (1979). Temperature dependence of the reaction HO 2 +NO -> OH+NO 2 . Journal of Chemical Physics 71, 2352-2359. 190 Hsu, C. C., Mebel, A. M. and Lin, M. C. (1996). Ab initio molecular orbital study of the HCO+O 2 reaction: Direct versus indirect abstraction channels. Journal of Chemical Physics 105, 2346-2352. Jackels, C. F. and Phillips, D. H. (1986). An ab initio investigation of possible intermediates in the reaction of the hydroxyl and hydroperoxyl radicals. Journal of Chemical Physics 84, 5013-5024. Janoschek, R. and Rossi, M. J. (2004). Thermochemical properties from G3MP2B3 calculations, Set-2: Free radicals with special consideration of CH 2 =CH- C • =CH 2 , cyclo- • C 5 H 5 , • CH 2 OOH, HO- • CO, and HC(O)O • . International Journal of Chemical Kinetics 36, 661-686. Ji, C., You, X. Q., Holley, A. T., Wang, Y. L., Egolfopoulos, F. N. and Wang, H. (2008). Propagation and extinction of n-dodecane/air flames: Experiments and modeling. Proceedings of the Combustion Institute 32. Jomaas, G., Zheng, X. L., Zhu, D. L. and Law, C. K. (2005). Experimental determination of counterflow ignition temperatures and laminar flame speeds of C2-C3 hydrocarbons at atmospheric and elevated pressures. Proceedings of the Combustion Institute 30, 193-200. Jones, J., Bacskay, G. B. and Mackie, J. C. (1997). Decomposition of the benzyl radical: Quantum chemical and experimental (shock tube) investigations of reaction pathways. Journal of Physical Chemistry A 101, 7105-7113. Joshi, A., You, X. Q., Barckholtz, T. A. and Wang, H. (2005). Thermal decomposition of ethylene oxide: Potential energy surface, master equation analysis, and detailed kinetic modeling. Journal of Physical Chemistry A 109, 8016-8027. Joshi, A. V. (2005). A Comprehensive Mechanism for Oxidation of Aromatic Hydrocarbon Fuels: Benzene and Toluene. Ph.D. Dissertation. University of Delaware, Newark. Joshi, A. V. and Wang, H. (2006). Master equation modeling of wide range temperature and pressure dependence of CO + OH -> products. International Journal of Chemical Kinetics 38, 57-73. Kalitan, D. M., Mertens, J. D., Crofton, M. W. and Petersen, E. L. (2007). Ignition and oxidation of lean CO/H 2 fuel blends in air. Journal of Propulsion and Power 23, 1291-1303. 191 Kappel, C., Luther, K. and Troe, J. (2002). Shock wave study of the unimolecular dissociation of H 2 O 2 in its falloff range and of its secondary reactions. Physical Chemistry Chemical Physics 4, 4392-4398. Kaufman, F. (1981). Laser studies of atmospheric reactions. Journal of Photochemistry 17, 397-404. Kee, R. J., Dixon-Lewis, G., Warnatz, J., Coltrin, M. E. and Miller, J. A. (1986). A Fortran computer code package for the evaluation of gas-phase, multicomponent transport properties. SAND86-8246. Sandia National Laboratories. Albequerque, NM. Kee, R. J., Grcar, J. F., Smooke, M. D. and Miller, J. A. (1985). A Fortran program for modeling steady laminar one-dimensional premixed flames. SAND85-8240. Sandia National Laboratories. Albequerque, NM. Kee, R. J., Rupley, F. M. and Miller, J. A. (1990). CHEMKIN-II: A Fortran chemical kinetics package for the analysis of gas-phase chemical kinetics. SAND89- 8009. Sandia National Laboratories. Kern, R. D., Singh, H. J. and Wu, C. H. (1988). Thermal decomposition of 1,2- butadiene. International Journal of Chemical Kinetics 20, 731-747. Kerr, J. A. and Parsonage, M. J. (1976). Evaluated kinetic data on gas phase hydrogen transfer reactions of methyl radicals. Butterworths, London. Keyser, L. F. (1988). Kinetics of the reaction OH+HO 2 -> H 2 O+O 2 from 254 K to 382 K. Journal of Physical Chemistry 92, 1193-1200. Khachatrian, M. S., Parsamian, N. I. and Azatyan, V. V. (1972). Reaction of HO 2 radical with carbon monoxide. Armyanskii Khimicheskii Zhurnal 25, 367. Kijewski, H. and Troe, J. (1971). Study of the pyrolysis of H 2 O 2 in the presence of H 2 and CO by use of UV absorption of HO 2 . International Journal of Chemical Kinetics 3, 223-235. Kim, T. J., Yetter, R. A. and Dryer, F. L. (1994). New results on moist CO oxidation: high pressure, high temperature experiments and comprehensive kinetic modeling. Symposium (International) on Combustion 25, 759-766. Klippenstein, S. J. (1990). Implementation of RRKM theory for highly flexible transition-states with a bond length as the reaction coordinate. Chemical Physics Letters 170, 71-77. 192 Klippenstein, S. J. (1991). A bond length reaction coordinate for unimolecular reactions. 2. Microcanonical and canonical implementations with application to the dissociation of NCNO. Journal of Chemical Physics 94, 6469-6482. Klippenstein, S. J. (1992). Variational optimizations in the Rice-Ramsberger-Kassel- Marcus theory calculations for unimolecular dissociations with no reverse barrier. Journal of Chemical Physics 96, 367-371. Klippenstein, S. J. (1994). An efficient procedure for evaluating the number of available states within a variably defined reaction coordinate framework. Journal of Physical Chemistry 98, 11459-11464. Klippenstein, S. J. and Harding, L. B. (2007). unpublished results. Klippenstein, S. J., Khundkar, L. R., Zewail, A. H. and Marcus, R. A. (1988). Application of unimolecular reaction-rate theory for highly flexible transition- states to the dissociation of NCNO into NC and NO. Journal of Chemical Physics 89, 4761-4770. Klippenstein, S. J. and Marcus, R. A. (1988). Unimolecular reaction rate theory for highly flexible transition states: use of conventional coordinates. Journal of Physical Chemistry 92, 3105-3109. Klippenstein, S. J. and Miller, J. A. (2005). The addition of hydrogen atoms to diacetylene and the heats of formation of i-C 4 H 3 and n-C 4 H 3 . Journal of Physical Chemistry A 109, 4285-4295. Klippenstein, S. J., Wagner, A. F., Dunbar, R. C., Wardlaw, D. M. and Robertson, S. H. (1999). VARIFLEX Version 1.0. Knispel, R., Koch, R., Siese, M. and Zetzsch, C. (1990). Adduct formation of OH radicals with benzene, toluene, and phenol and consecutive reactions of the adducts with NO x and O 2 . Berichte Der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics 94, 1375-1379. Knyazev, V. D., Bencsura, A., Stoliarov, S. I. and Slagle, I. R. (1996). Kinetics of the C 2 H 3 + H 2 ↔ H+C 2 H 4 and CH 3 +H 2 ↔ H+CH 4 reactions. Journal of Physical Chemistry 100, 11346-11354. Knyazev, V. D., Dubinsky, I. A., Slagle, I. R. and Gutman, D. (1994). Unimolecular decomposition of t-C 4 H 9 radical. Journal of Physical Chemistry 98, 5279- 5289. 193 Knyazev, V. D. and Slagle, I. R. (1996). Experimental and theoretical study of the C 2 H 3 ↔ H+C 2 H 2 reaction: tunneling and the shape of falloff curves. Journal of Physical Chemistry 100, 16899-16911. Knyazev, V. D. and Tsang, W. (1998). Nonharmonic degrees of freedom: densities of states and thermodynamic functions. Journal of Physical Chemistry A 102, 9167-9176. Ko, T., Adusei, G. Y. and Fontijn, A. (1991). Kinetics of the reactions between O( 3 P) and 1-butene from 335 to 1110 K. Journal of Physical Chemistry 95, 9366- 9370. Koshi, M., Fukuda, K., Kamiya, K. and Matsui, H. (1992). Temperature dependence of the rate constants for the reactions of C 2 H with C 2 H 2 , H 2 , and D 2 . Journal of Physical Chemistry 96, 9839-9843. Kreutz, T. G. and Law, C. K. (1996). Combustion and Flame 104, 157-175. Krokidis, X., Moriarty, N. W., Lester, W. A. and Frenklach, M. (2001). A quantum Monte Carlo study of energy differences in C 4 H 3 and C 4 H 5 isomers. International Journal of Chemical Kinetics 33, 808-820. Kudchadker, S. A. and Kudchadker, A. P. (1975). Thermodynamic properties of oxygen compounds III. Benzaldehyde and furfural (2-furaldehyde). Thermochimica Acta 12, 432-437. Kumar, K. and Sung, C. J. (2007). Laminar flame speeds and extinction limits of preheated n-decane/O 2 /N 2 and n-dodecane/O 2 /N 2 mixtures. Combustion and Flame 151, 209-224. Lambert, R. M., Christie, M. I. and Linnett, J. W. (1967). A novel reaction of hydrogen atoms. Chemical Communications, 388-&. Laskin, A. and Wang, H. (1999). On initiation reactions of acetylene oxidation in shock tubes: A quantum mechanical and kinetic modeling study. Chemical Physics Letters 303, 43-49. Laskin, A., Wang, H. and Law, C. K., (2000). Detailed kinetic modeling of 1,3- butadiene oxidation at high temperatures. International Journal of Chemical Kinetics 32, 589-614. Law, C. K., Sung, C. J., Wang, H. and Lu, T. F. (2003). Development of comprehensive detailed and reduced reaction mechanisms for combustion modeling. AIAA Journal 41, 1629-1646. 194 Lay, T. H., Bozzelli, J. W., Dean, A. M. and Ritter, E. R. (1995). Hydrogen atom bond increments for calculation of thermodynamic properties of hydrocarbon radical species. Journal of Physical Chemistry 99, 14514-14527. Lee, B. I. and Kesler, M. G. (1975). Generalized thermodynamic correlation based on 3-parameter corresponding states. AICHE Journal 21, 510-527. Lee, C., Yang, W. and Parr, R. G. (1988). Development of the Colle-Salvetti correlation energy formula into a functional of the electron density. Physical Review B 37, 785. Lee, T. J., Rendell, A. P. and Taylor, P. R. (1990). Comparison of the quadratic configuration interaction and coupled cluster approaches to electron correlation including the effect of triple excitations. Journal of Physical Chemistry 94, 5463-5468. Leung, K. M. and Lindstedt, R. P. (1995). Detailed kinetic modeling of C1-C3 alkane diffusion flames. Combustion and Flame 102, 129-160. Lewis, G. N. and Randall, M. (1961). Thermodynamics. McGraw-Hill, New York. Li, Z. and Wang, H. (2003). Drag force, diffusion coefficient, and electric mobility of small particles. Physical Review E 68, articles 061206 & 061207 Lide, D. R. (1990). Handbook of Chemistry and Physics. CRC Press, Boca Raton, FL. Lifshitz, A. and Benhamou, H. (1983). Thermal reactions of cyclic ethers at high temperatures I. pyrolysis of ethylene-oxide behind reflected shocks. Journal of Physical Chemistry 87, 1782-1787. Lifshitz, A. and Bidani, M. (1989). Thermal reactions of cyclic ethers at high temperatures V. Pyrolysis of 2,3-dihydrofuran behind reflected shocks. Journal of Physical Chemistry 93, 1139-1144. Lifshitz, A., Bidani, M. and Bidani, S. (1986a). Thermal reactions of cyclic ethers at high temperatures III. Pyrolysis of furan behind reflected shocks. Journal of Physical Chemistry 90, 5373-5377. Lifshitz, A., Bidani, M. and Bidani, S. (1986b). Thermal reactions of cyclic ethers at high temperatures IV. Pyrolysis of 2,5-dihydrofuran behind reflected shocks. Journal of Physical Chemistry 90, 6011-6014. 195 Lifshitz, A. and Tamburu, C. (1994). Isomerization and decomposition of propylene- oxide: studies with a single-pulse shock-tube. Journal of Physical Chemistry 98, 1161-1170. Lii, R. R., Gorse, R. A., Sauer, M. C. and Gordon, S. (1980). Rate constant for the reaction of OH with HO 2 . Journal of Physical Chemistry 84, 819-821. Lin, M. C. and Mebel, A. M. (1995). Ab initio molecular orbital study of the O+C 6 H 5 O reaction. Journal of Physical Organic Chemistry 8, 407-420. Lindstedt, R. P. and Maurice, L. Q. (1995). Detailed kinetic modelling of n-heptane combustion. Combustion Science and Technology 107, 317-353. Liu, A., Mulac, W. A. and Jonah, C. D. (1988). Rate constants for the gas-phase reactions of OH radicals with 1,3-butadiene and allene at 1 atm in Ar and over the temperature range 305-1173 K. Journal of Physical Chemistry 92, 131- 134. Lloyd, A. C. (1974). Evaluated and estimated kinetic data for phase reactions of hydroperoxyl radical. International Journal of Chemical Kinetics 6, 169-228. Mahmud, K., Marshall, P. and Fontijn, A. (1987). A high temperature photochemistry kinetics study of the reaction of O(3P) atoms with ethylene from 290 to 1510 K. Journal of Physical Chemistry 91, 1568-1573. Mansoori, G. A., Patel, V. K. and Edalat, M. (1980). The three-parameter corresponding states principle. International Journal of Thermophysics 1, 285- 298. Marenich, A. V. and Boggs, J. E. (2003). Coupled cluster CCSD(T) calculations of equilibrium geometries, anharmonic force fields, and thermodynamic properties of the formyl (HCO) and isoformyl (COH) radical species. Journal of Physical Chemistry A 107, 2343-2350. Martinez-Avila, M., Peiro-Garcia, J., Ramirez-Ramirez, V. M. and Nebot-Gil, I. (2003). Ab initio study on the mechanism of the HCO+O 2 -> HO 2 +CO reaction. Chemical Physics Letters 370, 313-318. Matheu, D. M., Green, W. H. and Grenda, J. M. (2003). Capturing pressure- dependence in automated mechanism generation: Reactions through cycloalkyl intermediates. International Journal of Chemical Kinetics 35, 95-119. McMillen, D. F. and Golden, D. M. (1982). Hydrocarbon bond dissociation energies. Annual Review of Physical Chemistry 33, 493-532. 196 McQuarrie, D. A. (1973). Statistical Mechanics. Happer & Row, New York. Mebel, A. M., Diau, E. W. G., Lin, M. C. and Morokuma, K. (1996). Ab initio and RRKM calculations for multichannel rate constants of the C 2 H 3 +O 2 reaction. Journal of the American Chemical Society 118, 9759-9771. Mebel, A. M., Lin, M. C., Chakraborty, D., Park, J., Lin, S. H. and Lee, Y. T. (2001). Ab initio molecular orbital/Rice-Ramsperger-Kassel-Marcus theory study of multichannel rate constants for the unimolecular decomposition of benzene and the H+C 6 H 5 reaction over the ground electronic state. Journal of Chemical Physics 114, 8421-8435. Mebel, A. M., Lin, M. C., Yu, T. and Morokuma, K. (1997). Theoretical study of potential energy surface and thermal rate constants for the C 6 H 5 +H 2 and C 6 H 6 +H reactions. Journal of Physical Chemistry A 101, 3189-3196. Middha, P. and Wang, H. (2005). First-principle calculation for the high temperature diffusion coefficients of small pairs: The H-Ar case. Combustion Theory and Modelling 9, 353-363. Middha, P., Yang, B. H. and Wang, H. (2003). A first-principle calculation of the binary diffusion coefficients pertinent to kinetic modeling of hydrogen/oxygen/helium flames. Proceedings of the Combustion Institute 29, 1361-1369. Miller, J. A. and Bowman, C. T. (1989). Mechanism and modeling of nitrogen chemistry in combustion. Progress in Energy and Combustion Science 15, 287-338. Miller, J. A., Kee, R. J. and Westbrook, C. K. (1990). Chemical kinetics and combustion modeling. Annual Review of Physical Chemistry 41, 345-387. Miller, J. A. and Klippenstein, S. J. (2000). Theoretical considerations in the NH 2 +NO reaction. Journal of Physical Chemistry A 104, 2061-2069. Miller, J. A. and Klippenstein, S. J. (2004). The H+C 2 H 2 (+M) ↔ C 2 H 3 (+M) and H+C 2 H 2 (+M) ↔ C 2 H 5 (+M) reactions: Electronic structure, variational transition-state theory, and solutions to a two-dimensional master equation. Physical Chemistry Chemical Physics 6, 1192-1202. Miller, J. A. and Melius, C. F. (1992). Kinetic and thermodynamic issues in the formation of aromatic compounds in flames of aliphatic fuels. Combustion and Flame 91, 21-39. 197 Miller, J. A., Mitchell, R. E., Smooke, M. D. and Kee, R. J. (1982). Toward a comprehensive chemical kinetic mechanism for the oxidation of acetylene: Comparison of model predictions with results from flame and shock tube experiments. Symposium (International) on Combustion 19, 181-196. Miller, J. L. (2004). Theoretical study of the straight-chain C 4 H 7 radical isomers and their dissociation and isomerization transition states. Journal of Physical Chemistry A 108, 2268-2277. Mittal, G., Sung, C. J., Fairweather, M., Tomlin, A. S., Griffiths, J. F. and Hughes, K. J. (2007). Significance of the HO 2 +CO reaction during the combustion of CO+H 2 mixtures at high pressures. Proceedings of the Combustion Institute 31, 419-427. Mittal, G., Sung, C. J. and Yetter, R. A. (2006). Autoignition of H 2 /CO at elevated pressures in a rapid compression machine. International Journal of Chemical Kinetics 38, 516-529. Montgomery, J. A., Jr., Frisch, M. J., Ochterski, J. W. and Petersson, G. A. (1999). A complete basis set model chemistry VI. Use of density functional geometries and frequencies. Journal of Chemical Physics 110, 2822-2827. Montgomery, J. A., Jr., Frisch, M. J., Ochterski, J. W. and Petersson, G. A. (2000). A complete basis set model chemistry VII. Use of the minimum population localization method. Journal of Chemical Physics 112, 6532-6542. Moskaleva, L. V. and Lin, M. C. (2000). Unimolecular isomerization/decomposition of cyclopentadienyl and related bimolecular reverse process: Ab initio MO/statistical theory study. Journal of Computational Chemistry 21, 415-425. Mozurkewich, M. (1986). Reactions of HO 2 with free-radicals. Journal of Physical Chemistry 90, 2216-2221. Mueller, M. A., Yetter, R. A. and Dryer, F. L. (1999). Flow reactor studies and kinetic modeling of the H 2 /O 2 /NO x and CO/H 2 O/O 2 /NO x reactions. International Journal of Chemical Kinetics 31, 705-724. Nam, G. J., Xia, W. S., Park, J. and Lin, M. C. (2000). The reaction of C 6 H 5 with CO: Kinetic measurement and theoretical correlation with the reverse process. Journal of Physical Chemistry A 104, 1233-1239. Nicovich, J. M., Gump, C. A. and Ravishankara, A. R. (1982). Rates of reactions of O( 3 P) with benzene and toluene. Journal of Physical Chemistry 86, 1684-1690. 198 Pang, G. A., Davidson, D. F. and Hanson, R. K. (2008). Experimental study and modeling of shock tube ignition delay times for hydrogen-oxygen-argon mixtures at low temperatures. Proceedings of the Combustion Institute 32. Park, J., Gheyas, S. and Lin, M. C. (2001). Kinetics of phenyl radical reactions with ethane and neopentane: Reactivity of C 6 H 5 toward the primary C-H bond of alkanes. International Journal of Chemical Kinetics 33, 64-69. Pedley, J. B., Naylor, R. O. and Kirby, S. P. (1986). Thermodynamic Data Organic Compounds. Chapman and Hall, London. Perry, R. A. (1984). Absolute rate measurements for the reaction of the OH radical with diacetylene over the temperature range of 296-688 K. Combustion and Flame 58, 221-227. Pfahl, U., Fieweger, K. and Adomeit, G. (1996). Self-ignition of diesel-relevant hydrocarbon-air mixtures under engine conditions. Symposium (International) on Combustion 26, 781-789. Pitzer, K. S. (1946). Energy levels and thermodynamic functions for molecules with internal rotation: II. Unsymmetrical tops attached to a rigid frame. Journal of Chemical Physics 14, 239-243. Pitzer, K. S. and Gwinn, W. D. (1942). Energy levels and thermodynamic functions for molecules with internal rotation I. Rigid frame with attached tops. Journal of Chemical Physics 10, 428-440. Prosen, E. J. and Rossini, F. D. (1945). Heats of combustion and formation of the paraffin hydrocarbons at 25 ºC. Journal of Research of the National Bureau of Standards 34, 263-269. Qin, Z. (1998). Ph.D. Dissertation. The University of Texas at Austin Qin, Z. W., Lissianski, V. V., Yang, H. X., Gardiner, W. C., Davis, S. G. and Wang, H. (2000). Combustion chemistry of propane: A case study of detailed reaction mechanism optimization. Proceedings of the Combustion Institute 28, 1663- 1669. Ranzi, E., Dente, M., Goldaniga, A., Bozzano, G. and Faravelli, T. (2001). Lumping procedures in detailed kinetic modeling of gasification, pyrolysis, partial oxidation and combustion of hydrocarbon mixtures. Progress in Energy and Combustion Science 27, 99-139. 199 Ranzi, E., Frassoldati, A., Granata, S. and Faravelli, T. (2005). Wide-range kinetic modeling study of the pyrolysis, partial oxidation, and combustion of heavy n- alkanes. Industrial & Engineering Chemistry Research 44, 5170-5183. Roth, W. R., Adamczak, O., Breuckmann, R., Lennartz, H. W. and Boese, R. (1991). Resonance energy calculation: the MM2ERW force-field. Chemische Berichte 124, 2499-2521. Rozenshtein, V. B., Gershenzon, Y. M., Ilin, S. D. and Kishkovitch, O. P. (1984). Reactions of HO 2 with NO, OH and HO 2 studied by EPR/LMR spectroscopy. Chemical Physics Letters 112, 473-478. Ruscic, B. (2004). Active Thermochemical Tables, in 2005 Yearbook of Science & Technology. McGraw-Hill, New York. Ruscic, B., Pinzon, R. E., Morton, M. L., Srinivasan, N. K., Su, M. C., Sutherland, J. W. and Michael, J. V. (2006). Active thermochemical tables: Accurate enthalpy of formation of hydroperoxyl radical, HO 2 . Journal of Physical Chemistry A 110, 6592-6601. Ruscic, B., Wagner, A. F., Harding, L. B., Asher, R. L., Feller, D., Dixon, D. A., Peterson, K. A., Song, Y., Qian, X. M., Ng, C. Y., Liu, J. B. and Chen, W. W. (2002). On the enthalpy of formation of hydroxyl radical and gas-phase bond dissociation energies of water and hydroxyl. Journal of Physical Chemistry A 106, 2727-2747. Schwab, J. J., Brune, W. H. and Anderson, J. G. (1989). Kinetics and mechanism of the OH+HO 2 reaction. Journal of Physical Chemistry 93, 1030-1035. Seiser, R., Pitsch, H., Seshadri, K., Pitz, W. J. and Gurran, H. J. (2000). Extinction and autoignition of n-heptane in counterflow configuration. Symposium (International) on Combustion 28, 2029-2037. Shin, K. S. and Michael, J. V. (1991). Rate constants (296-1700 K) for the reactions C 2 H+C 2 H 2 →C 4 H 2 +H and C 2 D+C 2 D 2 →C 4 D 2 +D. Journal of Physical Chemistry 95, 5864-5869. Simmie, J. M. (2003). Detailed chemical kinetic models for the combustion of hydrocarbon fuels. Progress in Energy and Combustion Science 29, 599-634. Simonaitis, R. and Heicklen, J. (1973). Reactions of HO 2 with carbon-monoxide and nitric-oxide and of O( 1 D) with water. Journal of Physical Chemistry 77, 1096- 1102. 