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Catalytic methane ignition over freely-suspended palladium nanoparticles

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Catalytic methane ignition over freely-suspended palladium nanoparticles

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Content CATALYTIC METHANE IGNITION OVER FREELY-SUSPENDED PALLADIUM NANOPARTICLES by Tsutomu Shimizu A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MECHANICAL ENGINEERING) May 2012 Copyright 2012 Tsutomu Shimizu ii Dedication This thesis is dedicated to my parents and my two friends, Peter Granz and Paula Fern. Their encouragement sustained me through some major hurdles, decisions, and challenges during my dissertation work. iii Acknowledgements I would like to thank my adviser, Professor Hai Wang. Through his mentorship, I was able to deepen my understanding of the combustion discipline from the physical chemistry point of view. He provided me with a wide variety of relevant research topics, and I was able to interact with a diverse group of people. These unique opportunities greatly enhanced and extended my research capabilities. I will remember the time during which I worked under Professor Wang as one of the most exciting and enjoyable periods of my life. I would also like to thank my committee members, Professors Paul Ronney, Dennis Phares, Charles Campbell and Theodore Tsotsis for their active participation in evaluating this work. I want to acknowledge the research collaborators, Dr. David Wickham, Dr. Jim Nabity and Jeffrey Engel at TDA Research, Inc. for their early preparation of the nanocatalyst flow reactor experiments. I also acknowledge Professor Scott Anderson at the University of Utah in the Department of Chemistry, who had insightful discussions with me and assisted the material synthesis work. Dr. He Lin at the Shanghai Jiao Tong University was very instrumental in conducting catalytic combustion experiments while he was a visiting scholar at USC. I would like to thank both former and current colleagues in the Combustion Kinetics Laboratory. Dr. Aamir Abid, Dr. Eric Tolmachoff, Saro Memarzadeh and Joaquin Camacho were actively involved in discussions about experimental problems and gave kind assistance when needed. Dr. David Sheen, Dr. Xiaoqing You, and Enoch Dames assisted with computational works. iv This work is supported by the U.S. Air Force Office of Scientific Research through the Multi University Research Initiatives (MURI) program. v Table of Contents Dedication ii Acknowledgements iii List of Tables vii List of Figures viii Abstract xiii Chapter 1 Introduction 1 1.1 Catalytic Methane Combustion–General Overview 1 1.2 Research Objectives and Methods of Study 8 Chapter 2 Experimental Methods 10 2.1 Introduction 10 2.2 Flow Reactor Apparatus 12 2.3 Liquid Atomizer 16 2.4 Scanning Mobility Particle Sizer 18 2.5 Particle Characterization 19 2.6 Catalyst Precursor 20 2.7 Summary 21 Chapter 3 Computational Methods 22 3.1 Introduction 22 3.2 Simulation Codes 24 3.3 Mathematical Formula 25 3.4 Chemical Kinetic Models 27 3.5 Temperature-Dependent Surface Kinetic Model 32 3.6 Validation of Hydrogen Oxidation Submodel 40 3.7 Summary 46 Chapter 4 Catalytic Methane Ignition by Freely-Suspended Palladium Nanoparticles 47 4.1 Introduction 47 4.2 Experimental Procedure 49 vi 4.3 Results and Discussion 54 4.4 Summary 83 Chapter 5 Particle Morphology and Composition 85 5.1 Introduction 85 5.2 Experimental Procedure 87 5.3 Results and Discussion 89 5.4 Summary 97 Chapter 6 Numerical Analysis of Optimum Catalyst Design 98 6.1 Introduction 98 6.2 Computational Methods 99 6.3 Ignition Delay Time 101 6.4 Sensitivity Analysis 105 6.5 Summary 113 Chapter 7 Conclusions and Future Works 114 7.1 Conclusions 114 7.2 Future Works 116 Bibliography 119 Appendices Appendix A Aerosol Plug-Flow Simulation code 128 Appendix B Ignition Delay Time Simulation code 138 vii List of Tables Table 3-1: Surface Reaction Model I 29 Table 3-2: Heat of desorption (∆H d , kJ/mol) on palladium chosen in this work. 33 Table 3-3: Vibrational frequency (ν, cm -1 ) of surface species on palladium 34 Table 3-4: Surface Reaction Model II; Surface reaction model for methane oxidation on palladium at 300 K – 1500 K. 35 Table 4-1: Summary of flow conditions and mixture compositions at reactor inlet 49 Table 4-2: Summary of experimental conditions and key results 51 Table 4-3: Summary of numerical conditions and key results 71 viii List of Figures Figure 1-1: Specific impulse – Mach number curve of various propulsion platforms for hydrogen and hydrocarbon fuels. (Cook and Hueter 2003) 2 Figure 1-2: The temperature programmed reaction (TPR) profiles for zirconia supported Pd catalyst in an alumina tubular reactor. Solid and open symbols represent for heating and cooling ramps, respectively. Influence of water vapor is also shown in the figure. (Ciuparu and Pfefferle 2001) 4 Figure 1-3: Reduction and re-oxidation of supported polycrystalline Pd/PdO catalysts as observed by thermogravimetric analysis (TGA) under different O 2 concentrations in N 2 at 1 bar. (Wolf et al. 2003) 5 Figure 1-4: Proposed mechanisms of molecular methane adsorption and dissociation steps over Pd/PdO surface. (Fujimoto et al. 1998) 7 Figure 2-1: Schematic of the experimental apparatus. 13 Figure 2-2: Schematic of the particle-probe sampling in the flow reactor. 15 Figure 3-1: Experimental (symbols, Hunter et al. 1994) and computed species profiles during homogeneous, non-catalytic oxidation of methane in a turbulent flow reactor. Left panels: 0.02CH 4 -0.205O 2 -0.775N 2 at 6 atm and ~953 K; middle panels: 0.02CH 4 -0.205O 2 -0.775N 2 at 10 atm and ~953 K; right panels: 0.021CH 4 -0.205O 2 -0.774N 2 at 6 atm and ~974 K. 27 Figure 3-2: Exponential prefactors (Top) and activation energies (Bottom) as a function of temperature. 39 Figure 3-3: Relative H 2 O and OH mole fractions as a function of the hydrogen mixing ratio α H2 . The symbols represent experimental data (Andrae et al. 2004) at 13 Pa and 100 SCCM flow rate and the lines are numerical predictions. 41 ix Figure 3-4a: Relative H 2 O and OH mole fractions as a function of the hydrogen mixing ratio α H2 . The symbols represent experimental data (Andrae et al. 2004) at 13 Pa and 100 SCCM flow rate and the lines are numerical predictions, comparing the SPIN and the PSR results. 43 Figure 3-4b: Relative H 2 O and OH mole fractions as a function of the hydrogen mixing ratio α H2 . The symbols represent experimental data (Andrae et al. 2004) at 26 Pa and 100 SCCM flow rate and the lines are numerical predictions, comparing the SPIN and the PSR results. 44 Figure 3-4c: Relative H 2 O and OH mole fractions as a function of the hydrogen mixing ratio α H2 . The symbols represent experimental data (Andrae et al. 2004) at 26 Pa and 200 SCCM flow rate and the lines are numerical predictions, comparing the SPIN and the PSR results. 45 Figure 4-1: Conceptual drawing of in situ generation of NPs followed by catalytic ignition in a fuel-oxidizer mixture in a flow reactor. (Shimizu et al. 2010) 48 Figure 4-2a: Background, centerline temperature T b,center measured in an N 2 flow (F-0 in Table 4-1) at several furnace temperatures T f . Symbols are experimental data and solid lines are fitted to data. The dashed lines were obtained from extrapolating the data from the measured data points for T f = 1173 K and 1273 K. 55 Figure 4-2b: Background, wall temperature profiles T b,wall measured in a N 2 flow (F-0 in Table 4-1) at several furnace temperatures T f . Symbols are data and solid lines are fitted to data. The dashed lines were obtained from extrapolating the data from measured data points for T f = 1173K and 1273 K. 56 Figure 4-3: CH 4 and CO 2 mole fractions observed for Runs 1 and 3 as a function of the furnace temperature of Zone I, T f-1 . 58 Figure 4-4: Selected particle size distributions observed for Run 3 at several furnace temperatures. 60 Figure 4-5: Representative particle size distributions (symbols) measured during Run 3. Lines are fitted into a tri-lognormal function whereas thinner lines indicate the three separate particle size modes. 63 x Figure 4-6: Particle median diameter <D p > and area-to-volume ratio ζ (STP) measured at the exit of the flow reactor during Run 3 and Run 4, as a function of the furnace temperature of Zone I, T f-1 . Square and round symbols represent Run 3 and Run 4, respectively. 64 Figure 4-7: CH 4 and CO 2 mole fractions measured during Run 5 as a function of the furnace temperature of Zone I, T f-1 . The wall of the reactor tube used for Run 5 was contaminated by wall coating of condensed- phase material from Pd(thd) 2 decomposition. 67 Figure 4-8: Selected particle size distribution functions at various testing times measured at the exit of the flow reactor during Run 7. Furnace temperature T f was kept at 973 K while the catalyst concentration was gradually increased. The mixture ignited 20 minutes after the start of the run. 69 Figure 4-9: Particle median diameter <D p > and area-to-volume ratio ζ measured at the exit of the flow reactor during Run 7. Round and rectangular symbols represent <D p > and ζ (STP), respectively. 70 Figure 4-10: Computational results of CH 4 and CO 2 mole fractions at the reactor exit as a function of furnace temperature T f for both non-catalytic (Simu-1) and catalytic (Simu-3 and -5) cases. The model used the centerline temperature T b,center as the input. For Simu-3, toluene was assumed to be completely oxidized to CO 2 and H 2 O before ignition, whereas for Simu-5 toluene was included as a reactant. For both catalytic cases, Pd particles with <D p > = 19 nm and ζ = 0.013 cm -1 (STP) were assumed. 73 Figure 4-11: Surface site fraction θ and centerline temperature T ceneter as a function of the distance from reactor inlet, computed for the furnace temperature T f = 954.7 K (Simu-3: <D p > = 19 nm and ζ = 0.013 cm -1 (STP)). Top panel: surface species in log-scale; bottom panel: O(S) site fraction in linear scale. 75 Figure 4-12: Sensitivity coefficients, –∆T f-ig /<T f-ig >, computed for Simu-3. A positive sensitivity coefficient indicates lowered ignition temperature. Reactions with noise-level sensitivities are omitted. 77 Figure 4-13: Particle size distributions measured at x = 23, 33, 43, 71 cm and the exhaust section from the reactor inlet. 79 xi Figure 4-14: Temperature profiles computed along the flow axis (x) using various input parameters for catalytic methane ignition. Particle radius (r d ) used for the simulation are also shown. Symbols are experimental values measured in this work. Also shown in the figure are the simulation results from a previous study. 81 Figure 5-1: TEM images of nanoparticles sampled in Run 8 (Left) and Run 9 (Right). The furnace temperature T f was kept at T f = 773 K and 973 K, respectively. The images were found to be mostly identical between the two runs. 90 Figure 5-2: HRTEM images of nanoparticles sampled in Run 8 (Left) and Run 9 (Right). The furnace temperature T f was kept at T f = 773 K and 973 K, respectively. Most particles were found to be rich in Pd metal. (Van Devener et al. 2009) 91 Figure 5-3: SAED pattern for Pd(thd) 2 catalyst after passage through reactor at 737 K in Run 8 (Left) and 937 K in Run 9 (Right). (Van Devener et al. 2009) 92 Figure 5-4: Pd 3d photoelectron spectra for particles passing through reactor at 737 K in Run 8 (Top) and 937 K in Run 9 (Bottom). (Van Devener et al. 2009) 94 Figure 6-1: Temperature-time histories computed for a stoichiometric methane/air mixture under adiabatic and isobaric conditions using Model I, showing the difference in ignition onset between catalytic and non-catalytic ignition of the mixture with initial temperature T 0 = 900 K and pressure p = 1 atm. The catalytic case used a median particle diameter <D p > = 19 nm and the surface-to-volume ratio ζ = 0.013 cm -1 (STP). The inset figure also shows the temperature history computed without considering gas-phase reactions. 102 Figure 6-2: Ignition delay time (τ) computed as a function of initial temperature (T 0 ) for a stoichiometric methane/air mixture under adiabatic and isobaric conditions. The catalytic cases used <D p > = 19 nm and ζ = 0.013 cm -1 (STP). 104 xii Figure 6-3: (Top) Computed ignition delay plot showing three temperature regions, Region I, II, and II. Model II in Table 3-4 is used for a stoichiometric methane/air gas-surface reactions. (Bottom) Temperature profiles as a function of nondimensional residence time t/τ ign , for three representative regions of ignition scheme, i.e. catalytic reaction dominant τ ign ≈ τ c (Region I), intermediate region τ ign ≈ τ c + τ g (Region II), and gas-phase reaction dominant τ ign ≈ τ g (Region III). 106 Figure 6-4: Sensitivity analysis of ignition delays for three representative gas temperatures T 0 = 800 K, 900 K, and 1000 K as a function of the desorption energy of surface oxygen at reference point of 300 K, E 300K (kJ/mol). Solid and dashed lines represent (τ c + τ g ) and τ c –only, respectively. 108 Figure 6-5a: Computed ignition delays as a function of the gas temperatures T 0 for stoichiometric methane/air mixture. Square, round-black line and round-red line symbols represent non-catalytic, catalytic with Model II, and catalytic with the oxygen desorption energy set to the minimum possible value (156 kJ/mol) in Model II, respectively. 110 Figure 6-5b: Computed ignition delays as a function of the gas temperatures T 0 for a fuel rich methane/air mixture (Φ = 1.5). Square, round-black line and round-red line symbols represent non-catalytic, catalytic with Model II, and catalytic with the oxygen desorption energy set to the minimum possible value (156 kJ/mol) in Model II, respectively. 111 Figure 6-5c: Computed ignition delays as a function of the gas temperatures T 0 for a fuel lean methane/air mixture (Φ = 0.7). Square, round-black line and round-red line symbols represent non-catalytic, catalytic with Model II, and catalytic with the oxygen desorption energy set to the minimum possible value (156 kJ/mol) in Model II, respectively. 112 Figure 7-1: Conceptual drawing of aerosol JSR-TFR test bed. Aerosol JSR serves as a particle generator. 118 xiii Abstract Catalytic methane ignition by palladium (Pd) nanoparticles (NPs) is examined both experimentally and numerically. NPs studied are freely suspended in a gas-phase fuel-oxidizer mixture. This research is motivated in part by ongoing research and development of hypersonic engines. One of the technological challenges is to effectively cool the engine utilizing a cryogenic fuel, and at the same time to maximize the thrust performance as well as the engine efficiency. As an alternative to cryogenic hydrogen and long-chain hydrocarbon jet fuels, it has been proposed that cryogenic methane could be a viable fuel of choice. Methane has a low tendency toward coking and has a high energy density. However, relatively long ignition delay of methane is a major drawback of this fuel. Thus, to pursue of any supportive means to overcome the poor ignition performance has been an active research area in the aeronautics community. Palladium is known as a highly efficient catalyst for the oxidation of hydrocarbon fuel including methane. Extensive research on the catalytic combustion over Pd-based catalyst has been carried out in the past several decades. Conventionally, supported palladium has been used in the fixed-bed reactors such as a stagnation flow reactor, a monolith reactor and a metal-coated flow reactor. The uniqueness of this dissertation work is that palladium tested is in the form of NPs, which are finely-dispersed in a stream of a gas mixture. A reactor test bed used in this work was built with a laminar flow reactor, in which Pd NPs are generated in situ in the flow reactor and catalyze the xiv methane oxidation processes to reach ignition at temperatures substantially lower than that of homogeneous gas-phase oxidation without catalyst. In the flow reactor, Pd NPs are expected to be generated through a sequential kinetic process initiated from the vaporization of Pd precursor followed by its decomposition into Pd atom or clusters. The Pd atoms or clusters undergo nucleation and coagulation. Palladium precursor was prepared with use of a Pd-based organometallic compound dissolved in an organic solvent. The precursor was injected into a reactor in the form of an aerosol generated through a nebulizer. NPs generated in a reactor were characterized in terms of detailed particle size distributions, surface densities and mass densities by a scanning mobility particle sizer (SMPS). A new probe sampling technique based on the Venturi effect was designed and utilized in this work, by which the gas sample may be rapidly diluted and reaction quenched. With use of this probe sampling technique, the time-resolved particle size distributions for in-situ generated Pd NPs were obtained along the flow passage of the reactor. Size distribution functions of NPs measured were primarily lognormal and the median diameter ranged from 10 to 30 nm. The particle sizes were not a strong function of the reactor gas temperatures but rather of the precursor loading and the residence time. The structure and morphology of the NPs was also examined with high resolution transmission electron microscopy (TEM) and x-ray photon spectroscopy (XPS) analysis. It was determined that NPs have a core-shell structure, with the core being the single- xv crystal Pd and a shell comprising of several atomic layers of PdO. The ratio of Pd to PdO is dependent of the oxygen concentrations and the gas temperatures in the reactor. A detailed kinetic model of methane oxidation over palladium surface was developed in this work. A trial surface kinetic model and a more detailed temperature- dependent model were proposed. The first trial model was taken from literature, and was used to predict the catalytic methane ignition demonstrated in this work. The flow reactor simulations show that methane oxidation over the surfaces of NPs causes gas temperature rise, which eventually leads to fuel ignition as observed in the flow reactor. The reaction rate parameters used in the trial model were re-evaluated based on the literature values for measured desorption energies and vibration frequencies of surface species in addition to some density functional theory analyses also available in literature. An analytical method that ensures micro-kinetic thermodynamic consistency between each reaction steps was employed not only to estimate the reaction rate parameters but also to include temperature dependency in the rate constants between 300 and 1500 K. The resulting model is thus thermodynamically-consistent as well as temperature-dependent. A hydrogen submodel in high temperature region was validated against the stagnation flow reactor experiments available in literature, which were carried out at 13 Pa and 1300 K of Pd surface temperature. The model provided fairly good agreements with the experiments. Design criteria of ideal nanocatalyst were discussed based on the ignition delay time computed using the proposed thermodynamically-consistent model. The sensitivity analysis against the reaction parameters suggests that the surface oxide formation and xvi desorption steps play a vital role for methane oxidation reactions. Methane ignition was found to occur in a two-stage process. In the first stage, catalytic heat release from the surface reaction leads to temperature rise. The rise in temperature eventually shuts off the catalytic reaction because of oxygen desorption, but gas-phase chain-branching and thermal runaway eventually brings the fuel air mixture to ignition. Design criteria for optimum nanocatalysts are discussed at the atomic scale on the basis of experimental and numerical analyses carried out in this dissertation work. Lastly, the future directions of the research on nanocatalysts are addressed. 1 Chapter 1 Introduction 1.1 Catalytic Methane Combustion–General Overview Supersonic combustion ramjets, known as scramjets, have received much attention by the international aviation communities over the past several decades (Sin-I 1989). Since early development of scramjets, use of hydrogen has been most favored due to short ignition delays, high specific energy, and specific heat (Cecere et al. 2011; Mitani and Kouchi 2005; Nishioka and Law 1997; Takita and Niioka 1996; Tsujikawa and Northam 1996). However, its low energy density could be a critical disadvantage with regard to the aerodynamic design. On the other hand, kerosene-based endothermic jet fuels have advantages over hydrgen in terms of energy density, heat capacity, cost and safety (see, Figure 1-1). The problem in this case, however, is that coking in the cooling lines during endothermic fuel cracking can cause significant degradation in heat transfer, which is an unwanted side effect of long-chain hydrocarbons. Cryogenic methane has gained some attention as an alternative fuel of choice since methane has a higher energy density than hydrogen but a lower coking tendency than jet fuels. More specifically, methane has a specific energy content of 50 MJ/kg, greater than those of conventional jet fuels (~43 MJ/kg). Methane also has a higher volumetric energy density (20.8 MJ/L) than hydrogen (8.2 MJ/L), both in their liquified states (Lewis 2001). However, owing to the large C-H bond strength (435 kJ/mol), the 2 use of methane is hampered by its poor ignition performance — one of a critical engine design parameters for scramjets (Curran 2001). Figure 1-1: Specific impulse – Mach number curve of various propulsion platforms for hydrogen and hydrocarbon fuels. (Cook and Hueter 2003) It would be of interest to note that for spark ignition engines known as the natural- gas driven vehicle (NGV) or the compressed natural gas vehicle (CNG), methane or natural gas can also be a superior fuel since it has a high octane number of 120, allowing engines to run at a high compression ratio (Pulkrabek 2003). On the other hand, it is anticipated that a cold unstart and a frequent misfiring during engine operation cycles can present technical challenges to utilization of natural-gas based transportation fuels (Lampert et al. 1997; Subramanian et al. 1992). 