200 Sirjean, B., Fournet, R., Glaude, P.-A. and Ruiz-Lo´pez, M. F. (2007). Extension of the composite CBS-QB3 method to singlet diradical calculations. Chemical Physics Letters 435, 152-156. Sivaramakrishnan, R., Comandini, A., Tranter, R. S., Brezinsky, K., Davis, S. G. and Wang, H. (2007). Combustion of CO/H 2 mixtures at elevated pressures. Proceedings of the Combustion Institute 31, 429-437. Slagle, I. R., Bencsura, A., Xing, S.-B. and Gutman, D. (1992). Kinetics and thermochemistry of the oxidation of unsaturated radicals: C 4 H 5 +O 2 . Symposium (International) on Combustion 24, 653-660. Slagle, I. R., Bernhardt, J. R. and Gutman, D. (1989). Kinetics of the reactions of unsaturated free radicals (methylvinyl and i-C 4 H 3 ) with molecular oxygen. Symposium (International) on Combustion 22, 953-962. Slagle, I. R. and Gutman, D. (1988). Kinetics of the reaction of C 3 H 3 with molecular oxygen from 293-900 K. Symposium (International) on Combustion 21, 875- 883. Smallbone, A. J., Liu, W., Law, C. K., You, X. Q. and Wang, H. (2008). Experiment and modeling study of laminar flame speed and nonpremixed counterflow ignition of n-heptane. Proceedings of the Combustion Institute 32. Smith, G. P., Golden, D. M., Frenklach, M., Eiteener, B., Goldenberg, M., Bowman, C. T., Hanson, R. K., Gardiner, W. C., Lissianski, V. V. and Qin, Z. W. (2000). GRI-Mech 3.0. http://www.me.berkeley.edu/gri_mech/. Smooke, M. D., Puri, I. K. and Seshadri, K. (1986). Proceedings of the Combustion Institute 21, 1783-1792. Sridharan, U. C., Qiu, L. X. and Kaufman, F. (1984). Rate-constant of the OH + HO 2 reaction from 252 K to 420 K. Journal of Physical Chemistry 88, 1281-1282. Srinivasan, N. K., Su, M. C., Sutherland, J. W., Michael, J. V. and Ruscic, B. (2006). Reflected shock tube studies of high-temperature rate constants for OH+NO 2 → HO 2 +NO and OH+HO 2 → H 2 O+O 2 . Journal of Physical Chemistry A 110, 6602-6607. Steele, W. V. and Chirico, R. D. (1993). Thermodynamic properties of alkenes (mono- olefins larger than C4). Journal of Physical and Chemical Reference Data 22, 377-430. 201 Sun, C. J., Sung, C. J., Wang, H. and Law, C. K. (1996). On the structure of nonsooting counterflow ethylene and acetylene diffusion flames. Combustion and Flame 107, 321-335. Sun, H. Y., Yang, S. I., Jomaas, G. and Law, C. K. (2007). High-pressure laminar flame speeds and kinetic modeling of carbon monoxide/hydrogen combustion. Proceedings of the Combustion Institute 31, 439-446. Tee, L. S., Gotoh, S. and Stewart, W. E. (1966). Molecular parameters for normal fluids: Lennard-Jones 12-6 potential. Industrial & Engineering Chemistry Fundamentals 5, 356-363. Temps, F. and Wagner, H. G. (1984). Rate constants for the reactions of OH radicals with CH 2 O and HCO. Berichte Der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics 88, 415-418. Thrush, B. A. and Wilkinson, J. P. T. (1981). The rate of reaction of HO 2 radicals with HO and with NO. Chemical Physics Letters 81, 1-3. Tokmakov, I. V. and Lin, M. C. (2001). Kinetics and mechanism for the H-for-X exchange process in the H+C 6 H 5 X reactions: A computational study. International Journal of Chemical Kinetics 33, 633-653. Tokmakov, I. V., Park, J., Gheyas, S. and Lin, M. C. (1999). Experimental and theoretical studies of the reaction of the phenyl radical with methane. Journal of Physical Chemistry A 103, 3636-3645. Toohey, D. W. and Anderson, J. G. (1989). Theoretical investigations of reactions of some radicals with HO 2 I. Hydrogen abstractions by direct mechanisms. Journal of Physical Chemistry 93, 1049-1058. Troe, J. (1983). Theory of thermal unimolecular reactions in the fall-off range I. strong collision rate constants. Berichte Der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics 87, 161-169. Tsang, W. (1988). Chemical kinetic database for combustion chemistry III. Propane. Journal of Physical and Chemical Reference Data 17, 887-952. Tsang, W. (1991). Chemical kinetic database for combustion chemistry V. Propene. Journal of Physical and Chemical Reference Data 20, 221-273. Tsang, W. (1996). Heats of formation of organic free radicals by kinetic methods. Energetics of Organic Free Radicals, 22-58. J. A. Martinho Simoes, A. Greenberg and J. F. Liebman. Blackie Academic and Professional, London. 202 Tsang, W. and Hampson, R. F. (1986). Chemical kinetic database for combustion chemistry I. Methane and related compounds. Journal of Physical and Chemical Reference Data 15, 1087-1279. Tully, F. P. (1988). Hydrogen-atom abstraction from alkenes by OH, ethene and 1- butene. Chemical Physics Letters 143, 510-514. Vagelopoulos, C. M., Egolfopoulos, F. N. and Law, C. K. (1994). Further considerations on the determination of laminar flame speeds with the counterflow twin-flame technique. Symposium (International) on Combustion 25, 1341-1347. Vandooren, J., Deguertechin, L. O. and Vantiggelen, P. J. (1986). Kinetics in a lean formaldehyde flame. Combustion and Flame 64, 127-139. Vardanyan, I. A., Sachyan, G. A. and Nalbandyan, A. B. (1975). Rate constant of reaction HO 2 + CO=CO2 + OH. International Journal of Chemical Kinetics 7, 23-31. Varshni, Y. P. (1957). Comparative study of potential energy functions for diatomic molecules. Reviews of Modern Physics 29, 664. Vasu, S. S., Davidson, D. F., Hong, Z., Vasudevan, V. and Hanson, R. K. (2008). N- dodecane oxidation at high pressures: measurements of ignition delay times and OH concentration time histories. Proceedings of the Combustion Institute 32. Vasudevan, V., Davidson, D. F. and Hanson, R. K. (2005a). Direct measurements of the reaction OH+CH 2 O → HCO+H 2 O at high temperatures. International Journal of Chemical Kinetics 37, 98-109. Vasudevan, V., Davidson, D. F. and Hanson, R. K. (2005b). High-temperature measurements of the reactions of OH with toluene and acetone. Journal of Physical Chemistry A 109, 3352-3359. Volman, D. H. and Gorse, R. A. (1972). Rate constant for reaction of HO 2 with carbon-monoxide. Journal of Physical Chemistry 76, 3301-3302. Wagman, D. D., Kilpatrick, J. E., Pitzer, K. S. and Rossini, F. D. (1945). Heats, equilibrium constants, and free energies of formation of the acetylene hydrocarbons through the pentynes, to 1500 K. Journal of Research of the National Bureau of Standards 35, 467-496. 203 Wagner, P. and Dugger, G. L. (1955). Flame propagation. V. Structural influences on burning velocity. Comparison of measured and calculated burning velocity. Journal of the American Chemical Society 77, 227-231. Walker, R. W. (1989). Reactions of HO 2 radicals in combustion chemistry. Symposium (International) on Combustion 22, 883-892. Wang, H. (1992). Detailed Kinetic Modeling of Soot Particle Formation in Laminar Premixed Hydrocarbon Flames. Ph.D. Dissertation. The Pennsylvania State University, University Park, PA. Wang, H. (1998). ACS Preprints, Div. Fuel Chem. 43, 113. Wang, H. (2001). A new mechanism for initiation of free-radical chain reactions during high-temperature, homogeneous oxidation of unsaturated hydrocarbons: Ethylene, propyne, and allene. International Journal of Chemical Kinetics 33, 698-706. Wang, H. and Brezinsky, K. (1998). Computational study on the thermochemistry of cyclopentadiene derivatives and kinetics of cyclopentadienone thermal decomposition. Journal of Physical Chemistry A 102, 1530-1541. Wang, H. and Frenklach, M. (1991). Detailed reduction of reaction mechanisms for flame modeling. Combustion and Flame 87, 365-370. Wang, H. and Frenklach, M. (1994a). Calculations of rate coefficients for the chemically activated reactions of acetylene with vinylic and aromatic radicals. Journal of Physical Chemistry 98, 11465-11489. Wang, H. and Frenklach, M. (1994b). Transport-properties of polycyclic aromatic- hydrocarbons for flame modeling. Combustion and Flame 96, 163-170. Wang, H. and Frenklach, M. (1997). A detailed kinetic modeling study of aromatics formation in laminar premixed acetylene and ethylene flames. Combustion and Flame 110, 173-221. Wang, H., Laskin, A., Moriarty, N. W. and Frenklach, M. (2000). On unimolecular decomposition of phenyl radical. Proceedings of the Combustion Institute 28, 1545-1555. 204 Werner, H.-J., Knowles, P. J., Lindh, R., Manby, F. R., Schütz, M., Celani, P., Korona, T., Rauhut, G., Amos, R. D., Bernhardsson, A., Berning, A., Cooper, D. L., Deegan, M. J. O., Dobbyn, A. J., Eckert, F., Hampel, C., Hetzer, G., Lloyd, A. W., McNicholas, S. J., Meyer, W., Mura, M. E., Nicklaß, A., Palmieri, P., Pitzer, R., Schumann, U., Stoll, H., Stone, A. J., Tarroni, R. and Thorsteinsson, T. (2006). MOLPRO, Cardiff, UK. Werner, H. J. (1996). Third-order multireference perturbation theory: The CASPT3 method. Molecular Physics 89, 645-661. Westbrook, C. K. (2000). Chemical kinetics of hydrocarbon ignition in practical combustion systems. Symposium (International) on Combustion 28, 1563- 1577. Westbrook, C. K. and Dryer, F. L. (1984). Chemical kinetic modeling of hydrocarbon combustion. Progress in Energy and Combustion Science 10, 1-57. Westbrook, C. K., Pitz, W. J., Curran, H. J., Boercker, J. and Kunrath, E. (2001). Chemical kinetic modeling study of shock tube ignition of heptane isomers. International Journal of Chemical Kinetics 33, 868-877. Westly, F., Herron, J. T., Cvetanovich, R. J., F., H. R. and Mallard, W. G. NIST - Chemical Kinetics Standard Reference Database 17, ver.5.0. Westmoreland, P. R., Dean, A. M., Howard, J. B. and Longwell, J. P. (1989). Forming benzene in flames by chemically activated isomerization. Journal of Physical Chemistry 93, 8171-8180. Wiberg, K. B., Crocker, L. S. and Morgan, K. M. (1991). Thermochemical studies of carbonyl-compounds. 5. Enthalpies of reduction of carbonyl groups. Journal of the American Chemical Society 113, 3447-3450. Wu, C. H. and Kern, R. D. (1987). Shock-tube study of allene pyrolysis. Journal of Physical Chemistry 91, 6291-6296. Wu, C. J. and Carter, E. A. (1990). Ab initio bond strengths in ethylene and acetylene. Journal of the American Chemical Society 112, 5893-5895. Wyrsch, D., Wendt, H. R. and Hunziker, H. E. (1974). Modulation kinetic spectroscopy in Hg-H 2 -O 2 -CO mixtures: Reactions of HgH and HO 2 . Berichte Der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics 78, 204. 205 Yoon, E. M., Selvaraj, L., Eser, S. and Coleman, M. M. (1996a). High-temperature stabilizers for jet fuels and similar hydrocarbon mixtures. 2. Kinetic studies. Energy & Fuels 10, 812-815. Yoon, E. M., Selvaraj, L., Song, C. S., Stallman, J. B. and Coleman, M. M. (1996b). High-temperature stabilizers for jet fuels and similar hydrocarbon mixtures. 1. Comparative studies of hydrogen donors. Energy & Fuels 10, 806-811. You, X. Q., Wang, H., Goos, E., Sung, C. J. and Klippenstein, S. J. (2007). Reaction kinetics of CO+HO 2 → products: Ab initio transition state theory study with master equation modeling. Journal of Physical Chemistry A 111, 4031-4042. Yu, H. G., Muckerman, J. T. and Sears, T. J. (2001). A theoretical study of the potential energy surface for the reaction OH+CO → H+CO 2 . Chemical Physics Letters 349, 547-554. Zeppieri, S. P., Klotz, S. D. and Dryer, F. L. (2000). Modeling concepts for larger carbon number alkanes: A partially reduced skeletal mechanism for n-decane oxidation and pyrolysis. Symposium (International) on Combustion 28, 1587- 1595. Zhang, H. R., Eddings, E. G. and Sarofim, A. F. (2007). Criteria for selection of components for surrogates of natural gas and transportation fuels. Proceedings of the Combustion Institute 31, 401-409. Zhong, X. and Bozzelli, J. W. (1997). Thermochemical and kinetic analysis on the addition reactions of H, O, OH, and HO 2 with 1,3-cyclopentadiene. International Journal of Chemical Kinetics 29, 893-913. Zhou, P. H., Hollis, O. L. and Crynes, B. L. (1987). Thermolysis of higher molecular- weight straight-chain alkanes C 9 -C 22 . Industrial & Engineering Chemistry Research 26, 846-852. 206 Appendix A Master Equation Code A.1 Input files for master equation code The main input file: mc.inp. CO+HO2-TS1->HOOCO-TS2-OH+CO2 ! Title 250.0 10.0 260.0 ! Max. energy (kcal/mol),Energy spacing(/cm)and-<Edown>(/cm) 1 5 ! No. of pressures and no of temperatures 7.6 ! Pressures (torr) 300. 400. 500. 600. 700. ! Temperatures (K) 1000000 ! No. of molecules 28.00 3.80 71.4 ! MW, LJ collision diameter, Well depth of the bath gas 1 1 2 ! No. of stable isomers, No. of products, No. of TS 3 2 ! Index of initial isomer and TS 1 ! Index of reactant CO+HO2 ! Name of reactant 1 ! No. of channels associated with reactant 2 ! Index of TS associated with reactant 3 ! Index of isomer HOOCO ! Name of isomer 6.5 ! Heat of formation of isomer at 0K 2 ! No. of channels associated with isomer 2 4 ! Index of TS associated with isomer 5 ! Index of product OH+CO2 ! Name of product 2 ! Index of TS TS1 ! Name of TS 17.9 ! Heat of formation of TS at 0K 1 3 ! Indices of reactant and product associated with TS 1 1 ! Reaction path degeneracy 4 ! Index of TS TS2 ! Name of TS 12.7 ! Heat of formation of TS at 0K 3 5 ! Indices of reactant and product associated with TS 1 1 ! Reaction path degeneracy 1. 0. 0. ! Equilibrium constant (E in kcal/mol) 207 Description file for isomer: HOOCO.dat HOOCO ! Name of isomer CCSD(T)/CBS ! Comment 60.993 4.79 211.7 ! Molecular wt., LJ parameters 0.1554 1 2 ! External inactive rotational constant(1/cm), symmetry number, dimension 1 ! Number of active rotors 2.244 1 1 ! External active rotational constant(1/cm), symmetry number, dimension 2 ! Number of hindered rotors 20.5 1 0.6 3.0 0.5 2.9 ! Hindered rotor rotational constant(1/cm), symmetry number, barrier heights (kcal/mol) 4.1 1 12.0 11.4 0.0 0.0 ! Hindered rotor rotational constant(1/cm), symmetry number, barrier heights (kcal/mol) 7 ! Number of vibrational frequencies 352.4 592.0 931.4 1047.3 1414.5 1861.4 3780.7 ! Vibrational frequencies (1/cm) Description file for transition state: TS1.dat TS1 ! Name of the transition state CCSD(T)/CBS ! Comment 0.1326 1 2 ! External inactive rotational constant(1/cm), symmetry number, dimension 1 ! Number of active rotors 1.899 1 1 ! External active rotational constant(1/cm), symmetry number, dimension 2 ! Number of hindered rotors 3.64 1 3.1 3.8 0.0 0.0 ! Hindered rotor rotational constant(1/cm), symmetry number, barrier heights (kcal/mol) 20.78 1 8.8 9.0 8.6 8.8 ! Hindered rotor rotational constant(1/cm), symmetry number, barrier heights (kcal/mol) 6 ! Number of vibrational frequencies 265 446 972 1429 2016 3748 ! Vibrational frequencies (1/cm) Description file for transition state: TS2.dat TS2 ! Name of the transition state CCSD(T)/CBS ! Comment 0.1489 1 2 ! External inactive rotational constant(1/cm), symmetry number, dimension 1 ! Number of active rotors 2.018 1 1 ! External active rotational constant(1/cm), symmetry number, dimension 1 ! Number of hindered rotors 19.56 1 2.8 0.0 0.0 0.0 ! Hindered rotor rotational constant(1/cm), symmetry number, barrier heights (kcal/mol) 7 ! Number of vibrational frequencies 322 343 784 928 1233 1916 3749 ! Vibrational frequencies (1/cm) 208 A.2 Source code for master equation solution The master equation code is composed of a main routine and several subroutines. The Fortran numerical library functions and subroutines which are not listed here should be provided to run the code. C*********************************************************************** C Program to determine rate constants for multi-channel reaction C networks using Monte Carlo approach. C C RRKM code: Hai Wang (1991). C Monte Carlo code: Ameya Joshi (2003). C C Modified by Xiaoqing You (2006) C*********************************************************************** PROGRAM Masterequation C BOLTZ is in units (/cm/K) IMPLICIT REAL*8 (A-H,O-Z) DIMENSION PRES(50),TEMP(50),ID(20),E00(20),Emin(20) DIMENSION WT(20),SIG(20),EPS(20),WTAVE(20),SIGMA(20),EPSLON(20) DIMENSION DELHF0(20),NCHAN(30),IDTS(20,10),TSINT(20,20) DIMENSION ROTX(20),SYMX(20),NDIMX(20),EQ(50),ATOT(20),HIGHP(20) DIMENSION NACROT(20),ROTACT(20,20),SYMACT(20,20) DIMENSION NDIMACT(20,20),NVIB(20),VIBX(20,100) DIMENSION REAC(20),PROD(20),IDEG(20,20),BARRIER(20),MGRAINS(20) DIMENSION QRSP(20),QVSP(20),QTOT(20),AKE(20) DIMENSION HIGH(20,50),ICOUNTER(20),ENTRK(50),Z(20) DIMENSION IFIT(20),FIT(20,15) DIMENSION NAHROT(20),ROTAH(20,20),SYMAH(20,20),VH(20,20) DIMENSION ROTH(20),SYMH(20),V(20) DIMENSION V1(20),V2(20), VH1(20,20),VH2(20,20) DIMENSION V3(20),V4(20), VH3(20,20),VH4(20,20) ALLOCATABLE P(:), PKE(:,:), DENS(:), GINIT(:) ALLOCATABLE PACT(:), PDEACT(:) ALLOCATABLE CIJ(:), PIJACT(:,:), PIJDEACT(:,:) ALLOCATABLE P2D(:,:), EINIT(:) REAL*8 KT,NTRIALS CHARACTER TITLE*50,NAME(20)*15, ANAME*15, CSTART, CSEED INTEGER ISEED(3) COMMON NARRAY, NTOL COMMON /DENSITY/ RO(0:120000,20) 209 COMMON /REACT/ VIB(100),ROT(20),SYM(20),NDIM(20),T,NV,NROT COMMON /RANDOM/ISEED DATA AVGD/6.0222E+23/,BOLTZ/0.695045/,PLANCK/3.3362E-11/, 1 PI/3.1415926/,SMALL/1.0D-78/,SPEED/2.9979E+10/ DATA ISEED(1),ISEED(2),ISEED(3)/1,10000,3000/ WRITE(*,*) 'ENTER SEED (1-9)' READ(*,*) ISEED(1) CALL TIME(time_start) IF(ISEED(1) .EQ. 1) CSEED = '1' IF(ISEED(1) .EQ. 2) CSEED = '2' IF(ISEED(1) .EQ. 3) CSEED = '3' IF(ISEED(1) .EQ. 4) CSEED = '4' IF(ISEED(1) .EQ. 5) CSEED = '5' IF(ISEED(1) .EQ. 6) CSEED = '6' IF(ISEED(1) .EQ. 7) CSEED = '7' IF(ISEED(1) .EQ. 8) CSEED = '8' IF(ISEED(1) .EQ. 9) CSEED = '9' OPEN (UNIT=15, FILE='mc.inp') OPEN (UNIT=16, FILE=CSEED//'.out') C EMAX = Maximum energy (input in kcal/mol) C DELTAE = Energy spacing between successive grains (/cm) C EDOWN = -<Edown>(/cm) C NPRES = Number of pressures C NTEMP = Number of temperatures C PRES = Pressures (torr) C TEMP = Temperatures (K) C NGRAINS = Total no. of grains C NTRIALS = No. of stochastic runs READ(15,500) TITLE READ(15,*) EMAX,DELTAE,EDOWN READ(15,*) NPRES,NTEMP WRITE(16,520) WRITE(16,530) TITLE WRITE(16,540) EMAX,DELTAE IF(NPRES.GT.50) THEN WRITE(*,*) ' Limit number of pressures is 50 -- abort' STOP ENDIF IF(NTEMP.GT.50) THEN WRITE(*,*) ' Limit number of temperature is 50 - abort' STOP ENDIF READ(15,*) (PRES(I),I=1,NPRES) READ(15,*) (TEMP(I),I=1,NTEMP) EMAX=EMAX*3.4964E2 ! /cm units NGRAINS=NINT(EMAX/DELTAE) 210 PTOL=1.0E-3 IF(NGRAINS.GT.120000) THEN WRITE(*,*) ' Maximum number of energy spacing exceeded' WRITE(*,*) ' Reduce EMAX or increase DELT' STOP ENDIF READ(15,*) NTRIALS C WTBATH = Molecular weight C SBATH = Lennard-Jones collision diameter C EBATH = Well depth of the bath gas READ(15,*) WTBATH,SBATH,EBATH C NISOMERS = No. of stable isomers, excluding reactants and products C NPRODUCTS = No. of products in reaction network C NTS = No. of Transition states C NSPECIES = Total no. of species READ(15,*) NISOMERS, NPRODUCTS, NTS NSPECIES = NISOMERS + NPRODUCTS + 1 WRITE(16,550) NTRIALS WRITE(16,560) WTBATH,SBATH,EBATH NMOLEC=NTRIALS NARRAY=NGRAINS+1 NTOL = NISOMERS+NPRODUCTS+NTS+1 allocate (P(0:NARRAY), PKE(NTOL,0:NARRAY), DENS(0:NARRAY)) allocate (GINIT(0:NARRAY), CIJ(0:NARRAY), EINIT(NMOLEC)) allocate (PACT(0:NARRAY), PDEACT(0:NARRAY)) allocate (PIJACT(NTOL,0:NARRAY),PIJDEACT(NTOL,0:NARRAY)) allocate (P2D(0:NARRAY,0:NARRAY)) C Read in data for reactants, isomers and products C ISINIT = ID of initial isomer C ID = Index of species C NAME = Name of species C NCHAN = No. of channels associated with isomer C IDTS, TEMPID = Indices of TS associated with isomer C TSINT = Internal index associated with isomer-channel pair C INCR = Integer serving as above index C WT = Molecular weight C SIG = Lennard-Jones collision diameter of species C EPS = Well depth of the species C DELHF0 = Heat of formation at 0K C I = 1 -- Reactant C = 2, NISOMERS+1 -- Isomers C = NISOMERS+2, NSPECIES -- Products C = NSPECIES+1, NSPECIES+NTS -- Transition states INCR = 1 READ(15,*) ISINIT, TSINIT READ(15,*) ID(1) ! Data for reactant READ(15,510) NAME(ID(1)) 211 READ(15,*) NCHAN(ID(1)) READ(15,*) (IDTS(ID(1),J),J=1,NCHAN(ID(1))) WRITE(16,565) DO 10 I = 2, NISOMERS+1 ! Data for isomers READ(15,*) ID(I) READ(15,510) ANAME READ(15,*) DELHF0(ID(I)) READ(15,*) NCHAN(ID(I)) READ(15,*) (IDTS(ID(I),J), J = 1, NCHAN(ID(I))) DO J = 1, NCHAN(ID(I)) TEMPID = IDTS(ID(I),J) TSINT(ID(I),TEMPID) = INCR INCR = INCR + 1 END DO C ICH = Integer locating first non-blank character in string C LCH = Integer locating last non-blank character in string ICH = IFIRCH(ANAME) LCH = ILASCH(ANAME) C Beginning of isomer card OPEN (UNIT=20, FILE=ANAME(ICH:LCH)//'.dat') READ(20,*) NAME(ID(I)) READ(20,*) READ(20,*) WT(ID(I)),SIG(ID(I)),EPS(ID(I)) IFIT(ID(I))=0 WTAVE(ID(I)) = WT(ID(I))*WTBATH/(WT(ID(I))+WTBATH) SIGMA(ID(I)) = (SIG(ID(I))+SBATH)/2.0 EPSLON(ID(I))= SQRT(EPS(ID(I))*EBATH) C ROTX = External inactive rotational constant C SYMX = Symmetry number C NDIMX = Dimension of external rotor (2 or 3) READ(20,*) ROTX(ID(I)),SYMX(ID(I)),NDIMX(ID(I)) C NACT, NACROT = Number of active rotors READ(20,*) NACT NACROT(ID(I)) = NACT C ROTACT = Rotational constant of active rotor C SYMACT = Symmetry number of active rotor C NDIMACT = Dimension of active rotor DO J=1,NACT READ(20,*) ROTACT(ID(I),J),SYMACT(ID(I),J),NDIMACT(ID(I),J) END DO C NAHROT = No of hindered rotors READ(20,*) NHROT NAHROT(ID(I))=NHROT C ROTH = Rotational constant of hindered rotor C SYMH = Symmetry number of hindered rotor C VH = Barrier of hindered rotor DO J=1,NHROT 212 READ(20,*) ROTAH(ID(I),J),SYMAH(ID(I),J),VH1(ID(I),J), 1 VH2(ID(I),J),VH3(ID(I),J),VH4(ID(I),J) VH1(ID(I),J)=VH1(ID(I),J)*3.4964E2 VH2(ID(I),J)=VH2(ID(I),J)*3.4964E2 VH3(ID(I),J)=VH3(ID(I),J)*3.4964E2 VH4(ID(I),J)=VH4(ID(I),J)*3.4964E2 END DO C NV, NVIB = Number of vibrational frequencies C VIBX = Vibrational frequencies READ(20,*) NV NVIB(ID(I)) = NV READ(20,*) (VIBX(ID(I),J),J=1,NV) CLOSE(20) C End of isomer card C*********************************************************** C Begin computing density of states for each isomer C*********************************************************** DO J=1,NV VIB(J)=VIBX(ID(I),J) END DO DO J=1,NACT ROT(J)=ROTACT(ID(I),J) SYM(J)=SYMACT(ID(I),J) NDIM(J)=NDIMACT(ID(I),J) END DO DO J=1,NHROT ROTH(J)=ROTAH(ID(I),J) SYMH(J)=SYMAH(ID(I),J) V1(J)=VH1(ID(I),J) V2(J)=VH2(ID(I),J) V3(J)=VH3(ID(I),J) V4(J)=VH4(ID(I),J) END DO C INDEX = 1 --- Returns density of state INDEX = 1 WRITE(*,*) 'Computing density of states of ', ANAME CALL BSCOUNT(VIB,NV,ROT,NACT,SYM,NDIM,EMAX,DELTAE,P,NGRAINS, 1 NHROT,ROTH,SYMH,V1,V2,V3,V4,INDEX) OPEN (UNIT=2, FILE=ANAME(ICH:LCH)//'.DEN.txt') WRITE(2,*) ' No. (cm-1) Density' DO J=0,NGRAINS RO(J,ID(I))=P(J) WRITE(2,*) J, J*DELTAE, P(J) END DO CLOSE(2) WRITE(16,570) NAME(ID(I)) WRITE(16,580) DELHF0(ID(I)) 213 WRITE(16,590) WT(ID(I)),SIG(ID(I)),EPS(ID(I)), 1 WTAVE(ID(I)),SIGMA(ID(I)),EPSLON(ID(I)) WRITE(16,600) ROTX(ID(I)) WRITE(16,610) SYMX(ID(I)) WRITE(16,620) NDIMX(ID(I)) WRITE(16,630) NACROT(ID(I)) WRITE(16,640) (ROTACT(ID(I),J),J=1,NACT) WRITE(16,650) (SYMACT(ID(I),J),J=1,NACT) WRITE(16,660) (NDIMACT(ID(I),J),J=1,NACT) WRITE(16,665) NHROT WRITE(16,666) (ROTAH(ID(I),J),J=1,NHROT) WRITE(16,667) (SYMAH(ID(I),J),J=1,NHROT) WRITE(16,668) (VH1(ID(I),J)/3.4964E2,J=1,NHROT) WRITE(16,668) (VH2(ID(I),J)/3.4964E2,J=1,NHROT) WRITE(16,668) (VH3(ID(I),J)/3.4964E2,J=1,NHROT) WRITE(16,668) (VH4(ID(I),J)/3.4964E2,J=1,NHROT) WRITE(16,670) WRITE(16,680) (VIBX(ID(I),J),J=1,NVIB(ID(I))) DELHF0(ID(I)) = DELHF0(ID(I))*3.4964E2 10 CONTINUE C*********************************************************** C End computing density of states for each isomer C*********************************************************** DO I = (NISOMERS+2), NSPECIES ! Data for products READ(15,*) ID(I) READ(15,510) NAME(ID(I)) END DO WRITE(16,685) DO 70 I = NSPECIES+1, NSPECIES+NTS ! Data for Transition States READ(15,*) ID(I) READ(15,510) ANAME READ(15,*) DELHF0(ID(I)) C REAC = Reactant ID for TS C PROD = Product ID for TS READ(15,*) REAC(ID(I)), PROD(ID(I)) C IDEG = Reaction path degeneracy READ(15,*) IDEG(REAC(ID(I)),ID(I)), IDEG(PROD(ID(I)),ID(I)) ICH = IFIRCH(ANAME) LCH = ILASCH(ANAME) C Beginning of TS card OPEN (UNIT=20, FILE=ANAME(ICH:LCH)//'.dat') READ(20,510) NAME(ID(I)) READ(20,*) READ(20,*) ROTX(ID(I)),SYMX(ID(I)),NDIMX(ID(I)) IF (ROTX(ID(I)) .LT. 0.0) THEN IFIT(ID(I))=1 READ(20,*) (FIT(ID(I),NFIT),NFIT=1,10) 214 ENDIF READ(20,*) NACT NACROT(ID(I)) = NACT DO J=1,NACT READ(20,*) ROTACT(ID(I),J),SYMACT(ID(I),J),NDIMACT(ID(I),J) END DO C NAHROT = No of hindered rotors READ(20,*) NHROT NAHROT(ID(I))=NHROT C ROTH = Rotational constant of hindered rotor C SYMH = Symmetry number of hindered rotor C VH = Barrier of hindered rotor DO J=1,NHROT READ(20,*) ROTAH(ID(I),J),SYMAH(ID(I),J),VH1(ID(I),J), 1 VH2(ID(I),J),VH3(ID(I),J),VH4(ID(I),J) VH1(ID(I),J)=VH1(ID(I),J)*3.4964E2 VH2(ID(I),J)=VH2(ID(I),J)*3.4964E2 VH3(ID(I),J)=VH3(ID(I),J)*3.4964E2 VH4(ID(I),J)=VH4(ID(I),J)*3.4964E2 END DO READ(20,*) NV NVIB(ID(I)) = NV READ(20,*) (VIBX(ID(I),J),J=1,NV) CLOSE(20) C*********************************************************** C Begin computing sum of states for TS C*********************************************************** DO J=1,NV VIB(J)=VIBX(ID(I),J) END DO DO J=1,NACT ROT(J)=ROTACT(ID(I),J) SYM(J)=SYMACT(ID(I),J) NDIM(J)=NDIMACT(ID(I),J) END DO DO J=1,NHROT ROTH(J)=ROTAH(ID(I),J) SYMH(J)=SYMAH(ID(I),J) V1(J)=VH1(ID(I),J) V2(J)=VH2(ID(I),J) V3(J)=VH3(ID(I),J) V4(J)=VH4(ID(I),J) END DO C INDEX = 2 --- Returns sum of state INDEX = 2 WRITE(*,*) 'Computing sum of states of ', ANAME 215 CALL BSCOUNT(VIB,NV,ROT,NACT,SYM,NDIM,EMAX,DELTAE,P,NGRAINS, 1 NHROT,ROTH,SYMH,V1,V2,V3,V4,INDEX) OPEN (UNIT=2, FILE=ANAME(ICH:LCH)//'.SUM.txt') WRITE(2,*) ' No. (cm-1) Sum of states' DO J=0,NGRAINS RO(J,ID(I))=P(J) WRITE(2,*) J, J*DELTAE, P(J) END DO CLOSE(2) C*********************************************************** C End computing sum of states for each TS C*********************************************************** WRITE(16,570) NAME(ID(I)) WRITE(16,580) DELHF0(ID(I)) WRITE(16,600) ROTX(ID(I)) WRITE(16,610) SYMX(ID(I)) WRITE(16,620) NDIMX(ID(I)) WRITE(16,630) NACROT(ID(I)) WRITE(16,640) (ROTACT(ID(I),J),J=1,NACT) WRITE(16,650) (SYMACT(ID(I),J),J=1,NACT) WRITE(16,660) (NDIMACT(ID(I),J),J=1,NACT) WRITE(16,665) NHROT WRITE(16,666) (ROTAH(ID(I),J),J=1,NHROT) WRITE(16,667) (SYMAH(ID(I),J),J=1,NHROT) WRITE(16,668) (VH1(ID(I),J)/3.4964E2,J=1,NHROT) WRITE(16,668) (VH2(ID(I),J)/3.4964E2,J=1,NHROT) WRITE(16,668) (VH3(ID(I),J)/3.4964E2,J=1,NHROT) WRITE(16,668) (VH4(ID(I),J)/3.4964E2,J=1,NHROT) WRITE(16,670) WRITE(16,680) (VIBX(ID(I),J),J=1,NVIB(ID(I))) WRITE(16,690) IDEG(REAC(ID(I)),ID(I)), IDEG(PROD(ID(I)),ID(I)) DELHF0(ID(I)) = DELHF0(ID(I))*3.4964E2 70 CONTINUE C End of TS card C AEQ,BEQ,EEQ : Parameters of equilibrium constant READ(15,*) AEQ,BEQ,EEQ WRITE(16,695) AEQ,BEQ,EEQ C Scan for first well C TSINIT = TS connecting reactants and isomer C ISINIT = First isomer formed from reactants C M1 = Index of first channel C MGR1 = Grain no. at critical energy of first channel IF(ISINIT .GT. 0) GOTO 162 DO I = NSPECIES+1, NSPECIES+NTS IF(REAC(ID(I)) .EQ. ID(1)) THEN TSINIT = ID(I) ISINIT = PROD(ID(I)) 216 ELSEIF(PROD(ID(I)) .EQ. ID(1)) THEN TSINIT = ID(I) ISINIT = REAC(ID(I)) ENDIF END DO 162 CONTINUE M1 = TSINT(ISINIT,TSINIT) ISINK = 0 WRITE(16,735) NTRIALS DO 120 IT=1,NTEMP T = TEMP(IT) KT = BOLTZ*T BETA = 1/KT EQ(IT) = AEQ*T**BEQ*EXP(-EEQ*1E3/1.9872/T) WRITE(*,*) 'TEMP = ', T WRITE(16,700) T C********************************************************** C Compute total partition function for each isomer C********************************************************** C IDIS= Temporary storage of ID of isomer WRITE(16,705) DO 130 I=2,NSPECIES+NTS IF (I .GE. NISOMERS+2 .AND. I .LE. NSPECIES) GOTO 130 IDIS = ID(I) IF(IFIT(ID(I)) .EQ. 1) THEN ROTX(ID(I))=0.0 RX=0.0 DO NFIT=1,10 RX = FIT(ID(I),NFIT)*T**(NFIT-1) ROTX(ID(I))=ROTX(ID(I))+RX END DO IF(ROTX(ID(I)) .LE. 0) ROTX(ID(I))=1.0E-6 ENDIF CALL QTOTAL(IDIS,T,NACROT,ROTX,SYMX,NDIMX,ROTACT,SYMACT, 1 NDIMACT,NAHROT,ROTAH,SYMAH,VH1,VH2,VH3,VH4,NVIB,VIBX,QTOT) WRITE(16,710) NAME(ID(I)),QTOT(ID(I)) 130 CONTINUE C***************************************************************** C Begin computing collision probability matrix for each isomer C***************************************************************** DO 201 I = 2,NISOMERS+1 DO J=0,NGRAINS DO K=0,NGRAINS P2D(J,K)=0.0 END DO END DO ANAME = NAME(ID(I)) 217 WRITE(*,*) 'Computing collision probability matrix for ',ANAME DO J=0,NGRAINS DENS(J)=RO(J,ID(I)) END DO CALL NORM(NGRAINS,DELTAE,DENS,EDOWN,BETA,CIJ) DO J = 0, NGRAINS DO K = 0, NGRAINS IF(J .GE. K) THEN P2D(K,J) = CIJ(J)*EXP(-DELTAE*(J-K)/EDOWN) ELSE P2D(K,J) = CIJ(K)*DENS(K)/DENS(J)*EXP(-(BETA+1/EDOWN)* 1 (DELTAE*(K-J))) ENDIF END DO END DO IF (NISOMERS .NE. 1) THEN ICH = IFIRCH(ANAME) LCH = ILASCH(ANAME) OPEN (UNIT=35,FORM='UNFORMATTED',FILE=ANAME(ICH:LCH)//'.prob') WRITE(*,*)'Writing collision probability matrix to scratch file' DO 214 J=0,NGRAINS WRITE(35) P2D(J,J) DO K1=(J+1),NGRAINS WRITE(35) P2D(K1,J) IF( P2D(K1,J)/P2D(J,J) .LT. PTOL) GOTO 211 END DO 211 DO K2=(J-1),0,-1 WRITE(35) P2D(K2,J) IF( P2D(K2,J)/P2D(J,J) .LT. PTOL) GOTO 214 END DO 214 CONTINUE CLOSE(35) END IF DO J = 0, NGRAINS PACT(J) = 0 DO K = J+1, NGRAINS PACT(J) = PACT(J) + P2D(K,J) END DO END DO DO J = 0, NGRAINS PDEACT(J) = 0 DO K = 0, J PDEACT(J) = PDEACT(J) + P2D(K,J) END DO END DO DO J=0,NGRAINS PIJACT(ID(I),J)=PACT(J) 218 PIJDEACT(ID(I),J)=PDEACT(J) END DO 201 CONTINUE C***************************************************************** C End computing collision probability matrix for each isomer C***************************************************************** C****************************************************************** C Begin loop for microcanonical and high pressure rate constants C for each channel C****************************************************************** C IDIS = Temporary storage of index of isomer C TEMPID = Temporary storage of index of TS associated with isomer C M = Temporary storage of internal index of isomer-channel pair C MGRAINS = Grain no. at critical energy WRITE(*,*) 'Computing microcanonical rate constants' WRITE(16,720) WRITE(16,725) DO 140 I=2,(NISOMERS+1) DO 150 J=1,NCHAN(ID(I)) IDIS = ID(I) TEMPID = IDTS(ID(I),J) DEGEN = IDEG(IDIS,TEMPID) M = TSINT(IDIS,TEMPID) E0 = DELHF0(TEMPID)-DELHF0(IDIS) BARRIER(M)=E0 E00(J)= DELHF0(TEMPID)-DELHF0(IDIS) IF (J .GE. 2) THEN If (E00(J) .LE. Emin(I)) THEN Emin(I)=E00(J) END IF ELSE Emin(I)=E00(1) END IF CALL MCRC(T,IDIS,TEMPID,M,DELTAE, 1 ROTX,NDIMX,SYMX,DEGEN,NGRAINS,BARRIER,MGRAINS,PKE) HIGH(M,IT) = DEGEN*KT/PLANCK*QTOT(TEMPID) 1 /QTOT(IDIS)*EXP(-BARRIER(M)/KT) MGR1 = MGRAINS(M1) WRITE(16,730) NAME(IDIS),NAME(TEMPID),HIGH(M,IT) 150 CONTINUE 140 CONTINUE C****************************************************************** C End of loop for microcanonical and high pressure rate constants C for each channel C****************************************************************** ENTRK(IT) = HIGH(M1,IT)*EQ(IT) 219 WRITE(16,736) ENTRK(IT) C Calculate the initial distribution of reactant for C chemically activated system as a function of energy C GINIT = Array containing above distribution CALL INDIST (T,M1,ISINIT,PKE,MGR1,NGRAINS,DELTAE,GINIT) C Begin the stochastic run C P5 = Pressure in torr C C5 = Concentration in mol/cm^3 C COUNTER = No. of molecules of particular species at end of simulation DO 180 IP = 1,NPRES P5=PRES(IP) C5=P5/760.0*1.013E-1/8.314/T WRITE(*,*) 'Stochastic run begun for pressure ', P5, ' torr' WRITE(16,740) P5 DO I = 1,NSPECIES ICOUNTER(ID(I)) = 0 END DO DO I = 2, NISOMERS+1 Z(ID(I))=ZLJ(T,WTAVE(ID(I)),SIGMA(ID(I)),EPSLON(ID(I)))*C5 END DO DO 190 NMOL=1,NTRIALS C******************************************************* C Determine initial energy of chosen molecule C******************************************************* C EINIT = Initial energy of chosen molecule C TIMER = Time of stochastic run for each molecule TIMER=0.0 CALL RAND(U) R1=U DO I = MGR1,NGRAINS IF(R1 .LE. GINIT(I)) THEN EINIT(NMOL)=DELTAE*(I)-(GINIT(I)-R1) 1 /(GINIT(I)-GINIT(I-1))*DELTAE GOTO 200 ENDIF END DO C************************************************** C Initial energy of chosen molecule determined C************************************************** C*************************************************************** C Begin loop to determine C (a) Time before molecule changes state C (b) Next process (activation/deactivation/isomerization) C (c) Energy at end of process if activation/deactivation C*************************************************************** C IDSPECIES = ID of isomer C E = Energy of molecule 220 C INEW = 0 -- molecule is same isomer as in previous time step C = 1 -- molecule has undergone isomerization in previous time step C Z = Collision frequency at P and T C ATOTAL = Sum of microcanonical rate constants and C collision frequency for isomer at energy E (/sec) C TAU = Time before molecule changes state 200 IDSPECIES = ISINIT IDOLD = ISINIT E = EINIT(NMOL) INEW=1 210 CONTINUE IF (INEW .EQ. 1) THEN E = E + DELHF0(IDOLD) - DELHF0(IDSPECIES) IDOLD = IDSPECIES NUM = NMOL/100 IF ((NUM*100) .EQ. NMOL) WRITE (*,*) NMOL IF (NISOMERS .NE. 1) THEN ANAME = NAME(IDSPECIES) ICH = IFIRCH(ANAME) LCH = ILASCH(ANAME) OPEN (UNIT=35,FORM='UNFORMATTED',FILE=ANAME(ICH:LCH)//'.prob') DO 215 J=0,NGRAINS READ (35) P2D(J,J) DO K1=(J+1),NGRAINS READ(35) P2D(K1,J) IF( P2D(K1,J)/P2D(J,J) .LT. PTOL) GOTO 212 END DO 212 DO K2=(J-1),0,-1 READ(35) P2D(K2,J) IF( P2D(K2,J)/P2D(J,J) .LT. PTOL) GOTO 215 END DO 215 CONTINUE CLOSE(35) END IF DO ITER = 0,NGRAINS IF (PIJACT(IDSPECIES,ITER) .GT. PIJDEACT(IDSPECIES,ITER) 1 .AND. PIJACT(IDSPECIES,ITER+1) .LT. PIJDEACT(IDSPECIES, 1 ITER+1)) THEN ISINK = ITER+1 ENDIF END DO ENDIF CALL RAND(U) R2 = U IF ( R2 .EQ. 0.0 ) R2 = SMALL ATOTAL = 0.0 DO 220 J=1,NCHAN(IDSPECIES) 221 TEMPID = IDTS(IDSPECIES,J) M = TSINT(IDSPECIES,TEMPID) C Interpolation to find k(E) from array PKE C AKE = Microcanonical rate constant at energy E, channel M C IGRAIN = Grain in which E lies DO IM = MGRAINS(M),NGRAINS IF(E .LT. DELTAE*(MGRAINS(M)-1)) THEN AKE(M) = 0.0 GOTO 230 ENDIF IF (E .LE. (DELTAE*IM)) THEN AKE(M) = PKE(M,IM-1)+(PKE(M,IM)-PKE(M,IM-1))* 1 (E-DELTAE*(IM-1))/DELTAE GOTO 230 ENDIF END DO 230 ATOT(J)=ATOTAL+AKE(M) ATOTAL = ATOT(J) 220 CONTINUE ATOTAL = ATOTAL + Z(IDSPECIES) TAU = -LOG(R2)/ATOTAL TIMER = TIMER + TAU CALL RAND(U) R3 = U C Check if process is activation/deactivation/isomerization C ICHECK = 0 -- activation/deactivation C ICHECK = 1 -- isomerization ICHECK = 0 DO J=1,NCHAN(IDSPECIES) IF(ATOT(J) .GE. (R3*ATOTAL)) THEN TEMPID = IDTS(IDSPECIES,J) !TS and respective channel selected IF(IDSPECIES .EQ. REAC(TEMPID)) THEN IDSPECIES = PROD(TEMPID) ICHECK = 1 INEW = 1 GOTO 240 ELSE IDSPECIES = REAC(TEMPID) ICHECK = 1 INEW = 1 GOTO 240 ENDIF ENDIF END DO C Check if species formed on isomerization is reactant / product 240 IF (IDSPECIES .EQ. ID(1)) THEN ICOUNTER(ID(1))=ICOUNTER(ID(1)) + 1 222 GOTO 190 ENDIF DO 250 IPROD = (NISOMERS+2), NSPECIES IF(IDSPECIES .EQ. ID(IPROD)) THEN ICOUNTER(ID(IPROD))=ICOUNTER(ID(IPROD)) + 1 GOTO 190 ENDIF 250 CONTINUE C Process is activating/deactivating collision IF(ICHECK .EQ. 0) THEN CALL STEP(IDSPECIES,DELTAE,DE,E,NGRAINS, 1 P2D,PIJACT,PIJDEACT,ENEW) E = ENEW INEW=0 IF ( E .LE. DELTAE*ISINK ) THEN ICOUNTER(IDSPECIES)=ICOUNTER(IDSPECIES) + 1 GOTO 190 ENDIF ENDIF GOTO 210 190 CONTINUE C*********************************************************** C Stochastic run complete for single molecule C*********************************************************** WRITE(16,750) DO I=1,NSPECIES FRAC = ICOUNTER(ID(I))/NTRIALS RES = FRAC * ENTRK(IT) WRITE(16,760) NAME(ID(I)),ICOUNTER(ID(I)),FRAC,RES END DO 180 CONTINUE C*********************************************************** C Calculation complete for single pressure C*********************************************************** 120 CONTINUE C*********************************************************** C Calculation complete for single temperature C*********************************************************** CALL TIME(time_end) WRITE(16,770) time_start WRITE(16,780) time_end C Format statements 500 FORMAT(A50) 510 FORMAT(A15) 520 FORMAT(10X,'Program for multichannel RRKM using 1Monte Carlo approach'/28X,'Ameya Joshi'/26X,'September 2003', 2/15X,'RRKM code adopted from Hai Wang, 1991',//80('*')) 223 530 FORMAT(//1X,A50) 540 FORMAT(//,80('-')//,'Maximum energy counted: ',1PE10.3,0P, 1 'kcal/mol'/'Energy spacing:',9X,1PE10.3,0P,'cm-1') 550 FORMAT('Number of molecules:',E10.2,//70('-')) 560 FORMAT(//,'Bath gas data',//45X,'Lennard-Jones',/15X, 1'Molecular Weight',4X,'Coll. Dia. (A)',4X,'Well Depth (K)'// 2T12,3(5X,F8.2,7X),//70('-')) 565 FORMAT(//,'Data for isomers') 570 FORMAT(//,A15) 580 FORMAT(//,'Relative Energy (kcal/mol)',10X,F6.2) 590 FORMAT(//,45X,'Lennard-Jones',/15X,'Molecular Weight',4X, 1'Coll. Dia. (A)',4X,'Well Depth (K)'//,'Isomer' 2T12,3(5X,F8.2,7X),/70('.')/'Average',T12,3(5X,F8.2,7X)) 600 FORMAT(//,'External rotational constant (/cm)',T41,2X,F6.2,2X) 610 FORMAT('Symmetry number',T41,4X,F6.2,5X) 620 FORMAT('Dimension of the external rotor',T41,4X,I1,5X) 630 FORMAT(/'No. of active rotors:',10X,I1) 640 FORMAT( 'Rotational constant (/cm)',T41,8(F8.4,2X)) 650 FORMAT( 'Symmetry number',T41,8(2X,F6.4,2X)) 660 FORMAT( 'Dimension',T41,8(2X,F6.4,2X)) 665 FORMAT(/'No. of hindered rotors:',10X,I1) 666 FORMAT( 'Rotational constant (/cm)',T41,8(F8.4,2X)) 667 FORMAT( 'Symmetry number',T41,8(2X,F6.4,2X)) 668 FORMAT( 'Barrier to rotation (kcal/mol)',T41,8(F8.4,2X)) 670 FORMAT(/'Vibrational frequencies (/cm):') 680 FORMAT(T41,F6.0) 685 FORMAT(//80('-'),//,'Data for Transition States') 690 FORMAT(/'Reaction path degeneracies:',T44,I2,2X,I2,2X/) 695 FORMAT(/,80('-'),//1X,'Equilibrium constant: A = ', 1 1PE10.3,0P,2X,'n =',F7.2,2X,'E = ',F7.3,' kcal/mol') 700 FORMAT(/,80('-'),//,25('*'),/2X,'Temperature =',F7.1,' K'/25('*')) 705 FORMAT(//,2X,'Total Partition Functions',/) 710 FORMAT(2X,'Partition function for',1X,A15,':',1PE10.3,0P) 720 FORMAT(//2X,'High pressure limit rate constants') 725 FORMAT(/,2X,'ISOMER ',5X,'TRANSITION STATE',5X,'Kinf') 730 FORMAT(2X,A15,5X,A15,5X,E10.3) 735 FORMAT(/,80('-'),//,'Number of molecules =',1PE10.3) 736 FORMAT(/,'k-High pressure for entrance channel',1PE10.3) 740 FORMAT(/1X,'Pressure = ',1PE10.3) 750 FORMAT(/,5X,'Channel',8X,'No. of molecules',5X,'Fraction',9X,'k'/) 760 FORMAT(A20,I8,15X,F5.3,5X,1PE10.3) 770 FORMAT(/,5X,'Time at start of program:',5X,A10) 780 FORMAT(/,5X,'Time at end of program:',7X,A10) STOP END 224 FUNCTION IFIRCH (STRING) C*********************************************************************** C DATE WRITTEN 850626 C REVISION DATE 850626 C CATEGORY NO. M4. C KEYWORDS CHARACTER STRINGS,SIGNIFICANT CHARACTERS C AUTHOR CLARK,G.L.,GROUP C-3 LOS ALAMOS NAT'L LAB C PURPOSE Determines first significant (non-blank) character C in character variable C*********************************************************************** IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER (I-N) CHARACTER* (*)STRING C FIRST EXECUTABLE STATEMENT IFIRCH NLOOP = LEN(STRING) IF (NLOOP.EQ.0 .OR. STRING.EQ.' ') THEN IFIRCH = 0 RETURN ENDIF DO I = 1, NLOOP IF (STRING(I:I) .NE. ' ') GO TO 120 END DO IFIRCH = 0 RETURN 120 CONTINUE IFIRCH = I END FUNCTION ILASCH (STRING) C*********************************************************************** C DATE WRITTEN 850626 C REVISION DATE 850626 C CATEGORY NO. M4. C KEYWORDS CHARACTER STRINGS,SIGNIFICANT CHARACTERS C AUTHOR CLARK,G.L.,GROUP C-3 LOS ALAMOS NAT'L LAB C PURPOSE Determines last significant (non-blank) character C in character variable C*********************************************************************** IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER (I-N) CHARACTER*(*) STRING C FIRST EXECUTABLE STATEMENT ILASCH NLOOP = LEN(STRING) IF (NLOOP.EQ.0 .OR. STRING.EQ.' ') THEN ILASCH = 0 RETURN ENDIF DO I = NLOOP, 1, -1 ILASCH = I 225 IF (STRING(I:I) .NE. ' ') RETURN END DO END SUBROUTINE INDIST (T,M,ISINIT,PKE,MGR,NGRAINS,DELTAE,GINIT) C*********************************************************************** C Subroutine to calculate the initial distribution of reactant for C chemically activated system as a function of energy C M = Index of first channel C MGR = Grain no. at critical energy of first channel C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) REAL*8 KT DATA AVGD/6.0222E+23/,BOLTZ/0.695045/,PLANCK/3.3362E-11/, 1 PI/3.1415926/,SMALL/1.0D-78/,SPEED/2.9979E+10/ COMMON NARRAY, NTOL COMMON /DENSITY/ RO(0:120000,20) DIMENSION GINIT(0:NARRAY), PKE(NTOL,0:NARRAY), TOTAL(0:NARRAY) KT = BOLTZ*T G = 0.0 DO I=0,NGRAINS GINIT(I) = 0.0 TOTAL(I) = 0.0 END DO C Integration of k(E)*Rho(E)*exp(-E/kT)dE DO ITER=MGR,NGRAINS G = RO(ITER,ISINIT)*EXP(-DELTAE*FLOAT(ITER)/KT) IF((ITER-MGR) .EQ. 0) THEN TOTAL(ITER)=TOTAL(ITER)+G*PKE(M,ITER)/2.0 ELSE TOTAL(ITER)=TOTAL(ITER-1)+G*PKE(M,ITER) ENDIF END DO C End of integration DO ITER=MGR,NGRAINS GINIT(ITER) = TOTAL(ITER)/TOTAL(NGRAINS) END DO RETURN END SUBROUTINE NORM(NGRAINS, DELTAE, DENS, EDOWN, BETA, CIJ) C*********************************************************************** C Subroutine to find the normalization constants associated with C the energy transfer probability matrix. The exponential down C model is used. C Based on the algorithm described in "Unimolecular Reactions" by C Holbrook, K.A., Pilling, M.J. and Robertson S.H. 226 C NGRAINS = No. of energy grains C DELTAE = Energy spacing between successive grains (/cm) C DENS(NGRAINS) = Array containing density of states in each grains C EDOWN = Average energy transferred per collision <Edown> C BETA = 1/kT C CIJ(NGRAINS) = Array containing normalization constants C*********************************************************************** IMPLICIT REAL*8 (A-H, O-Z) COMMON NARRAY, NTOL DIMENSION DENS(0:NARRAY),CIJ(0:NARRAY) F = -(BETA+1/EDOWN)*DELTAE DO 10 J = NGRAINS, 0, -1 SUM = 1.0 TOT = 0.0 IF (J .NE. NGRAINS) THEN DO I = NGRAINS, J+1, -1 SUM = SUM - CIJ(I) * DENS(I)/DENS(J) * EXP(F * (I-J)) END DO ENDIF DO K = 0, J TOT = TOT + EXP(DELTAE*(K-J)/EDOWN) END DO CIJ(J) = SUM/TOT 10 CONTINUE RETURN END DOUBLE PRECISION FUNCTION QR(B,N,SIGMA,ND,T) C*********************************************************************** C Function QR computes rotational partition function. C B = rotational constants in cm-1. C N = number of rotors. C SIGMA = symmetry numbers. C ND = dimension of the rotor C T = temperature, K. C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DIMENSION B(N),SIGMA(N),ND(N) DATA BOLTZ/0.695045/,PI/3.1415926/ C BOLTZ here is in unit of (/cm/K) QR=1.0 DO 10 I=1,N ID=ND(I) GOTO (20,30,40), ID C one-dimensional rotor 20 QR=QR*SQRT(PI*BOLTZ*T/B(I))/SIGMA(I) GOTO 10 227 C two-dimensional rotor 30 QR=QR*(BOLTZ*T/SIGMA(I)/B(I)) GOTO 10 C Three dimensional rotor 40 QR=QR*SQRT(PI)*(SQRT(BOLTZ*T/B(I)))**3/SIGMA(I) 10 CONTINUE RETURN END DOUBLE PRECISION FUNCTION QT(WT,T) C*********************************************************************** C Function QT computes the translational partition function C per unit volume (1/cm^3) C WT = molecular weight C T = temperature, K C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DATA AVGD/6.0222E+23/,BOLTZ/1.3806E-16/,PLANCK/6.6262E-27/, 1 PI/3.1415926/ WMASS=WT/AVGD QT=(2.0*PI*WMASS*BOLTZ*T)**(1.5)/PLANCK**3 RETURN END SUBROUTINE QTOTAL(IDIS,T,NACROT,ROTX,SYMX,NDIMX,ROTACT,SYMACT, 1 NDIMACT,NAHROT,ROTAH,SYMAH,VH1,VH2,VH3,VH4,NVIB,VIBX,QTOT) C*********************************************************************** C Subroutine to find the total partition function (including both C active and inactive rotations) of the desired species. C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DIMENSION ROT(20),SYM(20),ND(20),VIB(100) DIMENSION ROTX(20),SYMX(20),NDIMX(20) DIMENSION NACROT(20),ROTACT(20,20),SYMACT(20,20) DIMENSION NDIMACT(20,20),NVIB(20),VIBX(20,100) DIMENSION QRSP(20),QVSP(20),QTOT(20) DIMENSION VH1(20,20),VH2(20,20),VH3(20,20),VH4(20,20) DIMENSION NAHROT(20),ROTAH(20,20),SYMAH(20,20) DATA BOLTZ/0.695045/,PI/3.1415926/ C BOLTZ here is in unit of (/cm/K) C*********************************** C Rotational partition function C*********************************** QRH = 1.0 NROT=1+NACROT(IDIS) ROT(NROT)=ROTX(IDIS) SYM(NROT)=SYMX(IDIS) 228 ND(NROT)=NDIMX(IDIS) DO J=1,NACROT(IDIS) ROT(J)=ROTACT(IDIS,J) SYM(J)=SYMACT(IDIS,J) ND(J)=NDIMACT(IDIS,J) END DO QRSP(IDIS)=QR(ROT,NROT,SYM,ND,T) IF(NAHROT(IDIS) .GT. 0) THEN DO J=1,NAHROT(IDIS) ROTH=ROTAH(IDIS,J) SYMH=SYMAH(IDIS,J) V1=VH1(IDIS,J) ARG1=V1/2.0/BOLTZ/T V2=VH2(IDIS,J) ARG2=V2/2.0/BOLTZ/T V3=VH3(IDIS,J) ARG3=V3/2.0/BOLTZ/T V4=VH4(IDIS,J) ARG4=V4/2.0/BOLTZ/T IF (V3 .NE. 0.0) THEN QRH1=QR(ROTH,1,SYMH,1,T)*EXP(-ARG1)*BESSEL(ARG1) QRH2=QR(ROTH,1,SYMH,1,T)*EXP(-ARG2)*BESSEL(ARG2) QRH3=QR(ROTH,1,SYMH,1,T)*EXP(-ARG3)*BESSEL(ARG3) QRH4=QR(ROTH,1,SYMH,1,T)*EXP(-ARG4)*BESSEL(ARG4) QRH=QRH*1.0/4.0*(QRH1+QRH2+QRH3+QRH4) ELSEIF((V2 .NE. V1).AND.