3 One of the conventional methods to enhance methane ignition is through the use of a catalyst. The oxidation of fuel molecules is catalyzed on the surface of supported transition metals at targeted temperatures. In such cases, the overall activation energies methane oxidation can be much lower than those without catalytic surfaces. Palladium (Pd) is known as one of the most effective catalysts toward oxidation of hydrocarbons including methane. Extensive research has been carried out on catalytic methane combustion over Pd surfaces in recent years (Ciuparu et al. 2002). The kinetic mechanism of catalytic methane oxidation processes over Pd surface was found to be quite complex. Observations show surface oxygen on the Pd surface plays a vital role for methane oxidation below 1000 K (Ciuparu and Pfefferle 2001; Datye et al. 2000; Euzen et al. 1999; McCarty 1995; Salomonsson et al. 1995; Sekizawa et al. 1993; Thevenin et al. 2003; Thevenin et al. 2002). Metallic Pd surface can also be catalytically active, but this activity was observed at higher temperatures. Catalytic deactivation typically occurs around 1000 K (Figure 1-2). The presence of water vapor can also adversely impact the catalytic reactivity, as shown in Fig. 1-2. The deactivation is thought to to be caused of the formation of surface OH from reaction with water, which inhibits further surface reactions – a phenomenon known as OH poisoning (Persson et al. 2007). Oxygen desorption/adsorption leading to Pd/PdO surfaces is also responsible, in part, for the hysteresis behavior observed between 500 K and 1200 K (Figure 1-3). 4 Figure 1-2: The temperature programmed reaction (TPR) profiles for zirconia supported Pd catalyst in an alumina tubular reactor. Solid and open symbols represent for heating and cooling ramps, respectively. Influence of water vapor is also shown in the figure. (Ciuparu and Pfefferle 2001) 5 Figure 1-3: Reduction and re-oxidation of supported polycrystalline Pd/PdO catalysts as observed by thermogravimetric analysis (TGA) under different O 2 concentrations in N 2 at 1 bar. (Wolf et al. 2003) In an oxidizing environment, PdO is thermodynamically stable below 1055 K (Mallika et al. 1983). The equilibrium constant K p of 2PdO (s) = 2Pd(s) + O 2 (g) (1.1) is reported to be 2.2 × 10 -3 atm at 909 K and 0.64 atm at 1124 K (Rao 1985). These equilibrium constant values indeed suggest that the preferred thermodynamic state is PdO in air below ~ 900 K but it dissociates into O 2 (g) leaving behind vacant Pd (s) sites at temperatures above 1100 K. Kinetically, the surface oxidation can lead to diffusion of oxygen atoms into the bulk solid phase, creating local microstructures with kinks, islands and peninsulas where the catalytic reactivity could be enhanced compared to a crystalline 6 surface (Zheng and Altman 2000). An added complexity is that the Pd/PdO equilibrium constant and the catalytic reactivity of nanometer size Pd particles can be different from a single crystalline Pd(111) surface (Li and Wang 2005; Navrotsky et al. 2010; Tait et al. 2005). In addition to the competitive process between O 2 adsorption and desorption, the formation of PdO x by the oxygen migration into and from surface layers could also play a considerable role in the surface composition of the catalyst and in the hysteresis behavior just discussed (Wolf et al. 2003). Most of the research on catalytic methane combustion over Pd/PdO has been focused on observations of the global catalytic activites over a range of thermodynamic and composition conditions. Studies using detailed chemical kinetic modeling have also been reported in recent years (Moallemi et al. 1999; Sidwell et al. 2002). Moallemi et al. proposed a microkinetic model for Pd, which was built based on the existing model of platinum catalysis (Deutschmann et al. 1996), and they found that the model required considerable parameter changes to fit their experiments. Fujimoto et al. suggested that the presence of oxygen vacancies on PdO surfaces could play an important role for methane oxidation, as these vacancies allow for methane to adsorb onto the PdO surfaces. The adsorbed methane undergoes oxidative dissociation at mild temperatures around 973 K (Fujimoto et al. 1998). They proposed an additional reaction step as (see, Figure 1-4), CH 4 (g) + O(s) + Pd(s) → CH 3 (s) + OH(s) (1.2) 7 Figure 1-4: Proposed mechanisms of molecular methane adsorption and dissociation steps over Pd/PdO surface. (Fujimoto et al. 1998) Broclawik et al. (Broclawik et al. 1997; Broclawik et al. 1996) performed density functional theory (DFT) calculations and reported the potential energies for the above reaction. The model proposed by Sidwell et al. (Sidwell et al. 2002) includes step (1.2) in addition to the base model proposed by Deutschman et al. (Deutschmann et al. 1996). The model was tested for the stagnation flow reactor experiments at temperatures below 1200 K. It was shown that the proposed model was able to capture the rate of methane oxidation during the heating cycle fairly well. In general, all of the gas-surface reaction models proposed to date was tested for isolated experiments. A more detailed, comprehensive model that can fully describe the kinetic mechanism of catalytic methane oxidation over Pd/PdO surfaces over a wide range of condition is currently unavailable. 8 1.2 Research Objectives and Methods of Study In this dissertation work, methane ignition enhanced by a freely suspended nanoparticle Pd catalyst is studied as one of the viable means to make cryogenic methane applicable to high-speed combustion. Previously, catalytic combustion was almost exclusively studied in a fixed-bed device such as a monolith reactor typically applied to stationary gas turbine engines (Eguchi and Arai 1996; Ozawa et al. 1999; Schwiedernoch et al. 2003; Tsujikawa et al. 1995). Such approaches are not applicable to high speed combustion because of the extremely short residence times required and of continuous exposure of the catalyst to extremely high temperatures. Recently, researchers at TDA Research, Inc. proposed an innovative solution with use of fuel-soluble catalysts or catalyst precursor (Wickham et al. 2006). In the proposed approach, a fuel-dissolved catalyst is injected into the combustor inlet and mixed with a fuel-oxidizer mixture on a continuous basis. They demonstrated that catalyst precursor sprayed into a flow tube reactor could indeed lower the ignition temperature significantly for both methane and or even large hydrocarbon fuels. The objective of this dissertation research was to understand the nature of catalytic oxidation of methane over Pd nanoparticles, and with this understanding, the question concerning further improvements of the catalytic activities of Pd nanoparticles is addressed. The work is composed of two parts. In the first part, the kinetics of nanoparticle formation and the catalytic activities of the resulting particles are examined experimentally using a flow reactor. In the second part of the study, the gas-surface 9 oxidation reaction kinetics of methane over Pd surfaces was examined through detailed modeling. Key questions to be addressed include: • Can methane ignition be enhanced by in situ produced Pd nanocatalyst using a liquid Pd precursor? • What are the structure and composition of the nanoparticles, and how are these properties related to their catalytic activities? • Can the experimental observations be explained satisfactorily by a combined gas- phase and gas-surface kinetic model? • Which model parameters and reactions impact the catalytic process and are those parameters tunable to design more effective catalyst? In Chapter 2, the experimental setup and techniques employed will be described in detail. Chapter 3 discusses the computational methods and the reaction model used. Also described in this chapter are the chemical kinetic models proposed. Catalytic methane ignition over free-suspended Pd nanoparticles is discussed in detail in Chapter 4. Kinetics and formation mechanism of NPs generated in situ in a flow reactor are also discussed in detail based on measured PSDFs, along with computational analysis of the reaction mechanism through detailed modeling. In Chapter 5, particle morphology and chemical composition are analyzed on the basis of the surface science technology accessible at USC and University of Utah. In Chapter 6, the idea of an ideal nanocatalyst is explored on the basis of the reaction model developed. Conclusions of this dissertation works and possible future research directions are given in Chapter 7. 10 Chapter 2 Experimental Methods 2.1 Introduction One of the strategies to reduce the complications resulting from fluid dynamics, heat and mass transport during fuel oxidation is to continually stir the gas mixture to minimize gradients in concentration and temperature near or around on the boundary walls of a reactor. Jet-stirred reactor (Dagaut et al. 1995) and turbulent flow reactor (Hunter et al. 1994; Linteris et al. 1991; Lovell et al. 1989) were devised to achieve this purpose. In general, these reactors allow for studies of the time evolution of the concentrations of chemical species as a function of time under constant temperature and pressure conditions. Another common approach is to observe ignition delay time after shock or adiabatic compression of a gas mixture. Ignition delay time is one of the most important properties of a fuel-air mixture. Shock tube experiments (Ben-Dor et al. 2001; Culbertson and Brezinsky 2011; Haylett et al. 2012; Haylett et al. 2009) and a rapid compression machine (Griffiths et al. 1993; Westbrook et al. 1998) have been frequently used to measure ignition delays of fuel-oxidizer mixtures at elevated pressures and temperatures. The purpose of this work is to investigate a rather unique process of combustion that involve heterogeneous catalysis but over surfaces of freely-suspended nanoparticles. Following the work of Wickham et al. (Wickham et al. 2006), catalytic reactions were examined in a laminar flow reactor. Unlike their study in which the catalyst particles are 11 dissolved a liquid hydrocarbon fuel as an additive, the present study produces palladium nanoparticles in situ using a liquid, organometalic precursor. Although the initial flow reactor was provided by TDA, many modifications were made to accommodate the objective of this dissertation work. These included: • The catalyst precursor was introduced into the reactor as an ultrafine aerosol using an in-house miniature nebulizer. • The particle size distributions were followed along with detection of CH 4 and CO 2 concentrations at the exit of the reactor during the initial test run. In subsequent tests, time resolved measurement of the particle size distribution function was made by introducing sampling probes inside the reactor. The major components of the experimental setup employed in this work are described below. 12 2.2 Flow Reactor Apparatus Methane ignition was tested in a high-temperature flow reactor. In principle, chemical reactions and particle size growth evolve in time along the flow axis of the tube test section. The schematic flow-path diagram of the reactor rig employed in this study is presented in Figure 2-1. The furnace is MELLEN SV12, which is equipped with electrically heated coils, allowing for operations at the maximum oven temperature of 1373 K. The furnace is 94 cm in length and has a 5 cm inner diameter. The furnace is constructed with two zones. The upper part is referred to as Zone-I, and the lower part is termed Zone-II. The temperature in each zone may be controlled independently and monitored with K-type thermocouples (OMEGA) denoted as TC-1 and TC-2 for Zone-I and Zone-II, respectively. The temperatures measured are denoted as T f-1 and T f-2 , respectively. The furnace is fully computer-controlled by the LabVIEW TM program, which allows the furnace temperature to either ramp-up at constant heating rate or to keep it at fixed temperature. The test section of the flow reactor is made of a quartz tube and is housed inside of the furnace. The tube is 94 cm in length with 19 mm OD (17 mm ID). The space between the quartz tube and the inner wall of the furnace are covered with a silica insulation material. A mixture of the gases, composed of N 2 , O 2 and CH 4 were controlled using mass flow controllers (Porter Model 201) calibrated for each gas. In addition, an aerosol containing the catalyst precursor was generated in the miniature nebulizer and was carried into the reactor by a N 2 flow. Details of aerosol generation will be discussed in 13 section 2.2. The aerosol precursor and the fuel-oxidizer mixture were introduced into the reactor and mixed at its inlet before substantial heating occurred. Figure 2-1: Schematic of the experimental apparatus. The reacted gas was quenched by diluting it with a N 2 flow. During a test run, a small portion of the quenched exhaust gas was analyzed by a non-dispersed infrared (NDIR) CO 2 /CH 4 analyzer (Model 200 by the California Analytical Instruments) and a 1.9cm OD×1.7cm ID×94cm L Quartz Tube TC-3 Vent N 2 / O 2 / CH 4 Temperature Controlled Furnace Liquid Pump TC-1 N 2 NDIR CO 2 /CH 4 Analyzer Catalyst Solution N 2 TC-2 Liquid Atomizer PI-1 Vent Vent TSI 3080 EC Kr 85 n-DMA TSI 3025A UCPC ∆P SMPS System TEM Grid From liquid pump To reactor Liquid Pool N 2 T f-1 T f-2 Zone II Zone I L = 76cm 1.9cm OD×1.7cm ID×94cm L Quartz Tube TC-3 TC-3 Vent N 2 / O 2 / CH 4 Temperature Controlled Furnace Liquid Pump TC-1 TC-1 N 2 NDIR CO 2 /CH 4 Analyzer NDIR CO 2 /CH 4 Analyzer Catalyst Solution Catalyst Solution N 2 TC-2 TC-2 Liquid Atomizer PI-1 PI-1 Vent Vent TSI 3080 EC Kr 85 n-DMA Kr 85 Kr 85 n-DMA n-DMA TSI 3025A UCPC ∆P ∆P ∆P SMPS System TEM Grid From liquid pump To reactor Liquid Pool N 2 T f-1 T f-2 Zone II Zone I L = 76cm 14 scanning mobility particle sizer (TSI SMPS 3090) to measure the CO 2 /CH 4 concentrations and the particle size distributions, respectively. Detail of the SMPS operation is described in section 2.3. The data, including temperature, volumetric flow rates and species concentrations, were recorded at 1 Hz, whereas the particle data were taken and recorded separately when appropriate. The nanometer-size particles (NPs) in the flow stream were also collected on TEM grids affixed on top of an aluminum rod (0.6 cm in diameter) exposing to the reacted gas within a flow tube. The collected particles were then analyzed by X-ray photoionization spectroscopy and tranmision electron microscopy, as will be described in section 2.4. Within the flow residence time of ~ 1 s, NPs were generated and increase in size by surface growth and coagulation. Not only the final particle size but also the evolution of the size along the flow passage needs to be determined to capture the surface area of the nanoparticles. For this purpose, separate experiments were performed using a modified reactor setup. Figure 2-2 presents the modified parts of the apparatus. The particle-sampling probe made of a quartz tube (6 mm OD, 4 mm ID) was introduced in the flow passage crossing the flow. The sampling orifice is 0.5–0.7 mm in diameter and faces the oncoming flow. The probe was designed based on the principle of a Venturi tube, i.e., the pressure at the orifice section is lowered by making the flow passage narrower than that of the main flow (P 2 < P 1 and P 3 ). A N 2 dilution flow rate (Q 1 ) in the probe controls the dilution ratio (Q 1 +Q 3 )/Q 3 , which can reach up to about 1000. The dilution ratio was 15 determined through calibration using the CO 2 analyzer and a N 2 flow containing 10% (mol) CO 2 in N 2 . Details can be found in Chapter 4. Figure 2-2: Schematic of the particle-probe sampling in the flow reactor. Vent SMPS CO 2 Analyzer ! ! x Vent ! Vent SMPS CO 2 Analyzer ! ! x Vent ! 16 2.3 Liquid Atomizer Conventional spray nozzles produce relatively large droplets. They are used primarily for forming a spray with droplet size typically about 100 µ m. These nozzles are generally not useful to the present work. Rather, the desired method of catalyst precursor injection requires the aerosol to be composed of micron-sized droplets, which limits the vaporization rates to about 1 ms. Liquid atomizers (or nebulizers) capable of producing ultra small droplets have been used in studies of combustion reaction kinetics of liquid fuels in shock tubes (Haylett et al. 2012), flat burners (Abid 2009), and counterflow burners (Humer et al. 2007; Park et al. 2011). The requirements of the nebulizer performance for the current experiments are: • Aerosol droplets are smaller than 10 µm so that precursor is c ompletely vaporized in the reactor within about 1 ms. • Rate of liquid consumption needs to be as small as possible so that the influence of organic solvent on catalytic methane ignition is minimized. • Fluctuations in aerosol production and feed into the reactor must be minimal for experimental accuracy and reproducibility. A miniature atomizer was designed to produce an aerosol of the catalyst precursor with the droplet size below 10 µm. The carrier gas for the aerosol is N 2 . The atomizer utilizes a dual, concentric nozzles, as shown schematically in the inset of Fig. 2-1. The inner nozzle is made by a glass tubing (2 mm ID) with a tip diameter of 0.5 mm, and the outer nozzle is 4 mm ID glass tubing with a tip diameter of 1mm. Inside the atomizer, a liquid pool of a constant height was maintained by feeding the reservoir using a liquid 17 pump. A compressed N 2 flow passes through the inner nozzle at 8 – 12 PSIG using a needle valve. The flow rate was typically 2-3 L/min (STP). The compressed gas through the inner nozzle causes the Venturi effect, which pulls the liquid solution from the liquid reservoir through the narrow gap between the inner and outer tubes. Upon reaching the nozzle tip, the liquid was broken up to small droplets by the expanded gas. In this way, a fine spray is created. These droplets are then carried by a N 2 flow. The flow passage is made with a combination of metal tubing and conductive carbon-rubber tubing, and it has a couple of elbows serving as impactors, thus eliminating large droplets from the aerosol flow. The rate at which the aerosol was generated depends on several factors, including the liquid pool height relative to the bottom of the outer tube, the mass flow rate of the carrier gas, and the impactor arrangements. Under typical operating conditions (e.g., an upstream pressure of nitrogen at 8 PSIG), an aerosol can be produced at the rate of 0.19-0.22 ml/min. The liquid pool was replenished using a single-piston syringe pump (ISO-1000 by Chrom Tech). In some cases, it has been observed that aerosol solution can evaporate in the atomizer chamber, leading to non-steady state behavior in aerosol production. This problem was solved by chilling the atomizer with ice packs. 18 2.4 Scanning Mobility Particle Sizer SMPS has been utilized extensively in the aerosol science community in recent years for characterization of the size distribution of nanoparticles found in the atmosphere. SMPS has been utilized also for studying nascent soot formation in flames (Zhao et al. 2007; Zhao et al. 2006; Zhao et al. 2003a; Zhao et al. 2005; Zhao et al. 2003b). In these studies, the evolution of the particle size distribution was determined with the use of a dilution probe, often as a function of the distance from the flame surface. SMPS along with a probe-sampling technique was adopted also in the current work. The SMPS is composed of an electrostatic classifier (TSI Model 3080) and a particle counter (TSI Model 3025A). The classifier is equipped with a nano-differential mobility analyzer (n-DMA) (TSI Model 3085) and an ultrafine condensation particle counter (UCPC, model 3025). The diameter of the impactor nozzle is 0.0457 cm. The sheath flow rate in DMA is 3.0 L/min and the sample gas flow rate is 0.3 L/min, which are 10:1 ratio between them. The particle size was scanned from 4.53 to 160 nm in diameter. Each scan took 55 sec. The residence time between the sampling point and SMPS inlet was less than 0.6 second, which was short enough to prevent the particles from coagulating into each other at the level of particle number concentration employed. Various global properties about the size distribution may be obtained from the detailed particle size distribution, including the median diameter, the area-to-gas volume ratio and the particle mass concentration. 