(V2 .NE. 0.0).AND.(V3 .EQ. 0.0))THEN QRH1=QR(ROTH,1,SYMH,1,T)*EXP(-ARG1)*BESSEL(ARG1) QRH2=QR(ROTH,1,SYMH,1,T)*EXP(-ARG2)*BESSEL(ARG2) QRH3=0.0; QRH4=0.0 QRH=QRH*1.0/4.0*(QRH1+QRH2+QRH3+QRH4) ELSE QRH=QRH*QR(ROTH,1,SYMH,1,T)*EXP(-ARG1)*BESSEL(ARG1) END IF END DO END IF QRSP(IDIS)=QRSP(IDIS)*QRH C************************************* C Vibrational partition function C************************************* NV=NVIB(IDIS) DO J=1,NV VIB(J)=VIBX(IDIS,J) END DO QVSP(IDIS)=QV(VIB,NV,T) QTOT(IDIS)=QVSP(IDIS)*QRSP(IDIS) RETURN END 229 DOUBLE PRECISION FUNCTION BESSEL(R) C*********************************************************************** C Function to calculate the modified Bessel function of the first C kind of order zero I0(x) C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DATA PI/3.1415926/ DE=1.D-7 N=NINT(1.0D0/DE) BESSEL=0.0D0 DO I=0,N-1 T=DE*I BESSEL=BESSEL+DE*COSH(R*T)/SQRT(1.0D0-T**2) END DO BESSEL=BESSEL*2.0D0/PI RETURN END DOUBLE PRECISION FUNCTION QV(VIB,NVIB,T) C*********************************************************************** C Function QV computes the vibrational partitional function C VIB = vibrational frequencies, in /cm C NVIB = number of vibrational frequencies C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DIMENSION VIB(NVIB) DATA BOLTZ/0.695045/ QV=1.0 DO I=1,NVIB QV=QV/(1.0-EXP(-VIB(I)/BOLTZ/T)) END DO RETURN END SUBROUTINE RAND(U) C*********************************************************************** C Portable pseudo-random integer generator, especially for C microcomputers with a limitation of 16 bit integers. Translated from C original Pascal version(1) to Fortran 77 by H. D. Knoble, PSU. C*********************************************************************** INTEGER X,Y,Z REAL*8 U,V COMMON /RANDOM/X,Y,Z X=171*MOD(X,177)-2*(X/177) IF(X.LT.0) X=X+30269 Y=172*MOD(Y,176)-35*(Y/176) 230 IF(Y.LT.0) Y=Y+30307 Z=170*MOD(Z,178)-63*(Z/178) IF(Z.LT.0) Z=Z+30323 V=X/30269.0 + Y/30308.0 + Z/30323.0 U=V-INT(V) RETURN END SUBROUTINE MCRC(T,IDIS,TEMPID,M,DELTAE, 1 ROTX,NDIMX,SYMX,DEGEN,NGRAINS,BARRIER,MGRAINS,PKE) C*********************************************************************** C IDIS = Index of isomer C TEMPID = Index of TS associated with isomer C M = Temporary storage of internal index of isomer-channel pair C ROTX = External inactive rotational constant C SYMX = Symmetry number C NDIMX = Dimension of external rotor (2 or 3) C MGRAINS = No. of grains in energy barrier C PKE = Microcanonical rate constants C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) COMMON NARRAY, NTOL DIMENSION ROTX(20),SYMX(20),NDIMX(20) DIMENSION BARRIER(20),MGRAINS(20),PKE(NTOL,0:NARRAY) COMMON /DENSITY/ RO(0:120000,20) DATA AVGD/6.0222E+23/,BOLTZ/0.695045/,PLANCK/3.3362E-11/, 1 PI/3.1415926/,SMALL/1.0D-78/,SPEED/2.9979E+10/ E0 = BARRIER(M) MGRAINS(M) = NINT(E0/DELTAE) ROTIN=ROTX(IDIS) NDIMIN=NDIMX(IDIS) SYMIN=SYMX(IDIS) ROTTIN=ROTX(TEMPID) NDIMTIN=NDIMX(TEMPID) SYMTIN=SYMX(TEMPID) QRR=QR(ROTIN,1,SYMIN,NDIMIN,T) QRT=QR(ROTTIN,1,SYMTIN,NDIMTIN,T) OTHER=DEGEN*(QRT/QRR)/PLANCK DO I = 0,NGRAINS PKE(M,I) = 0.0 END DO DO ITER = MGRAINS(M),NGRAINS PKE(M,ITER) = OTHER*RO(ITER-MGRAINS(M),TEMPID) 1 /RO(ITER,IDIS) END DO RETURN END 231 SUBROUTINE STEP(ID,DELTAE,DE,E,NGRAINS, 1 PIJ,PIJACT,PIJDEACT,ENEW) C*********************************************************************** C Subroutine to determine : C (a) If the collision is activating / deactivating C (b) The new energy level after collision C R = Random number between 0 and 1 C DELTAE = Width of energy grain C E = Exact energy of molecule before collision C N1 = Energy grain before collision C NGRAINS = No. of energy grains C PIJACT(20,NARRAY) Summation of activation probabilities C PIJDEACT(20,NARRAY) Summation of deactivation probabilities C ENEW = New energy level after collision C*********************************************************************** IMPLICIT REAL*8 (A-H, O-Z) COMMON NARRAY, NTOL DIMENSION PIJACT(NTOL,0:NARRAY), PIJDEACT(NTOL,0:NARRAY) DIMENSION PIJ(0:NARRAY,0:NARRAY) ENEW = E CALL RAND(R) DO IM = 0, NGRAINS IF (E .LE. (DELTAE*IM)) THEN N1 = IM GOTO 5 ENDIF END DO 5 IF (R .LT. PIJACT(ID,N1)) THEN INDEX = 1 ! Collision is activating ELSE INDEX = 2 ! Collision is deactivating R=R-PIJACT(ID,N1) ENDIF IF (INDEX .EQ. 1) THEN ASUM1 = 0 DO 10 I = N1, NGRAINS ASUM2 = ASUM1 + PIJ(I,N1) IF (ASUM2 .GE. R) THEN ENEW = (R-ASUM1)/(ASUM2-ASUM1)*DELTAE + DELTAE*(I-1) GOTO 15 ENDIF ASUM1=ASUM2 10 CONTINUE ELSE DSUM1 = 0 DO 20 I = N1, 0, -1 232 DSUM2 = DSUM1 + PIJ(I,N1) IF (DSUM2 .GE. R) THEN ENEW = (DSUM1-R)/(DSUM2-DSUM1)*DELTAE + DELTAE*(I+1) GOTO 15 ENDIF DSUM1=DSUM2 20 CONTINUE ENDIF 15 RETURN END SUBROUTINE BSCOUNT(VIB,IVIB,ROT,IROT,SIGMA,NDIM,EMAX,DELTAE,P, 1 NMAX,NHROT,ROTH,SIGMAH,V1,V2,V3,V4,INDEX) C*********************************************************************** C Subroutine BSCOUNT performed ro-vibrational states counting. C The vibrational degrees of freedom are treated as hamonic oscillators. C The counting of rotational states are performed by using C the method described by Gilbert and Smith (R. O. Gilbert and C S. C. Smith, Theory of Unimolecular and Recombination Reactions, C Blackwell, Oxford, 1990, Chapter 3). C C IVIB = number of vibrational degrees of freedom, input; C VIB(I) = vibrational frequencies (cmˆ-1), input; C IROT = number of active (rigid) rotors, input; C (The maximum number of rotor is 4 for direct count.) C ROT(J) = rotational constant (cmˆ-1), input; C SIGMA(J) = symmetric number of the Jth rotor, input; C NDIM(J) = dimension of the Jth rotor, input; C EMAX = maximum energy (Evr, cmˆ-1), input; C DELTE = energy spacing; input (DELTE*NMAX=EMAX) C P = array containing density of states in DELTAE energy spacing. C INDEX = 1 --- returns density of state C = 2 --- returns sum of state C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DIMENSION VIB(IVIB),ROT(IROT),SIGMA(IROT),NDIM(IROT),P(0:NMAX) DIMENSION NVIB(200) DIMENSION ROTH(NHROT),SIGMAH(NHROT),V1(NHROT),V2(NHROT) DIMENSION V3(NHROT),V4(NHROT) ALLOCATABLE PD(:),PS(:),PP(:),S(:) IF(NHROT.EQ.0) THEN DE=DELTAE ELSE DE=1.0 ENDIF NN=NINT(DELTAE/DE) allocate (PD(0:NMAX*NN),PS(0:NMAX*NN),PP(0:NMAX*NN),S(0:NMAX*NN)) 233 DO 10 I=1,IVIB NVIB(I)=NINT(VIB(I)/DE) 10 CONTINUE C Initialize P array. IF(IROT.EQ.0) THEN C No active rotational degrees of freedom PD(0)=1.0 DO 20 I=1,NMAX*NN PD(I)=0.0 20 CONTINUE ELSE C with active rotational degress of freedom PD(0)=0.0 U=0.0 P2=0.0 C Count number if 1-diemnsional free rotors, U, and number of C 2-dimensional rotors, P2, and calculate the products PROD=1.0 DO 30 J=1,IROT IF(NDIM(J).EQ.1) THEN U=U+1 PROD=PROD/(SIGMA(J)*SQRT(ROT(J))) ENDIF IF(NDIM(J).EQ.2) THEN P2=P2+1 PROD=PROD/(SIGMA(J)*ROT(J)) ENDIF 30 CONTINUE C Assign intial value of rotational densitity of states to array P(I) PROD=PROD*3.1415926**(U/2.0)/DGAMMA(P2+U/2.0) EXPON=P2+U/2.0-1.0 DO 40 I=1,NMAX*NN ESUM=FLOAT(I)*DE PD(I)=PROD*ESUM**EXPON 40 CONTINUE ENDIF C Perform vibrational state counting. P(J),J=1,2,...,M contains C the number of energy states on level E(J)/DELTAE. CALL COUNT(NVIB,IVIB,NMAX*NN,PD) IF(IROT.EQ.0) THEN DO 45 I=1,NMAX*NN PD(I)=PD(I)/DE 45 CONTINUE ENDIF IF(INDEX.NE.1) THEN DO 50 I=1,NMAX*NN PS(I)=PS(I-1)+PD(I)*DE 234 50 CONTINUE END IF IF(NHROT .EQ. 0) GOTO 75 C Convolute with density of states of hindered rotor, if any DO IHROT=1,NHROT IF (V3(IHROT) .NE. 0.0) THEN CALL HINCOUNT3(ROTH(IHROT),SIGMAH(IHROT),V1(IHROT),V2(IHROT) 1 ,V3(IHROT),V4(IHROT),DE,NMAX*NN,S) ELSEIF((V2(IHROT) .NE. V1(IHROT)).AND.(V2(IHROT) .NE. 0.0) .AND. 1 (V3(IHROT) .EQ. 0.0))THEN CALL HINCOUNT2(ROTH(IHROT),SIGMAH(IHROT),V1(IHROT),V2(IHROT) 1 ,DE,NMAX*NN,S) ELSE CALL HINCOUNT(ROTH(IHROT),SIGMAH(IHROT),V1(IHROT),DE,NMAX*NN,S) END IF DO I=0,NMAX*NN RHS=0.0 DO K=0,I RHS=RHS+S(K)*PD(I-K)*DE END DO PP(I)=RHS END DO DO I=0,NMAX*NN PD(I)=PP(I) END DO END DO IF(INDEX.NE.1) THEN DO 60 I=1,NMAX*NN PS(I)=PS(I-1)+PD(I)*DE 60 CONTINUE END IF 75 DO I=1,NMAX IF(INDEX.EQ.1) THEN P(I)=PD(I*NN) ELSE P(I)=PS(I*NN) ENDIF END DO RETURN END SUBROUTINE HINCOUNT(ROT,SIGMA,V,DE,N,DEN) C*********************************************************************** C Subroutine HINCOUNT performed states counting for hindered rotors C The counting of rotational states are performed by using C the method described by Knyazev et al. (JPC,1994,98,5279) C ROT = rotational constant (cm-1), input; 235 C SIGMA = symmetric number of the Jth rotor, input; C V = Barrier height of rotor (cm-1), input; C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DIMENSION DEN(0:N) DATA PI/3.1415926/ DO I=0,N E=FLOAT(I)*DE ARG=V/E IF(E .GT. V) THEN ARG=SQRT(ARG) DEN(I)=2.0*EKP(ARG)/PI/SIGMA/SQRT(ROT*E) ELSE ARG=SQRT(1.0/ARG) DEN(I)=2.0*EKP(ARG)/PI/SIGMA/SQRT(ROT*V) ENDIF END DO RETURN END DOUBLE PRECISION FUNCTION EKP(ARG) C*********************************************************************** C Function to find the elliptic integral of the first kind C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) ARG2=ARG*ARG IF(ARG.LT.0.80) THEN EKP=3.1415926*(16.0-5.0*ARG2)/(2.0*(16.0-9.0*ARG2)) ELSE EKP=(5.0-ARG2)*log(16.0/(1.0-ARG2))/8.0-(1.0-ARG2)/4.0 ENDIF RETURN END SUBROUTINE HINCOUNT2(ROT,SIGMA,V1,V2,DE,N,DEN) C*********************************************************************** C Subroutine HINCOUNT2 performed states counting for hindered rotors C The counting of rotational states are performed by using C the method described by Knyazev et al. (JPC,1994,98,5279) C ROT = rotational constant (cm-1), input; C SIGMA = symmetric number of the Jth rotor, input; C V = Barrier height of rotor (cm-1), input; C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DIMENSION DEN(0:N) DATA PI/3.1415926/ DO I=0,N 236 E=FLOAT(I)*DE VV1=MIN(V1,V2) VV2=MAX(V1,V2) ARG1=VV1/E ARG2=VV2/E IF (E .GT. VV2) THEN ARG11=SQRT(ARG1) ARG22=SQRT(ARG2) DEN(I)=1.0/2.0*(EKP(ARG11)+EKP(ARG22))/PI/SIGMA/SQRT(ROT*E) ELSEIF((E .GE. VV1) .AND. (E.LT.VV2)) THEN ARG11=SQRT(ARG1) ARG22=SQRT(1.0/ARG2) DEN(I)=1.0/2.0/SIGMA/PI*(EKP(ARG11)/SQRT(ROT*E)+EKP(ARG22)/ 1 SQRT(ROT*VV2)) ELSE ARG11=SQRT(1.0/ARG1) ARG22=SQRT(1.0/ARG2) DEN(I)=1.0/2.0/PI/SIGMA*(EKP(ARG11)/SQRT(ROT*VV1)+EKP(ARG22)/ 1 SQRT(ROT*VV2)) ENDIF END DO RETURN END SUBROUTINE HINCOUNT3(ROT,SIGMA,V1,V2,V3,V4,DE,N,DEN) C*********************************************************************** C Subroutine HINCOUNT3 performed states counting for hindered rotors C The counting of rotational states are performed by using C the method described by Knyazev et al. (JPC,1994,98,5279) C ROT = rotational constant (cm-1), input; C SIGMA = symmetric number of the Jth rotor, input; C V = Barrier height of rotor (cm-1), input; C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DIMENSION DEN1(0:N),DEN2(0:N),DEN(0:N) DATA PI/3.1415926/ DO I=0,N E=FLOAT(I)*DE VV1=MIN(V1,V2) VV2=MAX(V1,V2) ARG1=VV1/E ARG2=VV2/E IF (E .GT. VV2) THEN ARG11=SQRT(ARG1) ARG22=SQRT(ARG2) DEN1(I)=1.0/2.0*(EKP(ARG11)+EKP(ARG22))/PI/SIGMA/SQRT(ROT*E) ELSEIF((E .GE. VV1) .AND. (E.LT.VV2)) THEN 237 ARG11=SQRT(ARG1) ARG22=SQRT(1.0/ARG2) DEN1(I)=1.0/2.0/SIGMA/PI*(EKP(ARG11)/SQRT(ROT*E)+EKP(ARG22)/ 1 SQRT(ROT*VV2)) ELSE ARG11=SQRT(1.0/ARG1) ARG22=SQRT(1.0/ARG2) DEN1(I)=1.0/2.0/PI/SIGMA*(EKP(ARG11)/SQRT(ROT*VV1)+EKP(ARG22) 1 /SQRT(ROT*VV2)) ENDIF END DO DO I=0,N E=FLOAT(I)*DE VV1=MIN(V3,V4) VV2=MAX(V3,V4) ARG1=VV1/E ARG2=VV2/E IF (E .GT. VV2) THEN ARG11=SQRT(ARG1) ARG22=SQRT(ARG2) DEN2(I)=1.0/2.0*(EKP(ARG11)+EKP(ARG22))/PI/SIGMA/SQRT(ROT*E) ELSEIF((E .GE. VV1) .AND. (E.LT.VV2)) THEN ARG11=SQRT(ARG1) ARG22=SQRT(1.0/ARG2) DEN2(I)=1.0/2.0/SIGMA/PI*(EKP(ARG11)/SQRT(ROT*E)+EKP(ARG22)/ 1 SQRT(ROT*VV2)) ELSE ARG11=SQRT(1.0/ARG1) ARG22=SQRT(1.0/ARG2) DEN2(I)=1.0/2.0/PI/SIGMA*(EKP(ARG11)/SQRT(ROT*VV1)+EKP(ARG22) 1 / SQRT(ROT*VV2)) ENDIF END DO DO I=0,N DEN(I)=DEN1(I)+DEN2(I) END DO RETURN END SUBROUTINE COUNT(IC,N,MCOUNT,P) C*********************************************************************** C The subroutine COUNT is taken from C T.Beyer and D.F.Swinehart, Commun. Assoc. Comput. Machin. 16, 379 C (1973). C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DIMENSION IC(N),P(0:MCOUNT) 238 C Perform state counting. DO 10 I=1,N J=IC(I) JP1=J+1 P(J)=P(J)+1.0 DO 20 M=JP1,MCOUNT MJ=M-J P(M)=P(M)+P(MJ) 20 CONTINUE 10 CONTINUE RETURN END DOUBLE PRECISION FUNCTION ZLJ(T,W,SIGMA,EPSLON) C*********************************************************************** C Function ZLJ evaluates Lennard-Jones collision frequency factor C*********************************************************************** IMPLICIT REAL*8 (A-H,O-Z) DATA BOLTZ/1.3806E-16/,PI/3.1415926/,AVGD/6.0222E+23/ IF(EPSLON.LE.0.0001D0) THEN OMEGA=1.0 ELSE TS=T/EPSLON OMEGA=1.16145/TS**0.14874 OMEGA=OMEGA+0.52487/EXP(0.7732*TS) OMEGA=OMEGA+2.16178/EXP(2.437887*TS) ENDIF WT=W/AVGD ZLJ=(SIGMA*1.0E-8)**2*SQRT(8.0*PI*BOLTZ*T/WT)*OMEGA*AVGD C This has units : cm^3/mol/sec RETURN END 239 Appendix B The Reaction Mechanism The detailed n-alkane (up to C 12 ) oxidation mechanism compiled in this study is presented in this appendix. The first 784 reactions are the update H 2 /CO/C 1 - C 4 model, and the rest are for the higher n-alkane model. The species names are listed first, and followed by the reactions and their forward rate coefficients. The reverse rate coefficients may be calculated via equilibrium constants. Parameters A, n, and Ea denote the A factor, the temperature exponent, and the activation energy, respectively, for the modified Arrhenius expression of the reaction rate coefficient (units: cm 3 , s, cal, mol). F is the uncertainty factor of the rate coefficient. For most unimolecular reactions, the rate coefficients are given in Troe’s fall-off form (Troe 1983), along with the third body collision efficiencies specified. The sources of the rate coefficient expression are provides in the last column of the table. These rate coefficients are either taken from literature, or fitted to experiments, or estimated based on analogous reactions. B.1 List of species Species Description H hydrogen radical O oxygen radical OH Hydroxyl radical HO2 hydroperoxy radical H2 molecular hydrogen 240 H2O water H2O2 hydrogen peroxide O2 molecular oxygen C carbon CH methylidyne CH2 methylene radical (triplet) CH2* methylene radical (singlet) CH3 methyl radical CH4 methane HCO formyl radical CH2O formaldehyde CH3O methoxy radical CH2OH hydromethyl radical CH3OH methanol CO carbon monoxide CO2 carbon dioxide C2O dicarbon monoxide C2H ethynyl radical C2H2 acetylene H2CC vinylidene C2H3 vinyl radical C2H4 ethylene C2H5 ethyl radical C2H6 ethane HCCO ethynyloxy radical HCCOH ethynol CH2CO ketene CH3CO acetyl radical CH2CHO vinyloxy radical CH2OCH oxiranyl radical CH3CHO acetyldehyde CH2OCH2 oxirane C3H3 propargyl pC3H4 propyne aC3H4 allene cC3H4 cyclopropene aC3H5 allyl radical CH3CCH2 2-propenyl CH3CHCH 1-propenyl C3H6 propene 241 nC3H7 1-propyl iC3H7 2-propyl C3H8 propane CH2CHCO CH2=CH-*CO C2H3CHO acrolein (CH2=CH-CH=O) CH3CHOCH2 propylene oxide CH3CH2CHO propanal CH3COCH3 acetone C4H2 diacetylene nC4H3 1-vinylacetylene radical (*CH=CH-CCH) iC4H3 2-vinylacetylene radical (CH2C*-CCH) C4H4 vinylacetylene nC4H5 1-butadienyl iC4H5 2-butadienyl C4H5-2 2-butyn-1-yl (CH3-CC-*CH2) c-C4H5 cyclopropenyl C4H6 1,3-butadiene C4H612 1,2-butadiene C4H6-2 2-butyne C4H7 but-3-en-1-yl radical (*CH2-CH2-CH=CH2) iC4H7 2-methylallyl radical C4H81 1-butene C4H82 2-butene iC4H8 isobutene pC4H9 1-butyl sC4H9 2-butyl iC4H9 iso-butyl tC4H9 tert-butyl C4H10 n-butane iC4H10 iso-butane H2C4O 1,2-epoxy-1-buten-3-yne (CH2=C=C=C=O) C4H4O furan CH2CHCHCHO *CH2-CH=CH-CHO CH3CHCHCO CH3-CH=CH-*CO C2H3CHOCH2 ethenyloxirane C4H6O23 2,3-dihydrofuran CH3CHCHCHO crotonaldehyde C4H6O25 2,5-dihydrofuran C5H4O 2,4-Cyclopentadien-1-one C5H5O(1,3) cyclopentadienyloxy radical 242 C5H5O(2,4) cyclopentadienyloxy radical C5H4OH cyclopentadienolyl radical C5H5OH cyclopentadienol C5H5 cyclopentadienyl C5H6 cyclopentadiene lC5H7 1,4-pentadien-3-yl radical C6H2 triacetylene C6H3 hexa-1,5-diyne-3-ene-3yl radical l-C6H4 1,5-hexadien-3-yl o-C6H4 ortho-benzyne C6H5 phenyl radical C6H6 benzene C6H5CH2 benzyl radical C6H5CH3 toluene C6H5C2H phenylacetylene C6H5O phenoxy radical C6H5OH phenol C6H4O2 p-benzoquinone C6H5CO benzoyl radical C6H5CHO benzodehyde C6H5CH2OH benzyl alcohol OC6H4CH3 methoxyphenyl radical HOC6H4CH3 methylphenol C6H4CH3 methylphenyl radical NC12H26 n-dodecane PXC12H25 1-dodecyl SXC12H25 2-dodecyl S2XC12H25 3-dodecyl S3XC12H25 4-dodecyl S4XC12H25 5-dodecyl S5XC12H25 6-dodecyl C12H24 1-dodecene C12H23 1-dodecenyl NC11H24 n-undecane PXC11H23 1-undecyl SXC11H23 2-undecyl S2XC11H23 3-undecyl S3XC11H23 4-undecyl S4XC11H23 5-undecyl S5XC11H23 6-undecyl C11H22 1-undecene 243 C11H21 1-undecenyl NC10H22 n-decane PXC10H21 1-decyl SXC10H21 2-decyl S2XC10H21 3-decyl S3XC10H21 4-decyl S4XC10H21 5-decyl C10H20 1-decene C10H19 1-decenyl NC9H20 n-nonane PXC9H19 1-nonyl SXC9H19 2-nonyl S2XC9H19 3-nonyl S3XC9H19 4-nonyl S4XC9H19 5-nonyl C9H18 1-nonene C9H17 1-nonenyl NC8H18 n-octane PXC8H17 1-octyl SXC8H17 2-octyl S2XC8H17 3-octyl S3XC8H17 4-octyl C8H16 1-octene C8H15 1-octenyl NC7H16 n-heptane PXC7H15 1-heptyl SXC7H15 2-heptyl S2XC7H15 3-heptyl S3XC7H15 4-heptyl C7H14 1-heptene c7H13 1-heptenyl NC6H14 n-hexane PXC6H13 1-hexyl SXC6H13 2-hexyl S2XC6H13 3-hexyl C6H12 1-hexene C6H11 1-hexenyl NC5H12 n-pentane PXC5H11 1-pentyl SXC5H11 2-pentyl 244 S2XC5H11 3-pentyl C5H10 1-pentene C5H9 1-pentenyl PC12H25O2 nC12peroxy radicals (C12H25O2) P12OOHX2 nC12hydroperoxyalkyl radicals (C12H25O2) SOO12OOH nC12hydroperoxyalkylperoxy radicals (C12H25O4) OC12OOH nC12ketohydroperoxydes (C12H24O3) B.2 Reactions and rate coefficients Reactions A n Ea F Reference 1 H+O2=O+OH 2.64E+16 -0.7 17041 1.1 (Davis et al. 2005) 2 O+H2=H+OH 4.59E+04 2.7 6260 1.3 (Davis et al. 2005) 3 OH+H2=H+H2O 1.73E+08 1.5 3430 1.3 (Davis et al. 2005) 4 OH+OH=O+H2O 3.97E+04 2.4 -2110 1.3 (Davis et al. 2005) 5 H+H+M=H2+M 1.78E+18 -1 0 2 (Davis et al. 2005) H2/0.0/ H2O/0.0/ CO2/0.0/ AR/0.63/ HE/0.63/ 6 H+H+H2=H2+H2 9.00E+16 -0.6 0 2 (Davis et al. 2005) 7 H+H+H2O=H2+H2O 5.62E+19 -1.2 0 2 (Davis et al. 2005) 8 H+H+CO2=H2+CO2 5.50E+20 -2 0 2 (Davis et al. 2005) 9 H+OH+M=H2O+M 4.40E+22 -2 0 2 (Davis et al. 2005) H2/2.0/ H2O/6.30/ CO/1.75/ CO2/3.6/ AR/0.38/ HE/0.38/ 10 O+H+M=OH+M 9.43E+18 -1 0 2 (Davis et al. 2005) H2/2.0/ H2O/12.0/ CO/1.75/ CO2/3.6/ AR/0.7/ HE/0.7/ 11 O+O+M=O2+M 1.20E+17 -1 0 3 (Davis et al. 2005) H2/2.4/ H2O/15.4/ CO/1.75/ CO2/3.6/ AR/0.83/ HE/0.83/ 12 H+O2(+M)=HO2(+M) 5.12E+12 0.4 0 1.2 (Davis et al. 2005) LOW-P LIMIT 6.33E+19 -1.4 0 TROE /0.5 1E-30 1E-30/ O2/0.85/ H2O/11.89/ CO/1.09/ CO2/2.18/ AR/0.40/ HE/0.46/ H2/0.75/ 13 H2+O2=HO2+H 5.92E+05 2.4 53502 1.2 (Davis et al. 2005) 14 OH+OH(+M)=H2O2(+M) 1.11E+14 -0.4 0 1.5 (Davis et al. 2005) LOW-P LIMIT 2.01E+17 -0.584-2293 TROE /0.7346 94 1756 5182/ H2/2.0/ H2O/6.00/ CO/1.75/ CO2/3.6/ AR/0.7/ HE/0.7/ 245 15 HO2+H=O+H2O 3.97E+12 0 671 3 (Davis et al. 2005) 16 HO2+H=OH+OH 7.48E+13 0 295 2 (Davis et al. 2005) 17 HO2+O=OH+O2 4.00E+13 0 0 2 (Davis et al. 2005) 18 HO2+HO2=O2+H2O2 1.30E+11 0 -1630 2 (Davis et al. 2005) 19 HO2+HO2=O2+H2O2 3.66E+14 0 12000 1.5 (Davis et al. 2005) 20 OH+HO2=H2O+O2 1.41E+18 -1.8 60 2 (Sivaramakrishnan et al. 2007) 21 OH+HO2=H2O+O2 1.12E+85 -22.3 26900 2 (Sivaramakrishnan et al. 2007) 22 OH+HO2=H2O+O2 5.37E+70 -16.7 32900 2 (Sivaramakrishnan et al. 2007) 23 OH+HO2=H2O+O2 2.51E+12 2 40000 2 (Sivaramakrishnan et al. 2007) 24 OH+HO2=H2O+O2 1.00E+136 -40 34800 2 (Sivaramakrishnan et al. 2007) 25 H2O2+H=HO2+H2 6.05E+06 2 5200 2 (Davis et al. 2005) 26 H2O2+H=OH+H2O 2.41E+13 0 3970 5 (Davis et al. 2005) 27 H2O2+O=OH+HO2 9.63E+06 2 3970 3 (Davis et al. 2005) 28 