19 2.5 Particle Characterization In addition to particle size distribution, morphology and chemical composition were also determined. Since SMPS measures the aerodynamic mobility size (Knutson and Whitby 1975), it does not have the ability to determine whether the particle is a single particle or aggregates of smaller particles. Such morphological difference could affect not only the determination of the surface area density but also our interpretation of the experiments. Of particular interest is the oxide state of the surface and the bulk composition since the coverage ratio between the surface oxygen and the metallic vacant sites is possibly one of the most critical factor impacting the catalytic activities of palladium particles. Another characteristic is the atomic structure of the particles. The binding energies of the surface species are expected to depend on crystalline structures and the grain size to some extent, all of which affect the catalytic reactivity. Particles sampled at the exit of the flow reactor were collected on a carbon grid (Electron Microscopy Science HC200-CU). The particles sampled were analyzed by the transmission electron microscopy (TEM, Philips EM420). Additional high-resolution analysis used a FEI Technai F30. The composition of the particles was explored by X- ray-photoionization spectroscopy (XPS). Both hi-RES TEM and XPS studies were carried out in collaboration with Professor Scott L. Anderson at the University of Utah (Van Devener et al. 2009). Hence, a detail description of these analyses is omitted here. Only key findings will be presented in Chapter 5. 20 2.6 Catalyst Precursor Catalyst precursor was made of an organometallic compound dissolved in an organic solvent. The organometallic compound used is Pd(thd) 2 (thd: 2,2,6,6-tetramethyl- 3,5-heptanedione) or Pd acetate (C 4 H 6 O 4 Pd). The precursor solution made of Pd(thd) 2 was supplied by TDA whereas Pd acetate was purchased from Sigma-Aldrich. Toluene was used as an organic solvent for both compounds. The conventional measure of catalyst input into the flow reactor is the palladium molar loading, defined as palladium moles per moles of fuel in the gas mixture, 4 4 4 / / CH4) moles Pd/ (moles Loading Catalyst CH CH CH cat tot cat MW Q MW Q & & ρ ρ = , (2-1) where MW cat and MW CH4 are molecular weights of the catalyst and methane, respectively, and ρ cat is the catalyst mass per unit volume of the gas, ρ CH4 is the mass density of methane, tot Q & is the total flow rate of the gas mixture at the exit of the reactor, 4 CH Q & is the flow rate of reactant methane, all of which were determined at the STP condition. It was assumed that the composition of the particle varies from pure palladium (ρ Pd = 12.0 g/cm 3 ) to palladium oxide (ρ PdO = 9.7 g/cm 3 ). Hence, the mass density of the catalyst particle was assumed to be 10 g/cm 3 . The total gas flow rate tot Q & was determined from the volumetric flow rates metered at the inlet, and the variation of the gas compositions due to toluene vaporization and oxidation was taken into account in the flow calculation. 21 2.7 Summary Experimental technique employed in this study is discussed in detail. Key points are summarized in what follows: • A miniature atomizer was developed to produce an ultrafine aerosol of catalyst precursor with minimum fluctuation in flow rates and droplet size at the injection rate ~0.2 ml/min. • A set of comprehensive diagnostic and sampling methods were developed, allowing for the reaction process to be monitored closely. Online measurements include CH 4 /CO 2 concentrations by NDIR and particle size distribution by SMPS. Offline analysis includes TEM and XPS for particles sampled on TEM grids. • The dilution probe designed and implemented is capable to almost instantaneous gas sample dilution, allowing for sample and measurement of the time evolution of the particle size distribution. 22 Chapter 3 Computational Methods 3.1 Introduction Computational analysis of combustion problems typically involves solving a system of equations of mass, momentum, energy, and species conservations. Practical combustion problems often need to consider multi-dimensional conservation equations. For instance, Bunsen-type flames stabilize through heat loss near the burner exit rim. Because of a 2-dimensional flow geometry, the conical shaped flame may be investigated computationally by a 2-D analysis (Bennett et al. 2001; Mokhov et al. 2007). Other well- known examples include 3-D turbulent flames (Jacqueline H 2011) and 2-D axisymmetric droplet combustion analysis under convective flow environment (Ackerman and Williams 2005). When kinetically controlled phenomena are investigated, a consideration of the detailed reaction kinetics and transport often makes the computation extremely demanding, not only because of the number of scalars one must solve, but also due to boundary conditions, which are not always well defined. Such cases include the analysis for the formation of NO x , flame ignition and extinction. Even though the computational power has increased dramatically in recent years, multi- dimensional reacting flow simulation coupled with detailed chemical kinetics is not viable practically or theoretically. To circumvent the above problem, reaction kinetics study is typically carried out by employing burners or reactors to generate quasi 0- or 1-D flow problem. Examples 23 include twin flames generated in a counter flow burner, 1-D flame in a burner-stabilized flat flame, and flows in a plug flow reactor, a perfectly-stirred reactor, a shock tube, a rapid compression machine, all of which can be treated as a 0-D, initial value problem. ChemKin software (Kee et al. 1989) is one of the most frequently used computational tools that includes several simulation codes such as the plug flow code (PLUG) (Larson 1996), the opposed-flow code (OPPDIF) (Lutz et al. 1996), the stagnation-flow code (SPIN) (Coltrin et al. 1991a), and the perfectly stirred reactor (PSR) (Glarborg 1986). In this dissertation work, Chemkin-PLUG, -SPIN, and -PSR are employed for the computational analysis of flow reactor experiments and the validation of a surface kinetic model, respectively. 24 3.2 Simulation Codes The catalytic ignition experiments performed in this work were simulated using PLUG (Larson 1996) and SURFICE KINETICS (Coltrin et al. 1991b) codes, both of which are provided as a part of the ChemKin package. In this dissertation work, these codes were revised to include gas-phase reaction kinetics. The resulting code was used for simulating the flow reactor experiments as well as for ignition delay time calculations. The source code used for the flow reactor simulation and the ignition delay time calculation are included in Appendix A and B, respectively. Chemkin SPIN was also used to simulate a set of the stagnation flow experimental data taken from literature. Since the stagnation flow experiments were performed under pressures as low as 13 Pa, the condition of the gas can deviate from the continuum approximation, where the conservation equations are no longer valid. To examine the impact of non-continuum effects, the PSR code was also used to simulate the stagnation flow experiments. The results represent what would be expected if the gas is in kinetic regime. The SPIN and PSR codes were used without modification. Only the PLUG-SURFACE KINETICS code programmed in this dissertation work is described below. 25 3.3 Mathematical Formula The underlying reacting flow problems are solved as an initial value problem, using a combed gas-phase and gas-surface reaction model. The flow regime in the flow reactor is laminar. Therefore, the flow is inherently two-dimensional and the flow velocity profile is parabolic. The fluid dynamics model in PLUG neglects the radial transport, which is a simplification in comparison to the actual experiments. Sensitivity analysis for various reactor parameters is performed to address the aforementioned issues. SURFACE CHEMKIN (Coltrin et al. 2004) was utilized to solve the system of equations and to calculate the rates for both gas-phase and gas-surface reactions. Convective time t was obtained from the gas velocity u and the axial position x of the flow reactor, 0 x t dx u = ∫ , (3-1) The gas-surface reaction rate constant was described as 2 8 B d i k T k r m γ π π = , (3-2) where γ is the reaction probability or sticking coefficient, k B the Boltzmann constant, m i the molecular mass of the i th gas-phase species, and r d the particle radius. The species conservation was written as, ( ) ρ ω ζ ω i w i s i g i M dt dY , , , & & + = , (3-3) 26 where Y is the mass fraction, M w the molecular weight, ρ the gas mass density, ζ the surface area to gas volume ratio of the catalyst, g ω & and s ω & are the gas-phase and gas- surface molar production rates, respectively. The rate of temperature change in the reactor is obtained by considering the heat release due to chemical reactions in addition to the convective heating/cooling, ( ) ∑ + − = i i w i i s i g p b M h c dt dT dt dT , , , 1 ω ζ ω ρ & & , (3-4) where h is the specific enthalpy, c p the specific heat capacity of the gas mixture. The first term on the right-hand side of the equation expresses the experimental temperature gradient obtained from a direct measurement for a non-reacting flow. As will be shown later, the particles formed are substantially smaller than the mean free path of the gas. Hence, the particles are treated as in free-molecular regime. The time evolution of the site fraction i for the i th surface is given as, Γ = i s i dt d , ω θ & , (3-5) where Γ is the catalytic surface site density. 27 3.4 Chemical Kinetic Models Figure 3-1: Experimental (symbols, Hunter et al. 1994) and computed species profiles during homogeneous, non-catalytic oxidation of methane in a turbulent flow reactor. Left panels: 0.02CH 4 -0.205O 2 -0.775N 2 at 6 atm and ~953 K; middle panels: 0.02CH 4 -0.205O 2 -0.775N 2 at 10 atm and ~953 K; right panels: 0.021CH 4 -0.205O 2 -0.774N 2 at 6 atm and ~974 K USC Mech II (Wang et al. 2007) was chosen as the gas-phase reaction model. The model is composed of 784 reactions and 111 species, and has been validated against a variety of experiments, including ignition delays, laminar flame speeds, and species profiles under the conditions relevant to the present flow reactor experiments. To verify the accuracy of USC Mech II for gas-phase methane oxidation under conditions comparable to the current flow reactor experiments, simulation results and comparison against the turbulent flow reactor data of Hunter et al. (Hunter et al. 1994) are reported here. In these experiments, methane was highly diluted and oxidized in an air-like 0 5000 10000 15000 20000 CH 4 CO CO 2 0 200 400 600 800 CH 2 O C 2 H 6 C 2 H 4 0 20 40 60 80 100 0 50 100 150 200 H 2 CH 3 OH Time (ms) 0 5000 10000 15000 20000 CH 4 CO CO 2 Mole Fraction (PPM) 0 200 400 600 800 1000 CH 2 O C 2 H 6 C 2 H 4 Mole Fraction (PPM) 0 50 100 150 200 0 40 80 120 160 200 240 280 320 Time (ms) H 2 CH 3 OH Mole Fraction (PPM) 0 5000 10000 15000 20000 CH 4 CO CO 2 0 200 400 600 800 1000 CH 2 O C 2 H 6 C 2 H 4 0 20 40 60 80 100 120 140 0 50 100 150 200 250 H 2 CH 3 OH Time (ms) 28 mixture at the pressures of 6 and 10 atm. The temperature along the reactor axis was nearly a constant and ranged from 950 to 975 K. As shown in Fig.3-1, major and minor species concentrations are predicted accurately by USC Mech II. The palladium surface reaction model proposed by Sidwell et al. (Sidwell et al. 2002) is one of the few models that are directly applicable to the present application. The model was developed for catalytic methane combustion over a palladium substituted hexaluminate substrate in a stagnation flow configuration at atmospheric pressure. The model describes the initial dissociative absorptions of CH 4 and O 2 followed by a sequence of surface reactions that lead to the formation and desorption of CO 2 and H 2 O from the catalytic surface. In this dissertation work, the Sidwell model was chosen as the starting trial model. On the basis of recent literature as well as the experimental results of catalytic ignition performed in this work, several revisions were made for the rate parameters, as will be discussed later. The resulting model, consisting of 5 reversible reactions and 7 irreversible (and perhaps semi-global) reactions with 4 gaseous species and 9 surface species, is shown in Table 3-1. This model is referred to as Surface Reaction Model I. Further revisions were made with an emphasis on thermodynamic constraints. The second model will be referred to as Surface Reaction Model II with details to be presented in Section 3.5. 29 Table 3-1: Surface Reaction Model I Rate Parameters a Reference/ comments No. Reaction b A β E 1f O 2 + 2Pd(S) → 2O(S) c 0.8 d –0.5 Wolf 03’ 1b 2O(S) → O 2 + 2Pd(S) 5.13×10 21 e 230 – 115θ O Wolf 03’ 2f H 2 O + Pd(S) → H 2 O(S) 0.75 d Deutsch. 96’ 2b H 2 O(S) → H 2 O + Pd(S) 1.00×10 13 44 Deutsch. 96’ 3f H(S) + O(S) → OH(S) + Pd(S) 5.13×10 21 e 94.5 f 3b OH(S) + Pd(S) → H(S) + O(S) 5.13×10 21 e 113.8 f 4f H(S) + OH(S) → H 2 O(S) + Pd(S) 5.13×10 21 e 31.1 f 4b H 2 O(S) + Pd(S) → H(S) + OH(S) 5.13×10 21 e 88.8 f 5f 2OH(S) → H 2 O(S) + O(S) 5.13×10 21 e 14.5 f 5b H 2 O(S) + O(S) → 2OH(S) 5.13×10 21 e 32.8 f 6 CO 2 (S) → CO 2 + Pd(S) 5.00×10 10 29 Sidwell 02’ 7 CO(S) + O(S) → CO 2 + Pd(S) 5.13×10 21 e 76 Sidwell 02’ 8 C(S) + O(S) → CO(S) + Pd(S) 5.13×10 21 e 62.8 Sidwell 02’ 30 Table 3-1 (Continued) Rate Parameters a Reference/ comments No. Reaction b A β E 9 CH 4 + 2Pd(S) → CH 3 (S) + H(S) c 4.00×10 5 d 196 Sidwell 02’ 10 CH 3 (S) + 3Pd(S) → C(S) + 3H(S) g 5.13×10 21 e 85.1 Sidwell 02’ 11 CH 4 + Pd(S) + O(S) → CH 3 (S) + OH(S) 4.20×10 -2 d 20 h 12 CH 3 (S) + 3O(S) → C(S) + 3OH(S) i 5.13×10 21 e 25.1 Sidwell 02’ a Arrhenius parameters for the rate constants written in k = AT β exp(–E/RT). The units of A are given in terms of mol, cm 3 , and sec. E is in kJ/mol. b The surface coverage is specified as the site fraction θ. Total site density of Pd is Γ = 1.95×10 –9 mol/cm 2 . c The coverage dependence is θ Pd(S) 2 . d Sticking coefficient. e The frequency factor is estimated from vibration frequency (10 13 s -1 ) and scaled by the total site density Γ. f The activation energies are based on the DFT results of {Cao and Chen 2006}. g The reaction order is 1 for Pd(S). h The sticking coefficient was taken from {Sidwell et al. 2002}. The activation energy was deduced from {Broclawik et al. 1996}. i The reaction order is 1 for O(s). In Model I, a notable modification was the oxygen adsorption/desorption step (reaction R1). It is known that the coverage of oxygen on palladium surface plays a critical role in catalytic oxidation of hydrocarbon fuels (Ciuparu et al. 2002; Sekizawa et al. 1993). The sticking coefficient of molecular oxygen (R1f) and the coverage-dependent oxygen desorption energy in (R1b) was taken from Wolf et al. (Wolf et al. 2003), who developed a model of palladium oxidation in a flow reactor at 1 atm. Their model captures the hysteresis behavior observed for oxygen desorption from a palladium oxide surface towards high temperatures and palladium re-oxidation towards low temperatures. 31 Modifications were made also for surface water formation reactions (reactions R3f-b through R5f-b). All of these steps are described by reversible processes based on extensive literature about H 2 oxidation over palladium (Andrae et al. 2004; Deutschmann et al. 1996; Johansson et al. 2003; Kramer et al. 2002; Seyed-Reihani and Jackson 2004). Notably, Cao et al. (Cao and Chen 2006) carried out a density functional theory calculation for surface H 2 O formation over a Pd(111) surface. They also reported the critical energies of reactions R3f-b through R5f-b, which form the basis for the activation energies adopted in Model I. The rate parameters of H 2 O adsorption and desorption (R2f-b) was adopted from the H 2 /O 2 /Pd reaction model of Deutsumann et al. (Deutschmann et al. 1996). The modified pre-exponential factor of 1×10 13 s -1 in (R2b) is a widely accepted literature value. The activation energy of dissociative adsorption of methane on a surface oxide site in (R11) was reduced from 38 kJ/mol to 20 kJ/mol. This downward revision is supported by the theoretical result of Broclawik et al. (Broclawik et al. 1997; Broclawik et al. 1996). Nonetheless, (R11) is probably a semi-global reaction. 32 3.5 Temperature-Dependent Surface Kinetic Model The principle of microkinetic thermodynamic constraints developed by Vlachos and coworkers (Mhadeshwar et al. 2003) may be illustrated by using the following example. Consider the gas-phase reaction H (g) + O (g) → OH (g) and its surface analog H(S) + O(S) → OH(S) with their heats of reaction given as gas H ∆ and surf H ∆ , respectively. Because thermodynamic properties are state functions, these heats of reaction are related through the heats of desorption of the surface species, surf gas d,OH d,H d,O H H H H H ∆ + ∆ − ∆ − ∆ = ∆ (3-6) where d,i H ∆ denotes the heat of desorption of the i th surface species. Let the forward and back rate coefficients take the forms of ,surf ,surf f f E RT f k A e − = and ,surf ,surf b b E RT b k A e − = , where R is the universal gas constant and T is the temperature. Likewise, the adsorption and desorption of H, O, and OH are given with their respective rate expressions as a , a a, i E RT i k A e − = and d , d d, i E RT i k A e − = , where the subscript a and d designate the adsorption and desorption steps. It may be shown that the activation energies of the surface reaction and the adsorption/desorption steps are related by the following algebraic expression, ( ) ( ) ( ) ,surf ,surf gas a,OH d,OH a,H d,H a,O d,O f b E E E E E E E E H − − − + − + − = ∆ (3-7) Similarly, the Arrhenius prefactors may be expressed as ( ) ( ) ( )( ) { } ,surf ,surf gas a,OH d,OH a,H d,H a,O d,O ln ln f b A A A A A A A A S R   − = ∆   (3-8) where gas S ∆ is the standard-state entropy of the gas-phase reaction. 33 To impose constraints on the rate parameters, heats of desorption of H 2 , O 2 , OH, H 2 O and CO on palladium were taken from literature (Anderson et al. 1992; Conrad et al. 1977; Conrad et al. 1974; Engel 1978; Stuve et al. 1984). The values are tabulated in Table 3-2. Also shown in Table 3-2 is the reference temperatures at which d H ∆ were measured. OH heat of desorption appears to be strongly dependent on the surface coverage (Anderson et al. 1992). This effect was taken into account by introducing a coverage-dependent desorption energy. Sensible heats of surface species were estimated from a statistical mechanics analysis. Data for the vibrational frequencies ν of molecules are tabulated in Table 3-3. Table 3-2: Heats of desorption (∆H d , kJ/mol) on palladium chosen in this work. Species ∆H d T ref (K) Ref. Species ∆H d T ref (K) Ref. H 2 88 368 Conrad 74’ OH 224 1300 Anderson 92’ O 2 230 900 Conrad 77’ H 2 O 43 173 Stuve 84’ CO 134 374 Engel 78’ 34 Table 3-3: Vibrational frequency (ν, cm -1 ) of surface species on palladium. Species ν (cm -1 ) mode Ref. Species ν (cm -1 ) mode Ref. H(S) 823 stretch Howard 78’ OH(S) 445 stretch Nyberg 84’; Stuve 84’ 916 bend Howard 78’ 930 bend Nyberg 84’; Stuve 84’ O(S) 355 stretch/bend Nyberg 84’ 3250 O-H stretch Stuve 84’ H 2 O(S) 235 Pd-O stretch Stuve 84’ CO(S) 375 Pd-C stretch Zou 96’ 810 bend/stretch Stuve 84’ 630 rocking Zou 96’; Morkel 05’ 3380 stretch Stuve 84’ 2050 C=O stretch Zou 96’; Morkel 05’ 1640 bend Stuve 84’ The information presented in Table 3-2 and Table 3-3 was used to determine the enthalpies of formation and the energies of desorption of surface species as a function of temperature. Thermodynamic data of gas-phase species were taken from USC Mech II (Wang et al. 2007). Model II is presented in Table 3-4. Total Pd site density is assumed to be Γ = 1.95×10 –9 mol/cm 2 , i.e., the average of the literature values for the Pd/PdO phases (Deutschmann et al. 1996; Kramer et al. 2002; Seyed-Reihani and Jackson 2004; Sidwell et al. 2002; Wolf et al. 2003). The Pd site occupancies of O(S), OH(S), and H 2 O(S) were assumed to be four, denoted as a superscript for each species (Andrae et al. 2004). This assumption was made on the basis of the maximum oxygen coverage over Pd(111) surface (Zheng and Altman 2000). 35 Table 3-4: Surface Model II; Surface reaction model for methane oxidation on palladium at 300 K –1500 K. Rate Parameters a Reference/ No. Reaction b A β µ E 300K comments 1f H 2 + 2Pd(S) → 2H(S) 1.0 d – 0.5 0.25 0 this work 1b 2H(S) → H 2 + 2Pd(S) 5.33×10 16 0.992 0.25 87.4 this work 2f O 2 + 8Pd(S) → 2O 4 (S) 1.0 d – 0.5 0.5 0 this work 2b 2O 4 (S) → O 2 + 8Pd(S) 5.01×10 15 1.336 0.5 241.1 – Bθ c this work 3f H(S) + O 4 (S) → OH 4 (S) + Pd(S) 2.91×10 18 1.264 0 94.6 – B/2θ c this work 3b OH 4 (S) + Pd(S) → H(S) + O 4 (S) 2.29×10 19 1.156 0 120.3 – Cθ c Cao 06’ 4f H(S) + OH 4 (S) → H 2 O 4 (S) + Pd(S) 6.56×10 15 1.403 0 31.8 this work 4b H 2 O 4 (S) + Pd(S) → H(S) + OH 4 (S) 2.11×10 18 1.134 0 83.8 + Cθ c Cao 06’ 5f 2OH 4 (S) → H 2 O 4 (S) + O 4 (S) 3.89×10 17 1.244 0 14.5 + B/2θ c this work 5b H 2 O 4 (S) + O 4 (S) → 2OH 4 (S) 1.40×10 19 1.1 0 40.7 + 2Cθ c Cao 06’ 6f H + Pd(S) → H(S) 1 d 0 0 0 this work 6b H(S) → H + Pd(S) 1.32×10 10 1.1 i 0 261.7 this work 7f O + 4Pd(S) → O 4 (S) 1 d 0 0 0 this work 7b O 4 (S) → O + 4Pd(S) 1.64×10 10 1.1 i 0 369.7 – B/2θ c this work 8f OH + 4Pd(S) → OH 4 (S) 1 d 0 0 0 this work 8b OH 4 (S) → OH + 4Pd(S) 1.60×10 10 1.1 i 0 227.5 – Cθ c this work 9f H 2 O + 4Pd(S) → H 2 O 4 (S) 1 d 0 0 0 this work 9b H 2 O 4 (S) → H 2 O + 4Pd(S) 1.62×10 10 1.1 i 0 43.8 this work 10 CO(S) + O 4 (S) → CO 2 + 5Pd(S) 1.00×10 19 1.115 i 0 59.8 Engel 78’ 11 C(S) + O 4 (S) → CO(S) + 4Pd(S) 1.01×10 19 1.115 i 0 62.8 Sidwell 02’ 12f CO + Pd(S) → CO(S) 1 d 0 0 0 this work 12b CO(S) → CO + Pd(S) 1.65×10 10 1.1 i 0 134 this work 36 Table 3-4 (Continued) Rate Parameters a Reference/ No. Reaction b A β µ E 300K comments 13 CH 4 + 2Pd(S) → CH 3 (S) + H(S) 4.0×10 5 d 0 0 196 Sidwell 02’, h 14 CH 3 (S) + 3Pd(S) → C(S) + 3H(S) e 1.07×10 19 1 i 0 85.1 Sidwell 02’, h 15 CH 4 + Pd(S) + O 4 (S) → CH 3 (S) + OH 4 (S) 4.2×10 –2 d 0 0 20 g Sidwell 02’, h 16 CH 3 (S) + 3O 4 (S) → C(S) + 3OH 4 (S) f 1.07×10 19 1 i 0 25.1 Sidwell 02’, h a Modified Arrhenius parameters for the rate constants written in k = A T β exp(-E/RT) 10 µ θ Pd . Unit of A are given in terms of mol, cm, and s. E is in kJ/mol. b Pd site occupancy of O(S), OH(S) and H 2 O(S) is set to 4. Total site density of Pd is Γ = 1.95×10 –9 mol/cm 2 . c θ is the total site fraction, i.e. θ = 1 – θ Pd . Coverage dependencies B = 156 kJ/mol and C = 30 kJ/mol. d Sticking coefficient. e The reaction order is 1 for Pd(S). f The reaction order is 1 for O(S). g The activation energies was deduced from {Broclawik et al.1996, 1997}. h Temperature dependency on the activation energies is not considered due to limited data available. i Linear temperature dependency on the exponential prefactors is derived based on the approximation A ~ (k/h)T, where k and h are Boltzmann constant and Plank’s constant, respectively. As in Model I, activation energies for the three Langmuir-Hinshelwood reactions (R3f-b through 5f-b) at 300 K were taken from the DFT study of Cao and Chen et al. (Cao and Chen 2006). Temperature dependency on the activation energies in reactions R3b, 4b, and 5b were estimated to be R∆T due to the loss of two hindered rotors in the transition state. This assumption was also applied for the CO oxidation step (R10). As a result, thermo-kinetic constrains are inherently satisfied in the Langmuir-Hinshelwood reactions. The entire hydrogen oxidation submodel is thermodynamically consistent at the enthalpy level. The prefactors of reaction R1b, 2b, 3f-b through 5f-b can be 37 determined by ensuring thermodynamic consistency at the entropy level. The exponential prefactors for R3b, 4b, and 5b were taken from Cao and Chen et al. (Cao and Chen 2006) and were assumed to be proportional to temperature. The forward reactions R3f, 4f, and 5f are then determined from molecular adsorption/desorption steps (R6–9). The exponential prefactors for H 2 and O 2 desorption steps (R1b and 2b) were calculated from the forward sticking coefficients of R1f and 2f, respectively. Sticking coefficients of H 2 and O 2 on Pd surface (R1f and 2f) are widely scattered in the literature (Andrae et al. 2004; Seyed-Reihani and Jackson 2004; Tait et al. 2005; Wolf et al. 2003; Yagi et al. 1999). In the current model, the H 2 and O 2 sticking coefficients were considered to be coverage-dependent. An expression of the rate equation k = γT β 10 µθ Pd was proposed for Model II, in which μ is a parameter fitted to experiments and θ Pd is the site fraction of the bare palladium site Pd(S). Here, the β value is set as β = –0.5 for both H 2 and O 2 due to the variation of mean gas velocity as a function of temperature. By fitting of the experiments of Rosen and coworkers (Johansson et al. 2003), µ was determined to be 0.7 and 0.5 for R1f and 2f, respectively. Because of limited kinetic data available for the reaction of carbon and hydrocarbon species, their reactions were assumed to be irreversible. Nevertheless, temperature dependency was included in the exponential prefactors of R11, 14, and 16. On the other hand, temperature dependencies for the activation energies in R11, 13–16 were neglected because their uncertainties remain relatively large. CO desorption may as well be a function the coverage. However, the coverage dependency was not taken into account because the simulation results are found to be insensitive to it because the step is 38 fast enough at the temperatures relevant to catalytic methane ignition, which is roughly above 773 K. In Figure 3-2, it is shown that the prefactors and activation energies deviate from those at the reference temperature of 300 K, ΔE = E(300K) – E(T) (kJ/mol). Inclusion of the temperature dependency can lead to up to an order of magnitude difference in the prefactors and as much as 40 kJ/mol difference in the activation energies over the temperature range considered. Accurate prediction at temperature exceeding 1000 K is important for the prediction of catalytic ignition behavior. In the following section, detail validation of the hydrogen submodel in Model II is reported for its predictive capability at high temperatures. 39 Figure 3-2: Exponential prefactors (Top) and activation energies (Bottom) as a function of temperature. 0 10 20 30 40 200 400 600 800 1000 1200 1400 E(300K) - E(T) (kJ/mol) 2H* H 2 H* + O* OH* H* + OH* H 2 O* 2OH* H 2 O* + O* Temperature, T (K) 2O* O 2 2O* O 2 10 18 10 19 10 20 10 21 10 22 200 400 600 800 1000 1200 1400 A (cm 2 /s) 2OH* H 2 O* + O* H* + O* OH* 2H* H 2 2O* O 2 H* + O* OH* 40 3.6 Validation of Hydrogen Oxidation Submodel Hydrogen oxidation submodel of Model II was validated at 1300 K against the stagnation flow reactor experiments reported by Johansson et al. (Johansson et al. 2001; Johansson et al. 2003). Temperature of the stagnation surface, reactor pressure, and flow rate were set to 1300 K, 13 or 26 Pa, and 100 or 200 cm 3 /min (STP), respectively. The stagnation flow problem was solved using the SPIN code along with SURFACE CHEMKIN (Coltrin et al. 1991b; Kee et al. 1989). The gas-phase reaction model was USC Mech II (Wang et al. 2007). Towards high temperatures and low pressures, the surface oxidation coverage tends to zero. Under the condition, the surface occupancy of O(S), OH(S), and H 2 O(S) are expected to be four, as discussed earlier. For high surface coverage, on the other hand, the occupancy tends to unity. This two limiting condition can cause some ambiguity in reaction order assignment. For flow reactor simulations at atmospheric pressure, it was found that the computational results were not very sensitive to reaction order, whereas the results of the stagnation flow reactor simulated for the low-pressure/ high-temperature experiments do. The occupancy numbers at the low surface coverage limit are used to simulate the latter experiments. In the stagnation flow reactor experiments reported by Johansson et al. (Johansson et al. 2003), the relative mole fractions of OH and H 2 O near the palladium surface were measured by laser-induced fluorescence and microcalorimetry, respectively. H 2 /O 2 mixture ratio was defined as α H2 = p H2 /(p H2 + p O2 ), where p H2 and p O2 are the partial pressures of H 2 and O 2 , respectively. Comparisons of the experimental and computed 41 relative OH and H 2 O mole fractions are shown in Fig. 3-3 for pressure at 13 Pa and flow rate at 100 cm 3 /min (STP). Figure 3-3: Relative H 2 O and OH mole fractions as a function of the hydrogen mixing ratio α H2 . The symbols represent experimental data (Andrae et al. 2004) at 13 Pa and 100 SCCM flow rate and the lines are numerical predictions. The model predicts the data rather well over the entire range of mixture ratio. We note that this agreement should be viewed with some caution, since the surface-coverage dependency of the rate constants for H 2 and O 2 adsorption on Pd surfaces is rather empirical and here, a fit to the data, the agreement seen is not surprising. In particular, it is noted that the coverage dependency must be dependent on the nature of local surface 0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 H 2 O OH Relative mole fraction H 2 mixing ratio, α α α α H2 42 species where adsorption/desorption takes place. This remains to be a weakness of the model proposed here. It is noted that treating this stagnation flow problem as if it is in the continuum regime is only an approximation since the mean free path of the gas is around 0.2 cm or a Knudsen number of the order of 0.1. Under this condition, the flow is rarefied. Simulations with SPIN show that the axial gradients in species concentrations and axial flow velocity are all close to zero at the surface. Hence, neither diffusion nor fluid momentum transport is of significant problems. What does matter is the gas-phase species temperature being lower than the surface temperature at the surface and the numerical formulation used effectively impacts the sticking probability. Hence, the simulation results should be considered as approximate. In fact, the underlying fluid problem is perhaps better described with the assumption made by the perfectly-stirred reactor. In order to clarify the above mentioned flow-regime problem, comparisons of the results calculated by SPIN and PSR are made for two different pressures (13 and 26 Pa) and flow rates at 100 and 200 cm 3 /min in this dissertation work. The results are plotted in Fig. 3-4a, 3-4b, and 3-4c for the flow conditions at {13 Pa, 100 cm 3 /min}, {26 Pa, 100 cm 3 /min}, and {26 Pa, 200 cm 3 /min}, respectively. As seen, the results obtained by the PSR code are not drastically different from those by SPIN. Hence, the hydrogen surface oxidation model in Model II appear to capture the experimental data at 1300 K rather well. 43 Figure 3-4a: Relative H 2 O and OH mole fractions as a function of the hydrogen mixing ratio α H2 . The symbols represent experimental data (Andrae et al. 2004) at 13 Pa and 100 SCCM flow rate and the lines are numerical predictions, comparing the SPIN and the PSR results. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 SPIN PSR H 2 mixing ratio, α α α α H2 H 2 O OH 13 Pa, 100 cm 3 /min Relative mole fraction 44 Figure 3-4b: Relative H 2 O and OH mole fractions as a function of the hydrogen mixing ratio α H2 . The symbols represent experimental data (Andrae et al. 2004) at 26 Pa and 100 SCCM flow rate and the lines are numerical predictions, comparing the SPIN and the PSR results. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 SPIN PSR H 2 mixing ratio, α α α α H2 H 2 O OH 26 Pa, 100 cm 3 /min Relative mole fraction 45 Figure 3-4c: Relative H 2 O and OH mole fractions as a function of the hydrogen mixing ratio α H2 . The symbols represent experimental data (Andrae et al. 2004) at 26 Pa and 200 SCCM flow rate and the lines are numerical predictions, comparing the SPIN and the PSR results. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 SPIN PSR H 2 mixing ratio, α α α α H2 H 2 O OH 26 Pa, 200 cm 3 /min Relative mole fraction 46 3.7 Summary Computational method for simulating catalytic ignition in a plug flow is presented. A code was programmed to include surface chemistry. Two gas-surface models were proposed for catalytic methane oxidation over palladium surface in this work. The first is a trial model termed as Model I. The second model, termed Model II, is an improved version of Model I. Model II includes temperature dependency and thermodynamic constrains of the rate parameters covering a wide range of temperature, from 300 to 1500 K. Principle of thermodynamic constrains is discussed. Literature sources of rate parameters are presented. The hydrogen submodel in Model II was validated against the stagnation flow reactor experiments in which palladium surface was kept at 1300 K. The model was shown to reproduce the experimental data rather well. 47 Chapter 4 Catalytic Methane Ignition by Freely-Suspended Palladium Nanoparticles 4.1 Introduction One of the objectives of this dissertation study was to demonstrate if catalytic ignition of methane could be achieved by freely-suspended Pd nanoparticles generated in situ in a flow reactor. The study combines flow reactor experiments, aerosol and surface sciences with kinetic modeling using detailed gas-phase and gas-surface reaction kinetics to explore the underlying mechanisms of methane ignition over Pd nanoparticles. A gas- phase coupled with gas-surface reaction model was proposed on the basis of previous studies (Deutschmann et al. 1996; Moallemi et al. 1999; Sidwell et al. 2002; Wang et al. 2007). Combined with particle mobility sizing and CO 2 /CH 4 species profiles, the numerical model was used to explain the observations made in the flow reactor. This was not meant to be a quantitative study. The use of a laminar flow reactor indeed limits the ability to account for local reaction conditions in a more precise manner. Nonetheless, the results described here are useful for designing a catalytic reaction process suited for high-speed combustion. Generation of palladium particles in-situ and the catalytic reaction of these particles leading to fuel ignition is schematically illustrated in Fig.4-1. The sequence of nanoparticles formation may be described as follows. At the reactor inlet, a liquid solution of catalyst precursor is injected in the form of micron-sized aerosol carried by a nitrogen stream. This flow was mixed with a stream of premixed CH 4 /O 2 /N 2 mixture. 48 Organometallic Pd compounds dissolved in toluene serves as the Pd precursor. Due to high temperature and small droplet size, the aerosol quickly evaporates in the inlet section of the reactor. Dissociation of the organometallic precursor followed due to heating, releasing Pd atoms or clusters. At high enough atom or cluster concentrations, Pd nucleates into small clusters which grow in size and mass by coagulation and surface condensation. The clusters or the surfaces of NPs become catalytically active at some point. The gas mixture is expected to undergo catalytic oxidation and eventually ignite in the flow reactor. Here, the concentrations of CH 4 and CO 2 were followed to monitor fuel ignition. Figure 4-1: Conceptual drawing of in situ generation of NPs followed by catalytic ignition in a fuel-oxidizer mixture in a flow reactor. 49 4.2 Experimental Procedure The total gas velocity U 0 and the mixture composition selected for the flow reactor experiments are summarized in Table 4-1. The residence time of the reactor was about 1 second. Under these conditions, the flow inside the reactor is laminar with the Reynolds number 568 ≥ Re ≥ 236 for 298 ≤ T (K) ≤ 1073. For reaction condition No.F-0, non-reacting background gas temperatures were measured under a N 2 flow at the steady- state furnace temperatures. Two furnace zone temperatures, T f-1 and T f-2 , were set to be equal (T f ) and the gas temperature profiles were determined along the center of the reactor for T f = 673-1073 K at 100 K interval. For temperature measurements, a K-type thermocouple (OMEGA) of 122 cm in length (denoted as TC-3 in Fig.2-1) was inserted from the bottom of the reactor. Table 4-1: Summary of flow conditions and mixture compositions No. Total gas velocity (STP) Mole fraction Equivalence Objective U 0 (cm/s) C 7 H 8 CH 4 O 2 N 2 ratio, Φ a F-0 52.9 - - - 1.000 0.00 Background temperature F-1 52.9 - 0.083 0.417 0.500 0.40 Non-catalytic ignition F-2 52.5 0.007 0.084 0.420 0.490 0.55 Catalytic ignition F-3 52.5 0.007 - 0.420 0.573 0.15 TEM analysis a Calculation of the equivalence ratio includes toluene. 50 Methane was injected into O 2 -rich flow to test ignition, which are termed as No.F- 1 and F-2 for non-catalytic and catalytic conditions, respectively. Particles were collected on TEM grids under the reactor flow condition identical to that of methane ignition test but without methane addition. This experiment is denoted as F-3. The results of TEM analysis will be presented separately in detail in Chapter 5. The toluene mole fraction is 0.007 given a liquid consumption rate of 0.22 ml/min, which was directly measured by balancing the liquid pool level and the liquid injection rate into the pool. The mass density of the Pd(thd) 2 /toluene solution was assumed to be identical to that of toluene at 0.87 g/ml. The catalyst flow rate at the exit of the atomizer may vary depending on the operating temperature of the atomizer. However, the fluctuations of the liquid injection rate during experiments were small (± 0.6 %). The mass fractions of the two batches of Pd(thd) 2 samples (706-90A and 706-84A, TDA Research, Inc.) are 50000 and 55800 ppm wt., respectively. Both catalyst samples were diluted with toluene to give a Pd(thd) 2 mass fraction of 19200 ppm, which contains 4.32 mg of pure palladium in 1 g of toluene. Summary of test conditions with various flow conditions given in Table 4-1 are presented in Table 4-2. Ignition tests were performed in two different ways. In one way (Run 1 though Run 5), the furnace was operated at the transient mode and the furnace temperatures were increased at a constant rate of 20 K/min until ignition occurs. During the ramp-up period, methane concentration and/or catalyst precursor input were kept at steady-state. In Runs 3 and Run 4, the mass concentration of Pd(thd) 2 used is 1.92% wt. This way gives a rough estimate of the ignition temperatures as well as precursor loading. 51 However, in the transient mode, the temperature profile could not be characterized well enough for detail computational analyses. Table 4-2: Summary of experimental condition and key results No. Ignition Flow type Furnace temp. (K) Molar ratio Median a Surface-to- volume ratio a type Table 4-1 T f-1 T f-2 χ Pd /χ CH4 <D p > ζ (1/cm) Transient furnace temperature at heating rate +20 K/min, constant injection rate. Run 1 Non-catalytic F-1 1149 1077 Run 2 Non-catalytic F-1 1142 1073 Run 3 Catalytic F-2 998 970 4.3×10 -4 24 0.023 Run 4 Catalytic F-2 954 916 4.7×10 -4 28 0.027 Run 5 Non-catalytic F-1 1179 1117 Constant furnace temperature, increase precursor loading over time. Run 6 Non-catalytic F-1 1113 1113 Run 7 Catalytic F-2 973 973 2.1×10 -4, c 19 c 0.013 c Controlled particle formation for TEM analysis. Run 8 No ignition F-3 773 773 - 26 0.016 Run 9 No ignition F-3 973 973 - 23 0.016 a Measured at reactor exit. b The reactor tube used was contaminated by wall coating. c Molar loading, particle diameter and surface area at point of ignition. One of the key experimental challenges in this work was to reduce the impact of wall deposits. In Run 5, the effect of the Pd deposited on the reactor wall was carefully investigated. The test was carried out without the input of catalyst precursor but with a quartz tube repetitively used in prior catalytic experiments. In all other runs, a fresh, new 52 tube was used to minimize the influence of the wall depositions, even though by visual inspection the tube was usually clean after an experiment. The other way tested (Run 6 through Run 9) is that the furnace was operated at the steady-state mode in which the temperature was maintained at a set value, and the composition of the inlet gas mixture was also held fixed. For the catalytic ignition test (Run 7), the catalyst loading was raised gradually until ignition occurs. Mass loading of the precursor is initially 0 % wt., therefore it is pure toluene, and then 1.92 % wt. of liquid precursor was added to the atomizer at a constant rate. This approach gives the minimum catalyst loading that causes ignition of methane under well-characterized temperature and flow fields at the specific furnace temperatures. In either approach, ignition tests were performed for non-catalytic cases to give the reference conditions for methane-only mixture to ignite. These are Runs 1, 2 and 6. In addition, Runs 8 and 9 were designed to produce Pd/PdO nanoparticles for TEM sampling. To avoid fuel ignition, only the mixture of O 2 and N 2 flows were used, and their combined flow rate was equal to those of catalytic experiments. The mass fraction of the Pd(thd) 2 in toluene was 1.2% wt., which is about the same as that in Run 7. In Run 9, the furnace temperatures were set equal to those in Run 7 whereas the furnace temperatures were lowered by 200 K in Run 8 to observe morphological or composition variations as a function of temperature. In Run 8, time-resolved particle size distributions were measured along the flow passage of the reactor. Palladium acetate was used as the precursor. The mass loading of Pd acetate was 0.6% wt. in toluene, which gives identical particle size distributions at the 53 exit of the flow reactor as those obtained in Run 7. The gas mixture was sampled at five different positions from the reactor inlet: x = 23, 33, 43, 71 cm, and at the reactor exit 76 cm. The gas sampled from the flow reactor was introduced into a scanning mobility particle sizer at a nominal flow rate of 0.3 L/min. The residence time from the reactor exit to the SMPS inlet is 0.1 sec, which is short enough to prevent particle losses. The diameter of the impactor nozzle used was 0.0457 cm. The particle size distribution was scanned from 4.53 to 160 nm in diameter. 54 4.3 Results and Discussion For the analysis of chemical kinetic behavior, the gas temperature profile needs to be characterized as precisely as possible. For the conditions tested here, the flow was laminar (568 ≥ Re ≥ 236). This creates a parabolic radial temperature profile, which can have relatively large radial temperature gradients. Moreover, in the axial tube direction, large temperature gradient also exists due to finite time for heating or cooling of the flow. For these reasons, the gas temperature was measured both along the centerline T b,center and adjacent to the wall T b,wall in pure N 2 flow at the total flow rate equal to the ignition tests (See, mixture F-0 of Table 4-1). The results are presented on Figs.4-2a and 4-2b, respectively. As seen, the centerline gas temperature undergoes heating in the first 2/3 of the reactor and cooling in the remaining section. As expected, the difference of temperature profiles between the centerline and the wall is quite large, by as much as 200 K. Along the centerline, gas temperature rises more gradually than that close to the wall and reaches the peak value further downstream than the temperature adjacent to the wall. The finite heating rate under the laminar flow condition could be in part responsible for this relatively long preheating period in the centerline of the reactor inlet. In comparison, Fig.4-2b shows that heating along the inner wall was more rapid. The highest temperature was reached closer to the inlet than along the centerline. 