H2O2+OH=HO2+H2O 2.00E+12 0 427 2 (Davis et al. 2005) 29 H2O2+OH=HO2+H2O 2.67E+41 -7 37600 2 (Davis et al. 2005) 30 CO+O(+M)=CO2(+M) 1.36E+10 0 2384 2 (Davis et al. 2005) LOW-P LIMIT 1.17E+24 -2.79 4191 H2/2.0/ H2O/12/ CO/1.75/ CO2/3.6/ AR/0.7/ HE/0.7/ 31 CO+OH=CO2+H 7.05E+04 2.1 -355.7 1.2 (Joshi and Wang 2006) 32 CO+OH=CO2+H 5.76E+12 -0.7 331.8 1.2 (Joshi and Wang 2006) 33 CO+O2=CO2+O 1.12E+12 0 47700 3 (Davis et al. 2005) 34 CO+HO2=CO2+OH 1.57E+05 2.2 17943 2 (You et al. 2007) 35 HCO+H=CO+H2 1.20E+14 0 0 2 (Davis et al. 2005) 36 HCO+O=CO+OH 3.00E+13 0 0 3 (Davis et al. 2005) 37 HCO+O=CO2+H 3.00E+13 0 0 3 (Davis et al. 2005) 38 HCO+OH=CO+H2O 3.02E+13 0 0 3 (Davis et al. 2005) 39 HCO+M=CO+H+M 1.87E+17 -1 17000 2 (Davis et al. 2005) H2/2.0/ H2O/0.0/ CO/1.75/ CO2/3.6/ 40 HCO+H2O=CO+H+H2O 2.24E+18 -1 17000 2 (Davis et al. 2005) 41 HCO+O2=CO+HO2 1.20E+10 0.8 -727 2 (Davis et al. 2005) 42 CO+H2(+M)=CH2O(+M) 4.30E+07 1.5 79600 2 (Frenklach et al. 1995) LOW-P LIMIT 5.07E+27 -3.42 84350 TROE /0.932 197 1540 10300/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 43 C+OH=CO+H 5.00E+13 0 0 2 (Frenklach et al. 1995) 44 C+O2=CO+O 5.80E+13 0 576 2 (Frenklach et al. 1995) 45 CH+H=C+H2 1.10E+14 0 0 2 (Frenklach et al. 1995) 46 CH+O=CO+H 5.70E+13 0 0 3 (Frenklach et al. 1995) 246 47 CH+OH=HCO+H 3.00E+13 0 0 2 (Frenklach et al. 1995) 48 CH+H2=CH2+H 1.11E+08 1.8 1670 3 (Frenklach et al. 1995) 49 CH+H2O=CH2O+H 5.71E+12 0 -755 10 (Frenklach et al. 1995) 50 CH+O2=HCO+O 3.30E+13 0 0 10 (Frenklach et al. 1995) 51 CH+CO(+M)=HCCO(+M) 5.00E+13 0 0 2 (Frenklach et al. 1995) LOW-P LIMIT 2.69E+28 -3.74 1936 TROE /0.5757 237 1652 5069/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 52 CH+CO2=HCO+CO 3.40E+12 0 690 1.3 Fitted to experiments 53 HCO+H(+M)=CH2O(+M) 1.09E+12 0.5 -260 1.3 (Frenklach et al. 1995) LOW-P LIMIT 1.35E+24 -2.57 1425 TROE /0.7824 271 2755 6570/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 54 CH2+H(+M)=CH3(+M) 2.50E+16 -0.8 0 1.7 (Frenklach et al. 1995) LOW-P LIMIT 3.20E+27 -3.14 1230 TROE /0.68 78 1995 5590/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 55 CH2+O=HCO+H 8.00E+13 0 0 3 (Frenklach et al. 1995) 56 CH2+OH=CH2O+H 2.00E+13 0 0 3 (Frenklach et al. 1995) 57 CH2+OH=CH+H2O 1.13E+07 2 3000 3 (Frenklach et al. 1995) 58 CH2+H2=H+CH3 5.00E+05 2 7230 3 Fitted to experiments 59 CH2+O2=HCO+OH 1.06E+13 0 1500 2 (Wang and Frenklach 1997) 60 CH2+O2=CO2+H+H 2.64E+12 0 1500 2 (Wang and Frenklach 1997) 61 CH2+HO2=CH2O+OH 2.00E+13 0 0 5 (Frenklach et al. 1995) 62 CH2+C=C2H+H 5.00E+13 0 0 5 (Frenklach et al. 1995) 63 CH2+CO(+M)=CH2CO(+M) 8.10E+11 0.5 4510 2 (Frenklach et al. 1995) LOW-P LIMIT 2.69E+33 -5.11 7095 TROE /0.5907 275 1226 5185/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 64 CH2+CH=C2H2+H 4.00E+13 0 0 2 (Frenklach et al. 1995) 65 CH2+CH2=C2H2+H2 3.20E+13 0 0 5 (Frenklach et al. 1995) 66 CH2*+N2=CH2+N2 1.50E+13 0 600 1.3 (Frenklach et al. 1995) 67 CH2*+AR=CH2+AR 9.00E+12 0 600 1.3 (Frenklach et al. 1995) 68 CH2*+H=CH+H2 3.00E+13 0 0 1.5 (Frenklach et al. 1995) 69 CH2*+O=CO+H2 1.50E+13 0 0 1.5 (Frenklach et al. 1995) 70 CH2*+O=HCO+H 1.50E+13 0 0 1.5 (Frenklach et al. 1995) 71 CH2*+OH=CH2O+H 3.00E+13 0 0 1.5 (Frenklach et al. 1995) 72 CH2*+H2=CH3+H 7.00E+13 0 0 2 (Frenklach et al. 1995) 247 73 CH2*+O2=H+OH+CO 2.80E+13 0 0 2 (Frenklach et al. 1995) 74 CH2*+O2=CO+H2O 1.20E+13 0 0 2 (Frenklach et al. 1995) 75 CH2*+H2O(+M)=CH3OH(+M) 2.00E+13 0 0 2 (Frenklach et al. 1995) LOW-P LIMIT 2.70E+38 -6.3 3100 TROE /0.1507 134 2383 7265/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ 76 CH2*+H2O=CH2+H2O 3.00E+13 0 0 2 (Frenklach et al. 1995) 77 CH2*+CO=CH2+CO 9.00E+12 0 0 2 (Frenklach et al. 1995) 78 CH2*+CO2=CH2+CO2 7.00E+12 0 0 2 (Frenklach et al. 1995) 79 CH2*+CO2=CH2O+CO 1.40E+13 0 0 2 (Frenklach et al. 1995) 80 CH2O+H(+M)=CH2OH(+M) 5.40E+11 0.5 3600 5 (Smith et al. 2000) LOW-P LIMIT 1.27E+32 -4.82 6530 TROE /0.7187 103 1291 4160/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ 81 CH2O+H(+M)=CH3O(+M) 5.40E+11 0.5 2600 2 (Smith et al. 2000) LOW-P LIMIT 2.20E+30 -4.8 5560 TROE /0.758 94 1555 4200/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ 82 CH2O+H=HCO+H2 2.30E+10 1.1 3275 3 (Smith et al. 2000) 83 CH2O+O=HCO+OH 3.90E+13 0 3540 2 (Frenklach et al. 1995) 84 CH2O+OH=HCO+H2O 3.43E+09 1.2 -447 1.5 (Vasudevan et al. 2005a) 85 CH2O+O2=HCO+HO2 1.00E+14 0 40000 3 (Frenklach et al. 1995) 86 CH2O+HO2=HCO+H2O2 1.00E+12 0 8000 2 (Eiteneer et al. 1998) 87 CH2O+CH=CH2CO+H 9.46E+13 0 -515 10 (Frenklach et al. 1995) 88 CH3+H(+M)=CH4(+M) 1.27E+16 -0.6 383 2 (Frenklach et al. 1995) LOW-P LIMIT 2.48E+33 -4.76 2440 TROE /0.783 74 2941 6964/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 89 CH3+O=CH2O+H 8.43E+13 0 0 2 (Frenklach et al. 1995) 90 CH3+OH(+M)=CH3OH(+M) 6.30E+13 0 0 5 (Frenklach et al. 1995) LOW-P LIMIT 2.70E+38 -6.3 3100 TROE /0.2105 83.5 5398 8370/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ 91 CH3+OH=CH2+H2O 5.60E+07 1.6 5420 5 (Frenklach et al. 1995) 92 CH3+OH=CH2*+H2O 2.50E+13 0 0 5 (Frenklach et al. 1995) 93 CH3+O2=O+CH3O 3.08E+13 0 28800 3 (Frenklach et al. 1995) 94 CH3+O2=OH+CH2O 3.60E+10 0 8940 3 (Frenklach et al. 1995) 248 95 CH3+HO2=CH4+O2 1.00E+12 0 0 3 (Frenklach et al. 1995) 96 CH3+HO2=CH3O+OH 1.34E+13 0 0 3 (Frenklach et al. 1995) 97 CH3+H2O2=CH4+HO2 2.45E+04 2.5 5180 2 (Frenklach et al. 1995) 98 CH3+C=C2H2+H 5.00E+13 0 0 10 (Frenklach et al. 1995) 99 CH3+CH=C2H3+H 3.00E+13 0 0 10 (Frenklach et al. 1995) 100 CH3+HCO=CH4+CO 8.48E+12 0 0 3 (Frenklach et al. 1995) 101 CH3+CH2O=CH4+HCO 3.32E+03 2.8 5860 2 (Frenklach et al. 1995) 102 CH3+CH2=C2H4+H 4.00E+13 0 0 3 (Frenklach et al. 1995) 103 CH3+CH2*=C2H4+H 1.20E+13 0 -570 1.5 (Frenklach et al. 1995) 104 CH3+CH3(+M)=C2H6(+M) 2.12E+16 -1 620 2 (Frenklach et al. 1995) LOW-P LIMIT 1.77E+50 -9.67 6220 TROE /0.5325 151 1038 4970/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 105 CH3+CH3=H+C2H5 4.99E+12 0.1 10600 5 (Frenklach et al. 1995) 106 CH3+HCCO=C2H4+CO 5.00E+13 0 0 10 Estimated 107 CH3+C2H=C3H3+H 2.41E+13 0 0 3 (Tsang and Hampson 1986) 108 CH3O+H(+M)=CH3OH(+M) 5.00E+13 0 0 3 (Frenklach et al. 1995) LOW-P LIMIT 8.60E+28 -4 3025 TROE /0.8902 144 2838 45569/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ 109 CH3O+H=CH2OH+H 3.40E+06 1.6 0 3 (Frenklach et al. 1995) 110 CH3O+H=CH2O+H2 2.00E+13 0 0 3 (Frenklach et al. 1995) 111 CH3O+H=CH3+OH 3.20E+13 0 0 3 (Frenklach et al. 1995) 112 CH3O+H=CH2*+H2O 1.60E+13 0 0 3 (Frenklach et al. 1995) 113 CH3O+O=CH2O+OH 1.00E+13 0 0 5 (Frenklach et al. 1995) 114 CH3O+OH=CH2O+H2O 5.00E+12 0 0 5 (Frenklach et al. 1995) 115 CH3O+O2=CH2O+HO2 4.28E-13 7.6 -3530 2 (Frenklach et al. 1995) 116 CH2OH+H(+M)=CH3OH(+M) 1.80E+13 0 0 3 (Frenklach et al. 1995) LOW-P LIMIT 3.00E+31 -4.8 3300 TROE /0.7679 338 1812 5081/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ 117 CH2OH+H=CH2O+H2 2.00E+13 0 0 3 (Frenklach et al. 1995) 118 CH2OH+H=CH3+OH 1.20E+13 0 0 3 (Frenklach et al. 1995) 119 CH2OH+H=CH2*+H2O 6.00E+12 0 0 3 (Frenklach et al. 1995) 120 CH2OH+O=CH2O+OH 1.00E+13 0 0 3 (Frenklach et al. 1995) 121 CH2OH+OH=CH2O+H2O 5.00E+12 0 0 5 (Frenklach et al. 1995) 122 CH2OH+O2=CH2O+HO2 1.80E+13 0 900 3 (Frenklach et al. 1995) 123 CH4+H=CH3+H2 6.60E+08 1.6 10840 2 (Frenklach et al. 1995) 249 124 CH4+O=CH3+OH 1.02E+09 1.5 8600 1.5 (Frenklach et al. 1995) 125 CH4+OH=CH3+H2O 1.00E+08 1.6 3120 1.5 (Frenklach et al. 1995) 126 CH4+CH=C2H4+H 6.00E+13 0 0 10 (Frenklach et al. 1995) 127 CH4+CH2=CH3+CH3 2.46E+06 2 8270 5 (Frenklach et al. 1995) 128 CH4+CH2*=CH3+CH3 1.60E+13 0 -570 5 (Frenklach et al. 1995) 129 CH4+C2H=C2H2+CH3 1.81E+12 0 500 5 (Tsang and Hampson 1986) 130 CH3OH+H=CH2OH+H2 1.70E+07 2.1 4870 3 (Frenklach et al. 1995) 131 CH3OH+H=CH3O+H2 4.20E+06 2.1 4870 10 (Frenklach et al. 1995) 132 CH3OH+O=CH2OH+OH 3.88E+05 2.5 3100 3 (Frenklach et al. 1995) 133 CH3OH+O=CH3O+OH 1.30E+05 2.5 5000 5 (Frenklach et al. 1995) 134 CH3OH+OH=CH2OH+H2O 1.44E+06 2 -840 5 (Frenklach et al. 1995) 135 CH3OH+OH=CH3O+H2O 6.30E+06 2 1500 5 (Frenklach et al. 1995) 136 CH3OH+CH3=CH2OH+CH4 3.00E+07 1.5 9940 3 (Frenklach et al. 1995) 137 CH3OH+CH3=CH3O+CH4 1.00E+07 1.5 9940 2 (Frenklach et al. 1995) 138 C2H+H(+M)=C2H2(+M) 1.00E+17 -1 0 3 (Frenklach et al. 1995) LOW-P LIMIT 3.75E+33 -4.8 1900 TROE /0.6464 132 1315 5566/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 139 C2H+O=CH+CO 5.00E+13 0 0 3 (Frenklach et al. 1995) 140 C2H+OH=H+HCCO 2.00E+13 0 0 5 (Frenklach et al. 1995) 141 C2H+O2=HCO+CO 5.00E+13 0 1500 3 (Frenklach et al. 1995) 142 C2H+H2=H+C2H2 4.90E+05 2.5 560 1.3 (Frenklach et al. 1995) 143 C2O+H=CH+CO 5.00E+13 0 0 3 (Miller and Melius 1992) 144 C2O+O=CO+CO 5.00E+13 0 0 2 (Miller and Melius 1992) 145 C2O+OH=CO+CO+H 2.00E+13 0 0 3 (Miller and Melius 1992) 146 C2O+O2=CO+CO+O 2.00E+13 0 0 3 (Miller and Melius 1992) 147 HCCO+H=CH2*+CO 1.00E+14 0 0 2 (Frenklach et al. 1995) 148 HCCO+O=H+CO+CO 1.00E+14 0 0 2 (Frenklach et al. 1995) 149 HCCO+O2=OH+2CO 1.60E+12 0 854 5 (Carl et al. 2001) 150 HCCO+CH=C2H2+CO 5.00E+13 0 0 5 (Frenklach et al. 1995) 151 HCCO+CH2=C2H3+CO 3.00E+13 0 0 5 (Frenklach et al. 1995) 152 HCCO+HCCO=C2H2+CO+CO 1.00E+13 0 0 5 (Frenklach et al. 1995) 153 HCCO+OH=C2O+H2O 3.00E+13 0 0 3 (Miller and Melius 1992) 154 C2H2(+M)=H2CC(+M) 8.00E+14 -0.5 50750 2 (Laskin and Wang 1999) LOW-P LIMIT 2.45E+15 -0.64 49700 H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/C2H6/3.0/C2H2/2.5/ C2H4/2.5/ 155 C2H3(+M)=C2H2+H(+M) 3.86E+08 1.6 37048 1.5 (Knyazev and Slagle 1996) LOW-P LIMIT 2.57E+27 -3.4 35799 250 TROE /1.9816 5383.7 4.2932 -0.0795/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ C2H2/3.00/ C2H4/3.00/ 156 C2H2+O=C2H+OH 4.60E+19 -1.4 28950 5 (Frenklach et al. 1995) 157 C2H2+O=CH2+CO 4.08E+06 2 1900 1.5 (Smith et al. 2000) 158 C2H2+O=HCCO+H 1.63E+07 2 1900 1.5 (Smith et al. 2000) 159 C2H2+OH=CH2CO+H 2.18E-04 4.5 -1000 5 (Frenklach et al. 1995) 160 C2H2+OH=HCCOH+H 5.04E+05 2.3 13500 5 (Frenklach et al. 1995) 161 C2H2+OH=C2H+H2O 3.37E+07 2 14000 2 (Frenklach et al. 1995) 162 C2H2+OH=CH3+CO 4.83E-04 4 -2000 5 (Frenklach et al. 1995) 163 C2H2+HCO=C2H3+CO 1.00E+07 2 6000 10 Estimated 164 C2H2+CH2=C3H3+H 1.20E+13 0 6620 2 (Bohland et al. 1988; Frank et al. 1988) 165 C2H2+CH2*=C3H3+H 2.00E+13 0 0 2 (Wang and Frenklach 1997) 166 C2H2+C2H=C4H2+H 9.60E+13 0 0 3 (Shin and Michael 1991; Koshi et al. 1992; Farhat et al. 1993) 167 C2H2+C2H(+M)=nC4H3(+M) 8.30E+10 0.9 -363 2 (Wang 1992) LOW-P LIMIT 1.24E+31 -4.7181871 TROE /1 100 5613 13387/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/C2H6/3.0/C2H2/2.5/ C2H4/2.5/ 168 C2H2+C2H(+M)=iC4H3(+M) 8.30E+10 0.9 -363 2 (Wang 1992) LOW-P LIMIT 1.24E+31 -4.7181871 TROE /1 100 5613 13387/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ C2H2/2.5/ C2H4/2.5/ 169 C2H2+HCCO=C3H3+CO 1.00E+11 0 3000 5 (Homann and Wellmann 1983; Miller and Bowman 1989) 170 C2H2+CH3=pC3H4+H 2.56E+09 1.1 13644 2 (Davis et al. 1999b) 171 C2H2+CH3=aC3H4+H 5.14E+09 0.9 22153 2 (Davis et al. 1999b) 172 C2H2+CH3=CH3CCH2 4.99E+22 -4.4 18850 2 (Davis et al. 1999b) 173 C2H2+CH3=CH3CHCH 3.20E+35 -7.8 13300 2 (Davis et al. 1999b) 174 C2H2+CH3=aC3H5 2.68E+53 -12.8 35730 2 (Davis et al. 1999b) 175 H2CC+H=C2H2+H 1.00E+14 0 0 5 Estimated 176 H2CC+OH=CH2CO+H 2.00E+13 0 0 5 Estimated 177 H2CC+O2=HCO+HCO 1.00E+13 0 0 2 (Laskin and Wang 1999) 178 H2CC+C2H2(+M)=C4H4(+M) 3.50E+05 2.1 -2400 2 (Laskin and Wang 1999) LOW-P LIMIT 1.40E+60 -12.6 7417 TROE /0.98 56 580 4164/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ C2H2/3.0/ C2H4/3.0/ 179 H2CC+C2H4=C4H6 1.00E+12 0 0 5 Estimated 180 CH2CO+H(+M)=CH2CHO(+M) 3.30E+14 -0.1 8500 2 Calculated, RRKM 251 LOW-P LIMIT 3.80E+41 -7.64 11900 TROE /0.337 1707 3200 4131/ H2/2/ H2O/6/ CH4/2/ CO/1.5/ CO2/2/ C2H6/3/ AR/0.7/ C2H2/3.00/ C2H4/3.00/ 181 CH2CO+H=HCCO+H2 5.00E+13 0 8000 10 (Frenklach et al. 1995) 182 CH2CO+H=CH3+CO 1.50E+09 1.4 2690 3 (Joshi et al. 2005) 183 CH2CO+O=HCCO+OH 1.00E+13 0 8000 10 (Frenklach et al. 1995) 184 CH2CO+O=CH2+CO2 1.75E+12 0 1350 10 (Frenklach et al. 1995) 185 CH2CO+OH=HCCO+H2O 7.50E+12 0 2000 10 (Frenklach et al. 1995) 186 HCCOH+H=CH2CO+H 1.00E+13 0 0 10 (Frenklach et al. 1995) 187 C2H3+H(+M)=C2H4(+M) 6.08E+12 0.3 280 2 (Frenklach et al. 1995) LOW-P LIMIT 1.40E+30 -3.86 3320 TROE /0.782 207.5 2663 6095/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ C2H2/3.00/ C2H4/3.00/ 188 C2H3+H=C2H2+H2 9.00E+13 0 0 5 (Tsang and Hampson 1986) 189 C2H3+H=H2CC+H2 6.00E+13 0 0 5 Estimated 190 C2H3+O=CH2CO+H 4.80E+13 0 0 3 (Tsang and Hampson 1986) 191 C2H3+O=CH3+CO 4.80E+13 0 0 3 (Tsang and Hampson 1986) 192 C2H3+OH=C2H2+H2O 3.01E+13 0 0 3 (Tsang and Hampson 1986) 193 C2H3+O2=C2H2+HO2 1.34E+06 1.6 -383.4 3 (Mebel et al. 1996) 194 C2H3+O2=CH2CHO+O 3.00E+11 0.3 11 3 (Mebel et al. 1996) 195 C2H3+O2=HCO+CH2O 4.60E+16 -1.4 1010 3 (Mebel et al. 1996) 196 C2H3+HO2=CH2CHO+OH 1.00E+13 0 0 5 Estimated 197 C2H3+H2O2=C2H4+HO2 1.21E+10 0 -596 5 (Tsang and Hampson 1986) 198 C2H3+HCO=C2H4+CO 9.03E+13 0 0 3 (Tsang and Hampson 1986) 199 C2H3+HCO=C2H3CHO 1.80E+13 0 0 3 (Tsang and Hampson 1986) 200 C2H3+CH3=C2H2+CH4 3.92E+11 0 0 3 (Tsang and Hampson 1986) 201 C2H3+CH3(+M)=C3H6(+M) 2.50E+13 0 0 3 (Tsang and Hampson 1986) LOW-P LIMIT 4.27E+58 -11.949770 TROE /0.175 1340.6 60000 10140/ H2/2/ H2O/6/ CH4/2/ CO/1.5/ CO2/2/ C2H6/3/ AR/0.7/C2H2/3.0/ C2H4/3.0/ 202 C2H3+CH3=aC3H5+H 1.50E+24 -2.8 18618 3 (Tsang and Hampson 1986) 203 C2H3+C2H2=C4H4+H 2.00E+18 -1.7 10600 2 (Wang and Frenklach 1997) 204 C2H3+C2H2=nC4H5 9.30E+38 -8.8 12000 2 (Wang and Frenklach 1997) 205 C2H3+C2H2=iC4H5 1.60E+46 -11 18600 2 (Wang and Frenklach 1997) 206 C2H3+C2H3=C4H6 1.50E+42 -8.8 12483 2 (Wang and Frenklach 1997) 207 C2H3+C2H3=iC4H5+H 1.20E+22 -2.4 13654 2 (Wang and Frenklach 1997) 208 C2H3+C2H3=nC4H5+H 2.40E+20 -2 15361 2 (Wang and Frenklach 1997) 252 209 C2H3+C2H3=C2H2+C2H4 9.60E+11 0 0 5 (Westly et al.) 210 CH2CHO=CH3+CO 7.80E+41 -9.1 46900 2 Calculated, RRKM 211 CH2CHO+H(+M)=CH3CHO(+M) 1.00E+14 0 0 2 Calculated, RRKM LOW-P LIMIT 5.20E+39 -7.2974700 TROE /0.55 8900 4350 7244/ H2/2/ H2O/6/ CH4/2/ CO/1.5/ CO2/2/ C2H6/3/ C2H2/3.0/ C2H4/3.0/ 212 CH2CHO+H=CH3CO+H 5.00E+12 0 0 5 Estimated 213 CH2CHO+H=CH3+HCO 9.00E+13 0 0 5 Estimated 214 CH2CHO+H=CH2CO+H2 2.00E+13 0 4000 5 (Miller et al. 1982) 215 CH2CHO+O=CH2CO+OH 2.00E+13 0 4000 5 (Miller et al. 1982) 216 CH2CHO+OH=CH2CO+H2O 1.00E+13 0 2000 5 (Miller et al. 1982) 217 CH2CHO+O2=CH2CO+HO2 1.40E+11 0 0 2 (Baulch et al. 1992) 218 CH2CHO+O2=CH2O+CO+OH 1.80E+10 0 0 2 (Baulch et al. 1992) 219 CH3+CO(+M)=CH3CO(+M) 4.85E+07 1.6 6150 2 Calculated, RRKM LOW-P LIMIT 7.80E+30 -5.3958600 TROE /0.258 598 21002 1773/ H2/2/ H2O/6/ CH4/2/ CO/1.5/ CO2/2/ C2H6/3/ AR/0.7/ C2H2/3.00/ C2H4/3.00/ 220 CH3CO+H(+M)=CH3CHO(+M) 9.60E+13 0 0 3 (Tsang and Hampson 1986) LOW-P LIMIT 3.85E+44 -8.5695500 TROE /1 2900 2900 5132/ H2/2/ H2O/6/ CH4/2/ CO/1.5/ CO2/2/ C2H6/3/ C2H2/3.0/ C2H4/3.0/ 221 CH3CO+H=CH3+HCO 9.60E+13 0 0 3 (Tsang and Hampson 1986) 222 CH3CO+O=CH2CO+OH 3.90E+13 0 0 5 (Baulch et al. 1992) 223 CH3CO+O=CH3+CO2 1.50E+14 0 0 5 (Tsang and Hampson 1986) 224 CH3CO+OH=CH2CO+H2O 1.20E+13 0 0 3 (Tsang and Hampson 1986) 225 CH3CO+OH=CH3+CO+OH 3.00E+13 0 0 3 (Tsang and Hampson 1986) 226 CH3CO+HO2=CH3+CO2+OH 3.00E+13 0 0 3 (Tsang and Hampson 1986) 227 CH3CO+H2O2=CH3CHO+HO2 1.80E+11 0 8226 3 (Tsang and Hampson 1986) 228 CH3+HCO(+M)=CH3CHO(+M) 1.80E+13 0 0 2 Calculated, RRKM LOW-P LIMIT 2.20E+48 -9.5885100 TROE /0.6173 13.076 2078 5093/ H2/2/ H2O/6/ CH4/2/ CO/1.5/ CO2/2/ C2H6/3/ C2H2/3.0/ C2H4/3.0/ 229 CH3CHO+H=CH3CO+H2 4.10E+09 1.2 2400 3 (Baulch et al. 1992) 230 CH3CHO+H=CH4+HCO 5.00E+10 0 0 3 (Lambert et al. 1967) 231 CH3CHO+O=CH3CO+OH 5.80E+12 0 1800 2 (Baulch et al. 1992) 232 CH3CHO+OH=CH3CO+H2O 2.35E+10 0.7 -1110 2 (Baulch et al. 1992) 233 CH3CHO+CH3=CH3CO+CH4 2.00E-06 5.6 2460 2 (Baulch et al. 1992) 234 CH3CHO+HCO=CO+HCO+CH4 8.00E+12 0 10400 10 (Westly et al.) 253 235 CH3CHO+O2=CH3CO+HO2 3.00E+13 0 39100 10 (Baulch et al. 1992) 236 CH2OCH2=CH3+HCO 3.63E+13 0 57200 2 (Joshi et al. 2005) 237 CH2OCH2=CH3CHO 7.26E+13 0 57200 2 (Joshi et al. 2005) 238 CH2OCH2=CH4+CO 1.21E+13 0 57200 2 (Joshi et al. 2005) 239 CH2OCH2+H=CH2OCH+H2 2.00E+13 0 8300 2 (Joshi et al. 2005) 240 CH2OCH2+H=C2H3+H2O 5.00E+09 0 5000 2 (Lifshitz and Benhamou 1983) 241 CH2OCH2+H=C2H4+OH 9.51E+10 0 5000 2 (Lifshitz and Benhamou 1983) 242 CH2OCH2+O=CH2OCH+OH 1.91E+12 0 5250 2 (Bogan and Hand 1978) 243 CH2OCH2+OH=CH2OCH+H2O 1.78E+13 0 3610 2 (Baldwin et al. 1984) 244 CH2OCH2+CH3=CH2OCH+CH4 1.07E+12 0 11830 2 (Baldwin et al. 1984) 245 CH2OCH+M=CH3+CO+M 3.16E+14 0 12000 2 (Joshi et al. 2005) 246 CH2OCH+M=CH2CHO+M 5.00E+09 0 0 2 (Joshi et al. 2005) 247 CH2OCH+M=CH2CO+H+M 3.00E+13 0 8000 2 (Joshi et al. 2005) 248 C2H4(+M)=H2+H2CC(+M) 8.00E+12 0.4 88770 2 (Frenklach et al. 1995) LOW-P LIMIT 7.00E+50 -9.31 99860 TROE /0.7345 180 1035 5417/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 249 C2H4+H(+M)=C2H5(+M) 1.37E+09 1.5 1355 2 (Miller and Klippenstein 2004) LOW-P LIMIT 2.03E+39 -6.6425769 TROE /-0.569 299 9147 -152.4/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 250 C2H4+H=C2H3+H2 5.07E+07 1.9 12950 2 (Knyazev et al. 1996) 251 C2H4+O=C2H3+OH 1.51E+07 1.9 3740 2 (Mahmud et al. 1987) 252 C2H4+O=CH3+HCO 1.92E+07 1.8 220 2 (Mahmud et al. 1987) 253 C2H4+O=CH2+CH2O 3.84E+05 1.8 220 2 (Mahmud et al. 1987) 254 C2H4+OH=C2H3+H2O 3.60E+06 2 2500 2 (Tully 1988) 255 C2H4+HCO=C2H5+CO 1.00E+07 2 8000 5 Estimated 256 C2H4+CH=aC3H4+H 3.00E+13 0 0 5 Estimated 257 C2H4+CH=pC3H4+H 3.00E+13 0 0 5 Estimated 258 C2H4+CH2=aC3H5+H 2.00E+13 0 6000 5 Estimated 259 C2H4+CH2*=H2CC+CH4 5.00E+13 0 0 5 Estimated 260 C2H4+CH2*=aC3H5+H 5.00E+13 0 0 5 Estimated 261 C2H4+CH3=C2H3+CH4 2.27E+05 2 9200 5 (Frenklach et al. 1995) 262 C2H4+CH3=nC3H7 3.30E+11 0 7700 1.3 (Tsang and Hampson 1986) 263 C2H4+C2H=C4H4+H 1.20E+13 0 0 3 (Tsang and Hampson 1986) 264 C2H4+O2=C2H3+HO2 4.22E+13 0 60800 5 (Tsang and Hampson 1986) 265 C2H4+C2H3=C4H7 7.93E+38 -8.5 14220 2 (Wang and Frenklach 1997) 266 C2H4+HO2=CH2OCH2+OH 2.82E+12 0 17100 1.7 (Baulch et al. 1992) 254 267 C2H5+H(+M)=C2H6(+M) 5.21E+17 -1 1580 2 (Frenklach et al. 1995) LOW-P LIMIT 1.99E+41 -7.08 6685 TROE /0.8422 125 2219 6882/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 268 C2H5+H=C2H4+H2 2.00E+12 0 0 3 (Frenklach et al. 1995) 269 C2H5+O=CH3+CH2O 1.60E+13 0 0 2 (Tsang and Hampson 1986) 270 C2H5+O=CH3CHO+H 8.02E+13 0 0 2 (Tsang and Hampson 1986) 271 C2H5+O2=C2H4+HO2 2.00E+10 0 0 5 (Bozzelli and Dean 1990) 272 C2H5+HO2=C2H6+O2 3.00E+11 0 0 2 (Tsang and Hampson 1986) 273 C2H5+HO2=C2H4+H2O2 3.00E+11 0 0 2 (Tsang and Hampson 1986) 274 C2H5+HO2=CH3+CH2O+OH 2.40E+13 0 0 2 (Tsang and Hampson 1986) 275 C2H5+H2O2=C2H6+HO2 8.70E+09 0 974 5 (Tsang and Hampson 1986) 276 C2H5+CH3(+M)=C3H8(+M) 4.90E+14 -0.5 0 3 (Tsang 1988) LOW-P LIMIT 6.80E+61 -13.426000 TROE /1 1000 1433.9 5328.8/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 277 C2H5+C2H3(+M)=C4H81(+M) 1.50E+13 0 0 3 (Tsang and Hampson 1986) LOW-P LIMIT 1.55E+56 -11.798985 TROE /0.198 2277.9 60000 5723.