55 Figure 4-2a: Background, centerline temperature T b,center measured in an N 2 flow (F-0 in Table 4-1) at several furnace temperatures T f . Symbols are experimental data and solid lines are fitted to data. The dashed lines were obtained from extrapolating the data from the measured data points for T f = 1173 K and 1273 K. 400 600 800 1000 1200 0 10 20 30 40 50 60 70 Background centerline temperature, T b,center (K) Distance from reactor inlet, x (cm) T f =673 K 773 K 873 K 973 K 1073 K 1173 K 1273 K 56 Figure 4-2b: Background, wall temperature profiles T b,wall measured in a N 2 flow (F-0 in Table 4-1) at several furnace temperatures T f . Symbols are data and solid lines are fitted to data. The dashed lines were obtained from extrapolating the data from measured data points for T f = 1173K and 1273 K. 400 600 800 1000 1200 0 10 20 30 40 50 60 70 Background wall temperature, T b,wall (K) Distance from reactor inlet, x (cm) T f =673 K 773 K 873 K 973 K 1073 K 1173 K 1273 K 57 The observed radial temperature gradient makes it difficult to interpret the data quantitatively. A realistic modeling approach would have to simulate the problem as a two-dimensional, laminar reacting flow problem. Because of the computational difficulties involved, this will not be attempted hereby. Rather, both the centerline and the near-wall temperatures were used as the initial input for numerical simulation, which will give upper and lower bounds of the predictions. Results of ignition tests, Runs 1 through 4 in Table 4-2, are to be examined first. For these tests, the furnace temperature was transient and increased at a rate of 20 K/min. The furnace temperatures T f-1 and T f-2 , at the point of ignition were recorded and shown in Table 4-2. The experiments were found to be reproducible (cf. Runs 1 and 2). Figure 4-3 shows the variations of CH 4 and CO 2 concentrations plotted as a function of the Zone-I furnace temperature T f-1 . It is seen that for all cases the CH 4 mole fractions drop and the CO 2 mole fractions rise quite abruptly at the point of ignition. For the catalytic Runs 3 and 4, the rise of the CO 2 mole fractions prior to the disappearance of CH 4 was caused by catalytic oxidation of toluene. These oxidation processes appear to be gradual and non- explosive. Experimentally, it was confirmed that toluene itself could hardly affect the ignition temperature of methane under non-catalytic conditions. 58 Figure 4-3: CH 4 and CO 2 mole fractions observed for Runs 1 and 3 as a function of the furnace temperature of Zone I, T f-1 . Methane ignited non-catalytically at around 1100 K furnace temperatures as were Runs 1 and 2, corresponding to a maximum gas temperature of roughly 950 K along the centerline of the reactor as seen in Fig.4-2a. The use of Pd catalyst generated in situ leads to a reduction of the furnace temperature by about 150 K at the point of ignition, using a Pd loading of ζ ~ 0.025 cm -1 ( ζ: catalyst surface area to total gas volume or surface density) as shown in Table 4-2. Under this condition, the atomic Pd to CH 4 ratio was around 4.5×10 -4 corresponding to about 3 mg Pd/gm-CH 4 . Runs 3 and 4 were designed to test the operation of the atomizer. In Run 3, the atomizer was covered by ice 0.00 0.02 0.04 0.06 0.08 0.10 0.12 800 900 1000 1100 1200 Run 4 Non-Catalytic CH 4 Furnace Temperature, T f-1 (K) Mole Fraction Catalytic Run 3 CO 2 59 packs, reducing its temperature down to ~278 K. For Run 4, the atomizer was operated at a somewhat higher temperature ~283 K. Because of the temperature dependencies of the viscosity and the surface tension of droplets, the mass of aerosol generated changed. When the atomizer was chilled, a lesser amount of aerosol was introduced into the reactor, leading to a smaller median diameter and the surface area-to-volume ratio than those when the atomizer was operated at 283 K. The impact of this temperature difference in catalyst mass loading was captured by the two experiments. With a higher catalyst loading (by about 10%), the furnace temperature at ignition was reduced by about 50 K as shown in Table 4-2 and Fig.4-3. During the methane ignition runs under the transient furnace operation mode, the particle size distribution functions (PSDFs) were determined at the exit of the reactor tube. Figure 4-4 presents several PSDFs obtained during Run 3 at various furnace temperatures. These samples were collected with the dilution ratio of ~10 and an aerosol transmission time of 0.6 s. Since the number density of the particles is of the order of 10 8 cm -3 at the exit of the reactor, this density drops to 10 7 cm -3 after dilution. Assuming the coagulation rate constant to be the collision-limit ~10 -9 cm 3 /s, the characteristic coagulation time was calculated as 1/ (10 7 × 10 -9 ) ~ 100 s. Hence, this analysis shows little to no coagulation losses are expected for the aerosol sampled. 60 Figure 4-4: Selected particle size distributions observed for Run 3 at several furnace temperatures. As seen, the median diameter of the particles was 20 to 30 nm. Without injecting the Pd(thd) 2 precursor solution, the same measurement yielded only trace of particles with number density similar to the ambient background. Although the particle diameters are mobility diameters, they should be very close to the true diameters for particles in the observed size range (Li and Wang 2003a; Li and Wang 2003b; Wang 2008). While the furnace temperature was being ramped up over a period of 20 minute, the PSDFs remain 0 1x10 9 2x10 9 10 100 800 850 900 950 1000 1050 dN/dlog(D p ) (#/cm 3 ) Particle Diameter, D p (nm) Furnace temperature, T f-1 (K) 61 almost identical. This indicates that the precursor injection rate is steady, and the processes of aerosol evaporation and precursor decomposition followed by particles nucleation and growth are independent of temperature for the furnace temperatures above 800 K. It also suggests that these processes are complete or almost complete near the inlet region of the reactor and at temperatures substantially below the peak temperature of the gas. Hence, the observed catalytic effect on methane ignition arises from the catalyst particles generated in situ. Further detail PSDFs within the reactor tube will be examined later in this section. All of the PSDFs observed are roughly log-normal with median diameter as expected for particle size growth dominated by particle-particle coagulation. Additionally, the tail towards the small size end of the distribution is again expected, and is indicative of persistent particle nucleation, perhaps due to the residue Pd vapor in the flow tube. The small shoulder towards the large particle size is probably indicative of the presence of aggregates. This type of the PSDFs has been commonly observed in homogeneous soot nucleation and growth (Abid et al. 2008; Abid et al. 2009; Singh et al. 2006; Zhao et al. 2007; Zhao et al. 2003a; Zhao et al. 2005; Zhao et al. 2003b), and is not indicative of particles produced from aerosol drying or breakup. Given the mass fraction of Pd(thd) 2 in toluene and the initial aerosol droplet size, the particles would be about 100 nm in diameter if they were produced purely from toluene evaporation. If the particles were produced from a combination of aerosol drying and breakup, the size distribution would be significantly wider than observed. 62 The homogeneous nucleation mechanism for particle formation is also supported by the second order of coagulation kinetics. Suppose that the initial Pd vapor, Pd(v), is the monomer at the concentration of N 0 = 2 × 10 14 cm -3 as calculated from the initial Pd(thd) 2 loading for Runs 3 and 4, and is uniformly dispersed in the gaseous reactant mixture, and assume that the sticking probability is unity and the bimolecular coagulation rate constant is β = 1 ×10 -9 cm 3 /s, then it can be estimated that the number density of Pd particle after 1 s is 9 3 0 0 ~ ~ 10 cm 1 N N N t β − + (4-1) This is consistent with the observation shown in Fig.4-5. In addition, the particle diameter may be estimated from the number of atoms in each particle ~ 2×10 5 and an assumed mass density of 10 g/cm 3 . This gives a mean diameter of 20 nm, which is close to the experimental observation ~ 25 nm. Of course, the initial non-uniform distribution of the aerosol could cause the local Pd(v) concentration to exceed 2 × 10 14 cm -3 . This would result in the effectively shortened coagulation time for particle production. The measured PSDFs can be fitted into a tri-lognormal distribution function, ( ) ( ) 2 3 2 1 log exp log 2 log 2 log p p k k p k k k D D dN N d D π σ σ =         = −       ∑ , (4-2) where D p is the particle diameter, N k , p k D and σ k are the number density, the median diameter, and the geometric standard deviation of the k th size mode, respectively. 63 Figure 4-5: Representative particle size distributions (symbols) measured during Run 3. Lines are fitted into a tri-lognormal function whereas thinner lines indicate the three separate particle size modes. Figure 4-5 shows a sample of the fit to data taken from Run 3. Aside from the fact that the PSDF parameters are roughly invariant with respect to the furnace temperature (especially the dominant, second mode), the most important feature here is that σ 2 = 1.53, which is slightly larger but close to that of the self-preserved distribution function of 1.46 (Landgrebe and Pratsinis 1989). Hence, the particles measured are conclusively those from nucleation and growth out of the gas-phase precursors. As discussed earlier, the PSDFs were found to be insensitive to the temperature for T f > 800 10 7 10 8 10 9 10 10 10 100 Growth Mode N 2 = 7.5x10 8 (cm -3 ) σ 2 = 1.53 <D p > 2 = 23 nm Nucleation mode N 1 = 5.8x10 9 (cm -3 ) σ 1 = 1.34 <D p > 1 = 2.3 nm Aggregates N 3 = 4.2x10 6 (cm -3 ) σ 3 = 1.36 <D p > 3 = 98 nm dN/dlogD p (#/cm 3 ) Particle diameter, D p (nm) T f-1 = 911 K 64 K. Below that temperature, however, this is not the case. Figure 4-6 shows that below 800 K the median particle diameter <D p > can rise up to 40 nm in some cases, whereas the surface area-to-volume ratio ζ (integrated from the distribution function) remains relatively constant. Figure 4-6: Particle median diameter <D p > and area-to-volume ratio ζ (STP) measured at the exit of the flow reactor during Run 3 and Run 4, as a function of the furnace temperature of Zone I, T f-1 . Square and round symbols represent Run 3 and Run 4, respectively. The rise in the median diameter towards low temperature was caused perhaps by coke formation or carbon deposition, since the aerosol was injected into the reactor in a 0 5 10 15 20 25 30 35 40 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 700 800 900 1000 1100 Median diameter, <D p > (nm) Area-to-volume ratio, ζ ζ ζ ζ (cm -1 ) Furnace temperature, T f-1 (K) Ignition Run 3 Run 4 Run 3 Run 4 Ignition 65 nitrogen stream and locally the precursor flow was extremely fuel rich for a period of time. Meanwhile, toluene undergoes pyrolysis either homogeneously or catalyzed by dissociation of Pd(thd) 2 and Pd/PdO clusters formed thereafter. Regardless, the observed variations in the median size below 800 K do not affect the interpretation of the experiment since ignition was observed above that temperature. More details of these size distributions of low temperature regions will be examined in the context of the time- resolved particle formation later in this section. One of the concerns that could influence the catalytic ignition results is that methane could be catalytically oxidized on the Pd contaminated tube wall and ignition could occur near the catalytic wall. In the aerosol flow reactor experiments performed in this dissertation work, it is nearly impossible to completely eliminate condensed matter deposition on the tube wall because of the finite surface to volume ratio of the reactor. Hence, our effort was directly at minimizing wall catalysis. The liquid atomizer used was designed specifically for that purpose. Because of the use of multiple impactors, the Stokes’ number of the droplets is relatively small, which makes the aerosol followed the flow closely; and the droplets have little possibility to impinge onto the reactor wall before they disintegrate. In addition, the unburned reactant gas (CH 4 /O 2 /N 2 ) can act as a sheath surrounding the aerosol injection tube at the inlet of the reactor. This design further prevents the aerosol from reaching the reactor wall, at least before they are in contact with the unburned gas. Apart from this situation, there could still remain a minor possibility that the actual ignition was induced by catalytic reaction on the reactor wall, on which a few atomic layers of palladium might be deposited. 66 In order to examine the influence of catalysis on the reactor wall independently, Run 5 is carried out without injecting the Pd(thd) 2 precursor but using a quartz tube with a visible coating from a prior experiment with an overloaded precursor to induce a large amount of wall deposition. Figure 4-7 shows the CO 2 and CH 4 profiles as a function of the Zone-I furnace temperature. It is seen that the “contaminated” tube caused the methane mole fraction to drop, starting at around T f-1 = 730 K. It reached the plateau at around T f-1 = 1000 K. Interestingly, the ignition occurs at T f-1 ~ 1180 K (Table 4-2), about 30 K higher than those tested in clean and unused tubes (Runs 1 and 2). The above observation may be interpreted in what follows. In Run 5, wall catalysis indeed occurs, leading to the formation of the plateaus in the concentration profiles. Ignition at a furnace temperature ~1180 K was caused by homogeneous process. The ignition was delayed because methane concentration was reduced from the gaseous mixture due to catalytic conversion on the wall. This delay also indicates that the heat transfer process from the catalytic wall into the gas-phase bulk flow was not very efficient. Hence, it is clear that in this case, wall catalysis would rather retard the ignition process. More importantly, the lack of plateaus in the CH 4 concentration profiles coupled with a reduced ignition temperature as observed for Runs 3 and 4 (Fig.4-3) indicates that (a) wall catalysis is sufficiently suppressed and (b) ignition is indeed induced by nanoparticles produced from Pd(thd) 2 . 67 Figure 4-7: CH 4 and CO 2 mole fractions measured during Run 5 as a function of the furnace temperature of Zone I, T f-1 . The wall of the reactor tube used for Run 5 was contaminated by wall coating of condensed-phase material from Pd(thd) 2 decomposition. Runs 6 and 7 were made to facilitate model comparisons. For these runs, the furnace temperature was kept fixed so that the flow and the temperature fields were kept at steady-state conditions. These runs were more suitable for model comparisons than the transient operations, considering that the temperature profiles along the reactor tube could be measured only under the condition of steady reactor operation. Under the transient conditions, the rise in the gas temperature lags further behind. For these reasons, though the results of Runs 3 and 4 are useful for examining the response of methane ignition to furnace temperature, they cannot be modeled with certainty because the actual gas temperature prior to ignition cannot be measured accurately. 0.00 0.02 0.04 0.06 0.08 0.10 700 800 900 1000 1100 1200 CH 4 CO 2 Mole fraction Furnace temperature, T f-1 (K) 68 For background non-catalytic ignition of methane in Run 6, the furnace temperature is elevated at a 5-K interval. The reactor was allowed to equilibrate for 30 min at each furnace temperature until ignition was observed. For the mixture composition given as F-1, the ignition was observed at T f = 1113 K with an uncertainty of ±5 K. This temperature was about 35 K lower than that of Runs 1 and 2, which is reasonable considering that the furnace temperature is transient in those runs. In Run 7, the furnace temperature was held fixed at 973 K. The Pd(thd) 2 loading was increased gradually while the Pd particle size distribution was continuously measured. Figure 4-8 shows selected PSDFs data at various times over the course of the run. Both the median diameter of the particles and the particle surface density continued to increase as seen in Fig.4-9 while the total number density remains nearly the same over the 20-min of run period. When the particles grow to a median diameter around 20 nm (the filled symbols in Fig.4-9), ignition occurred. At that point, the atomic Pd-to-CH 4 ratio was 2×10 -4 and the surface area-to-gas volume ratio ζ was 0.013 cm -1 , as shown in Table 4-2. As before, the PSDFs are trimodal and the main mode is log-normal. This set of the experiments was highly reproducible and was used as the basis of modeling studies. 69 Figure 4-8: Selected particle size distribution functions at various testing times measured at the exit of the flow reactor during Run 7. Furnace temperature T f was kept at 973 K while the catalyst concentration was gradually increased. The mixture ignited 20 minutes after the start of the run. 0 1x10 9 2x10 9 10 100 0 5 10 15 20 dN/dlogD p (#/cm 3 ) Particle diameter, <D p > (nm) Time (ms) ζ ζ ζ ζ = 2.6×10 -3 cm -1 3.3×10 -3 5.5×10 -3 7.9×10 -3 9.1×10 -3 1.0×10 -2 1.3×10 -2 Ignition 0 1x10 9 2x10 9 10 100 0 5 10 15 20 dN/dlogD p (#/cm 3 ) Particle diameter, <D p > (nm) Time (ms) ζ ζ ζ ζ = 2.6×10 -3 cm -1 3.3×10 -3 5.5×10 -3 7.9×10 -3 9.1×10 -3 1.0×10 -2 1.3×10 -2 Ignition 70 Figure 4-9: Particle median diameter <D p > and area-to-volume ratio ζ measured at the exit of the flow reactor during Run 7. Round and rectangular symbols represent <D p > and ζ (STP), respectively. Flow reactor simulation was performed first using the trial surface model, Model I discussed in Chapter 3. In addition, the particle size was set as a constant throughout the reactor, and the size measured at the exit of the reactor was chosen. The influence of particle size change during the course of reaction will be addressed later. The computational results are summarized in Table 4-3. Simu-1 and 2 correspond to the non-catalytic methane ignition cases of Run 6. Simu-3 through 6 represents Pd- dispersed catalytic methane ignition cases of Run 7. In these simulations, the measured non-reacting background temperatures (Figs 4-2a or b) were used as a model input, i.e., 10 15 20 0.00 0.01 0.02 0 5 10 15 20 25 T f = 973 K Median diameter, <D p > (nm) Area-to-volume ratio, ζ ζ ζ ζ (cm -1 ) Test time (min) Ignition 71 the first term on the right-hand side of eq.3-4. Heat release was accounted for in the second term of that equation. Of course, that description is not mathematically rigorous since local heat release would affect the first term because of sensitivity of heat conduction and convection towards local temperature. This uncertainty, however, is expected to be smaller than the non-uniform temperature in the reactor. In the simulations, either the measured centerline (T b,center ) or the near-wall temperature (T b,wall ) was used as model input and they are treated as the two limiting cases. Table 4-3: Summary of numerical conditions and key results No. Ignition type Background temp. Flow type Table 4-1 Ignition furnace temp. T f-ign (K) Difference from measured a ∆T Simu-1 Non-catalytic T b, center F-1 1127 +14 Simu-2 Non-catalytic T b, wall F-1 1039 –74 Simu-3 Catalytic T b, center F-2 b 956 –17 Simu-4 Catalytic T b, wall F-2 b 880 –93 Simu-5 Catalytic T b, center F-2 c 960 –13 Simu-6 Catalytic T b, wall F-2 c 885 –88 a Run 6 and Run 7 in Table 4-2 are used for comparison with non-catalytic and catalytic cases, respectively. b Toluene is converted to CO 2 and H 2 O; U 0 = 52.8 cm/s, Φ = 0.47, χ CH4 / χ O2 / χ CO2 / χ H2O / χ N2 = 0.083/ 0.356/ 0.047/ 0.027/ 0.486. c Toluene was included as a reactant. d <D p > = 19 nm and ζ = 0.013 cm -1 (STP), the ignition condition of Run 7 in Table 4-2. In case of Simu-1 when the centerline temperature was used as the model input, the predicted furnace temperature at the point of ignition was only 14 K higher than the experimental value (also, see Fig.4-10). Considering all of the experimental and model 72 uncertainties, the close agreement is perhaps fortuitous but encouraging nonetheless. If the near wall temperature was used in the simulation (Simu-2), the furnace temperature of ignition is predicted to be 74 K lower than the observation. The results computed with the two limiting temperatures bracket the experimental value, as expected. Considering that the wall quenching of the free radicals was not considered in either computational case, the current results are considered as more than acceptable. In what follows, only computations carried out with the centerline temperature will be discussed, though computational results using the near wall temperatures are reported in Table 4-3 for all cases. Figure 4-10 shows the CH 4 and CO 2 profiles computed as a function of the furnace temperature as well as the experimental data points of Runs 6 and 7, comparing the non-catalytic case (Simu-1 and Run 6) with the catalytic cases (Simu-3 and -5, and Run 7). As seen, the computed temperatures are within 20 K of the experimental values for both non-catalytic and catalytic cases. Under comparable conditions, the model predicts a reduction of 171 K in the furnace temperature at a catalyst loading of 2×10 -4 (atomic Pd-to-CH 4 ratio) and a corresponding surface area-to-gas volume ratio ζ of 0.013 cm -1 whereas the experimental value is 140 K. Since toluene was used as the solvent for Pd(thd) 2 , its impact on the gas-phase reaction kinetics was considered in the simulation. USC Mech II has a limited number of reactions for toluene pyrolysis and oxidation. It predicts the laminar flame speed and ignition delay of toluene-oxidizer mixtures reasonably well (Djurisic et al. 2001). However, USC Mech II does not include some of the reactions that may be of importance 73 to toluene oxidation in the temperature range of the current experiments. Hence, the simulation was performed by assuming all of the carbon in toluene was converted to CO 2 (Simu-3 and -4) or by assuming all of toluene remains as the reactant at the onset of the reaction (Simu-5 and -6). Figure 4-10: Computational results of CH 4 and CO 2 mole fractions at the reactor exit as a function of furnace temperature T f for both non-catalytic (Simu-1) and catalytic (Simu-3 and -5) cases. The model used the centerline temperature T b,center as the input. For Simu-3, toluene was assumed to be completely oxidized to CO 2 and H 2 O before ignition, whereas for Simu-5 toluene was included as a reactant. For both catalytic cases, Pd particles with <D p > = 19 nm and ζ = 0.013 cm -1 (STP) were assumed. 0.00 0.02 0.04 0.06 0.08 0.10 0.12 800 900 1000 1100 1200 CH 4 CO 2 Mole fraction Furnace temperature, T f (K) Non-Catalytic Simu-1 Catalytic Exp. Run 7 Non-Catalytic Exp. Run 6 Catalytic Simu-3 Catalytic Simu-5 74 Unlike the experimental observation, Simu-5 did yield noticeable toluene consumption and CO 2 production prior to ignition as seen in Fig.4-10. The reason, of course, is probably catalytic processes during Pd cluster and particle formation not accounted for by the model. On the other hand, the computed ignition temperature was not at all sensitive to the toluene chemistry. Simu-3 and 5 yielded basically the same results. Overall, the combined gas-phase and gas-surface model predicts the experimental results well. Analysis of the computational results indicates that the ignition process involves both thermal and radical runaway. Fig.4-11 presents the computational results of Simu-3 wherein the evolution of catalyst surface coverage just before ignition is plotted against the axial position of the flow reactor as well as the reaction time. The model predicts that the surface is nearly saturated by O(S), in agreement with the XPS results as will be presented in Chapter 5. The initial rise in temperature is caused by heating of the gas until about 20 cm from the inlet. The subsequent rise in temperature is the result of heating and heat release due to catalytic reactions. From 20 to 60 cm, almost all CH 4 consumption and CO 2 production is the result of catalysis. At the same time, the reaction becomes autocatalytic, in that the rise in temperature causes an increase in the catalytic reaction rate. At about 70 cm from the inlet, the temperature is brought to ~1000 K at which point the increased desorption of oxygen leads a rapid rise in other surface sites and the overall reaction rate. The temperature now increases rapidly. At about 1000 K, the gas-phase reactions take over, leading to both thermal and radical runaways. 75 Figure 4-11: Surface site fraction θ and centerline temperature T ceneter as a function of the distance from reactor inlet, computed for the furnace temperature T f = 954.7 K (Simu-3: <D p > = 19 nm and ζ = 0.013 cm -1 (STP)). Top panel: surface species in log-scale; bottom panel: O(S) site fraction in linear scale. 0.0 0.1 0.2 0.3 0.4 200 400 600 800 1000 1200 Residence time, t (sec) T center T b,center O 2 CH 4 CO 2 H 2 O Gas temperature, T (K) 0.00 0.15 0.27 0.36 0.44 0.51 0.58 0.64 Mole fraction 10 -10 10 -8 10 -6 10 -4 H O OH H 2 HO 2 CO CH 2 O Mole fraction 10 -9 10 -7 10 -5 10 -3 10 -1 0.96 0.97 0.98 0.99 1.00 0 10 20 30 40 50 60 70 Distance from reactor inlet, x (cm) Surface site fraction, θ θ θ θ O(S) site fraction, θ θ θ θ Ο Ο Ο Ο O(S) OH(S) CO(S) H 2 O(S) C(S) Pd(S) CH 3 (S) H(S) 76 In order to understand further the impact of surface reactions on ignition, the sensitivity analysis for the simulation discussed above was performed. The sensitivity coefficient was calculated by as –∆T f-ig /<T f-ig >, where ∆T f-ig is the change in the furnace temperature of ignition resulting from perturbing the pre-factors by a factor of 2, and <T f-ig > is the average before and after the perturbation. The results are shown in Fig.4-12. It is seen that the key steps are adsorption and desorption of O 2 (R1f-b in Table 3-1) and the oxidative dissociation of CH 4 on a vacant site (R11 in Table 3-1). These results are in agreement with what Fujimoto et al. (Fujimoto et al. 1998) reported on CH 4 oxidation over PdO surface from 500 to 800 K. The overall catalytic reaction rate appears to be limited by reversible oxygen adsorption and desorption (R1f- b), as the reaction controls the vacant Pd sites needed for CH 4 oxidative dissociation on catalyst surfaces. Water or hydroxyl poisoning was predicted to play a minor role under the conditions studied. At around 900 K, the major pathway for water formation is the surface metathesis reaction between two surface OH sites. 77 Figure 4-12: Sensitivity coefficients, –∆T f-ig /<T f-ig >, computed for Simu-3. A positive sensitivity coefficient indicates lowered ignition temperature. Reactions with noise-level sensitivities are omitted. A couple of questions are to be asked in regards to the validity of the assumptions imposed in the preliminary interpretations given above about the Pd NPs dispersed catalytic ignition phenomena. First assumption is that the particle size is fixed throughout the computational domain in the reactor tube. This assumption was removed by the time- resolved particle size measurements to be presented below. The second is that the reaction rate parameters in the surface model (Model I) is independent of temperature -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 R1f R1b R2f R2b R5f R5b R11 Sensitivity coefficient, -∆∆ ∆ ∆ T f-ig /<T f-ig > O 2 +2Pd(S) 2O(S) O 2 +2Pd(S) 2O(S) H 2 O+Pd(S) H 2 O(S) H 2 O(S) H 2 O+Pd(S) 2OH(S) H 2 O(S)+O(S) H 2 O(S)+O(S) 2OH(S) CH 4 +Pd(S)+O(S) CH 3 (S)+OH(S) 78 whereas the computed gas temperature varies over a wide range of values. This assumption was to be removed by replacing the surface model by Model II, and recalculating the flow reactor model. A critical test of the particle sampling procedure is the dependence of the particle size distribution function measured as a function of dilution ratio. This technique was used in the earlier studies of nascent soot formation in premixed flames (Zhao et al. 2003a; Zhao et al. 2003b). To ensure that particles do not undergo substantial coagulation in the sample probe, the dilution ratio must reach a critical value above which the size distribution should become insensitive to the dilution level. Figure 4-13 shows selected PSDFs of Pd nanoparticles determined by SMPS. The reactor condition was identical to that of Run 9 in Table 4-2, in which the reactor temperature was set to the catalytic ignition point, T f = 973 K. It is seen that the distribution function is insensitive to the dilution ratio employed, indicating that particle losses in the probe is minimal. 79 Figure 4-13: Particle size distributions measured at x = 23, 33, 43, 71 cm and the exhaust section from the reactor inlet. For x ≥ 33 cm, the distribution shows the classical log-normal function indicative of particle growth chemistry to be dominated by coagulation in the flow reactor. Particles nucleate out of the vapor phase at around 33 cm. They grow to a median diameter of approximately 7 nm at 43 cm and 10 nm at 71 cm. Below 33 cm, the distribution is broad with little presence of small particles. At that point, much of the particle mass is above 200 nm, as the aerosol droplet is still undergoing evaporation. 10 7 10 8 10 9 10 10 10 100 83 506 221 160 390 69 80 8 dN/dlogD p (#/cm 3 ) Particle diameter, D p (nm) 33cm x = 43cm 71cm 23cm Dilution ratio Exhaust 80 Using a mass density value of 10 g/cm 3 , which is between the density of palladium (12 g/cm 3 ) and palladium oxide (9.7 g/cm 3 ), the mass concentration of the Pd particles at each sample position was determined. The results show that for x ≥ 43 cm, the total mass concentration of the Pd particles is in agreement with the palladium acetate loading. Below this position, the mass concentration measured in the particle size range of 5 to 160 nm is substantially lower than the precursor loading, indicating the aerosol is either still being converted to vapor-phase palladium acetate, or because of finite-rate kinetics for particle nucleation. Having validated a wide-temperature range in the gas-surface reaction model, and with improved measurement of particle size distribution function presented above, in Fig.4-14 the new simulation results will be presented for the earlier flow reactor experiments. Mixture mole fractions are CH 4 / O 2 / CO 2 / H 2 O/ N 2 = 0.083/ 0.356/ 0.047/ 0.027/ 0.486. As in the previous work, the measured non-reactive temperature profiles were used as the background in the form of a heat flux. The heat release from catalytic and gas-phase reactions were added to this heat flux to determine the reactive temperature profiles. Time-resolved particle size measurements were used to model particle size variations, as shown in Fig.4-14. 81 Figure 4-14: Temperature profiles computed along the flow axis (x) using various input parameters for catalytic methane ignition. Particle radius (r d ) used for the simulation are also shown. Symbols are experimental values measured in this work. Also shown in the figure are the simulation results from a previous study. It was assumed that particles nucleate out of the gas phase 30 cm from the reactor inlet. Downstream from this position, the particle radius (r d ) was interpolated as a linear function between measured data at 43 cm and 71 cm. Using the input parameters described above, the current combined gas-phase and gas-surface model predicted that in a mixture with 8.4% CH 4 , 42% O 2 , 49% N 2 , 0.7% toluene, and with 4×10 -4 (mol) Pd/CH 4 catalyst loading, the furnace temperature was T f = 998 K at the ignition point, in good agreement with the measurement (970 K). In comparison, the experimental and computed furnace temperatures are 1113 and 1127 K, respectively, without Pd precursor 400 800 1200 1600 2000 4 8 12 0 10 20 30 40 50 60 70 Temperature, T (K) Particle radius, r d (nm) Distance from inlet, x (cm) T f = 1022 K r d - previous particle model r d - current particle model T - current particle model T - previous particle model T - previous surface model T - current surface model 82 injection. Furthermore, to compare the current surface/particle models with those proposed previously, simulations were performed at a furnace temperature of T f = 1022 K with the catalyst loading at 2×10 -4 (mol) Pd/CH 4 . The predicted temperature profiles are plotted along the reactor axis (x) in Fig.4-14. The modeling results show that the improved gas-surface and particle models do lead to some differences in the predicted temperature profiles, but the fundamental interpretation of the data remains the same. 83 4.4 Summary Freely suspended palladium nanoparticles were generated in-situ in a laminar flow reactor from an aerosol composed of organometallic dissolved in toluene. Mixing the aerosol with a flow of methane-oxygen-nitrogen mixture (equivalence ratio Φ ~ 0.5) can lead to a notable reduction in the ignition temperature of the unburned mixture, as compared to homogeneous non-catalytic methane oxidation without palladium NPs. Measurement of the particle size distribution shows that the median particle diameter is around 20 nm and the surface-to-gas volume fraction is ~0.02 cm -1 (STP). The observed size distribution is consistent with particle formation mechanism dominated by homogeneous nucleation and particle size growth by coagulation and surface condensation. Numerical simulation using a detailed, combined gas-phase and gas-surface reaction model show that the experimental results are well captured by the model. Simulation results suggested that the surfaces of Pd nanoparticles give rise to catalytic reactions at a temperature which would otherwise not lead to substantial gas-phase reactions. The heat release resulting from catalysis eventually brings the gas to a temperature where the catalytic reaction is overtaken by the gas-phase reactions, which eventually lead to thermal and radical runaway, and fuel ignition. The key surface reaction steps are found to be the reversible oxygen adsorption/desorption, which governs the vacant Pd site density and the overall rate of the catalytic reaction. Methane oxidative dissociation on a vacant Pd site is the rate-limiting step for catalytic conversion of methane to CO and hence the heat release. 84 As a continued effort of the gas-surface model development, a temperature- dependent surface reaction model of methane oxidation on palladium was developed with an emphasis on the thermodynamic consistency of the underlying model parameters. Heats of desorption and vibrational frequencies for H 2 , O 2 , OH, H 2 O and CO were taken from literature. The hydrogen submodel was validated against the experiments of H 2 oxidation on palladium at 1300 K. The methane model was tested against a previous flow reactor experiment. The particle size and concentration were modeled based on improved measurements for PSDFs performed in this work. Simulation results are found in good agreement with previous flow reactor data. After improvements made to the reaction model as well as the experimental technique, the first trial interpretations and conclusions drawn from the preliminary analysis are confirmed to remain valid. 85 Chapter 5 Particle Morphology and Composition 5.1 Introduction In the previous chapter, catalytic ignition of methane was demonstrated in a flow reactor. The ignition mechanism was examined using detailed kinetic modeling of the catalytic reaction process over the freely-suspended palladium (Pd) nanoparticles (NPs). Size distributions of Pd NPs were measured at the exit of the flow reactor tube and at the several positions along the flow tube passage. It was confirmed that the size distributions were lognormal with a median diameter about 20 nm near or at the point of catalytic ignition. The chemical kinetic model showed that Pd surfaces become reactive towards methane oxidation close to the temperature of ~ 973 K at which catalytic ignition was observed. The sensitivity analysis revealed that molecular oxygen adsorption, oxide formation, and desorption from the surface reaction processes play a dominant role in the reactivity of Pd surfaces. These observations and interpretations were further verified by microscopy and composition analysis of the synthesized Pd NPs. Size distribution measured by SMPS was based on the mobility size of the particles, and SMPS does not yield sufficient information to discern the actual shape or morphology of the particle sample. In the current work, the SMPS results were compared to or verified against imaging by transmission electron microscopy (TEM). X-ray photoelectron spectroscopy (XPS) was used to measure the chemical composition of the particles. Both hi-res TEM and XPS 86 studies were carried out in collaboration with University of Utah. The summary of the results related to the catalysis performance are presented in this chapter. 87 5.2 Experimental Procedure For studies of morphology and material composition, Runs 8 and 9 were designed to produce Pd/PdO nanoparticles as the experimental conditions shown in Table 4-2. It is important to note that in experiments where ignition was observed, there was a large spike in gas temperature that would presumably cause substantial modification of the particle properties, in particular, the particle surface chemistry of interest for ignition catalysis. To avoid this problem, in experiments where particles were collected for microscopy and surface analysis, the reactor flows contained only oxygen and nitrogen but had total gas velocity of 52.5 cm/s and flow composition otherwise identical to the ignition experiments (mole fractions: 0.007 toluene, 0.420 O 2 , and 0.573 N 2 ). The mass fraction of the Pd(thd) 2 in toluene was 1.2% wt., which was about the same as that of ignition condition in Run 7. In Run 9, the furnace temperatures were set to 973 K, which was determined in Run 7 as ignition condition, whereas the furnace temperature in Run 8 was operated at 773 K, 200 K lowered than that of Run 9 to observe the variation of morphology and composition as a function of temperature, and the correlation to ignition. After passing through the flow reactor, the particle-containing gas mixture was diluted eight times in cold nitrogen in order to quench the reaction and minimize post- reactor changes in the particles. In the exhaust section, a TEM carbon grid (Electron Microscopy Science HC200-CU) was placed in the flow line so that the grid was exposed directly to the diluted exhaust flow, flowing parallel to the grid surface. The linear flow rate was 13 m/s over the grid. Under this condition, the flow is turbulent and the principal mechanism of particle collection is diffusion of the particles across the laminar boundary 88 layer near the surface. As will be discussed below, diffusion-mediated collection biases against large particles since the particle diffusivity is inversely proportional to the diameter squared. The morphological structure of particles dispersed on the grid was first analyzed by the transmission electron microscopy (TEM, Philips EM420) located at the Center of Electron Microscope and Microanalysis (CEMMA) at USC. Then, the TEM samples were analyzed in more detail at University of Utah by the following methods. High- resolution transmission electron microscopy (HRTEM) and selected electron diffraction (SAED) was done using an FEI Technai F30 at 300 keV beam energy. Sannning transmission electron microscopy (STEM) analysis was performed on an FEI Technai F20 operated at 200 keV, with a high-angle annular dark field (HAADF) detector. The STEM was also used for energy dispersive X-ray (EDX) analysis of elemental compositions. Spectra were background-subtracted, integrated, and converted to elemental compositions using k-factors supplied by EDAX Inc. X-ray photoelectron spectra (XPS) were collected using the monochromatic Al Kα source (1486.7 eV) on a Kratos Axis Ultra DLD instrument. A brief summary of the results and the findings relevant to ignition catalysis are presented in the next section. 89 5.3 Results and Discussion There are several general points to be made before discussing the particle properties. As the N 2 flow in which the Pd(thd) 2 /toluene aerosol was entrained mixed with the bulk CH 4 /O 2 /N 2 mixture and enters the heated section of the reactor, the aerosol droplets are expected to evaporate rapidly (b.p. toluene = 384 K, T sublimation Pd(thd) 2 ~ 423 K), releasing the Pd(thd) 2 vapor into the flow. Pd(thd) 2 is a weakly-bound coordination complex, expected to decompose at relatively low temperatures, releasing Pd atoms into the flow. As will be shown below, the Pd atoms nucleate to form nanoparticles, which catalyze ignition of methane at 873 K gas temperature (973 K furnace temperature). One question is whether Pd(thd) 2 decomposition is fast enough at the temperature of interest, so that nanoparticle growth is complete, or nearly so, before the exit of the flow tube. It is found that the particle size distribution is, essentially independent of reactor temperature from at least 773 K to 1073 K. If the Pd(thd) 2 decomposition rate were a significant factor controlling nanoparticle nucleation and growth, the particle size distribution would change significantly over such a broad temperature range. Figure 5-1 shows the low-magnification TEM images from Runs 8 and 9. Both TEM grids were exposed to the exhaust flow for 6 minutes. The two images were almost identical, an observation consistent with the mobility size measurement. Most of the particles are somewhat smaller than the median diameter <D p > observed by SMPS. This could be due to the fact that the current particle collection mechanism relies on the particle diffusion towards the grid. The collection efficiency would be, therefore, biased against larger particles. 