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 278 C2H5+C2H3=aC3H5+CH3 3.90E+32 -5.2 19747 3 (Tsang and Hampson 1986) 279 C2H6+H=C2H5+H2 1.15E+08 1.9 7530 2 (Frenklach et al. 1995) 280 C2H6+O=C2H5+OH 8.98E+07 1.9 5690 2 (Frenklach et al. 1995) 281 C2H6+OH=C2H5+H2O 3.54E+06 2.1 870 1.5 (Frenklach et al. 1995) 282 C2H6+CH2*=C2H5+CH3 4.00E+13 0 -550 3 (Frenklach et al. 1995) 283 C2H6+CH3=C2H5+CH4 6.14E+06 1.7 10450 1.5 (Frenklach et al. 1995) 284 C3H3+H=pC3H4 1.50E+13 0 0 10 (Davis et al. 1999b) 285 C3H3+H=aC3H4 2.50E+12 0 0 10 (Davis et al. 1999b) 286 C3H3+O=CH2O+C2H 2.00E+13 0 0 3 (Miller and Bowman 1989) 287 C3H3+O2=CH2CO+HCO 3.00E+10 0 2868 2 (Slagle and Gutman 1988) 288 C3H3+HO2=OH+CO+C2H3 8.00E+11 0 0 10 (Davis et al. 1999a) 289 C3H3+HO2=aC3H4+O2 3.00E+11 0 0 3 (Davis et al. 1999a) 290 C3H3+HO2=pC3H4+O2 2.50E+12 0 0 3 (Davis et al. 1999a) 291 C3H3+HCO=aC3H4+CO 2.50E+13 0 0 10 (Davis et al. 1999a) 292 C3H3+HCO=pC3H4+CO 2.50E+13 0 0 10 (Davis et al. 1999a) 293 C3H3+HCCO=C4H4+CO 2.50E+13 0 0 10 (Davis et al. 1999a) 294 C3H3+CH=iC4H3+H 5.00E+13 0 0 5 (Davis et al. 1999a) 295 C3H3+CH2=C4H4+H 5.00E+13 0 0 3 (Miller and Melius 1992) 255 296 C3H3+CH3(+M)=C4H612(+M) 1.50E+12 0 0 2 (Wang and Frenklach 1997) LOW-P LIMIT 2.60E+57 -11.949770 TROE /0.175 1340.6 60000 9769.8/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 297 C3H3+C2H2=C5H5 6.87E+55 -12.5 42025 3 (Moskaleva and Lin 2000) 298 C3H3+C3H3=>C6H5+H 5.00E+12 0 0 3 (Wang and Frenklach 1997) 299 C3H3+C3H3=>C6H6 2.00E+12 0 0 3 300 C3H3+C4H4=C6H5CH2 6.53E+05 1.3 -4611 2 (Jones et al. 1997) 301 C3H3+C4H6=C6H5CH3+H 6.53E+05 1.3 -4611 3 Estimated 302 aC3H4+H=C3H3+H2 1.30E+06 2 5500 2 (Davis et al. 1999b) 303 aC3H4+H=CH3CHCH 5.40E+29 -6.1 16300 2 (Davis et al. 1999b) 304 aC3H4+H=CH3CCH2 9.46E+42 -9.4 11190 2 (Davis et al. 1999b) 305 aC3H4+H=aC3H5 1.52E+59 -13.5 26949 2 (Davis et al. 1999b) 306 aC3H4+O=C2H4+CO 2.00E+07 1.8 1000 2 (Davis et al. 1998) 307 aC3H4+OH=C3H3+H2O 5.30E+06 2 2000 2 (Wang and Frenklach 1997) 308 aC3H4+CH3=C3H3+CH4 1.30E+12 0 7700 2 (Wu and Kern 1987) 309 aC3H4+CH3=iC4H7 2.00E+11 0 7500 2 (Davis et al. 1999b) 310 aC3H4+C2H=C2H2+C3H3 1.00E+13 0 0 2 (Wang and Frenklach 1997) 311 pC3H4=cC3H4 1.20E+44 -9.9 69250 2 (Davis et al. 1999b) 312 pC3H4=aC3H4 5.15E+60 -13.9 91117 2 (Davis et al. 1999b) 313 pC3H4+H=aC3H4+H 6.27E+17 -0.9 10079 2 (Davis et al. 1999b) 314 pC3H4+H=CH3CCH2 1.66E+47 -10.6 13690 2 (Davis et al. 1999b) 315 pC3H4+H=CH3CHCH 5.50E+28 -5.7 4300 2 (Davis et al. 1999b) 316 pC3H4+H=aC3H5 4.91E+60 -14.4 31644 2 (Davis et al. 1999b) 317 pC3H4+H=C3H3+H2 1.30E+06 2 5500 2 (Wang and Frenklach 1997) 318 pC3H4+C3H3=aC3H4+C3H3 6.14E+06 1.7 10450 5 Estimated 319 pC3H4+O=HCCO+CH3 7.30E+12 0 2250 2 (Adusei et al. 1996) 320 pC3H4+O=C2H4+CO 1.00E+13 0 2250 2 (Adusei et al. 1996) 321 pC3H4+OH=C3H3+H2O 1.00E+06 2 100 2 (Davis et al. 1998) 322 pC3H4+C2H=C2H2+C3H3 1.00E+13 0 0 5 Estimated 323 pC3H4+CH3=C3H3+CH4 1.80E+12 0 7700 2 (Wu and Kern 1987) 324 cC3H4=aC3H4 4.89E+41 -9.2 49594 2 (Davis et al. 1999b) 325 aC3H5+H(+M)=C3H6(+M) 2.00E+14 0 0 3 (Tsang 1991) LOW-P LIMIT 1.33E+60 -12 5968 TROE /0.02 1096.6 1096.6 6859.5/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 326 aC3H5+H=aC3H4+H2 1.80E+13 0 0 3 (Tsang 1991) 327 aC3H5+O=C2H3CHO+H 6.00E+13 0 0 2.5(Tsang 1991) 256 328 aC3H5+OH=C2H3CHO+H+H 4.20E+32 -5.2 30126 2 (Tsang 1991) 329 aC3H5+OH=aC3H4+H2O 6.00E+12 0 0 2 (Tsang 1991) 330 aC3H5+O2=aC3H4+HO2 4.99E+15 -1.4 22428 2 (Bozzelli and Dean 1993) 331 aC3H5+O2=CH3CO+CH2O 1.19E+15 -1 20128 2 (Bozzelli and Dean 1993) 332 aC3H5+O2=C2H3CHO+OH 1.82E+13 -0.4 22859 2 (Bozzelli and Dean 1993) 333 aC3H5+HO2=C3H6+O2 2.66E+12 0 0 3 (Baulch et al. 1992) 334 aC3H5+HO2=OH+C2H3+CH2O 6.60E+12 0 0 3 (Baulch et al. 1992) 335 aC3H5+HCO=C3H6+CO 6.00E+13 0 0 5 (Tsang 1991) 336 aC3H5+CH3(+M)=C4H81(+M) 1.00E+14 -0.3 -262.31.5(Tsang 1991) LOW-P LIMIT 3.91E+60 -12.816250 TROE /0.104 1606 60000 6118.4/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 337 aC3H5+CH3=aC3H4+CH4 3.00E+12 -0.3 -131 3 (Tsang 1991) 338 aC3H5=CH3CCH2 7.06E+56 -14.1 75868 2 (Davis et al. 1999b) 339 aC3H5=CH3CHCH 5.00E+51 -13 73300 2 (Davis et al. 1999b) 340 aC3H5+C2H2=lC5H7 8.38E+30 -6.2 12824 3 (Dean 1990) 341 CH3CCH2=CH3CHCH 1.50E+48 -12.7 53900 2 (Davis et al. 1999b) 342 CH3CCH2+H=pC3H4+H2 3.34E+12 0 0 2 (Davis et al. 1999b) 343 CH3CCH2+O=CH3+CH2CO 6.00E+13 0 0 5 Estimated 344 CH3CCH2+OH=CH3+CH2CO+H 5.00E+12 0 0 5 Estimated 345 CH3CCH2+O2=CH3CO+CH2O 1.00E+11 0 0 2 (Davis et al. 1999b) 346 CH3CCH2+HO2=CH3+CH2CO+OH 2.00E+13 0 0 5 Estimated 347 CH3CCH2+HCO=C3H6+CO 9.00E+13 0 0 5 Estimated 348 CH3CCH2+CH3=pC3H4+CH4 1.00E+11 0 0 3 (Davis et al. 1999b) 349 CH3CCH2+CH3=iC4H8 2.00E+13 0 0 5 (Davis et al. 1999b) 350 CH3CHCH+H=pC3H4+H2 3.34E+12 0 0 3 Estimated 351 CH3CHCH+O=C2H4+HCO 6.00E+13 0 0 5 Estimated 352 CH3CHCH+OH=C2H4+HCO+H 5.00E+12 0 0 5 Estimated 353 CH3CHCH+O2=CH3CHO+HCO 1.00E+11 0 0 3 Estimated 354 CH3CHCH+HO2=C2H4+HCO+OH 2.00E+13 0 0 5 Estimated 355 CH3CHCH+HCO=C3H6+CO 9.00E+13 0 0 5 Estimated 356 CH3CHCH+CH3=pC3H4+CH4 1.00E+11 0 0 5 Estimated 357 C3H6+H(+M)=nC3H7(+M) 1.33E+13 0 3261 1.5(Tsang 1991) LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 358 C3H6+H(+M)=iC3H7(+M) 1.33E+13 0 1560 2 (Tsang 1991) LOW-P LIMIT 8.70E+42 -7.5 4722 257 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 359 C3H6+H=C2H4+CH3 8.00E+21 -2.4 11180 2 (Tsang 1991) 360 C3H6+H=aC3H5+H2 1.73E+05 2.5 2490 2 (Tsang 1991) 361 C3H6+H=CH3CCH2+H2 4.00E+05 2.5 9790 2 (Tsang 1991) 362 C3H6+H=CH3CHCH+H2 8.04E+05 2.5 12283 2 (Tsang 1991) 363 C3H6+O=CH2CO+CH3+H 8.00E+07 1.6 327 1.3(Tsang 1991) 364 C3H6+O=C2H3CHO+H+H 4.00E+07 1.6 327 1.3(Tsang 1991) 365 C3H6+O=C2H5+HCO 3.50E+07 1.6 -972 1.3(Tsang 1991) 366 C3H6+O=aC3H5+OH 1.80E+11 0.7 5880 3 (Tsang 1991) 367 C3H6+O=CH3CCH2+OH 6.00E+10 0.7 7630 3 (Tsang 1991) 368 C3H6+O=CH3CHCH+OH 1.21E+11 0.7 8960 3 (Tsang 1991) 369 C3H6+OH=aC3H5+H2O 3.10E+06 2 -298 2 (Tsang 1991) 370 C3H6+OH=CH3CCH2+H2O 1.10E+06 2 1450 2 (Tsang 1991) 371 C3H6+OH=CH3CHCH+H2O 2.14E+06 2 2778 2 (Tsang 1991) 372 C3H6+HO2=aC3H5+H2O2 9.60E+03 2.6 13910 10 (Tsang 1991) 373 C3H6+CH3=aC3H5+CH4 2.20E+00 3.5 5675 1.4(Tsang 1991) 374 C3H6+CH3=CH3CCH2+CH4 8.40E-01 3.5 11660 10 (Tsang 1991) 375 C3H6+CH3=CH3CHCH+CH4 1.35E+00 3.5 12848 10 (Tsang 1991) 376 C3H6+C2H3=C4H6+CH3 7.23E+11 0 5000 3 (Tsang 1991) 377 C3H6+HO2=CH3CHOCH2+OH 1.09E+12 0 14200 2 (Baldwin et al. 1985) 378 C2H3CHO+H=C2H4+HCO 1.08E+11 0.5 5820 3 Estimated 379 C2H3CHO+O=C2H3+OH+CO 3.00E+13 0 3540 3 Estimated 380 C2H3CHO+O=CH2O+CH2CO 1.90E+07 1.8 220 3 Estimated 381 C2H3CHO+OH=C2H3+H2O+CO 3.43E+09 1.2 -447 3 Estimated 382 C2H3CHO+CH3=CH2CHCO+CH4 2.00E+13 0 11000 5 Estimated 383 C2H3CHO+C2H3=C4H6+HCO 2.80E+21 -2.4 14720 3 Estimated 384 CH2CHCO=C2H3+CO 1.00E+14 0 27000 10 Estimated 385 CH2CHCO+H=C2H3CHO 1.00E+14 0 0 5 Estimated 386 CH3CHOCH2=CH3CH2CHO 1.84E+14 0 58500 3 (Flowers 1977) 387 CH3CHOCH2=C2H5+HCO 2.45E+13 0 58500 2 (Lifshitz and Tamburu 1994) 388 CH3CHOCH2=CH3+CH2CHO 2.45E+13 0 58800 2 (Lifshitz and Tamburu 1994) 389 CH3CHOCH2=CH3COCH3 1.01E+14 0 59900 3 (Flowers 1977) 390 CH3CHOCH2=CH3+CH3CO 4.54E+13 0 59900 2 (Lifshitz and Tamburu 1994) 391 iC3H7+H(+M)=C3H8(+M) 2.40E+13 0 0 2 (Tsang 1988) LOW-P LIMIT 1.70E+58 -12.0811264 TROE /0.649 1213.1 1213.1 13370/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 258 392 iC3H7+H=CH3+C2H5 1.40E+28 -3.9 15916 2 (Tsang 1988) 393 iC3H7+H=C3H6+H2 3.20E+12 0 0 2 (Tsang 1988) 394 iC3H7+O=CH3CHO+CH3 9.60E+13 0 0 2 (Tsang 1988) 395 iC3H7+OH=C3H6+H2O 2.40E+13 0 0 3 (Tsang 1988) 396 iC3H7+O2=C3H6+HO2 1.30E+11 0 0 3 (Tsang 1988) 397 iC3H7+HO2=CH3CHO+CH3+OH 2.40E+13 0 0 2 (Tsang 1988) 398 iC3H7+HCO=C3H8+CO 1.20E+14 0 0 3 (Tsang 1988) 399 iC3H7+CH3=CH4+C3H6 2.20E+14 -0.7 0 1.5(Tsang 1988) 400 nC3H7+H(+M)=C3H8(+M) 3.60E+13 0 0 2 (Tsang 1988) LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 401 nC3H7+H=C2H5+CH3 3.70E+24 -2.9 12505 2 (Tsang 1988) 402 nC3H7+H=C3H6+H2 1.80E+12 0 0 2 (Tsang 1988) 403 nC3H7+O=C2H5+CH2O 9.60E+13 0 0 2 (Tsang 1988) 404 nC3H7+OH=C3H6+H2O 2.40E+13 0 0 3 (Tsang 1988) 405 nC3H7+O2=C3H6+HO2 9.00E+10 0 0 3 (Tsang 1988) 406 nC3H7+HO2=C2H5+OH+CH2O 2.40E+13 0 0 2 (Tsang 1988) 407 nC3H7+HCO=C3H8+CO 6.00E+13 0 0 5 (Tsang 1988) 408 nC3H7+CH3=CH4+C3H6 1.10E+13 0 0 1.7(Tsang 1988) 409 C3H8+H=H2+nC3H7 1.30E+06 2.5 6756 3 (Tsang 1988) 410 C3H8+H=H2+iC3H7 1.30E+06 2.4 4471 3 (Tsang 1988) 411 C3H8+O=nC3H7+OH 1.90E+05 2.7 3716 2 (Tsang 1988) 412 C3H8+O=iC3H7+OH 4.76E+04 2.7 2106 2 (Tsang 1988) 413 C3H8+OH=nC3H7+H2O 1.40E+03 2.7 527 1.5(Tsang 1988) 414 C3H8+OH=iC3H7+H2O 2.70E+04 2.4 393 1.5(Tsang 1988) 415 C3H8+O2=nC3H7+HO2 4.00E+13 0 50930 10 (Tsang 1988) 416 C3H8+O2=iC3H7+HO2 4.00E+13 0 47590 10 (Tsang 1988) 417 C3H8+HO2=nC3H7+H2O2 4.76E+04 2.5 16490 10 (Tsang 1988) 418 C3H8+HO2=iC3H7+H2O2 9.64E+03 2.6 13910 10 (Tsang 1988) 419 C3H8+CH3=CH4+nC3H7 9.03E-01 3.6 7153 1.5 (Tsang 1988) 420 C3H8+CH3=CH4+iC3H7 1.51E+00 3.5 5480 1.5 (Tsang 1988) 421 C4H2+H=nC4H3 1.10E+42 -8.7 15300 2 (Wang and Frenklach 1997) 422 C4H2+H=iC4H3 1.10E+30 -4.9 10800 2 (Wang and Frenklach 1997) 423 C4H2+OH=H2C4O+H 6.60E+12 0 -410 3 (Perry 1984) 424 C4H2+C2H=C6H2+H 9.60E+13 0 0 5 Estimated 425 C4H2+C2H=C6H3 4.50E+37 -7.7 7100 2 (Wang and Frenklach 1997) 426 H2C4O+H=C2H2+HCCO 5.00E+13 0 3000 2 (Miller and Melius 1992) 427 H2C4O+OH=CH2CO+HCCO 1.00E+07 2 2000 2 (Miller and Melius 1992) 259 428 nC4H3=iC4H3 4.10E+43 -9.5 53000 2 (Wang 1992) 429 nC4H3+H=iC4H3+H 2.50E+20 -1.7 10800 2 (Wang 1992); 430 nC4H3+H=C2H2+H2CC 6.30E+25 -3.3 10014 2 (Wang 1992); 431 nC4H3+H=C4H4 2.00E+47 -10.3 13070 2 (Wang 1992); 432 nC4H3+H=C4H2+H2 3.00E+13 0 0 10 Estimated 433 nC4H3+OH=C4H2+H2O 2.00E+12 0 0 10 Estimated 434 nC4H3+C2H2=l-C6H4+H 2.50E+14 -0.6 10600 2 (Wang and Frenklach 1997) 435 nC4H3+C2H2=C6H5 9.60E+70 -17.8 31300 2 (Wang and Frenklach 1997) 436 nC4H3+C2H2=o-C6H4+H 6.90E+46 -10 30100 2 (Wang and Frenklach 1997) 437 iC4H3+H=C2H2+H2CC 2.80E+23 -2.5 10780 2 (Wang 1992); 438 iC4H3+H=C4H4 3.40E+43 -9 12120 2 (Wang 1992); 439 iC4H3+H=C4H2+H2 6.00E+13 0 0 10 Estimated 440 iC4H3+OH=C4H2+H2O 4.00E+12 0 0 10 Estimated 441 iC4H3+O2=HCCO+CH2CO 7.86E+16 -1.8 0 5 (Slagle et al. 1989) 442 C4H4+H=nC4H5 1.30E+51 -11.9 16500 2 (Wang and Frenklach 1997) 443 C4H4+H=iC4H5 4.90E+51 -11.9 17700 2 (Wang and Frenklach 1997) 444 C4H4+H=nC4H3+H2 6.65E+05 2.5 12240 2 (Wang and Frenklach 1997) 445 C4H4+H=iC4H3+H2 3.33E+05 2.5 9240 2 (Wang and Frenklach 1997) 446 C4H4+OH=nC4H3+H2O 3.10E+07 2 3430 2 (Wang and Frenklach 1997) 447 C4H4+OH=iC4H3+H2O 1.55E+07 2 430 2 (Wang and Frenklach 1997) 448 C4H4+O=C3H3+HCO 6.00E+08 1.4 -860 5 Estimated 449 C4H4+C2H=l-C6H4+H 1.20E+13 0 0 5 Estimated 450 nC4H5=iC4H5 1.50E+67 -16.9 59100 2 (Wang and Frenklach 1997) 451 nC4H5+H=iC4H5+H 3.10E+26 -3.4 17423 2 (Wang and Frenklach 1997) 452 nC4H5+H=C4H4+H2 1.50E+13 0 0 3 (Wang and Frenklach 1997) 453 nC4H5+OH=C4H4+H2O 2.00E+12 0 0 3 (Wang and Frenklach 1997) 454 nC4H5+HCO=C4H6+CO 5.00E+12 0 0 3 (Wang and Frenklach 1997) 455 nC4H5+HO2=C2H3+CH2CO+OH 6.60E+12 0 0 3 (Wang and Frenklach 1997) 456 nC4H5+H2O2=C4H6+HO2 1.21E+10 0 -596 2 (Wang and Frenklach 1997) 457 nC4H5+HO2=C4H6+O2 6.00E+11 0 0 5 Estimated 458 nC4H5+O2=CH2CHCHCHO+O 3.00E+11 0.3 11 5 Estimated 459 nC4H5+O2=HCO+C2H3CHO 9.20E+16 -1.4 1010 5 Estimated 460 nC4H5+C2H2=C6H6+H 1.60E+16 -1.3 5400 2 (Wang and Frenklach 1997) 461 nC4H5+C2H3=C6H6+H2 1.84E-13 7.1 -3611 2 (Westmoreland et al. 1989) 462 iC4H5+H=C4H4+H2 3.00E+13 0 0 3 (Wang and Frenklach 1997) 463 iC4H5+H=C3H3+CH3 2.00E+13 0 2000 5 (Wang and Frenklach 1997) 464 iC4H5+OH=C4H4+H2O 4.00E+12 0 0 3 (Wang and Frenklach 1997) 465 iC4H5+HCO=C4H6+CO 5.00E+12 0 0 3 (Wang and Frenklach 1997) 466 iC4H5+HO2=C4H6+O2 6.00E+11 0 0 5 Estimated 260 467 iC4H5+HO2=C2H3+CH2CO+OH 6.60E+12 0 0 3 (Wang and Frenklach 1997) 468 iC4H5+H2O2=C4H6+HO2 1.21E+10 0 -596 3 (Wang and Frenklach 1997) 469 iC4H5+O2=CH2CO+CH2CHO 2.16E+10 0 2500 3 Estimated 470 C4H5-2=iC4H5 1.50E+67 -16.9 59100 3 Estimated 471 iC4H5+H=C4H5-2+H 3.10E+26 -3.4 17423 3 Estimated 472 C4H5-2+HO2=OH+C2H2+CH3CO 8.00E+11 0 0 10 Estimated 473 C4H5-2+O2=CH3CO+CH2CO 2.16E+10 0 2500 3 (Slagle et al. 1992) 474 C4H5-2+C2H2=C6H6+H 5.00E+14 0 25000 5 Estimated 475 C4H5-2+C2H4=C5H6+CH3 5.00E+14 0 25000 5 Estimated 476 C4H6=iC4H5+H 5.70E+36 -6.3 11235 3 2 (Wang and Frenklach 1997) 477 C4H6=nC4H5+H 5.30E+44 -8.6 12967 7. 2 (Wang and Frenklach 1997) 478 C4H6=C4H4+H2 2.50E+15 0 94700 2 (Hidaka et al. 1996) 479 C4H6+H=nC4H5+H2 1.33E+06 2.5 12240 3 Estimated 480 C4H6+H=iC4H5+H2 6.65E+05 2.5 9240 5 Estimated 481 C4H6+H=C2H4+C2H3 1.46E+30 -4.3 21647 2 (Wang and Frenklach 1997) 482 C4H6+H=pC3H4+CH3 2.00E+12 0 7000 10 (Wang and Frenklach 1997) 483 C4H6+H=aC3H4+CH3 2.00E+12 0 7000 10 Estimated 484 C4H6+O=nC4H5+OH 7.50E+06 1.9 3740 10 Estimated 485 C4H6+O=iC4H5+OH 7.50E+06 1.9 3740 10 Estimated 486 C4H6+O=CH3CHCHCO+H 1.50E+08 1.4 -860 3 (Adusei et al. 1996) 487 C4H6+O=CH2CHCHCHO+H 4.50E+08 1.4 -860 3 (Adusei et al. 1996) 488 C4H6+OH=nC4H5+H2O 6.20E+06 2 3430 3 (Liu et al. 1988) 489 C4H6+OH=iC4H5+H2O 3.10E+06 2 430 5 Estimated 490 C4H6+HO2=C4H6O25+OH 1.20E+12 0 14000 5 Estimated 491 C4H6+HO2=C2H3CHOCH2+OH 4.80E+12 0 14000 5 Estimated 492 C4H6+CH3=nC4H5+CH4 2.00E+14 0 22800 3 (Hidaka et al. 1996) 493 C4H6+CH3=iC4H5+CH4 1.00E+14 0 19800 3 (Hidaka et al. 1996) 494 C4H6+C2H3=nC4H5+C2H4 5.00E+13 0 22800 3 (Hidaka et al. 1996) 495 C4H6+C2H3=iC4H5+C2H4 2.50E+13 0 19800 3 (Hidaka et al. 1996) 496 C4H6+C3H3=nC4H5+aC3H4 1.00E+13 0 22500 3 (Hidaka et al. 1996) 497 C4H6+C3H3=iC4H5+aC3H4 5.00E+12 0 19500 3 (Hidaka et al. 1996) 498 C4H6+aC3H5=nC4H5+C3H6 1.00E+13 0 22500 5 Estimated 499 C4H6+aC3H5=iC4H5+C3H6 5.00E+12 0 19500 5 Estimated 500 C4H6+C2H3=C6H6+H2+H 5.62E+11 0 3240 3 (Leung and Lindstedt 1995) 501 C4H612=iC4H5+H 4.20E+15 0 92600 3 (Leung and Lindstedt 1995) 502 C4H612+H=C4H6+H 2.00E+13 0 4000 10 Estimated 503 C4H612+H=iC4H5+H2 1.70E+05 2.5 2490 5 Estimated 504 C4H612+H=aC3H4+CH3 2.00E+13 0 2000 3 (Wang and Frenklach 1997) 261 505 C4H612+H=pC3H4+CH3 2.00E+13 0 2000 3 (Wang and Frenklach 1997) 506 C4H612+CH3=iC4H5+CH4 7.00E+13 0 18500 3 (Kern et al. 1988) 507 C4H612+O=CH2CO+C2H4 1.20E+08 1.6 327 3 Estimated 508 C4H612+O=iC4H5+OH 1.80E+11 0.7 5880 3 Estimated 509 C4H612+OH=iC4H5+H2O 3.10E+06 2 -298 3 Estimated 510 C4H612=C4H6 3.00E+13 0 65000 3 (Hidaka et al. 1996) 511 C4H6-2=C4H6 3.00E+13 0 65000 3 (Hidaka et al. 1996) 512 C4H6-2=C4H612 3.00E+13 0 67000 3 (Hidaka et al. 1996) 513 C4H6-2+H=C4H612+H 2.00E+13 0 4000 5 Estimated 514 C4H6-2+H=C4H5-2+H2 3.40E+05 2.5 2490 3 Estimated 515 C4H6-2+H=CH3+pC3H4 2.60E+05 2.5 1000 3 (Hidaka et al. 1996) 516 C4H6-2=H+C4H5-2 5.00E+15 0 87300 3 (Hidaka et al. 1996) 517 C4H6-2+CH3=C4H5-2+CH4 1.40E+14 0 18500 5 Estimated 518 C2H3CHOCH2=C4H6O23 2.00E+14 0 50600 5 (Crawford et al. 1976) 519 C4H6O23=CH3CHCHCHO 1.95E+13 0 49400 2 (Lifshitz and Bidani 1989) 520 C4H6O23=C2H4+CH2CO 5.75E+15 0 69300 2 (Lifshitz and Bidani 1989) 521 C4H6O23=C2H2+CH2OCH2 1.00E+16 0 75800 2 (Lifshitz and Bidani 1989) 522 C4H6O25=C4H4O+H2 5.30E+12 0 48500 2 (Lifshitz et al. 1986b) 523 C4H4O=CO+pC3H4 1.78E+15 0 77500 2 (Lifshitz et al. 1986a) 524 C4H4O=C2H2+CH2CO 5.01E+14 0 77500 2 (Lifshitz et al. 1986a) 525 CH3CHCHCHO=C3H6+CO 3.90E+14 0 69000 5 Estimated 526 CH3CHCHCHO+H=CH2CHCHCHO+H 2 1.70E+05 2.5 2490 5 Estimated 527 CH3CHCHCHO+H=CH3CHCHCO+H2 1.00E+05 2.5 2490 10 Estimated 528 CH3CHCHCHO+H=CH3+C2H3CHO 4.00E+21 -2.4 11180 5 Estimated 529 CH3CHCHCHO+H=C3H6+HCO 4.00E+21 -2.4 11180 5 Estimated 530 CH3CHCHCHO+CH3=CH2CHCHCHO +CH4 2.10E+00 3.5 5675 5 Estimated 531 CH3CHCHCHO+CH3=CH3CHCHCO+C H4 1.10E+00 3.5 5675 10 Estimated 532 CH3CHCHCHO+C2H3=CH2CHCHCHO +C2H4 2.21E+00 3.5 4682 5 Estimated 533 CH3CHCHCHO+C2H3=CH3CHCHCO+ C2H4 1.11E+00 3.5 4682 10 Estimated 534 CH3CHCHCO=CH3CHCH+CO 1.00E+14 0 30000 5 Estimated 535 CH3CHCHCO+H=CH3CHCHCHO 1.00E+14 0 0 5 Estimated 536 CH2CHCHCHO=aC3H5+CO 1.00E+14 0 25000 5 Estimated 537 CH2CHCHCHO+H=CH3CHCHCHO 1.00E+14 0 0 5 Estimated 538 C4H7=C4H6+H 2.48E+53 -12.3 52000 2 (Wang and Frenklach 1997) 539 C4H7+H(+M)=C4H81(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ 262 H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 540 C4H7+H=CH3+aC3H5 2.00E+21 -2 11000 5 Estimated 541 C4H7+H=C4H6+H2 1.80E+12 0 0 5 Estimated 542 C4H7+O2=C4H6+HO2 1.00E+11 0 0 10 Estimated 543 C4H7+HO2=CH2O+OH+aC3H5 2.40E+13 0 0 5 Estimated 544 C4H7+HCO=C4H81+CO 6.00E+13 0 0 5 Estimated 545 C4H7+CH3=C4H6+CH4 1.10E+13 0 0 5 Estimated 546 iC4H7+H(+M)=iC4H8(+M) 2.00E+14 0 0 2 Estimated LOW-P LIMIT 1.33E+60 -12 5968 TROE /0.02 1096.6 1096.6 6859.5/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 547 iC4H7+H=CH3CCH2+CH3 2.60E+45 -8.2 37890 2 Estimated 548 iC4H7+O=CH2O+CH3CCH2 9.00E+13 0 0 10 Estimated 549 iC4H7+HO2=CH3CCH2+CH2O+OH 4.00E+12 0 0 10 Estimated 550 C4H81+H(+M)=pC4H9(+M) 1.33E+13 0 3261 3 Estimated LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 551 C4H81+H(+M)=sC4H9(+M) 1.33E+13 0 1560 3 Estimated LOW-P LIMIT 8.70E+42 -7.5 4722 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 552 C4H81+H=C2H4+C2H5 1.60E+22 -2.4 11180 3 Estimated 553 C4H81+H=C3H6+CH3 3.20E+22 -2.4 11180 5 Estimated 554 C4H81+H=C4H7+H2 6.50E+05 2.5 6756 5 Estimated 555 C4H81+O=nC3H7+HCO 3.30E+08 1.4 -402 2 (Ko et al. 1991) 556 C4H81+O=C4H7+OH 1.50E+13 0 5760 2 (Ko et al. 1991) 557 C4H81+O=C4H7+OH 2.60E+13 0 4470 2 (Ko et al. 1991) 558 C4H81+OH=C4H7+H2O 7.00E+02 2.7 527 3 Estimated 559 C4H81+O2=C4H7+HO2 2.00E+13 0 50930 3 Estimated 560 C4H81+HO2=C4H7+H2O2 1.00E+12 0 14340 2 (Walker 1989) 561 C4H81+CH3=C4H7+CH4 4.50E-01 3.6 7153 3 Estimated 562 C4H82+H(+M)=sC4H9(+M) 1.33E+13 0 1560 3 Estimated LOW-P LIMIT 8.70E+42 -7.5 4722 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 563 C4H82+H=C4H7+H2 3.40E+05 2.5 2490 3 Estimated 263 564 C4H82+O=C2H4+CH3CHO 2.40E+08 1.6 327 3 Estimated 565 C4H82+OH=C4H7+H2O 6.20E+06 2 -298 3 Estimated 566 C4H82+O2=C4H7+HO2 5.00E+13 0 53300 5 Estimated 567 C4H82+HO2=C4H7+H2O2 1.90E+04 2.6 13910 3 Estimated 568 C4H82+CH3=C4H7+CH4 4.40E+00 3.5 5675 3 Estimated 569 iC4H8+H(+M)=iC4H9(+M) 1.33E+13 0 3261 3 Estimated LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 570 iC4H8+H=iC4H7+H2 1.20E+06 2.5 6760 3 Estimated 571 iC4H8+H=C3H6+CH3 8.00E+21 -2.4 11180 3 Estimated 572 iC4H8+O=CH3+CH3+CH2CO 1.20E+08 1.6 327 3 Estimated 573 iC4H8+O=iC3H7+HCO 3.50E+07 1.6 -972 3 Estimated 574 iC4H8+O=iC4H7+OH 2.90E+05 2.5 3640 3 Estimated 575 iC4H8+OH=iC4H7+H2O 1.50E+08 1.5 775 3 Estimated 576 iC4H8+HO2=iC4H7+H2O2 2.00E+04 2.5 15500 3 Estimated 577 iC4H8+O2=iC4H7+HO2 2.70E+13 0 50900 3 Estimated 578 iC4H8+CH3=iC4H7+CH4 9.10E-01 3.6 7150 3 Estimated 579 C2H4+C2H5=pC4H9 1.50E+11 0 7300 3 Estimated 580 pC4H9+H(+M)=C4H10(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 581 pC4H9+H=C2H5+C2H5 3.70E+24 -2.9 12505 3 Estimated 582 pC4H9+H=C4H81+H2 1.80E+12 0 0 3 Estimated 583 pC4H9+O=nC3H7+CH2O 9.60E+13 0 0 3 Estimated 584 pC4H9+OH=C4H81+H2O 2.40E+13 0 0 3 Estimated 585 pC4H9+O2=C4H81+HO2 2.70E+11 0 0 5 Estimated 586 pC4H9+HO2=nC3H7+OH+CH2O 2.40E+13 0 0 5 Estimated 587 pC4H9+HCO=C4H10+CO 9.00E+13 0 0 5 Estimated 588 pC4H9+CH3=C4H81+CH4 1.10E+13 0 0 5 Estimated 589 C3H6+CH3(+M)=sC4H9(+M) 1.70E+11 0 7404 2 Estimated LOW-P LIMIT 2.31E+28 -4.27 1831 TROE /0.565 60000 534.2 3007.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 590 sC4H9+H(+M)=C4H10(+M) 2.40E+13 0 0 3 Estimated LOW-P LIMIT 1.70E+58 -12.0811264 TROE /0.649 1213.1 1213.1 13370/ 264 H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 591 sC4H9+H=C2H5+C2H5 1.40E+28 -3.9 15916 3 Estimated 592 sC4H9+H=C4H81+H2 3.20E+12 0 0 3 Estimated 593 sC4H9+H=C4H82+H2 2.10E+12 0 0 3 Estimated 594 sC4H9+O=CH3CHO+C2H5 9.60E+13 0 0 3 Estimated 595 sC4H9+OH=C4H81+H2O 2.40E+13 0 0 3 Estimated 596 sC4H9+OH=C4H82+H2O 1.60E+13 0 0 3 Estimated 597 sC4H9+O2=C4H81+HO2 5.10E+10 0 0 3 Estimated 598 sC4H9+O2=C4H82+HO2 1.20E+11 0 0 3 Estimated 599 sC4H9+HO2=CH3CHO+C2H5+OH 2.40E+13 0 0 5 Estimated 600 sC4H9+HCO=C4H10+CO 1.20E+14 0 0 5 Estimated 601 sC4H9+CH3=CH4+C4H81 2.20E+14 -0.7 0 5 Estimated 602 sC4H9+CH3=CH4+C4H82 1.50E+14 -0.7 0 5 Estimated 603 C3H6+CH3(+M)=iC4H9(+M) 9.60E+10 0 8004 2 Estimated LOW-P LIMIT 1.30E+28 -4.27 2431 TROE /0.565 60000 534.2 3007.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 604 iC4H9+H(+M)=iC4H10(+M) 3.60E+13 0 0 2 Estimated LOW-P LIMIT 3.27E+56 -11.746431 TROE /0.506 1266.6 1266.6 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 605 iC4H9+H=iC3H7+CH3 1.90E+35 -5.8 22470 2 Estimated 606 iC4H9+H=iC4H8+H2 9.00E+11 0 0 2 Estimated 607 iC4H9+O=iC3H7+CH2O 9.60E+13 0 0 2 Estimated 608 iC4H9+OH=iC4H8+H2O 1.20E+13 0 0 2 Estimated 609 iC4H9+O2=iC4H8+HO2 2.40E+10 0 0 2 Estimated 610 iC4H9+HO2=iC3H7+CH2O+OH 2.41E+13 0 0 3 Estimated 611 iC4H9+HCO=iC4H10+CO 3.60E+13 0 0 2 Estimated 612 iC4H9+CH3=iC4H8+CH4 6.00E+12 -0.3 0 2 Estimated 613 tC4H9(+M)=iC4H8+H(+M) 8.30E+13 0 38150 2 Estimated LOW-P LIMIT 1.90E+41 -7.36 36632 TROE /0.293 649 60000 3425.9/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 614 tC4H9+H(+M)=iC4H10(+M) 2.40E+13 0 0 2 Estimated LOW-P LIMIT 1.47E+61 -12.948000 TROE /0 1456.4 1000 10000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 265 615 tC4H9+H=iC3H7+CH3 2.60E+36 -6.1 25640 2 Estimated 616 tC4H9+H=iC4H8+H2 5.42E+12 0 0 2 Estimated 617 tC4H9+O=iC4H8+OH 1.80E+14 0 0 2 Estimated 618 tC4H9+O=CH3COCH3+CH3 1.80E+14 0 0 2 Estimated 619 tC4H9+OH=iC4H8+H2O 1.80E+13 0 0 2 Estimated 620 tC4H9+O2=iC4H8+HO2 4.80E+11 0 0 2 Estimated 621 tC4H9+HO2=CH3+CH3COCH3+OH 1.80E+13 0 0 2 Estimated 622 tC4H9+HCO=iC4H10+CO 6.00E+13 0 0 2 Estimated 623 tC4H9+CH3=iC4H8+CH4 3.80E+15 -1 0 2 Estimated 624 CH3COCH3+H=H2+CH2CO+CH3 1.30E+06 2.5 6756 3 Estimated 625 CH3COCH3+O=OH+CH2CO+CH3 1.90E+05 2.7 3716 3 Estimated 626 CH3COCH3+OH=H2O+CH2CO+CH3 3.20E+07 1.8 934 3 Estimated 627 CH3+CH3CO=CH3COCH3 4.00E+15 -0.8 0 2 Estimated 628 nC3H7+CH3(+M)=C4H10(+M) 1.93E+14 -0.3 0 2 Estimated LOW-P LIMIT 2.68E+61 -13.246000 TROE /1 1000 1433.9 5328.8/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 629 C2H5+C2H5(+M)=C4H10(+M) 1.88E+14 -0.5 0 2 Estimated LOW-P LIMIT 2.61E+61 -13.426000 TROE /1 1000 1433.9 5328.8/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 630 C4H10+H=pC4H9+H2 9.20E+05 2.5 6756 3 Estimated 631 C4H10+H=sC4H9+H2 2.40E+06 2.4 4471 3 Estimated 632 C4H10+O=pC4H9+OH 4.90E+06 2.4 5500 3 Estimated 633 C4H10+O=sC4H9+OH 4.30E+05 2.6 2580 3 Estimated 634 C4H10+OH=pC4H9+H2O 3.30E+07 1.8 954 3 Estimated 635 C4H10+OH=sC4H9+H2O 5.40E+06 2 -596 3 Estimated 636 C4H10+O2=pC4H9+HO2 4.00E+13 0 50930 3 Estimated 637 C4H10+O2=sC4H9+HO2 8.00E+13 0 47590 3 Estimated 638 C4H10+HO2=pC4H9+H2O2 4.76E+04 2.5 16490 3 Estimated 639 C4H10+HO2=sC4H9+H2O2 1.90E+04 2.6 13910 3 Estimated 640 C4H10+CH3=pC4H9+CH4 9.03E-01 3.6 7153 3 Estimated 641 C4H10+CH3=sC4H9+CH4 3.00E+00 3.5 5480 3 Estimated 642 iC3H7+CH3(+M)=iC4H10(+M) 1.40E+15 -0.7 0 2 Estimated LOW-P LIMIT 4.16E+61 -13.333903 TROE /0.931 60000 1265.3 5469.8/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 643 iC4H10+H=iC4H9+H2 1.80E+06 2.5 6760 2 Estimated 266 644 iC4H10+H=tC4H9+H2 6.00E+05 2.4 2580 2 Estimated 645 iC4H10+O=iC4H9+OH 4.30E+05 2.5 3640 2 Estimated 646 iC4H10+O=tC4H9+OH 1.57E+05 2.5 1110 2 Estimated 647 iC4H10+OH=iC4H9+H2O 2.30E+08 1.5 775 2 Estimated 648 iC4H10+OH=tC4H9+H2O 5.73E+10 0.5 64 2 Estimated 649 iC4H10+HO2=iC4H9+H2O2 3.00E+04 2.5 15500 2 Estimated 650 iC4H10+HO2=tC4H9+H2O2 3.60E+03 2.5 10500 2 Estimated 651 iC4H10+O2=iC4H9+HO2 4.00E+13 0 50900 2 Estimated 652 iC4H10+O2=tC4H9+HO2 4.00E+13 0 44000 2 Estimated 653 iC4H10+CH3=iC4H9+CH4 1.36E+00 3.6 7150 2 Estimated 654 iC4H10+CH3=tC4H9+CH4 9.00E-01 3.5 4600 2 Estimated 655 C6H2+H=C6H3 1.10E+30 -4.9 10800 2 (Wang and Frenklach 1997) 656 C6H3+H=C4H2+C2H2 2.80E+23 -2.5 10780 2 (Wang and Frenklach 1997) 657 C6H3+H=l-C6H4 3.40E+43 -9 12120 2 (Wang and Frenklach 1997) 658 C6H3+H=C6H2+H2 3.00E+13 0 0 2 (Wang and Frenklach 1997) 659 C6H3+OH=C6H2+H2O 4.00E+12 0 0 2 (Wang and Frenklach 1997) 660 l-C6H4+H=C6H5 1.70E+78 -19.7 31400 2 (Wang and Frenklach 1997) 661 l-C6H4+H=o-C6H4+H 1.40E+54 -11.7 34500 2 (Wang and Frenklach 1997) 662 l-C6H4+H=C6H3+H2 1.33E+06 2.5 9240 5 (Wang and Frenklach 1997) 663 l-C6H4+OH=C6H3+H2O 3.10E+06 2 430 5 (Wang and Frenklach 1997) 664 C4H2+C2H2=o-C6H4 5.00E+78 -19.3 67920 2 (Wang et al. 2000) 665 o-C6H4+OH=CO+C5H5 1.00E+13 0 0 5 (Wang and Frenklach 1997) 666 C6H5+CH3=C6H5CH3 1.38E+13 0 46 3 (Tokmakov et al. 1999) 667 C6H5CH3+O2=C6H5CH2+HO2 3.00E+14 0 42992 2 (Eng et al. 1998) 668 C6H5CH3+OH=C6H5CH2+H2O 1.62E+13 0 2770 2 (Vasudevan et al. 2005b) 669 C6H5CH3+OH=C6H4CH3+H2O 1.33E+08 1.4 1450 3 Estimated 670 C6H5CH3+H=C6H5CH2+H2 1.26E+14 0 8359 2 (Hippler et al. 1991) 671 C6H5CH3+H=C6H6+CH3 1.93E+06 2.2 4163 2 (Tokmakov and Lin 2001) 672 C6H5CH3+O=OC6H4CH3+H 2.60E+13 0 3795 3 (Nicovich et al. 1982) 673 C6H5CH3+CH3=C6H5CH2+CH4 3.16E+11 0 9500 3 (Kerr and Parsonage 1976) 674 C6H5CH3+C6H5=C6H5CH2+C6H6 2.10E+12 0 4400 3 (Fahr and Stein 1989) 675 C6H5CH3+HO2=C6H5CH2+H2O2 3.98E+11 0 14069 3 (Baulch et al. 1994) 676 C6H5CH3+HO2=C6H4CH3+H2O2 5.42E+12 0 28810 3 (Baulch et al. 1994) 677 C6H5CH2+H(+M)=C6H5CH3(+M) 1.00E+14 0 0 3 Calculated, RRKM LOW-P LIMIT 1.1E+103 -24.6314590 TROE /0.431 383 152 4730/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ 678 C6H5CH2+H=C6H5+CH3 1.50E+66 -13.9 64580 2 Calculated, RRKM 679 C6H5CH2+O=C6H5CHO+H 4.00E+14 0 0 2 (Hippler et al. 1991) 267 680 C6H5CH2+OH=C6H5CH2OH 2.00E+13 0 0 2 (Hippler et al. 1991) 681 C6H5CH2+HO2=C6H5CHO+H+OH 5.00E+12 0 0 2 (Hippler et al. 1991) 682 C6H5CH2+C6H5OH=C6H5CH3+C6H5 O 1.05E+11 0 9500 5 (Emdee et al. 1992) 683 C6H5CH2+HOC6H4CH3=C6H5CH3 +OC6H4CH3 1.05E+11 0 9500 5 (Emdee et al. 1992) 684 C6H5CH2OH+OH=C6H5CHO+H2O+H 5.00E+12 0 0 3 (Hippler et al. 1991) 685 C6H5CH2OH+H=C6H5CHO+H2+H 8.00E+13 0 8235 5 (Emdee et al. 1992) 686 C6H5CH2OH+H=C6H6+CH2OH 1.20E+13 0 5148 5 (Emdee et al. 1992) 687 C6H5CH2OH+C6H5=C6H5CHO+C6H6 +H 1.40E+12 0 4400 5 (Emdee et al. 1992) 688 C6H5+HCO=C6H5CHO 1.00E+13 0 0 5 Estimated 689 C6H5CHO=C6H5CO+H 3.98E+15 0 86900 5 (Grela and Colussi 1986) 690 C6H5CHO+O2=C6H5CO+HO2 1.02E+13 0 38950 5 Estimated 691 C6H5CHO+OH=C6H5CO+H2O 2.35E+10 0.7 -1110 5 Estimated 692 C6H5CHO+H=C6H5CO+H2 4.10E+09 1.2 2400 5 Estimated 693 C6H5CHO+H=C6H6+HCO 1.93E+06 2.2 4163 5 Estimated 694 C6H5CHO+O=C6H5CO+OH 5.80E+12 0 1800 5 Estimated 695 C6H5CHO+C6H5CH2=C6H5CO+C6H5 CH3 2.00E-06 5.6 2460 5 Estimated 696 C6H5CHO+CH3=C6H5CO+CH4 2.00E-06 5.6 2460 5 Estimated 697 C6H5CHO+C6H5=C6H5CO+C6H6 2.10E+12 0 4400 5 Estimated 698 C6H5CO+H2O2=C6H5CHO+HO2 1.80E+11 0 8226 5 Estimated 699 OC6H4CH3+H(+M)=HOC6H4CH3(+M)1.00E+14 0 0 5 Estimated LOW-P LIMIT 4.00E+93 -21.8413880 TROE /0.043 304.2 60000 5896.4/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ 700 OC6H4CH3+H=C6H5O+CH3 1.93E+06 2.2 4163 5 Estimated 701 OC6H4CH3+O=C6H4O2+CH3 8.00E+13 0 0 5 Estimated 702 HOC6H4CH3+OH=OC6H4CH3+H2O 6.00E+12 0 0 3 (He et al. 1988) 703 HOC6H4CH3+H=OC6H4CH3+H2 1.15E+14 0 12400 3 (He et al. 1988) 704 HOC6H4CH3+H=C6H5CH3+OH 2.21E+13 0 7910 3 (He et al. 1988) 705 HOC6H4CH3+H=C6H5OH+CH3 1.20E+13 0 5148 5 (Emdee et al. 1992) 706 C6H5CO=C6H5+CO 5.27E+14 0 29013 3 (Nam et al. 2000) 707 C6H5+H(+M)=C6H6(+M) 1.00E+14 0 0 2 Calculated, RRKM LOW-P LIMIT 6.60E+75 -16.3 7000 TROE /1 0.1 584.9 6113/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ 708 C6H6+OH=C6H5+H2O 3.98E+05 2.3 1058 2 (Joshi 2005) 709 C6H6+OH=C6H5OH+H 1.30E+13 0 10600 2 (Baulch et al. 1992) 710 C6H6+O=C6H5O+H 1.39E+13 0 4910 2 (Baulch et al. 1994) 268 711 C6H6+O=C5H5+HCO 1.39E+13 0 4530 2 (Baulch et al. 1994) 712 C6H5+H2=C6H6+H 5.71E+04 2.4 6273 2 (Mebel et al. 1997) 713 C6H5(+M)=o-C6H4+H(+M) 4.30E+12 0.6 77313 2 (Wang et al. 2000) LOW-P LIMIT 1.00E+84 -18.8790064 TROE /0.902 696 358 3856/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ (Mebel et al. 2001) 714 C6H5+H=o-C6H4+H2 2.00E+11 1.1 24500 2 (Frank et al. 1994) 715 C6H5+O2=C6H5O+O 2.60E+13 0 6120 3 (Frank et al. 1994) 716 C6H5+O2=C6H4O2+H 3.00E+13 0 8980 3 (Frank et al. 1994) 717 C6H5+O=C5H5+CO 1.00E+14 0 0 3 Estimated 718 C6H5+OH=C6H5O+H 3.00E+13 0 0 5 Estimated 719 C6H5+HO2=C6H5O+OH 3.00E+13 0 0 5 Estimated 720 C6H5+HO2=C6H6+O2 1.00E+12 0 0 5 (Tokmakov et al. 1999) 721 C6H5+CH4=C6H6+CH3 3.89E-03 4.6 5256 3 (Park et al. 2001) 722 C6H5+C2H6=C6H6+C2H5 2.10E+11 0 4443 3 (Choi et al. 2000) 723 C6H5+CH2O=C6H6+HCO 8.55E+04 2.2 38 3 (Frank et al. 1994) 724 C6H4O2=C5H4O+CO 7.40E+11 0 59000 3 Estimated 725 C6H4O2+H=CO+C5H5O(1,3) 4.30E+09 1.4 3900 5 Estimated 726 C6H4O2+O=2CO+C2H2+CH2CO 3.00E+13 0 5000 10 Estimated 727 C6H5O+H=C5H5+HCO 1.00E+13 0 12000 5 Estimated 728 C6H5O+H=C5H6+CO 5.00E+13 0 0 5 (Wang 1998) 729 C6H5O=CO+C5H5 3.76E+54 -12.1 72800 3 (Lin and Mebel 1995) 730 C6H5O+O=C6H4O2+H 2.60E+10 0.5 795 3 (Horn et al. 1998) 731 C6H5OH=C5H6+CO 1.00E+12 0 60808 3 (Knispel et al. 1990) 732 C6H5OH+OH=C6H5O+H2O 2.95E+06 2 -1312 3 (He et al. 1988) 733 C6H5OH+H=C6H5O+H2 1.15E+14 0 12398 3 (Emdee et al. 1992) 734 C6H5OH+O=C6H5O+OH 2.81E+13 0 7352 5 (Emdee et al. 1992) 735 C6H5OH+C2H3=C6H5O+C2H4 6.00E+12 0 0 5 (Emdee et al. 1992) 736 C6H5OH+nC4H5=C6H5O+C4H6 6.00E+12 0 0 5 (Fahr and Stein 1989) 737 C6H5OH+C6H5=C6H5O+C6H6 4.91E+12 0 4400 3 (Zhong and Bozzelli 1997) 738 C5H6+H=C2H2+aC3H5 7.74E+36 -6.2 32890 3 (Zhong and Bozzelli 1997) 739 C5H6+H=lC5H7 8.27E+126 -32.3 82348 3 (Zhong and Bozzelli 1997) 740 C5H6+H=C5H5+H2 3.03E+08 1.7 5590 3 (Zhong and Bozzelli 1997) 741 C5H6+O=C5H5+OH 4.77E+04 2.7 1106 5 (Zhong and Bozzelli 1997) 742 C5H6+O=C5H5O(1,3)+H 8.91E+12 -0.1 590 3 (Zhong and Bozzelli 1997) 743 C5H6+O=C5H5O(1,3)+H 5.60E+12 -0.1 200 3 (Zhong and Bozzelli 1997) 744 C5H6+O=nC4H5+CO+H 8.70E+51 -11.1 33240 3 (Zhong and Bozzelli 1997) 745 C5H6+OH=C5H5+H2O 3.08E+06 2 0 5 (Zhong and Bozzelli 1997) 746 C5H6+HO2=C5H5+H2O2 1.10E+04 2.6 12900 5 (Zhong and Bozzelli 1997) 269 747 C5H6+O2=C5H5+HO2 4.00E+13 0 37150 5 (Zhong and Bozzelli 1997) 748 C5H6+HCO=C5H5+CH2O 1.08E+08 1.9 16000 5 (Zhong and Bozzelli 1997) 749 C5H6+CH3=C5H5+CH4 1.80E-01 4 0 5 (Frank et al. 1994) 750 C5H5+H(+M)=C5H6(+M) 1.00E+14 0 0 3 (Wang and Frenklach 1997) LOW-P LIMIT 4.40E+80 -18.2812994 TROE /0.068 400.7 4135.8 5501.9/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ 751 C5H5+O2=C5H5O(2,4)+O 7.78E+15 -0.7 48740 3 (Zhong and Bozzelli 1997) 752 C5H5+O=C5H5O(2,4) 1.12E-12 5.9 -17310 3 (Zhong and Bozzelli 1997) 753 C5H5+O=C5H4O+H 5.81E+13 0 20 3 (Zhong and Bozzelli 1997) 754 C5H5+O=nC4H5+CO 3.20E+13 -0.2 440 3 (Zhong and Bozzelli 1997) 755 C5H5+OH=C5H4OH+H 3.51E+57 -12.2 48350 3 (Zhong and Bozzelli 1997) 756 C5H5+OH=C5H5O(2,4)+H 1.36E+51 -10.5 57100 3 (Zhong and Bozzelli 1997) 757 C5H5+HO2=C5H5O(2,4)+OH 6.27E+29 -4.7 11650 3 (Zhong and Bozzelli 1997) 758 C5H5+OH=C5H5OH 6.49E+14 -0.8 -2730 3 (Zhong and Bozzelli 1997) 759 C5H5+OH=C5H5OH 1.15E+43 -8.8 18730 3 (Zhong and Bozzelli 1997) 760 C5H5+OH=C5H5OH 1.06E+59 -13.1 33450 3 (Zhong and Bozzelli 1997) 761 C5H5+O2=C5H4O+OH 1.80E+12 0.1 18000 3 Calculated, RRKM 762 C5H5OH+H=C5H5O(2,4)+H2 1.15E+14 0 15400 5 Estimated 763 C5H5OH+H=C5H4OH+H2 1.20E+05 2.5 1492 5 Estimated 764 C5H5OH+OH=C5H5O(2,4)+H2O 6.00E+12 0 0 5 Estimated 765 C5H5OH+OH=C5H4OH+H2O 3.08E+06 2 0 5 Estimated 766 C5H5O(2,4)+H=C5H5OH 1.00E+14 0 0 5 Estimated 767 C5H5O(2,4)=C5H4O+H 2.00E+13 0 30000 5 Estimated 768 C5H5O(2,4)+O2=C5H4O+HO2 1.00E+11 0 0 5 Estimated 769 C5H4O+H=C5H5O(1,3) 2.00E+13 0 2000 5 Estimated 770 C5H5O(1,3)=c-C4H5+CO 1.00E+12 0 36000 5 Estimated 771 C5H5O(1,3)+O2=C5H4O+HO2 1.00E+11 0 0 5 Estimated 772 C5H4OH=C5H4O+H 2.10E+13 0 48000 5 (Emdee et al. 1992) 773 C5H4O=2C2H2+CO 6.20E+41 -7.9 98700 3 (Wang and Brezinsky 1998) 774 C5H4O+H=CO+c-C4H5 4.30E+09 1.4 3900 5 Estimated 775 C5H4O+O=CO+HCO+C3H3 6.20E+08 1.4 -858 5 Estimated 776 c-C4H5+H=C4H6 1.00E+13 0 0 5 Estimated 777 c-C4H5+H=C2H4+C2H2 1.00E+13 0 0 5 Estimated 778 c-C4H5+O=CH2CHO+C2H2 1.00E+14 0 0 5 Estimated 779 c-C4H5+O2=CH2CHO+CH2CO 4.80E+11 0 19000 5 Estimated 780 c-C4H5=C4H4+H 3.00E+12 0 52000 5 Estimated 781 c-C4H5=C2H3+C2H2 2.00E+12 0 58000 5 Estimated 782 aC3H5+C2H3=lC5H7+H 1.00E+13 0 0 10 Estimated 270 783 lC5H7+O=C2H3CHO+C2H3 5.00E+13 0 0 10 Estimated 784 lC5H7+OH=C2H3CHO+C2H4 2.00E+13 0 0 10 Estimated 785 C5H9+H(+M)=C5H10(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 786 C5H9+H=CH3+C4H7 2.00E+21 -2 11000 5 Estimated 787 C5H9+HO2=CH2O+OH+C4H7 2.40E+13 0 0 5 Estimated 788 C5H9+HCO=C5H10+CO 6.00E+13 0 0 5 Estimated 789 C2H4+aC3H5=C5H9 3.00E+11 0 7300 3 Estimated 790 C5H10+H(+M)=PXC5H11(+M) 1.33E+13 0 3261 3 Estimated LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 791 C5H10+H(+M)=SXC5H11(+M) 1.33E+13 0 1560 3 Estimated LOW-P LIMIT 8.70E+42 -7.5 4722 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 792 C5H10+H=C2H4+nC3H7 8.00E+21 -2.4 11180 3 Estimated 793 C5H10+H=C3H6+C2H5 1.60E+22 -2.4 11180 5 Estimated 794 C5H10+H=C5H9+H2 6.50E+05 2.5 6756 5 Estimated 795 C5H10+O=pC4H9+HCO 3.30E+08 1.4 -402 2 Estimated 796 C5H10+O=C5H9+OH 1.50E+13 0 5760 2 Estimated 797 C5H10+O=C5H9+OH 2.60E+13 0 4470 2 Estimated 798 C5H10+OH=C5H9+H2O 7.00E+02 2.7 527 3 Estimated 799 C5H10+O2=C5H9+HO2 2.00E+13 0 50930 3 Estimated 800 C5H10+HO2=C5H9+H2O2 1.00E+12 0 14340 2 Estimated 801 C5H10+CH3=C5H9+CH4 4.50E-01 3.6 7153 3 Estimated 802 C3H6+C2H5=SXC5H11 3.00E+11 0 7300 3 Estimated 803 SXC5H11+H(+M)=NC5H12(+M) 2.40E+13 0 0 3 Estimated LOW-P LIMIT 1.70E+58 -12.0811264 TROE /0.649 1213.1 1213.1 13370/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 804 SXC5H11+H=nC3H7+C2H5 1.40E+28 -3.9 15916 3 Estimated 805 SXC5H11+H=C5H10+H2 3.20E+12 0 0 3 Estimated 806 SXC5H11+O=CH3CHO+nC3H7 9.60E+13 0 0 3 Estimated 807 SXC5H11+OH=C5H10+H2O 2.40E+13 0 0 3 Estimated 808 SXC5H11+O2=C5H10+HO2 1.30E+11 0 0 3 Estimated 271 809 SXC5H11+HO2=CH3CHO+nC3H7+OH2.40E+13 0 0 5 Estimated 810 SXC5H11+HCO=NC5H12+CO 1.20E+14 0 0 5 Estimated 811 SXC5H11+CH3=CH4+C5H10 2.20E+14 -0.7 0 5 Estimated 812 C4H81+CH3(+M)=S2XC5H11(+M) 1.70E+11 0 7404 3 Estimated LOW-P LIMIT 2.31E+28 -4.27 1831 TROE /0.565 60000 534.2 3007.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 813 S2XC5H11+O2=C5H10+HO2 1.30E+11 0 0 3 Estimated 814 C2H4+nC3H7=PXC5H11 3.00E+11 0 7300 3 Estimated 815 PXC5H11+H(+M)=NC5H12(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 816 PXC5H11+H=nC3H7+C2H5 3.70E+24 -2.9 12505 3 Estimated 817 PXC5H11+H=C5H10+H2 1.80E+12 0 0 3 Estimated 818 PXC5H11+O=pC4H9+CH2O 9.60E+13 0 0 3 Estimated 819 PXC5H11+OH=C5H10+H2O 2.40E+13 0 0 3 Estimated 820 PXC5H11+O2=C5H10+HO2 9.00E+10 0 0 5 Estimated 821 PXC5H11+HO2=pC4H9+OH+CH2O 2.40E+13 0 0 5 Estimated 822 PXC5H11+HCO=NC5H12+CO 9.00E+13 0 0 5 Estimated 823 PXC5H11+CH3=C5H10+CH4 1.10E+13 0 0 5 Estimated 824 pC4H9+CH3=NC5H12 1.93E+14 -0.3 0 3 Estimated 825 nC3H7+C2H5=NC5H12 1.88E+14 -0.5 0 3 Estimated 826 NC5H12+H=PXC5H11+H2 1.30E+06 2.5 6756 3 Estimated 827 NC5H12+H=SXC5H11+H2 2.60E+06 2.4 4471 3 Estimated 828 NC5H12+O=PXC5H11+OH 1.90E+05 2.7 3716 3 Estimated 829 NC5H12+O=SXC5H11+OH 9.52E+04 2.7 2106 3 Estimated 830 NC5H12+OH=PXC5H11+H2O 1.40E+03 2.7 527 3 Estimated 831 NC5H12+OH=SXC5H11+H2O 5.40E+04 2.4 393 3 Estimated 832 NC5H12+O2=PXC5H11+HO2 4.00E+13 0 50930 3 Estimated 833 NC5H12+O2=SXC5H11+HO2 8.00E+13 0 47590 3 Estimated 834 NC5H12+HO2=PXC5H11+H2O2 4.76E+04 2.5 16490 3 Estimated 835 NC5H12+HO2=SXC5H11+H2O2 1.90E+04 2.6 13910 3 Estimated 836 NC5H12+CH3=PXC5H11+CH4 9.03E-01 3.6 7153 3 Estimated 837 NC5H12+CH3=SXC5H11+CH4 3.00E+00 3.5 5480 3 Estimated 838 C6H11+H(+M)=C6H12(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ 272 H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 839 C6H11+H=CH3+C5H9 2.00E+21 -2 11000 5 Estimated 840 C6H11+HO2=CH2O+OH+C5H9 2.40E+13 0 0 5 Estimated 841 C6H11+HCO=C6H12+CO 6.00E+13 0 0 5 Estimated 842 C2H4+C4H7=C6H11 3.00E+11 0 7300 3 Estimated 843 C6H12+H(+M)=PXC6H13(+M) 1.33E+13 0 3261 3 Estimated LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 844 C6H12+H(+M)=SXC6H13(+M) 1.33E+13 0 1560 3 Estimated LOW-P LIMIT 8.70E+42 -7.5 4722 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 845 C6H12+H=C2H4+pC4H9 8.00E+21 -2.4 11180 3 Estimated 846 C6H12+H=C3H6+nC3H7 1.60E+22 -2.4 11180 5 Estimated 847 C6H12+H=C6H11+H2 6.50E+05 2.5 6756 5 Estimated 848 C6H12+O=PXC5H11+HCO 3.30E+08 1.4 -402 2 Estimated 849 C6H12+O=C6H11+OH 1.50E+13 0 5760 2 Estimated 850 C6H12+O=C6H11+OH 2.60E+13 0 4470 2 Estimated 851 C6H12+OH=C6H11+H2O 7.00E+02 2.7 527 3 Estimated 852 C6H12+O2=C6H11+HO2 2.00E+13 0 50930 3 Estimated 853 C6H12+HO2=C6H11+H2O2 1.00E+12 0 14340 2 Estimated 854 C6H12+CH3=C6H11+CH4 4.50E-01 3.6 7153 3 Estimated 855 C2H4+pC4H9=PXC6H13 3.00E+11 0 7300 3 Estimated 856 PXC6H13+H(+M)=NC6H14(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 857 PXC6H13+H=pC4H9+C2H5 3.70E+24 -2.9 12505 3 Estimated 858 PXC6H13+H=C6H12+H2 1.80E+12 0 0 3 Estimated 859 PXC6H13+O=PXC5H11+CH2O 9.60E+13 0 0 3 Estimated 860 PXC6H13+OH=C6H12+H2O 2.40E+13 0 0 3 Estimated 861 PXC6H13+O2=C6H12+HO2 9.00E+10 0 0 5 Estimated 862 PXC6H13+HO2=PXC5H11+OH+CH2O 2.40E+13 0 0 5 Estimated 863 PXC6H13+HCO=NC6H14+CO 9.00E+13 0 0 5 Estimated 864 PXC6H13+CH3=C6H12+CH4 1.10E+13 0 0 5 Estimated 865 C3H6+nC3H7=SXC6H13 3.00E+11 0 7300 3 Estimated 866 SXC6H13+H(+M)=NC6H14(+M) 2.40E+13 0 0 3 Estimated 273 LOW-P LIMIT 1.70E+58 -12.0811264 TROE /0.649 1213.1 1213.1 13370/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 867 SXC6H13+H=pC4H9+C2H5 1.40E+28 -3.9 15916 3 Estimated 868 SXC6H13+H=C6H12+H2 3.20E+12 0 0 3 Estimated 869 SXC6H13+O=CH3CHO+pC4H9 9.60E+13 0 0 3 Estimated 870 SXC6H13+OH=C6H12+H2O 2.40E+13 0 0 3 Estimated 871 SXC6H13+O2=C6H12+HO2 1.30E+11 0 0 3 Estimated 872 SXC6H13+HO2=CH3CHO+pC4H9+OH2.40E+13 0 0 5 Estimated 873 SXC6H13+HCO=NC6H14+CO 1.20E+14 0 0 5 Estimated 874 SXC6H13+CH3=CH4+C6H12 2.20E+14 -0.7 0 5 Estimated 875 C2H5+C4H81=S2XC6H13 3.00E+11 0 7300 3 Estimated 876 C5H10+CH3(+M)=S2XC6H13(+M) 1.70E+11 0 7404 3 Estimated LOW-P LIMIT 2.31E+28 -4.27 1831 TROE /0.565 60000 534.2 3007.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 877 S2XC6H13+O2=C6H12+HO2 1.30E+11 0 0 3 Estimated 878 PXC5H11+CH3=NC6H14 1.93E+14 -0.3 0 3 Estimated 879 pC4H9+C2H5=NC6H14 1.88E+14 -0.5 0 3 Estimated 880 nC3H7+nC3H7=NC6H14 1.88E+14 -0.5 0 3 Estimated 881 NC6H14+H=PXC6H13+H2 1.30E+06 2.5 6756 3 Estimated 882 NC6H14+H=SXC6H13+H2 2.60E+06 2.4 4471 3 Estimated 883 NC6H14+O=PXC6H13+OH 1.90E+05 2.7 3716 3 Estimated 884 NC6H14+O=SXC6H13+OH 9.52E+04 2.7 2106 3 Estimated 885 NC6H14+OH=PXC6H13+H2O 1.40E+03 2.7 527 3 Estimated 886 NC6H14+OH=SXC6H13+H2O 5.40E+04 2.4 393 3 Estimated 887 NC6H14+O2=PXC6H13+HO2 4.00E+13 0 50930 3 Estimated 888 NC6H14+O2=SXC6H13+HO2 8.00E+13 0 47590 3 Estimated 889 NC6H14+HO2=PXC6H13+H2O2 4.76E+04 2.5 16490 3 Estimated 890 NC6H14+HO2=SXC6H13+H2O2 1.90E+04 2.6 13910 3 Estimated 891 NC6H14+CH3=PXC6H13+CH4 9.03E-01 3.6 7153 3 Estimated 892 NC6H14+CH3=SXC6H13+CH4 3.00E+00 3.5 5480 3 Estimated 893 C7H13+H(+M)=C7H14(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 894 C7H13+H=CH3+C6H11 2.00E+21 -2 11000 5 Estimated 895 C7H13+HO2=CH2O+OH+C6H11 2.40E+13 0 0 5 Estimated 274 896 C7H13+HCO=C7H14+CO 6.00E+13 0 0 5 Estimated 897 C2H4+C5H9=C7H13 3.00E+11 0 7300 3 Estimated 898 C7H14+H(+M)=PXC7H15(+M) 1.33E+13 0 3261 3 Estimated LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 899 C7H14+H(+M)=SXC7H15(+M) 1.33E+13 0 1560 3 Estimated LOW-P LIMIT 8.70E+42 -7.5 4722 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 900 C7H14+H=C2H4+PXC5H11 8.00E+21 -2.4 11180 3 Estimated 901 C7H14+H=C3H6+pC4H9 1.60E+22 -2.4 11180 5 Estimated 902 C7H14+H=C7H13+H2 6.50E+05 2.5 6756 5 Estimated 903 C7H14+O=PXC6H13+HCO 3.30E+08 1.4 -402 2 Estimated 904 C7H14+O=C7H13+OH 1.50E+13 0 5760 2 Estimated 905 C7H14+O=C7H13+OH 2.60E+13 0 4470 2 Estimated 906 C7H14+OH=C7H13+H2O 7.00E+02 2.7 527 3 Estimated 907 C7H14+O2=C7H13+HO2 2.00E+13 0 50930 3 Estimated 908 C7H14+HO2=C7H13+H2O2 1.00E+12 0 14340 2 Estimated 909 C7H14+CH3=C7H13+CH4 4.50E-01 3.6 7153 3 Estimated 910 C2H4+PXC5H11=PXC7H15 3.00E+11 0 7300 3 Estimated 911 PXC7H15+H(+M)=NC7H16(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 912 PXC7H15+H=PXC5H11+C2H5 3.70E+24 -2.9 12505 3 Estimated 913 PXC7H15+H=C7H14+H2 1.80E+12 0 0 3 Estimated 914 PXC7H15+O=PXC6H13+CH2O 9.60E+13 0 0 3 Estimated 915 PXC7H15+OH=C7H14+H2O 2.40E+13 0 0 3 Estimated 916 PXC7H15+O2=C7H14+HO2 9.00E+10 0 0 5 Estimated 917 PXC7H15+HO2=PXC6H13+OH+CH2O 2.40E+13 0 0 5 Estimated 918 PXC7H15+HCO=NC7H16+CO 9.00E+13 0 0 5 Estimated 919 PXC7H15+CH3=C7H14+CH4 1.10E+13 0 0 5 Estimated 920 pC4H9+C3H6=SXC7H15 3.00E+11 0 7300 3 Estimated 921 SXC7H15+H(+M)=NC7H16(+M) 2.40E+13 0 0 3 Estimated LOW-P LIMIT 1.70E+58 -12.0811264 TROE /0.649 1213.1 1213.1 13370/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 275 922 SXC7H15+H=PXC5H11+C2H5 1.40E+28 -3.9 15916 3 Estimated 923 SXC7H15+H=C7H14+H2 3.20E+12 0 0 3 Estimated 924 SXC7H15+O=CH3CHO+PXC5H11 9.60E+13 0 0 3 Estimated 925 SXC7H15+OH=C7H14+H2O 2.40E+13 0 0 3 Estimated 926 SXC7H15+O2=C7H14+HO2 1.30E+11 0 0 3 Estimated 927 SXC7H15+HO2=CH3CHO+PXC5H11 +OH 2.40E+13 0 0 5 Estimated 928 SXC7H15+HCO=NC7H16+CO 1.20E+14 0 0 5 Estimated 929 SXC7H15+CH3=CH4+C7H14 2.20E+14 -0.7 0 5 Estimated 930 nC3H7+C4H81=S2XC7H15 3.00E+11 0 7300 3 Estimated 931 C6H12+CH3(+M)=S2XC7H15(+M) 1.70E+11 0 7404 3 Estimated LOW-P LIMIT 2.31E+28 -4.27 1831 TROE /0.565 60000 534.2 3007.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 932 S2XC7H15+O2=C7H14+HO2 1.30E+11 0 0 3 Estimated 933 C2H5+C5H10=S3XC7H15 3.00E+11 0 7300 3 Estimated 934 S3XC7H15+O2=C7H14+HO2 1.30E+11 0 0 3 Estimated 935 PXC6H13+CH3=NC7H16 1.93E+14 -0.3 0 3 Estimated 936 PXC5H11+C2H5=NC7H16 1.88E+14 -0.5 0 3 Estimated 937 pC4H9+nC3H7=NC7H16 1.88E+14 -0.5 0 3 Estimated 938 NC7H16+H=PXC7H15+H2 1.30E+06 2.5 6756 3 Estimated 939 NC7H16+H=SXC7H15+H2 2.60E+06 2.4 4471 3 Estimated 940 NC7H16+O=PXC7H15+OH 1.90E+05 2.7 3716 3 Estimated 941 NC7H16+O=SXC7H15+OH 9.52E+04 2.7 2106 3 Estimated 942 NC7H16+OH=PXC7H15+H2O 1.40E+03 2.7 527 3 Estimated 943 NC7H16+OH=SXC7H15+H2O 5.40E+04 2.4 393 3 Estimated 944 NC7H16+O2=PXC7H15+HO2 4.00E+13 0 50930 3 Estimated 945 NC7H16+O2=SXC7H15+HO2 8.00E+13 0 47590 3 Estimated 946 NC7H16+HO2=PXC7H15+H2O2 4.76E+04 2.5 16490 3 Estimated 947 NC7H16+HO2=SXC7H15+H2O2 1.90E+04 2.6 13910 3 Estimated 948 NC7H16+CH3=PXC7H15+CH4 9.03E-01 3.6 7153 3 Estimated 949 NC7H16+CH3=SXC7H15+CH4 3.00E+00 3.5 5480 3 Estimated 950 C8H15+H(+M)=C8H16(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 951 C8H15+H=CH3+C7H13 2.00E+21 -2 11000 5 Estimated 952 C8H15+HO2=CH2O+OH+C7H13 2.40E+13 0 0 5 Estimated 953 C8H15+HCO=C8H16+CO 6.00E+13 0 0 5 Estimated 276 954 C2H4+C6H11=C8H15 3.00E+11 0 7300 3 Estimated 955 C8H16+H(+M)=PXC8H17(+M) 1.33E+13 0 3261 3 Estimated LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 956 C8H16+H(+M)=SXC8H17(+M) 1.33E+13 0 1560 3 Estimated LOW-P LIMIT 8.70E+42 -7.5 4722 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 957 C8H16+H=C2H4+PXC6H13 8.00E+21 -2.4 11180 3 Estimated 958 C8H16+H=C3H6+PXC5H11 1.60E+22 -2.4 11180 5 Estimated 959 C8H16+H=C8H15+H2 6.50E+05 2.5 6756 5 Estimated 960 C8H16+O=PXC7H15+HCO 3.30E+08 1.4 -402 2 Estimated 961 C8H16+O=C8H15+OH 1.50E+13 0 5760 2 Estimated 962 C8H16+O=C8H15+OH 2.60E+13 0 4470 2 Estimated 963 C8H16+OH=C8H15+H2O 7.00E+02 2.7 527 3 Estimated 964 C8H16+O2=C8H15+HO2 2.00E+13 0 50930 3 Estimated 965 C8H16+HO2=C8H15+H2O2 1.00E+12 0 14340 2 Estimated 966 C8H16+CH3=C8H15+CH4 4.50E-01 3.6 7153 3 Estimated 967 C2H4+PXC6H13=PXC8H17 3.00E+11 0 7300 3 Estimated 968 PXC8H17+H(+M)=NC8H18(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 969 PXC8H17+H=PXC6H13+C2H5 3.70E+24 -2.9 12505 3 Estimated 970 PXC8H17+H=C8H16+H2 1.80E+12 0 0 3 Estimated 971 PXC8H17+O=PXC7H15+CH2O 9.60E+13 0 0 3 Estimated 972 PXC8H17+OH=C8H16+H2O 2.40E+13 0 0 3 Estimated 973 PXC8H17+O2=C8H16+HO2 9.00E+10 0 0 5 Estimated 974 PXC8H17+HO2=PXC7H15+OH+CH2O 2.40E+13 0 0 5 Estimated 975 PXC8H17+HCO=NC8H18+CO 9.00E+13 0 0 5 Estimated 976 PXC8H17+CH3=C8H16+CH4 1.10E+13 0 0 5 Estimated 977 PXC5H11+C3H6=SXC8H17 3.00E+11 0 7300 3 Estimated 978 SXC8H17+H(+M)=NC8H18(+M) 2.40E+13 0 0 3 Estimated LOW-P LIMIT 1.70E+58 -12.0811264 TROE /0.649 1213.1 1213.1 13370/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 979 SXC8H17+H=PXC6H13+C2H5 1.40E+28 -3.9 15916 3 Estimated 277 980 SXC8H17+H=C8H16+H2 3.20E+12 0 0 3 Estimated 981 SXC8H17+O=CH3CHO+PXC6H13 9.60E+13 0 0 3 Estimated 982 SXC8H17+OH=C8H16+H2O 2.40E+13 0 0 3 Estimated 983 SXC8H17+O2=C8H16+HO2 1.30E+11 0 0 3 Estimated 984 SXC8H17+HO2=CH3CHO+PXC6H13 +OH 2.40E+13 0 0 5 Estimated 985 SXC8H17+HCO=NC8H18+CO 1.20E+14 0 0 5 Estimated 986 SXC8H17+CH3=CH4+C8H16 2.20E+14 -0.7 0 5 Estimated 987 pC4H9+C4H81=S2XC8H17 3.00E+11 0 7300 3 Estimated 988 C7H14+CH3(+M)=S2XC8H17(+M) 1.70E+11 0 7404 3 Estimated LOW-P LIMIT 2.31E+28 -4.27 1831 TROE /0.565 60000 534.2 3007.