90 Figure 5-1: TEM images of nanoparticles sampled in Run 8 (Left) and Run 9 (Right). The furnace temperature T f was kept at T f = 773 K and 973 K, respectively. The images were found to be mostly identical between the two runs. Figure 5-2 shows HRTEM images collected for particles representative of the samples. They are confirmed to be identical regardless of the reactor temperature difference of about 200 K. The images show the typical primary particles, roughly ~ 10 nm in diameter with well developed lattice fringes. The 2.28 Å lattice spacing clearly corresponds to the spacing between Pd (111) planes. This same spacing is seen in high- resolution images of most particles examined, confirming that the bulk of the particles is crystalline metallic Pd. 91 Figure 5-2: HRTEM images of nanoparticles sampled in Run 8 (Left) and Run 9 (Right). The furnace temperature T f was kept at T f = 773 K and 973 K, respectively. Most particles were found to be rich in Pd metal. (Van Devener et al. 2009) Bulk structure of the particles are also analyzed by the selected area electron diffraction (SAED). The SAED pattern measured for these samples is shown in Fig.5-3. As seen, both images are again identical, and most of the lattice distances measured is found to be in close agreement with the lattice parameters for Pd metal. Although in both cases of Run 8 and Run 9 formation of PdO is thermodynamically favorable (Rao 1985), no evidence of PdO was found from these SAED patterns, consistent conclusion drawn from the HRTEM images discussed above. Given that PdO is more active catalytic active state for methane combustion as discussed in the previous chapter, it seems worthwhile to examine the surface chemistry of the particles to see if it differs significantly from the particle bulk. 92 Figure 5-3: SAED pattern for Pd(thd) 2 catalyst after passage through reactor at 737 K in Run 8 (Left) and 937 K in Run 9 (Right). (Van Devener et al. 2009) XPS is sensitive to the top few nanometers of the sample surface, providing a means to look for chemical modification of the particle surfaces. Figure 5-4 shows XPS spectra collected for both the Run 8 and Run 9 samples. The samples were collected on TEM grids in the same manner as was done for microscopy experiments, with the only difference being higher particle density to obtain better signal-to-noise ratio to aid chemical state identification. The spectra were analyzed by subtracting a Shirley background, then fitting with Gaussian/Lorentzian functions. The largest peak at 335.9 eV is metallic Pd denoted as Pd 0 , which represents the bulk (interior) of the particles. The smaller peak shifted 1.5 eV toward higher binding energy is from some oxidized Pd species denoted as Pd OX . The high-biding-energy region of the experimental peak is asymmetrically broadened, which is fit by adding a small peak at 338.7 eV. The origin of 93 this high energy broadening is not clear. For the purpose of estimating the amount of oxidized Pd present, here it is simply considered all intensity outside the metallic Pd 0 peak to be oxidized Pd as Pd OX . Taking the XPS and TEM results together, it is clear that while the bulk of the particles formed in Run 9 at T f = 973 K is metallic Pd, there is oxidized surface layer. For the Run 8 sample, the Pd OX signal is barely detectable, indicating formation of much less surface oxide. It is possible to estimate the thickness of the oxide layer by modeling the ratio of Pd OX to Pd 0 signals. The method of estimation is beyond the scope of this dissertation work, however, the detail description can be found elsewhere (Van Devener et al. 2009). Only the results of calculation are presented below. It was determined that, on the basis of the observed intensity ratios, the oxide layer is ~ 0.36 nm thick for the Run 9 sample and 0.09 nm thick for the Run 8 sample, assuming a uniform oxide layer over the particle surfaces. 0.36 nm corresponds to essentially one monolayer of oxidized Pd on the particle surfaces at 973 K and partial monolayer coverage at 773 K. These oxidized Pd layers are too thin to observe in the TEM images and are probably not ordered well enough to contribute to structure in the electron diffraction patterns. 94 Figure 5-4: Pd 3d photoelectron spectra for particles passing through reactor at 973 K in Run 9 (Top) and 773 K in Run 8 (Bottom). (Van Devener et al. 2009) 95 The observed temperature dependence suggests that oxide formation may be kinetically controlled—an observation also supported by findings in the literature for bulk Pd surfaces over much longer residence time (Datye et al. 2000; Wolf et al. 2003), and also with the observation that PdO is more catalytically active than Pd. An appreciable amount of SiO 2 or partially oxidized silicon was also detected in the particle sample. Additional XPS experiments show that the source of silicon contamination was the toluene solvent used to dissolve the Pd(thd) 2 precursor. Because silica is a stable, chemically inert oxide, its participation directly in the catalysis process is quite unlikely. This is also because the Pd particles are relatively large. The presence of this silica contamination should not have much effect on the catalytic chemistry of the Pd particles. Indeed, non-catalytic runs with toluene solvent only show the ignition temperature to be nearly identical to that without toluene injection. SMPS, TEM and XPS evidence all points to a mechanism of ignition induced by the catalytic activity of the Pd/PdO nanoparticles produced in situ from the decomposition of the Pd(thd) 2 /toluene aerosol. Summarizing the above results, a phenomenological description of the particle formation mechanism and its catalytic activities are to be discussed here. The kinetic processes of catalyst particle formation may be described by the following processes: 1. Pd(thd) 2 droplets (1-10 µm) fragment into Pd vapor or Pd i clusters 2. Pd(v) + Pd(v) → Pd 2 3. Pd(v) + Pd 2 → Pd 3 4. Pd 2 + Pd 2 → Pd 4 96 5. …… 6. Pd i + Pd j → Pd i+j This coalescence process leads for the formation of Pd NPs, as observed in Figs.5- 1 and 5-2. The surface of the Pd particles becomes oxidized at some point, leading to enhanced catalytic activities, which eventually lead to the gas mixture to ignite. What remains unclear is why the oxide does not form at an early stage of cluster and particle formation. The reason may be thermodynamic and/or kinetic in nature. It is possible for small particles the formation of palladium oxides is not favorable thermodynamically. A more plausible cause for the lack of bulk PdO formation is the finite mixing time required. As the aerosol is injected into the reactor and undergoes evaporation and decomposition, this flow stream is not yet mixed locally with oxygen in the sheath. Hence, the initial particle nucleation process takes place in spatial regions depleted of oxygen. If oxygen is present locally, it would have been depleted by toluene decomposition and oxidation, as evidenced by the early rise of CO 2 in Fig.4-3. The burst of nucleation followed by coagulation causes the Pd(v) to condense onto existing particle surface rapidly, before the particles have opportunities to mix by diffusion with the sheath oxygen. The result is a particle with a Pd core and a few PdO atomic layers on the surface, as confirmed by TEM and XPS results. 97 5.4 Summary Particles collected at flow reactor temperatures below 773 K and above 973 K at which catalytic ignition was observed for methane mixture were found to have essentially identical size distributions and particle morphologies with one important exception. Those collected above the ignition temperature were found to have ~ 1 monolayer of oxidized palladium on their surfaces where particles collected below the ignition temperature had little oxide present. The similarity in other particle properties presumably reflects a particle formation mechanism in which Pd(thd) 2 decomposes, and Pd NPs condense as the precursor is carried into the reactor, and the carrier gas heat it up. Evidently, at 737 K, the kinetic of Pd oxidation are sufficiently slow that not even a monolayer of oxidized Pd forms during the flow residence time ~ 1 s. By 973 K, the Pd oxidation kinetics is fast enough to form a monolayer of oxidized Pd, and this oxidation appears to activate the particles for methane ignition. The presence of such an oxide layer on Pd surface under ignition condition supports the interpretation of catalytic ignition mechanism made by the gas-surface kinetic model studies presented in the previous chapter, Chapter 4. Additional implications as the results of this particle morphology and composition studies may be that the flow and temperature profiles must be such that the particles have time to oxidize, before significant catalytic ignition can be expected. 98 Chapter 6 Numerical Analysis of Optimal Catalyst Design 6.1 Introduction Computational model for catalytic methane ignition by freely-suspended Pd NPs in a gaseous mixture has developed on the basis of a detailed gas-phase and gas-surface model. In order to avoid the computational complexities by considering the multi- dimensional flow domain and yet to closely model the experiments, the background temperature profiles measured along the centerline and near the wall of the reactor tube were used separately as an initial condition so that the result of each temperature profiles give the upper or lower limits of prediction. A trial gas-surface model (Model I) and a more refined detailed temperature-dependent gas-surface model (Model II) predicted the experiments well within the uncertainties expected from the temperature gradient developed in the laminar flow tube. Based on the validated gas-surface models, in this chapter, additional fundamental insight was gained by numerically calculating the ignition delay times at adiabatic conditions. The analysis is further extended to give guidelines towards optimal nano- catalyst design on the basis of model sensitivity analysis with the goal of maximizing the catalytic reactivity and minimizing ignition delays. This chapter is intended to provide the possible future research directions as well as the fundamental nature of nanocatalysis. 99 6.2 Computational Methods Chemical kinetic models used here are the same as those introduced previously in Chapters 3 and 4. USC Mech-II was used as a gas-phase reaction kinetic model, and Model I or Model II, shown in Tables 3-1 and 3-4, respectively, were used as a gas- surface kinetic model. Adiabatic ignition problems were solved as an initial value problem. Radial transport problems encountered in the previous flow reactor model do not need to be considered in this problem since any flow motion is not taken into account in the system. SURFACE CHEMKIN (Coltrin et al. 2004) was utilized to solve the system of equations and to calculate the chemical reaction rates for both gas-phase and gas-surface processes. The model produces the evolution of chemical species over time. The gas-surface reaction rate constant is described as 2 8 B d i k T k r m γ π π = , (6-1) where γ is the reaction probability or sticking coefficient, k B the Boltzmann constant, m i the molecular mass of i th gas-phase species, and r d the particle radius. The species conservation is written as, ( ) ρ ω ζ ω i w i s i g i M dt dY , , , & & + = , (6-2) where Y is the mass fraction, M w the molecular weight, ρ the gas mass density, ζ the surface area to gas volume ratio of the catalyst, g ω & and s ω & are the gas-phase and gas- 100 surface molar production rates, respectively. The rate of temperature change is obtained by considering the heat release due to chemical reactions only, ( ) ∑ + − = i i w i i s i g p M h c dt dT , , , 1 ω ζ ω ρ & & , (6-3) where h is the specific enthalpy, c p the specific heat capacity of the gas mixture. As before, the particles formed are substantially smaller than the mean free path of the gas. Hence, the particles are treated as in free-molecular regime. The time evolution of the site fraction i for the i th surface is given as, Γ = i s i dt d , ω θ & , (6-4) where Γ is the catalytic surface site density. The code used for computing the ignition delay times is presented in Appendix B. 101 6.3 Ignition Delay Time Ignition delay times (τ) for stoichiometric methane oxidation in air under the adiabatic and isobaric conditions at an initial temperature of 900 K and 1 atm pressure were computed first using Model I. The temperature-time histories with and without Pd NPs are shown in Fig.6-1. The calculation for catalytic oxidation used typical Pd loading and size measured in the experiment with <D p > = 19 nm and the surface-to-volume ratio equal to 0.013 cm -1 (STP). Under the Pd loading chosen, the ignition delay time is shortened by two orders of magnitude compared to homogeneous non-catalytic methane oxidation. For the catalytic case, the rise in the initial temperature occurred at around 10 -2 s appears to be entirely caused by heat release from surface reactions. Interestingly, in that case, the temperature levels off at around 1400 K just before it takes off again some 10 -2 s later. This behavior is explored more closely, as shown in the inset of Fig.6-1. Without considering gas-phase reactions, the predicted temperature plateaus at around 1400 K, far below the adiabatic flame temperature. In other words, the catalytic reaction shuts itself off at that temperature because surface desorption of O 2 becomes so rapid that the catalytic activity is lost. Yet, because the catalytic reactions had brought the gas temperature up to ~ 1400 K, close to the cross-over temperature of H + O 2 chain branching and termination under that pressure, homogeneous gas-phase reactions become active. Eventually ignition occurs because of both gas-phase thermal and radical runaways. 102 Figure 6-1: Temperature-time histories computed for a stoichiometric methane/air mixture under adiabatic and isobaric conditions using Model I, showing the difference in ignition onset between catalytic and non-catalytic ignition of the mixture with initial temperature T 0 = 900 K and pressure p = 1 atm. The catalytic case used a median particle diameter <D p > = 19 nm and the surface-to-volume ratio ζ = 0.013 cm -1 (STP). The inset figure also shows the temperature history computed without considering gas-phase reactions. Hence, the present analysis suggests a two-step process to ignition. That is, catalytic reactions result in initial heat release and raise the gas temperature. Although the temperature rise would shut off the catalytic activity at some point, gas-phase radical chain branching takes over eventually and completes the ignition process. As shown 800 1000 1200 1400 1600 1800 2000 2200 10 -4 10 -3 10 -2 10 -1 10 0 Temperature, T (K) Time, t (sec) Catalytic Non-Catalytic Heat release due to catalytic oxidation Ignition due to gas-phase oxidation 1000 1200 1400 1600 1800 0.02 0.03 T (K) t (s) w/o gas-phase reactions with gas-phase reactions 103 below, these interpretations of catalytic ignition process is essentially the same when Model II was used for the analysis. To assess any influence of the initial temperature on the ignition delay time, the above calculation was extended to a range of 700 – 1500 K. Figure 6-2 is a plot of the computed ignition delay time as a function of the initial gas temperature (T 0 ) where the two catalytic cases using either Model I or Model II. Compared with the trial surface model (Model I), the modified surface model (Model II) predicts somewhat longer delay times below T 0 ~ 1200 K but shorter delay times at higher temperatures. Nevertheless, the qualitative as well as quantitative difference between Model I and Model II is not very significant, and the Model II still predicts ignition delay times shorter than those of homogeneous non-catalytic case by up to two orders of magnitude upon catalyst loading for below T 0 ~ 1200 K. When the initial temperature is high enough near 1400 K, the catalytic and non- catalytic ignition delay is identical because the catalyst activity is suppressed for reasons already discussed and also because gas-phase reaction kinetics tend to dominate at such high temperatures. Over the range of temperature shown in Fig.6-2, the ignition mechanism remains the same. That is, ignition takes place by a sequential, two-step process in which the catalytic reaction dominates initially, but the gas-phase reactions take over after catalytic processes are deactivated by the rising temperature. 104 Figure 6-2: Ignition delay time (τ) computed as a function of initial temperature (T 0 ) for a stoichiometric methane/air mixture under adiabatic and isobaric conditions. The catalytic cases used <D p > = 19 nm and ζ = 0.013 cm -1 (STP). 10 -3 10 -2 10 -1 10 0 10 1 10 2 600 800 1000 1200 1400 1600 Stoichiometric CH 4 -Air mixture P = 1 atm Ignition delay time, τ τ τ τ (sec) Initial temperature, T 0 (K) Non-catalytic Catalytic Model-II Model-I 105 6.4 Sensitivity Analysis Several questions critical to the further development of palladium nanocatalysis are addressed here. They include: • Is it possible to shortned the ignition delay further? • What are the minimum possible ignition delay times, and what are the limiting factors? • Which physical parameters need to be tuned to make further enhancement of ignition delays possible? • Is it physically feasible to tune such physical parameters? The top panel of Fig.6-3 shows the ignition delay times computed for the stoichiometric methane-air mixtures at 1 atm over a wide range of temperature. In the catalytic case, the particles have <D p > = 19 nm and the surface-to-volume ratio equal to 0.013 cm -1 (STP), as before. Dashed line represents the catalytic ignition delays (τ c ) computed without gas-phase reaction kinetics. There appear to be three distinct regions of temperatures that govern the ignition scheme. The top figure also depicts such regions where catalytic ignition is dominant below about 900 K (Region I), both the catalytic and gas-phase reactions contribute to ignition for 900 K < T 0 < 1100 K (Region II), and the gas-phase ignition is dominant above ~1100 K (Region III). A clear distinction between these three regions may be seen by plotting each temperature history. 106 Figure 6-3: (Top) Computed ignition delay plot showing three temperature regions, Region I, II, and II. Model II in Table 3-4 is used for a stoichiometric methane/air gas-surface reactions. (Bottom) Temperature profiles as a function of nondimensional residence time t/τ ign , for three representative regions of ignition scheme, i.e. catalytic reaction dominant τ ign ≈ τ c (Region I), intermediate region τ ign ≈ τ c + τ g (Region II), and gas-phase reaction dominant τ ign ≈ τ g (Region III). 10 -6 10 -4 10 -2 10 0 10 2 600 800 1000 1200 1400 1600 φ = 1.0 Ignition delay time, τ τ τ τ (s) Initial temperature, T 0 (K) Catalytic r d = 9.5nm, ζ = 0.013 cm -1 Homogeneous τ c Region I Region II Region III 600 800 1000 1200 1400 1600 1800 0 0.2 0.4 0.6 0.8 1 T (K) Nondimensional residence time, t /τ τ τ τ ign Region III Region II Region I τ g τ c 107 The bottom panel of Fig.6-3 shows representative temperature histories as a function of the non-dimensional residence time (t/τ ign ), which is normalized by the total ignition delay time τ ign for the initial gas temperature T 0 equal to 800, 1100 and 1300 K for Regions I, II and III, respectively. As seen, with T 0 = 800 K the overall induction period is dictated by the catalytic ignition delays (τ c ). For T 0 = 1300 K, ignition delay time is limited by the gas-phase chemistry (τ g ). Region II is an intermediate region where the catalytic ignition delay and gas-phase ignition delay contribute almost equally to the total ignition delay time (τ ign = τ c + τ g ). The two-stage ignition process discussed in the previous section is clearly seen in this intermediate region. In all cases, it is seen that the gas-phase kinetics is initiated just above 1400 K. As discussed before, the role of Pd NPs is to bring the temperature up to this point. If a nanocatalyst is to be designed to maximize its catalytic reactivity, gas-phase reactions must be the rate limiting process, which leads to a minimal ignition delay time on the order of 1 millisecond for all gas temperatures below 1500 K. Reducing the overall ignition delay times is viable if the catalytic reactivity of nanocatalyst towards lower temperatures could be controlled by tuning the material properties at the atomic scale. In order to investigate this feasibility, the ignition delay times are plotted in Fig.6-4 for various desorption energies of surface oxygen in reaction step R2b, using Model II for the analysis. Three representative gas temperatures, 800, 900 and 1000 K are used again as examples. 108 Figure 6-4: Sensitivity analysis of ignition delays for three representative gas temperatures T 0 = 800 K, 900 K, and 1000 K as a function of the desorption energy of surface oxygen at reference point of 300 K, E 300K (kJ/mol). Solid and dashed lines represent (τ c + τ g ) and τ c –only, respectively. As presented in the previous chapters, the modeling studies and particle characterization results suggest that reaction steps R2f-b is the most influential to catalytic reactivity. Figure 6-4 indeed shows that oxygen desorption energy is the key parameter for catalyst design at least for palladium. For simplicity of analysis, the sticking probability of oxygen molecule in reaction step R2f was assumed to be identical to the original value in Model II for these computations. As before, the total ignition delay time (τ ign ) and the catalytic ignition delay time (τ c ) are shown by the solid and 10 -4 10 -3 10 -2 10 -1 10 0 160 180 200 220 240 2O(S) -> O 2 + 2Pd(S) Ignition delay time, τ τ τ τ (sec) Oxygen desorption energy E 300K , kJ/mol 1000 K 900 K T 0 =800 K PdO τ c Limitted by gas-phase kinetics 109 dashed lines, respectively. As expected, the ignition delay times decreases monotonically as the oxygen desorption energy is reduced; the total ignition delay time tends asymptotically to the limiting value of ~10 -3 s. The above findings are applicable to a wide range of conditions, as shown in Figs.6-5a, 6-5b, and 6-5c for the equivalence ratios of 1.0, 1.5, and 0.7. The desorption energy explored range from 156 kJ/mol to 241.1 kJ/mol. The latter is the nominal value experimentally determined for Pd-O desorption (Conrad et al. 1977), which is evaluated at 300 K in R2b of Model II in Table 3-4. The 156 kJ/mol value derives from B value for which desorption energy is minimum i.e. E des = 156 – 156θ where θ ~ 1 at atmospheric pressure. Solid and dashed lines represent the total and catalytic ignition delay times, respectively. These results show that a lowered oxygen desorption energy promote the catalytic activity under all conditions. The effect is the greatest towards lower equivalence ratio, where surface kinetics is more sensitive to oxygen desorption. The results presented here suggest that a further enhancement of the catalytic activity of palladium nanoparticle is possible if the desorption energy of oxygen on palladium surface can be reduced. Possibilities for engineering the desorption energy reduction include a significantly reduced particle size, leading to weaken interactions between the Pd surface atoms with chemisorbed oxygen, doping, or functionalizing the Pd particles on other nanoparticles as the support. These possibilities can be explored in future studies. 