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 989 S2XC8H17+O2=C8H16+HO2 1.30E+11 0 0 3 Estimated 990 nC3H7+C5H10=S3XC8H17 3.00E+11 0 7300 3 Estimated 991 C6H12+C2H5=S3XC8H17 3.00E+11 0 7300 3 Estimated 992 S3XC8H17+O2=C8H16+HO2 1.30E+11 0 0 3 Estimated 993 PXC7H15+CH3=NC8H18 1.93E+14 -0.3 0 3 Estimated 994 PXC6H13+C2H5=NC8H18 1.88E+14 -0.5 0 3 Estimated 995 PXC5H11+nC3H7=NC8H18 1.88E+14 -0.5 0 3 Estimated 996 pC4H9+pC4H9=NC8H18 1.88E+14 -0.5 0 3 Estimated 997 NC8H18+H=PXC8H17+H2 1.30E+06 2.5 6756 3 Estimated 998 NC8H18+H=SXC8H17+H2 2.60E+06 2.4 4471 3 Estimated 999 NC8H18+O=PXC8H17+OH 1.90E+05 2.7 3716 3 Estimated 1000 NC8H18+O=SXC8H17+OH 9.52E+04 2.7 2106 3 Estimated 1001 NC8H18+OH=PXC8H17+H2O 1.40E+03 2.7 527 3 Estimated 1002 NC8H18+OH=SXC8H17+H2O 5.40E+04 2.4 393 3 Estimated 1003 NC8H18+O2=PXC8H17+HO2 4.00E+13 0 50930 3 Estimated 1004 NC8H18+O2=SXC8H17+HO2 8.00E+13 0 47590 3 Estimated 1005 NC8H18+HO2=PXC8H17+H2O2 4.76E+04 2.5 16490 3 Estimated 1006 NC8H18+HO2=SXC8H17+H2O2 1.90E+04 2.6 13910 3 Estimated 1007 NC8H18+CH3=PXC8H17+CH4 9.03E-01 3.6 7153 3 Estimated 1008 NC8H18+CH3=SXC8H17+CH4 3.00E+00 3.5 5480 3 Estimated 1009 C9H17+H(+M)=C9H18(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1010 C9H17+H=CH3+C8H15 2.00E+21 -2 11000 5 Estimated 1011 C9H17+HO2=CH2O+OH+C8H15 2.40E+13 0 0 5 Estimated 278 1012 C9H17+HCO=C9H18+CO 6.00E+13 0 0 5 Estimated 1013 C2H4+C7H13=C9H17 3.00E+11 0 7300 3 Estimated 1014 C9H18+H(+M)=PXC9H19(+M) 1.33E+13 0 3261 3 Estimated LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1015 C9H18+H(+M)=SXC9H19(+M) 1.33E+13 0 1560 3 Estimated LOW-P LIMIT 8.70E+42 -7.5 4722 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1016 C9H18+H=C2H4+PXC7H15 8.00E+21 -2.4 11180 3 Estimated 1017 C9H18+H=C3H6+PXC6H13 1.60E+22 -2.4 11180 5 Estimated 1018 C9H18+H=C9H17+H2 6.50E+05 2.5 6756 5 Estimated 1019 C9H18+O=PXC8H17+HCO 3.30E+08 1.4 -402 2 Estimated 1020 C9H18+O=C9H17+OH 1.50E+13 0 5760 2 Estimated 1021 C9H18+O=C9H17+OH 2.60E+13 0 4470 2 Estimated 1022 C9H18+OH=C9H17+H2O 7.00E+02 2.7 527 3 Estimated 1023 C9H18+O2=C9H17+HO2 2.00E+13 0 50930 3 Estimated 1024 C9H18+HO2=C9H17+H2O2 1.00E+12 0 14340 2 Estimated 1025 C9H18+CH3=C9H17+CH4 4.50E-01 3.6 7153 3 Estimated 1026 C2H4+PXC7H15=PXC9H19 3.00E+11 0 7300 3 Estimated 1027 PXC9H19+H(+M)=NC9H20(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1028 PXC9H19+H=PXC7H15+C2H5 3.70E+24 -2.9 12505 3 Estimated 1029 PXC9H19+H=C9H18+H2 1.80E+12 0 0 3 Estimated 1030 PXC9H19+O=PXC8H17+CH2O 9.60E+13 0 0 3 Estimated 1031 PXC9H19+OH=C9H18+H2O 2.40E+13 0 0 3 Estimated 1032 PXC9H19+O2=C9H18+HO2 9.00E+10 0 0 5 Estimated 1033 PXC9H19+HO2=PXC8H17+OH+CH2O 2.40E+13 0 0 5 Estimated 1034 PXC9H19+HCO=NC9H20+CO 9.00E+13 0 0 5 Estimated 1035 PXC9H19+CH3=C9H18+CH4 1.10E+13 0 0 5 Estimated 1036 C3H6+PXC6H13=SXC9H19 3.00E+11 0 7300 3 Estimated 1037 SXC9H19+H(+M)=NC9H20(+M) 2.40E+13 0 0 3 Estimated LOW-P LIMIT 1.70E+58 -12.0811264 TROE /0.649 1213.1 1213.1 13370/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 279 1038 SXC9H19+H=PXC7H15+C2H5 1.40E+28 -3.9 15916 3 Estimated 1039 SXC9H19+H=C9H18+H2 3.20E+12 0 0 3 Estimated 1040 SXC9H19+O=CH3CHO+PXC7H15 9.60E+13 0 0 3 Estimated 1041 SXC9H19+OH=C9H18+H2O 2.40E+13 0 0 3 Estimated 1042 SXC9H19+O2=C9H18+HO2 1.30E+11 0 0 3 Estimated 1043 SXC9H19+HO2=CH3CHO+PXC7H15 +OH 2.40E+13 0 0 5 Estimated 1044 SXC9H19+HCO=NC9H20+CO 1.20E+14 0 0 5 Estimated 1045 SXC9H19+CH3=CH4+C9H18 2.20E+14 -0.7 0 5 Estimated 1046 PXC5H11+C4H81=S2XC9H19 3.00E+11 0 7300 3 Estimated 1047 C8H16+CH3(+M)=S2XC9H19(+M) 1.70E+11 0 7404 3 Estimated LOW-P LIMIT 2.31E+28 -4.27 1831 TROE /0.565 60000 534.2 3007.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1048 S2XC9H19+O2=C9H18+HO2 1.30E+11 0 0 3 Estimated 1049 pC4H9+C5H10=S3XC9H19 3.00E+11 0 7300 3 Estimated 1050 C7H14+C2H5=S3XC9H19 3.00E+11 0 7300 3 Estimated 1051 S3XC9H19+O2=C9H18+HO2 1.30E+11 0 0 3 Estimated 1052 nC3H7+C6H12=S4XC9H19 3.00E+11 0 7300 3 Estimated 1053 S4XC9H19+O2=C9H18+HO2 1.30E+11 0 0 3 Estimated 1054 PXC8H17+CH3=NC9H20 1.93E+14 -0.3 0 3 Estimated 1055 PXC7H15+C2H5=NC9H20 1.88E+14 -0.5 0 3 Estimated 1056 PXC6H13+nC3H7=NC9H20 1.88E+14 -0.5 0 3 Estimated 1057 PXC5H11+pC4H9=NC9H20 1.88E+14 -0.5 0 3 Estimated 1058 NC9H20+H=PXC9H19+H2 1.30E+06 2.5 6756 3 Estimated 1059 NC9H20+H=SXC9H19+H2 2.60E+06 2.4 4471 3 Estimated 1060 NC9H20+O=PXC9H19+OH 1.90E+05 2.7 3716 3 Estimated 1061 NC9H20+O=SXC9H19+OH 9.52E+04 2.7 2106 3 Estimated 1062 NC9H20+OH=PXC9H19+H2O 1.40E+03 2.7 527 3 Estimated 1063 NC9H20+OH=SXC9H19+H2O 5.40E+04 2.4 393 3 Estimated 1064 NC9H20+O2=PXC9H19+HO2 4.00E+13 0 50930 3 Estimated 1065 NC9H20+O2=SXC9H19+HO2 8.00E+13 0 47590 3 Estimated 1066 NC9H20+HO2=PXC9H19+H2O2 4.76E+04 2.5 16490 3 Estimated 1067 NC9H20+HO2=SXC9H19+H2O2 1.90E+04 2.6 13910 3 Estimated 1068 NC9H20+CH3=PXC9H19+CH4 9.03E-01 3.6 7153 3 Estimated 1069 NC9H20+CH3=SXC9H19+CH4 3.00E+00 3.5 5480 3 Estimated 1070 C10H19+H(+M)=C10H20(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ 280 H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1071 C10H19+H=CH3+C9H17 2.00E+21 -2 11000 5 Estimated 1072 C10H19+HO2=CH2O+OH+C9H17 2.40E+13 0 0 5 Estimated 1073 C10H19+HCO=C10H20+CO 6.00E+13 0 0 5 Estimated 1074 C2H4+C8H15=C10H19 3.00E+11 0 7300 3 Estimated 1075 C10H20+H(+M)=PXC10H21(+M) 1.33E+13 0 3261 3 Estimated LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1076 C10H20+H(+M)=SXC10H21(+M) 1.33E+13 0 1560 3 Estimated LOW-P LIMIT 8.70E+42 -7.5 4722 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1077 C10H20+H=C2H4+PXC8H17 8.00E+21 -2.4 11180 3 Estimated 1078 C10H20+H=C3H6+PXC7H15 1.60E+22 -2.4 11180 5 Estimated 1079 C10H20+H=C10H19+H2 6.50E+05 2.5 6756 5 Estimated 1080 C10H20+O=PXC9H19+HCO 3.30E+08 1.4 -402 2 Estimated 1081 C10H20+O=C10H19+OH 1.50E+13 0 5760 2 Estimated 1082 C10H20+O=C10H19+OH 2.60E+13 0 4470 2 Estimated 1083 C10H20+OH=C10H19+H2O 7.00E+02 2.7 527 3 Estimated 1084 C10H20+O2=C10H19+HO2 2.00E+13 0 50930 3 Estimated 1085 C10H20+HO2=C10H19+H2O2 1.00E+12 0 14340 2 Estimated 1086 C10H20+CH3=C10H19+CH4 4.50E-01 3.6 7153 3 Estimated 1087 C2H4+PXC8H17=PXC10H21 3.00E+11 0 7300 3 Estimated 1088 PXC10H21+H(+M)=NC10H22(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1089 PXC10H21+H=PXC8H17+C2H5 3.70E+24 -2.9 12505 3 Estimated 1090 PXC10H21+H=C10H20+H2 1.80E+12 0 0 3 Estimated 1091 PXC10H21+O=PXC9H19+CH2O 9.60E+13 0 0 3 Estimated 1092 PXC10H21+OH=C10H20+H2O 2.40E+13 0 0 3 Estimated 1093 PXC10H21+O2=C10H20+HO2 9.00E+10 0 0 5 Estimated 1094 PXC10H21+HO2=PXC9H19+OH+CH2O2.40E+13 0 0 5 Estimated 1095 PXC10H21+HCO=NC10H22+CO 9.00E+13 0 0 5 Estimated 1096 PXC10H21+CH3=C10H20+CH4 1.10E+13 0 0 5 Estimated 1097 C3H6+PXC7H15=SXC10H21 3.00E+11 0 7300 3 Estimated 1098 SXC10H21+H(+M)=NC10H22(+M) 2.40E+13 0 0 3 Estimated 281 LOW-P LIMIT 1.70E+58 -12.0811264 TROE /0.649 1213.1 1213.1 13370/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1099 SXC10H21+H=PXC8H17+C2H5 1.40E+28 -3.9 15916 3 Estimated 1100 SXC10H21+H=C10H20+H2 3.20E+12 0 0 3 Estimated 1101 SXC10H21+O=CH3CHO+PXC8H17 9.60E+13 0 0 3 Estimated 1102 SXC10H21+OH=C10H20+H2O 2.40E+13 0 0 3 Estimated 1103 SXC10H21+O2=C10H20+HO2 1.30E+11 0 0 3 Estimated 1104 SXC10H21+HO2=CH3CHO+PXC8H17 +OH 2.40E+13 0 0 5 Estimated 1105 SXC10H21+HCO=NC10H22+CO 1.20E+14 0 0 5 Estimated 1106 SXC10H21+CH3=CH4+C10H20 2.20E+14 -0.7 0 5 Estimated 1107 PXC6H13+C4H81=S2XC10H21 3.00E+11 0 7300 3 Estimated 1108 C9H18+CH3(+M)=S2XC10H21(+M) 1.70E+11 0 7404 3 Estimated LOW-P LIMIT 2.31E+28 -4.27 1831 TROE /0.565 60000 534.2 3007.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1109 S2XC10H21+O2=C10H20+HO2 1.30E+11 0 0 3 Estimated 1110 PXC5H11+C5H10=S3XC10H21 3.00E+11 0 7300 3 Estimated 1111 C8H16+C2H5=S3XC10H21 3.00E+11 0 7300 3 Estimated 1112 S3XC10H21+O2=C10H20+HO2 1.30E+11 0 0 3 Estimated 1113 pC4H9+C6H12=S4XC10H21 3.00E+11 0 7300 3 Estimated 1114 C7H14+nC3H7=S4XC10H21 3.00E+11 0 7300 3 Estimated 1115 S4XC10H21+O2=C10H20+HO2 1.30E+11 0 0 3 Estimated 1116 PXC9H19+CH3=NC10H22 1.93E+14 -0.3 0 3 Estimated 1117 PXC8H17+C2H5=NC10H22 1.88E+14 -0.5 0 3 Estimated 1118 PXC7H15+nC3H7=NC10H22 1.88E+14 -0.5 0 3 Estimated 1119 PXC6H13+pC4H9=NC10H22 1.88E+14 -0.5 0 3 Estimated 1120 PXC5H11+PXC5H11=NC10H22 1.88E+14 -0.5 0 3 Estimated 1121 NC10H22+H=PXC10H21+H2 1.30E+06 2.5 6756 3 Estimated 1122 NC10H22+H=SXC10H21+H2 2.60E+06 2.4 4471 3 Estimated 1123 NC10H22+O=PXC10H21+OH 1.90E+05 2.7 3716 3 Estimated 1124 NC10H22+O=SXC10H21+OH 9.52E+04 2.7 2106 3 Estimated 1125 NC10H22+OH=PXC10H21+H2O 1.40E+03 2.7 527 3 Estimated 1126 NC10H22+OH=SXC10H21+H2O 5.40E+04 2.4 393 3 Estimated 1127 NC10H22+O2=PXC10H21+HO2 4.00E+13 0 50930 3 Estimated 1128 NC10H22+O2=SXC10H21+HO2 8.00E+13 0 47590 3 Estimated 1129 NC10H22+HO2=PXC10H21+H2O2 4.76E+04 2.5 16490 3 Estimated 1130 NC10H22+HO2=SXC10H21+H2O2 1.90E+04 2.6 13910 3 Estimated 282 1131 NC10H22+CH3=PXC10H21+CH4 9.03E-01 3.6 7153 3 Estimated 1132 NC10H22+CH3=SXC10H21+CH4 3.00E+00 3.5 5480 3 Estimated 1133 C11H21+H(+M)=C11H22(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1134 C11H21+H=CH3+C10H19 2.00E+21 -2 11000 5 Estimated 1135 C11H21+HO2=CH2O+OH+C10H19 2.40E+13 0 0 5 Estimated 1136 C11H21+HCO=C11H22+CO 6.00E+13 0 0 5 Estimated 1137 C2H4+C9H17=C11H21 3.00E+11 0 7300 3 Estimated 1138 C11H22+H(+M)=PXC11H23(+M) 1.33E+13 0 3261 3 Estimated LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1139 C11H22+H(+M)=SXC11H23(+M) 1.33E+13 0 1560 3 Estimated LOW-P LIMIT 8.70E+42 -7.5 4722 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1140 C11H22+H=C2H4+PXC9H19 8.00E+21 -2.4 11180 3 Estimated 1141 C11H22+H=C3H6+PXC8H17 1.60E+22 -2.4 11180 5 Estimated 1142 C11H22+H=C11H21+H2 6.50E+05 2.5 6756 5 Estimated 1143 C11H22+O=PXC10H21+HCO 3.30E+08 1.4 -402 2 Estimated 1144 C11H22+O=C11H21+OH 1.50E+13 0 5760 2 Estimated 1145 C11H22+O=C11H21+OH 2.60E+13 0 4470 2 Estimated 1146 C11H22+OH=C11H21+H2O 7.00E+02 2.7 527 3 Estimated 1147 C11H22+O2=C11H21+HO2 2.00E+13 0 50930 3 Estimated 1148 C11H22+HO2=C11H21+H2O2 1.00E+12 0 14340 2 Estimated 1149 C11H22+CH3=C11H21+CH4 4.50E-01 3.6 7153 3 Estimated 1150 C2H4+PXC9H19=PXC11H23 3.00E+11 0 7300 3 Estimated 1151 PXC11H23+H(+M)=NC11H24(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1152 PXC11H23+H=PXC9H19+C2H5 3.70E+24 -2.9 12505 3 Estimated 1153 PXC11H23+H=C11H22+H2 1.80E+12 0 0 3 Estimated 1154 PXC11H23+O=PXC10H21+CH2O 9.60E+13 0 0 3 Estimated 1155 PXC11H23+OH=C11H22+H2O 2.40E+13 0 0 3 Estimated 1156 PXC11H23+O2=C11H22+HO2 9.00E+10 0 0 5 Estimated 283 1157 PXC11H23+HO2=PXC10H21+OH +CH2O 2.40E+13 0 0 5 Estimated 1158 PXC11H23+HCO=NC11H24+CO 9.00E+13 0 0 5 Estimated 1159 PXC11H23+CH3=C11H22+CH4 1.10E+13 0 0 5 Estimated 1160 PXC8H17+C3H6=SXC11H23 3.00E+11 0 7300 3 Estimated 1161 SXC11H23+H(+M)=NC11H24(+M) 2.40E+13 0 0 3 Estimated LOW-P LIMIT 1.70E+58 -12.0811264 TROE /0.649 1213.1 1213.1 13370/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1162 SXC11H23+H=PXC9H19+C2H5 1.40E+28 -3.9 15916 3 Estimated 1163 SXC11H23+H=C11H22+H2 3.20E+12 0 0 3 Estimated 1164 SXC11H23+O=CH3CHO+PXC9H19 9.60E+13 0 0 3 Estimated 1165 SXC11H23+OH=C11H22+H2O 2.40E+13 0 0 3 Estimated 1166 SXC11H23+O2=C11H22+HO2 1.30E+11 0 0 3 Estimated 1167 SXC11H23+HO2=CH3CHO+PXC9H19 +OH 2.40E+13 0 0 5 Estimated 1168 SXC11H23+HCO=NC11H24+CO 1.20E+14 0 0 5 Estimated 1169 SXC11H23+CH3=CH4+C11H22 2.20E+14 -0.7 0 5 Estimated 1170 PXC7H15+C4H81=S2XC11H23 3.00E+11 0 7300 3 Estimated 1171 C10H20+CH3(+M)=S2XC11H23(+M) 1.70E+11 0 7404 3 Estimated LOW-P LIMIT 2.31E+28 -4.27 1831 TROE /0.565 60000 534.2 3007.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1172 S2XC11H23+O2=C11H22+HO2 1.30E+11 0 0 3 Estimated 1173 PXC6H13+C5H10=S3XC11H23 3.00E+11 0 7300 3 Estimated 1174 C9H18+C2H5=S3XC11H23 3.00E+11 0 7300 3 Estimated 1175 S3XC11H23+O2=C11H22+HO2 1.30E+11 0 0 3 Estimated 1176 PXC5H11+C6H12=S4XC11H23 3.00E+11 0 7300 3 Estimated 1177 C8H16+nC3H7=S4XC11H23 3.00E+11 0 7300 3 Estimated 1178 S4XC11H23+O2=C11H22+HO2 1.30E+11 0 0 3 Estimated 1179 pC4H9+C7H14=S5XC11H23 3.00E+11 0 7300 3 Estimated 1180 S5XC11H23+O2=C11H22+HO2 1.30E+11 0 0 3 Estimated 1181 PXC10H21+CH3=NC11H24 1.93E+14 -0.3 0 3 Estimated 1182 PXC9H19+C2H5=NC11H24 1.88E+14 -0.5 0 3 Estimated 1183 PXC8H17+nC3H7=NC11H24 1.88E+14 -0.5 0 3 Estimated 1184 PXC7H15+pC4H9=NC11H24 1.88E+14 -0.5 0 3 Estimated 1185 PXC6H13+PXC5H11=NC11H24 1.88E+14 -0.5 0 3 Estimated 1186 NC11H24+H=PXC11H23+H2 1.30E+06 2.5 6756 3 Estimated 1187 NC11H24+H=SXC11H23+H2 2.60E+06 2.4 4471 3 Estimated 1188 NC11H24+O=PXC11H23+OH 1.90E+05 2.7 3716 3 Estimated 284 1189 NC11H24+O=SXC11H23+OH 9.52E+04 2.7 2106 3 Estimated 1190 NC11H24+OH=PXC11H23+H2O 1.40E+03 2.7 527 3 Estimated 1191 NC11H24+OH=SXC11H23+H2O 5.40E+04 2.4 393 3 Estimated 1192 NC11H24+O2=PXC11H23+HO2 4.00E+13 0 50930 3 Estimated 1193 NC11H24+O2=SXC11H23+HO2 8.00E+13 0 47590 3 Estimated 1194 NC11H24+HO2=PXC11H23+H2O2 4.76E+04 2.5 16490 3 Estimated 1195 NC11H24+HO2=SXC11H23+H2O2 1.90E+04 2.6 13910 3 Estimated 1196 NC11H24+CH3=PXC11H23+CH4 9.03E-01 3.6 7153 3 Estimated 1197 NC11H24+CH3=SXC11H23+CH4 3.00E+00 3.5 5480 3 Estimated 1198 C12H23+H(+M)=C12H24(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1199 C12H23+H=CH3+C11H21 2.00E+21 -2 11000 5 Estimated 1200 C12H23+HO2=CH2O+OH+C11H21 2.40E+13 0 0 5 Estimated 1201 C12H23+HCO=C12H24+CO 6.00E+13 0 0 5 Estimated 1202 C2H4+C10H19=C12H23 3.00E+11 0 7300 3 Estimated 1203 C12H24+H(+M)=PXC12H25(+M) 1.33E+13 0 3261 3 Estimated LOW-P LIMIT 6.26E+38 -6.66 7000 TROE /1 1000 1310 48097/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1204 C12H24+H(+M)=SXC12H25(+M) 1.33E+13 0 1560 3 Estimated LOW-P LIMIT 8.70E+42 -7.5 4722 TROE /1 1000 645.4 6844.3/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1205 C12H24+H=C2H4+PXC10H21 8.00E+21 -2.4 11180 3 Estimated 1206 C12H24+H=C3H6+PXC9H19 1.60E+22 -2.4 11180 5 Estimated 1207 C12H24+H=C12H23+H2 6.50E+05 2.5 6756 5 Estimated 1208 C12H24+O=PXC11H23+HCO 3.30E+08 1.4 -402 2 Estimated 1209 C12H24+O=C12H23+OH 1.50E+13 0 5760 2 Estimated 1210 C12H24+O=C12H23+OH 2.60E+13 0 4470 2 Estimated 1211 C12H24+OH=C12H23+H2O 7.00E+02 2.7 527 3 Estimated 1212 C12H24+O2=C12H23+HO2 2.00E+13 0 50930 3 Estimated 1213 C12H24+HO2=C12H23+H2O2 1.00E+12 0 14340 2 Estimated 1214 C12H24+CH3=C12H23+CH4 4.50E-01 3.6 7153 3 Estimated 1215 C2H4+PXC10H21=PXC12H25 3.00E+11 0 7300 3 Estimated 1216 PXC12H25+H(+M)=NC12H26(+M) 3.60E+13 0 0 3 Estimated LOW-P LIMIT 3.01E+48 -9.32 5834 285 TROE /0.498 1314 1314 50000/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ 1217 C3H6+PXC9H19=SXC12H25 3.00E+11 0 7300 3 Estimated 1218 SXC12H25+H=PXC10H21+C2H5 1.40E+28 -3.9 15916 3 Estimated 1219 SXC12H25+H=C12H24+H2 3.20E+12 0 0 3 Estimated 1220 SXC12H25+O=CH3CHO+PXC10H21 9.60E+13 0 0 3 Estimated 1221 SXC12H25+OH=C12H24+H2O 2.40E+13 0 0 3 Estimated 1222 SXC12H25+O2=C12H24+HO2 1.30E+11 0 0 3 Estimated 1223 SXC12H25+HO2=CH3CHO+PXC10H21 +OH 2.40E+13 0 0 5 Estimated 1224 SXC12H25+CH3=CH4+C12H24 2.20E+14 -0.7 0 5 Estimated 1225 C4H81+PXC8H17=S2XC12H25 3.00E+11 0 7300 3 Estimated 1226 C11H22+CH3(+M)=S2XC12H25(+M) 1.70E+11 0 7404 3 Estimated 1227 LOW-P LIMIT 2.31E+28 -4.27 1831 TROE /0.565 60000 534.2 3007.2/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ S2XC12H25+O2=C12H24+HO2 1.30E+11 0 0 3 Estimated 1228 C5H10+PXC7H15=S3XC12H25 3.00E+11 0 7300 3 Estimated 1229 C10H20+C2H5=S3XC12H25 3.00E+11 0 7300 3 Estimated 1230 S3XC12H25+O2=C12H24+HO2 1.30E+11 0 0 3 Estimated 1231 C6H12+PXC6H13=S4XC12H25 3.00E+11 0 7300 3 Estimated 1232 C9H18+nC3H7=S4XC12H25 3.00E+11 0 7300 3 Estimated 1233 S4XC12H25+O2=C12H24+HO2 1.30E+11 0 0 3 Estimated 1234 C7H14+PXC5H11=S5XC12H25 3.00E+11 0 7300 3 Estimated 1235 C8H16+pC4H9=S5XC12H25 3.00E+11 0 7300 3 Estimated 1236 S5XC12H25+O2=C12H24+HO2 1.30E+11 0 0 3 Estimated 1237 PXC12H25=SXC12H25 3.56E+10 0.9 39000 3 (Matheu et al. 2003) 1238 PXC11H23=SXC11H23 3.56E+10 0.9 39000 3 (Matheu et al. 2003) 1239 PXC10H21=SXC10H21 3.56E+10 0.9 39000 3 (Matheu et al. 2003) 1240 PXC9H19=SXC9H19 3.56E+10 0.9 39000 3 (Matheu et al. 2003) 1241 PXC8H17=SXC8H17 3.56E+10 0.9 39000 3 (Matheu et al. 2003) 1242 PXC7H15=SXC7H15 3.56E+10 0.9 39000 3 (Matheu et al. 2003) 1243 PXC6H13=SXC6H13 3.56E+10 0.9 39000 3 (Matheu et al. 2003) 1244 PXC5H11=SXC5H11 3.56E+10 0.9 39000 3 (Matheu et al. 2003) 1245 PXC12H25=S2XC12H25 3.80E+10 0.7 37500 3 (Matheu et al. 2003) 1246 PXC11H23=S2XC11H23 3.80E+10 0.7 37500 3 (Matheu et al. 2003) 1247 PXC10H21=S2XC10H21 3.80E+10 0.7 37500 3 (Matheu et al. 2003) 1248 PXC9H19=S2XC9H19 3.80E+10 0.7 37500 3 (Matheu et al. 2003) 1249 PXC8H17=S2XC8H17 3.80E+10 0.7 37500 3 (Matheu et al. 2003) 286 1250 PXC7H15=S2XC7H15 3.80E+10 0.7 37500 3 (Matheu et al. 2003) 1251 PXC6H13=S2XC6H13 3.80E+10 0.7 37500 3 (Matheu et al. 2003) 1252 PXC5H11=S2XC5H11 3.80E+10 0.7 37500 3 (Matheu et al. 2003) 1253 PXC12H25=S3XC12H25 7.85E+11 -0.1 22200 3 (Matheu et al. 2003) 1254 PXC11H23=S3XC11H23 7.85E+11 -0.1 22200 3 (Matheu et al. 2003) 1255 PXC10H21=S3XC10H21 7.85E+11 -0.1 22200 3 (Matheu et al. 2003) 1256 PXC9H19=S3XC9H19 7.85E+11 -0.1 22200 3 (Matheu et al. 2003) 1257 PXC8H17=S3XC8H17 7.85E+11 -0.1 22200 3 (Matheu et al. 2003) 1258 PXC7H15=S3XC7H15 7.85E+11 -0.1 22200 3 (Matheu et al. 2003) 1259 PXC12H25=S4XC12H25 3.67E+12 -0.6 14400 3 (Matheu et al. 2003) 1260 PXC11H23=S4XC11H23 3.67E+12 -0.6 14400 3 (Matheu et al. 2003) 1261 PXC10H21=S4XC10H21 3.67E+12 -0.6 14400 3 (Matheu et al. 2003) 1262 PXC9H19=S4XC9H19 3.67E+12 -0.6 14400 3 (Matheu et al. 2003) 1263 PXC12H25=S5XC12H25 2.80E+10 0 18400 3 (Matheu et al. 2003) 1264 PXC11H23=S5XC11H23 2.80E+10 0 18400 3 (Matheu et al. 2003) 1265 PXC11H23+CH3=NC12H26 1.93E+14 -0.3 0 3 Estimated 1266 PXC10H21+C2H5=NC12H26 1.88E+14 -0.5 0 3 Estimated 1267 PXC9H19+nC3H7=NC12H26 1.88E+14 -0.5 0 3 Estimated 1268 PXC8H17+pC4H9=NC12H26 1.88E+14 -0.5 0 3 Estimated 1269 PXC7H15+PXC5H11=NC12H26 1.88E+14 -0.5 0 3 Estimated 1270 PXC6H13+PXC6H13=NC12H26 1.88E+14 -0.5 0 3 Estimated 1271 NC12H26+H=PXC12H25+H2 1.30E+06 2.5 6756 3 Estimated 1272 NC12H26+H=SXC12H25+H2 1.30E+06 2.4 4471 3 Estimated 1273 NC12H26+H=S2XC12H25+H2 1.30E+06 2.4 4471 3 Estimated 1274 NC12H26+H=S3XC12H25+H2 1.30E+06 2.4 4471 3 Estimated 1275 NC12H26+H=S4XC12H25+H2 1.30E+06 2.4 4471 3 Estimated 1276 NC12H26+H=S5XC12H25+H2 1.30E+06 2.4 4471 3 Estimated 1277 NC12H26+O=PXC12H25+OH 1.90E+05 2.7 3716 3 Estimated 1278 NC12H26+O=SXC12H25+OH 4.76E+04 2.7 2106 3 Estimated 1279 NC12H26+O=S2XC12H25+OH 4.76E+04 2.7 2106 3 Estimated 1280 NC12H26+O=S3XC12H25+OH 4.76E+04 2.7 2106 3 Estimated 1281 NC12H26+O=S4XC12H25+OH 4.76E+04 2.7 2106 3 Estimated 1282 NC12H26+O=S5XC12H25+OH 4.76E+04 2.7 2106 3 Estimated 1283 NC12H26+OH=PXC12H25+H2O 1.40E+03 2.7 527 3 Estimated 1284 NC12H26+OH=SXC12H25+H2O 2.70E+04 2.4 393 3 Estimated 1285 NC12H26+OH=S2XC12H25+H2O 2.70E+04 2.4 393 3 Estimated 1286 NC12H26+OH=S3XC12H25+H2O 2.70E+04 2.4 393 3 Estimated 1287 NC12H26+OH=S4XC12H25+H2O 2.70E+04 2.4 393 3 Estimated 1288 NC12H26+OH=S5XC12H25+H2O 2.70E+04 2.4 393 3 Estimated 287 1289 NC12H26+O2=PXC12H25+HO2 4.00E+13 0 50930 3 Estimated 1290 NC12H26+O2=SXC12H25+HO2 4.00E+13 0 47590 3 Estimated 1291 NC12H26+O2=S2XC12H25+HO2 4.00E+13 0 47590 3 Estimated 1292 NC12H26+O2=S3XC12H25+HO2 4.00E+13 0 47590 3 Estimated 1293 NC12H26+O2=S4XC12H25+HO2 4.00E+13 0 47590 3 Estimated 1294 NC12H26+O2=S5XC12H25+HO2 4.00E+13 0 47590 3 Estimated 1295 NC12H26+HO2=PXC12H25+H2O2 4.76E+04 2.5 16490 3 Estimated 1296 NC12H26+HO2=SXC12H25+H2O2 9.50E+03 2.6 13910 3 Estimated 1297 NC12H26+HO2=S2XC12H25+H2O2 9.50E+03 2.6 13910 3 Estimated 1298 NC12H26+HO2=S3XC12H25+H2O2 9.50E+03 2.6 13910 3 Estimated 1299 NC12H26+HO2=S4XC12H25+H2O2 9.50E+03 2.6 13910 3 Estimated 1300 NC12H26+HO2=S5XC12H25+H2O2 9.50E+03 2.6 13910 3 Estimated 1301 NC12H26+CH3=PXC12H25+CH4 1.81E+00 3.6 7153 3 Estimated 1302 NC12H26+CH3=SXC12H25+CH4 3.00E+00 3.5 5480 3 Estimated 1303 NC12H26+CH3=S2XC12H25+CH4 3.00E+00 3.5 5480 3 Estimated 1304 NC12H26+CH3=S3XC12H25+CH4 3.00E+00 3.5 5480 3 Estimated 1305 NC12H26+CH3=S4XC12H25+CH4 3.00E+00 3.5 5480 3 Estimated 1306 NC12H26+CH3=S5XC12H25+CH4 3.00E+00 3.5 5480 3 Estimated 1307 PXC12H25+O2=PC12H25O2 5.00E+12 0.0 0.0 10 Estimated 1308 SXC12H25+O2=PC12H25O2 5.00E+12 0.0 0.0 10 Estimated 1309 S2XC12H25+O2=PC12H25O2 5.00E+12 0.0 0.0 10 Estimated 1310 S3XC12H25+O2=PC12H25O2 5.00E+12 0.0 0.0 10 Estimated 1311 S4XC12H25+O2=PC12H25O2 5.00E+12 0.0 0.0 10 Estimated 1312 S5XC12H25+O2=PC12H25O2 5.00E+12 0.0 0.0 10 Estimated 1313 PC12H25O2=>P12OOHX2 2.00E+12 0.0 17017 10 Estimated 1314 P12OOHX2=>PC12H25O2 1.00E+11 0.0 12500 10 Estimated 1315 P12OOHX2=C12H24+HO2 8.50E+12 0.0 25574 10 Estimated 1316 P12OOHX2+O2=SOO12OOH 5.00E+12 0.0 0.0 10 Estimated 1317 SOO12OOH=OC12OOH+OH 1.50E+12 0.0 0.0 10 Estimated 1318 OC12OOH=CH2O+4C2H4+C2H5+OH+ CO 7.00E+14 0.0 42065.10 Estimated
Abstract (if available)
Abstract
Basic understanding of the combustion kinetics of jet fuels is critical to optimal design of gas-turbine engines. Because jet fuels contain a large number of compounds, a current approach to their combustion kinetics is to use a surrogate, containing several compounds, to mimic jet-fuel behaviors. Towards the goal of developing a combustion kinetic model for jet-fuel surrogates, a theoretical study was undertook here, focusing largely on a particular class of surrogate component, namely, the normal alkanes.
Linked assets
University of Southern California Dissertations and Theses
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Asset Metadata
Creator
You, Xiaoqing
(author)
Core Title
A theoretical study of normal alkane combustion
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Publication Date
07/01/2008
Defense Date
06/13/2008
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
combustion kinetics,jet fuels,kinetic models,normal alkane,OAI-PMH Harvest,theoretical studies
Language
English
Advisor
Wang, Hai (
committee chair
), Egolfopoulos, Fokion N. (
committee member
), Krylov, Anna I. (
committee member
), Ronney, Paul D. (
committee member
)
Creator Email
xyou@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m1308
Unique identifier
UC1158805
Identifier
etd-You-20080701 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-84124 (legacy record id),usctheses-m1308 (legacy record id)
Legacy Identifier
etd-You-20080701.pdf
Dmrecord
84124
Document Type
Dissertation
Rights
You, Xiaoqing
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
combustion kinetics
jet fuels
kinetic models
normal alkane
theoretical studies