110 Figure 6-5a: Computed ignition delays as a function of the gas temperatures T 0 for stoichiometric methane/air mixture. Square, round-black line and round-red line symbols represent non-catalytic, catalytic with Model II, and catalytic with the oxygen desorption energy set to the minimum possible value (156 kJ/mol) in Model II, respectively. 10 -6 10 -4 10 -2 10 0 10 2 600 800 1000 1200 1400 1600 φ φ φ φ=1.0 =1.0 =1.0 =1.0 Ignition delay time, τ τ τ τ (sec) Initial temperature, T 0 (K) E 300K = 241 kJ/mol Homogeneous E 300K = 156 kJ/mol τ c 111 Figure 6-5b: Computed ignition delays as a function of the gas temperatures T 0 for a fuel rich methane/air mixture (Φ = 1.5). Square, round-black line and round-red line symbols represent non-catalytic, catalytic with Model II, and catalytic with the oxygen desorption energy set to the minimum possible value (156 kJ/mol) in Model II, respectively. 10 -6 10 -4 10 -2 10 0 10 2 600 800 1000 1200 1400 1600 φ φ φ φ=1.5 =1.5 =1.5 =1.5 E 300K = 241 kJ/mol Homogeneous E 300K = 156 kJ/mol τ c Ignition delay time, τ τ τ τ (sec) Initial temperature, T 0 (K) 112 Figure 6-5c: Computed ignition delays as a function of the gas temperatures T 0 for a fuel lean methane/air mixture (Φ = 0.7). Square, round-black line and round-red line symbols represent non-catalytic, catalytic with Model II, and catalytic with the oxygen desorption energy set to the minimum possible value (156 kJ/mol) in Model II, respectively. 10 -6 10 -4 10 -2 10 0 10 2 600 800 1000 1200 1400 1600 φ φ φ φ=0.7 =0.7 =0.7 =0.7 E 300K = 241 kJ/mol Homogeneous E 300K = 156 kJ/mol τ c Ignition delay time, τ τ τ τ (sec) Initial temperature, T 0 (K) 113 6.5 Summary The mechanism and potential enhancement of catalytic methane ignition over free-suspended Pd NPs was explored by detailed kinetic modeling. Typical temperature- time history shows that catalytic ignition is accomplished through a two-stage process with the first stage being catalytic, causing heat release and gas temperature increase, and this accelerates gas-phase high-temperature chain branching in the second stage at 1400- 1500 K, eventually leading to thermal runaway and fuel ignition. The reduction of the catalytic reaction zone in the first stage of the ignition process helps to enhance the overall ignition performance. Sensitivity analysis demonstrates that enhanced catalytic activity can be expected if the desorption energy of surface oxygen can be reduced, leading shortened ignition delay of methane over a wide range of temperature and equivalence ratio. The limiting ignition delay time is dictated by gas-phase kinetics and is around 1 millisecond. 114 Chapter 7 Conclusions and Future Works 7.1 Conclusions Catalytic ignition of methane over freely-suspended Pd NPs was studied experimentally and numerically. This dissertation work was intended to serve as an integral element of a feasibility study of cryogenic methane as a fuel of choice for hypersonic combustion. Experimentally, an aerosol flow reactor was used to demonstrate catalytic methane ignition by in-situ generated Pd NPs under the flow residence time ~ 1 s. Catalytic ignition was observed to occur at a temperature about 150 K lower than that of non-catalytic ignition. Catalytic particles were characterized in terms of size distributions, morphology, and chemical composition. A gas-surface chemical kinetic model is proposed to capture the catalytic behavior of Pd NPs. The model identified key reaction steps that played important roles in the fuel ignition process. Molecular oxygen adsorption/desorption, O 2 + 2Pd(S) = 2O(S), and the oxidative adsorption of methane onto a vacant Pd site CH 4 + Pd(S) + O(S) → CH 3 (S) + OH(S) appear to be two critical steps that control the catalytic activity. The kinetic model was further developed to ensure thermokinetic consistency. The hydrogen submodel was validated against literature stagnation flow reactor experiments at 1300 K. The modified surface kinetic model also captured the flow tube experiments very well with time-resolved particle size distributions measured at several positions along the major axis of the reactor. 115 Mobility sizing decidedly show the particle size to be log-normally distributed. TEM analysis confirms that the particles produced are mostly single, crystalline particles. These results consistently indicate that the particles are formed from an aerosol dynamics process starting from Pd vapors. The vaporization and subsequent thermal decomposition of the aerosol precursor provides the Pd vapor necessary for particle nucleation and size growth. Combined TEM and XPS analyses confirmed that particles have a core-shell structure in which the bulk particle is crystalline Pd with a few atomic layers of PdO covering the particle surface. The observation of surface covered oxygen supports the results of numerical analysis using the gas-surface kinetic model. Numerical analysis suggests that catalytic ignition occur through a two-stage process. In the first stage, heat release due to catalytic oxidation leads to temperature rises. In the second stage, gas-phase chain-branching and thermal runaway processes become dominant, eventually leading to ignition. Sensitivity analysis suggests that an enhancement of catalyst activities can be achieved by lowering the oxygen desorption energy. Depending on the fuel equivalence ratio, the ignition delay time can be as low as 1 ms at temperature above 800 K. 116 7.2 Future Works Throughout this dissertation work, nanocatalyst ignition was characterized with regard to ignition delay times and material morphology. It was found that nanocatalysts dispersed in a fuel-oxidizer mixture significantly changes ignition characteristics. This nanocatalyst combustion can potentially become one of the key topics in combustion since the behavior of nanocatalyst in combustion has not been well characterized in the past, perhaps due to limited opportunity to collaborate with the nanotechnology and surface science communities. Change of combustion characteristics by nanocatalyst may inspire the development of practical applications in combustion devices, as well. Additionally, in order to preserve the environment and its natural resources, the development of high-performance aerosol precipitators or filtration systems, as well as metal recovery and recycling systems, will become essential for practical implementations. As for combustion phenomena, behavior of nanocatalysts may be studied in different aspects other than ignition phenomena, for instance, under turbulent flames or a flamelet where ignition and extinction characteristics play important roles. The effect of burning rate may be studied under the Bunsen type of burner. An aerosol shock tube or an aerosol rapid compression machine may also provide new insight to the kinetics of nanocatalysts. Ignition characteristics themselves may be studied in much broader aspects. For example, they may be combined with different hydrocarbon fuels and equivalence ratios, temperature and pressure conditions, particle concentrations and materials. 117 Correlation between the particle size and the Pd/PdO equilibrium constant is of particular interest for high-performance nanocatalyst design. In regards to different materials, the effect of nanocomposite and support material over catalytic reactivity can be tested, and high-performance catalysts to achieve desired performance may be engineered at an atomic scale by choosing the optimum material and cluster size. The flow reactor ignition experiments and the gas-surface kinetic modeling studies carried out in this dissertation work leave room for many other interesting studies. As an example, consider that the catalytic ignition experiments were performed under the flow residence time of ~ 1 s. More detailed catalytic fuel oxidation needs to be investigated in a millisecond time scale. In order to obtain more fundamental information about the interaction between NPs and fuel molecules, NPs would be better generated and formed separately before they are mixed with a fuel so that precursor vaporization and atom nucleation processes are independent of fuel oxidation processes. If a complex heat release process can be eliminated by creating a constant temperature profile without a preheating zone in the reactor, it would provide more fundamental data to study detail rate parameters in the gas-surface chemical kinetic model. In an attempt to resolve these issues, an aerosol Jet-Stirred Reactor (JSR) and Turbulent Flow Reactor (TFR) platform has been under development. Figure 7-1 shows a schematic diagram of the aerosol JSR-TFR concept. In an aerosol JSR section, particles are generated and formed in the nanometer size range from an aerosol precursor mixed in N 2 -O 2 gas mixture. At the exit of JSR, a test fuel is injected into the mixing nozzle, and then the particles/fuel/N 2 /O 2 mixture is introduced into the TFR test section. By running 118 the fuel oxidation test in a turbulent flow, radial transport may be neglected so that the computational plug flow model better resembles the experiments. This proposed platform is expected to provide more fundamental information about nanocatalyized combustion. The basic performance test is currently underway. Figure 7-1: Conceptual drawing of aerosol JSR-TFR test bed. Aerosol JSR serves as a particle generator. 119 Bibliography Abid, A. D. (2009). 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"The Oxidation of Pd(111)." Surface Science, 462, 151-168. 128 Appendix A Aerosol Plug-Flow Simulation Code PROGRAM SKFLOW C**********************************************************************C C This is the user's Fortran code that models nanoparticle-dispersed C gas mixture in plug flow. Background temperature profile is also C programmed to be computed based on the inlet gas temperature. C By T. Shimizu, University of Southern California 2012 C**********************************************************************C IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER(I-N) C PARAMETER (LENIWK=60000, LENRWK=1200000, LENCWK=800, 1 ITOL=1, IOPT=0, LIN=15, LOUT=16, LOUTG=17, LOUTS=18, 2 LINKCK=25, LINKSK=27, KMAX=800, 3 RTOL=1.0E-3, ITASK=1, ATOL=1.0E-12) C DIMENSION IWORK(LENIWK), RWORK(LENRWK), X(KMAX), Z(KMAX) C COMMON /SURFACE/ RD1, RD2, AVRAT1, AVRAT2, CATST COMMON /RCONS/ P, RU C COMMON /ICONS/ KK, KKS, KKB, KKTOT, NFSURF, NLSURF, NFBULK, 1 NLBULK, NISK, NIPKK, NIPKF, NIPKL, NRSK, NSDEN, 2 NRCOV, NX, NZ, NWDOT, NWT, NACT, NHMS, NSDOT, 3 NSITDT, NNSURF, NNBULK COMMON /PV/ TCONST C common /furnace/ Tf, SLPM, area, XL C CHARACTER*16 CWORK(LENCWK), KSYM(KMAX) DATA IWORK/LENIWK*0/, RWORK/LENRWK*0.0/, CWORK/LENCWK*' '/ CHARACTER*80 LINE C LOGICAL KERR, IERR, TCONST EXTERNAL FUN DATA KERR/.FALSE./, X/KMAX*0.0/, KSYM/KMAX*' '/ C----------------------------------------------------------------------C open(unit=25,file='cklink',form='unformatted') open(unit=27,file='sklink',form='unformatted') open(unit=15,file='input',form='formatted') open(unit=16,file='output',form='formatted') open(unit=17,file='outputg',form='formatted') open(unit=18,file='outputs',form='formatted') open(unit=26,file='save',form='unformatted') C----------------------------------------------------------------------C C Initialize CHEMKIN and SURFACE CALL CKLEN (LINKCK, LOUT, LENI, LENR, LENC) CALL SKLEN (LINKSK, LOUT, LENIS, LENRS, LENCS) C LITOT = LENI + LENIS LRTOT = LENR + LENRS LCTOT = MAX(LENC, LENCS) 129 C CALL CKINIT (LENI, LENR, LENC, LINKCK, LOUT, IWORK, RWORK, 1 CWORK) CALL CKINDX (IWORK, RWORK, MM, KK, II, NFIT) C NISK = LENI + 1 NRSK = LENR + 1 CALL SKINIT (LENIS, LENRS, LENCS, LINKSK, LOUT, IWORK(NISK), 1 RWORK(NRSK), CWORK) CALL SKINDX (IWORK(NISK), NELEM, KK, KKS, KKB, 1 KKTOT, NNPHAS, NNSURF, NFSURF, NLSURF, 2 NNBULK, NFBULK, NLBULK, IISUR) C IKSYM = LCTOT + 1 IPSYM = IKSYM + KKTOT LCTOT = IPSYM + NNPHAS - 1 C NIPKK = NISK + LENIS NIPKF = NIPKK + NNPHAS NIPKL = NIPKF + NNPHAS NICOV = NIPKL + NNPHAS NEQ = KKTOT + 3 + NNSURF NIODE = NICOV + KKTOT LIW = 30 + NEQ ITOT = NIODE + LIW - 1 C NSDEN = NRSK + LENRS NRCOV = NSDEN + NNPHAS NX = NRCOV + KKTOT NZ = NX + KKTOT NWDOT = NZ + KKTOT + 3 + NNSURF NWT = NWDOT + KK NACT = NWT + KKTOT NHMS = NACT + KKTOT NSDOT = NHMS + KKTOT NSITDT= NSDOT + KKTOT NRODE = NSITDT + NNPHAS LRW = 22 + 9*NEQ + 2*NEQ**2 NTOT = NRODE + LRW - 1 C IF (LENIWK.LT.ITOT .OR. LENRWK.LT.NTOT .OR. LENCWK.LT.LCTOT 1 .OR. KMAX.LT.KKTOT) THEN IF (LENIWK .LT. ITOT) WRITE (LOUT, *) 1 ' ERROR: LENIWK must be at least ', ITOT IF (LENRWK .LT. NTOT) WRITE (LOUT, *) 1 ' ERROR: LENRWK must be at least ', NTOT IF (LENCWK .LT. LCTOT) WRITE (LOUT,*) 1 ' ERROR: LENCWK must be at least ', LCTOT IF (KMAX .LT. KKTOT) WRITE (LOUT, *) 1 ' ERROR: KMAX must be at least ', KKTOT GO TO 1111 ENDIF C CALL SKPKK (IWORK(NISK), IWORK(NIPKK), IWORK(NIPKF), 1 IWORK(NIPKL)) CALL SKSDEN (IWORK(NISK), RWORK(NRSK), RWORK(NSDEN)) CALL SKCOV (IWORK(NISK), IWORK(NICOV)) C DO 30 K = 1, KKTOT RWORK(NRCOV + K - 1) = IWORK(NICOV + K - 1) 130 RWORK(NX + K - 1) = 0.0 30 CONTINUE C CALL SKSYMS (IWORK(NISK), CWORK, LOUT, CWORK(IKSYM), IERR) KERR = KERR.OR.IERR CALL SKSYMP (IWORK(NISK), CWORK, LOUT, CWORK(IPSYM), IERR) KERR = KERR.OR.IERR C CALL SKWT (IWORK(NISK), RWORK(NRSK), RWORK(NWT)) CALL SKRP (IWORK(NISK), RWORK(NRSK), RU, RUC, PATM) IF (KERR) THEN WRITE (LOUT, *) 1 'STOP...ERROR INITIALIZING CONSTANTS...' GO TO 1111 ENDIF C C Initial non-zero moles WRITE (LOUT, '(/A)') 1 ' INPUT INITIAL ACTIVITY OF NEXT SPECIES' 40 CONTINUE LINE = ' ' READ (LIN, '(A)', END=45) LINE WRITE (LOUT, '(1X,A)') LINE ILEN = INDEX (LINE, '!') IF (ILEN .EQ. 1) GO TO 40 C ILEN = ILEN - 1 IF (ILEN .LE. 0) ILEN = LEN(LINE) IF (INDEX(LINE(:ILEN), 'END') .EQ. 0) THEN IF (LINE(:ILEN) .NE. ' ') THEN CALL SKSNUM (LINE(1:ILEN), 1, LOUT, CWORK(IKSYM), 1 KKTOT, CWORK(IPSYM), NPHASE, IWORK(NIPKK), 2 KNUM, NKF, NVAL, VAL, IERR) IF (IERR) THEN WRITE (LOUT,*) ' Error reading moles...' KERR = .TRUE. ELSE RWORK(NX + KNUM - 1) = VAL ENDIF ENDIF GO TO 40 ENDIF C 45 CONTINUE C TCONST=.FALSE. READ(LIN, *) 46 READ(LIN,7000) LINE IF(LINE(1:1).EQ.'*') GOTO 47 IF(LINE(1:1).EQ.'T') TCONST=.TRUE. GOTO 46 47 CONTINUE C C Final time and print interval (in microseconds) WRITE (LOUT, '(/A)') ' INPUT FINAL TIME AND DT' READ (LIN, *) T2, DT WRITE (LOUT,7105) T2, DT T2=T2/1.0E6 DT=DT/1.0E6 C 131 WRITE (LOUT, '(/A)') 1 ' INPUT INITIAL PRESSURE (ATM) AND TEMPERATURE (K)' READ (LIN, *) PA, SLPM, area, XL READ(*,*) Tf WRITE (LOUT,7105) PA, Tf IF (TCONST) THEN c Tf = Tf(K) T = Tf ELSE c Tf = Tf(C) T = TFLOW(0.0D0) ENDIF C5=PA/82.0578/T P = PA*PATM C C Surface area to volume ratio WRITE (LOUT, '(/A)') ' OUTPUT RD (NM) AND AVRAT (1/CM)' READ (LIN, *) RD1, RD2, AVRAT1, AVRAT2, CATST C C Normalize the mole fractions for each phase DO 60 N = 1, NNPHAS XTOT = 0.0 KFIRST = IWORK(NIPKF + N - 1) KLAST = IWORK(NIPKL + N - 1) DO 50 K = KFIRST, KLAST XTOT = XTOT + RWORK(NX + K - 1) 50 CONTINUE IF (XTOT .NE. 0.0) THEN DO 55 K = KFIRST, KLAST RWORK(NX + K - 1) = RWORK(NX + K - 1) / XTOT 55 CONTINUE ELSE WRITE (LOUT, *) 1 ' ERROR...NO SPECIES WERE INPUT FOR PHASE ', 2 CWORK(IPSYM+N-1) KERR = .TRUE. ENDIF 60 CONTINUE C IF (KERR) THEN WRITE (LOUT, *) 'STOP...ERROR INITIALIZING SOLUTION...' GO TO 1111 ENDIF C C Initial conditions and mass fractions TT1 = 0.0 RWORK(NZ+KKTOT) = T CALL CKXTY (RWORK(NX), IWORK, RWORK, RWORK(NZ)) RWORK(NZ+KKTOT+1) = 0.0 RWORK(NZ+KKTOT+2) = RD2 C IF (NNSURF .GT. 0) THEN C Initial surface site fractions KFIRST = IWORK(NIPKF + NFSURF - 1) KLAST = IWORK(NIPKL + NLSURF - 1) DO 110 K = KFIRST, KLAST RWORK(NZ+K-1) = RWORK(NX + K - 1) 110 CONTINUE ENDIF IF (NNBULK .GT. 0) THEN 132 C Initial bulk deposit amounts KFIRST = IWORK(NIPKF + NFBULK - 1) KLAST = IWORK(NIPKL + NLBULK - 1) DO 120 K = KFIRST, KLAST RWORK(NZ+K-1) = 0.0 120 CONTINUE ENDIF C Initilal gas-phase mass density CALL CKRHOY (P, RWORK(NZ+KKTOT), RWORK(NZ), IWORK, RWORK, RHO) C IF (NNSURF .GT. 0) THEN DO 130 N = NFSURF, NLSURF IZ = NZ + KKTOT + 3 + N - NFSURF RWORK(IZ) = RWORK(NSDEN + N - 1) 130 CONTINUE ENDIF C C Integration control parameters for VODE TT2 = TT1 MF = 22 ISTATE= 1 C C Print page heading C WRITE (LOUT,*) ' ' WRITE (LOUT,7050) CALL PRT1 (KK, CWORK(IKSYM), LOUTG, RWORK(NX)) C IF (NNSURF .GT. 0) THEN KKPHAS = IWORK(NIPKK + NFSURF - 1) KFIRST = IWORK(NIPKF + NFSURF - 1) CALL PRT1 (KKPHAS, CWORK(IKSYM+KFIRST-1), LOUTS, 1 RWORK(NZ+KFIRST-1)) ENDIF C C+++++++++++++++++++++++++Integration loop+++++++++++++++++++++++++++++C 250 CONTINUE C C========Print the solution============================================C CALL CKRHOY (P, RWORK(NZ+KKTOT), RWORK(NZ), IWORK, RWORK, RHO) T = RWORK(NZ+KKTOT) PA = P / PATM X1 = RWORK(NZ+KKTOT+1) IF (X1 .LE. CATST*XL) THEN AVRAT = 0.0 RD0 = 0.0 ELSE AVRAT = (AVRAT1*X1+AVRAT2)*298.5/T RD0 = RWORK(NZ+KKTOT+2) ENDIF WRITE (LOUT,7100) TT2*1.0E+3, X1, PA, T, RHO, AVRAT, RD0*1.0E+7 C CALL CKYTX (RWORK(NZ), IWORK, RWORK, RWORK(NX)) CALL PRT2 (KK, CWORK(IKSYM), LOUTG, RWORK(NX)) C IF (NNSURF .GT. 0) THEN KKPHAS = IWORK(NIPKK + NFSURF - 1) KFIRST = IWORK(NIPKF + NFSURF - 1) CALL PRT2 (KKPHAS, CWORK(IKSYM+KFIRST-1), LOUTS, 1 RWORK(NZ+KFIRST-1)) 133 ENDIF IF (X1 .GT. XL) GOTO 1111 C ENDIF TT2 = MIN(TT2 + DT, T2) C C-------Call the differential equation solver--------------------------C 350 CONTINUE CALL DVODE(FUN, NEQ, RWORK(NZ), TT1, TT2, ITOL, RTOL, ATOL, 1 ITASK, ISTATE, IOPT, RWORK(NRODE), LRW, 2 IWORK(NIODE), LIW, JAC, MF, RWORK, IWORK) C IF (ISTATE .LE. -2) THEN IF (ISTATE .EQ. -1) THEN ISTATE = 2 GO TO 350 ELSE WRITE (LOUT,*) ' ISTATE=',ISTATE GO TO 1111 ENDIF ENDIF GO TO 250 C 1111 CONTINUE C CALL PRT3 (KK, CWORK(IKSYM), RWORK(NX)) C IF (NNSURF .GT. 0) THEN KKPHAS = IWORK(NIPKK + NFSURF - 1) KFIRST = IWORK(NIPKF + NFSURF - 1) CALL PRT4 (KKPHAS, CWORK(IKSYM+KFIRST-1), 1 RWORK(NZ+KFIRST-1)) ENDIF C C++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++C 7000 FORMAT (A) 7050 FORMAT (1X,'t(ms)',8X,'x(cm)',8X,'P(atm)',7X,'T(K)',9X, 1 'RHO(g/cc)',4X,'AVRAT(1/cm)',1X,'RD(nm)') 7100 FORMAT (7(1PE12.5,0P,1X)) 7105 FORMAT (1X,12E10.3) C----------------------------------------------------------------------C END C***********************************************************************C SUBROUTINE FUN (NEQ, TIME, Z, ZP, RWORK, IWORK) C IMPLICIT DOUBLE PRECISION(A-H,O-Z), INTEGER(I-N) C DIMENSION Z(NEQ), ZP(NEQ), RWORK(*), IWORK(*) C COMMON /SURFACE/ RD1, RD2, AVRAT1, AVRAT2, CATST COMMON /RCONS/ P, RU COMMON /ICONS/KK, KKS, KKB, KKTOT, NFSURF, NLSURF, NFBULK, 1 NLBULK, NISK, NIPKK, NIPKF, NIPKL, NRSK, NSDEN, 2 NRCOV, NX, NZ, NWDOT, NWT, NACT, NHMS, NSDOT, 3 NSITDT, NNSURF, NNBULK COMMON /PV/ TCONST common /furnace/ Tf, SLPM, area, XL LOGICAL TCONST C ----------------------------------------------------------------------C C Variables in Z are: Z(K) = Y(K), K=1,KK 134 C Z(K) = SURFACE SITE FRACTIONS, C K=KFIRST(NFSURF), KLAST(NLSURF) C Z(K) = BULK SPECIES MASS, C K=KFIRST(NFBULK), KLAST(NLBULK) C Z(K) = TEMPERATURE, K=KKTOT+1 C Z(K) = x, K=KKTOT+2 C Z(K) = RD0, K=KKTOT+3 C Z(K) = SURFACE SITE MOLAR DENSITIES, C K=KKTOT+4, KKTOT+3+NNSURF C ----------------------------------------------------------------------C C Call CHEMKIN and SURFACE CHEMKIN subroutines C ----------------------------------------------------------------------C RWORK(NZ+KKTOT) = Z(KKTOT+1) RWORK(NZ+KKTOT+1) = Z(KKTOT+2) RWORK(NZ+KKTOT+2) = Z(KKTOT+3) C CALL CKRHOY (P, Z(KKTOT+1), Z(1), IWORK, RWORK, RHO) CALL CKCPBS (Z(KKTOT+1), Z(1), IWORK, RWORK, CPB) CALL CKWYP (P, Z(KKTOT+1), Z(1), IWORK, RWORK, RWORK(NWDOT)) CALL CKYTX (Z(1), IWORK, RWORK, RWORK(NACT)) C IF (Z(KKTOT+2) .LE. CATST*XL) THEN AVRAT0 = 0.0 ELSE AVRAT0 = (AVRAT1*RWORK(NZ+KKTOT+1)+AVRAT2)*298.5/ 1 RWORK(NZ+KKTOT) ENDIF C IF (NNSURF .GT. 0) THEN KFIRST = IWORK(NIPKF + NFSURF - 1) KLAST = IWORK(NIPKL + NLSURF - 1) DO 100 K = KFIRST, KLAST RWORK(NACT + K - 1) = Z(K) 100 CONTINUE ENDIF C IF (NNBULK .GT. 0) THEN KFIRST = IWORK(NIPKF + NFBULK - 1) KLAST = IWORK(NIPKL + NLBULK - 1) DO 150 K = KFIRST, KLAST RWORK(NACT + K - 1) = RWORK(NX + K - 1) 150 CONTINUE ENDIF C IF (NNSURF .GT. 0) THEN DO 160 N = NFSURF, NLSURF RWORK(NSDEN + N - 1) = Z(KKTOT+4+N-NFSURF) 160 CONTINUE ENDIF C CALL SKHMS (RWORK(NZ+KKTOT), IWORK(NISK), RWORK(NRSK), 1 RWORK(NHMS)) CALL SKRAT (P, RWORK(NZ+KKTOT+2), RWORK(NZ+KKTOT), 1 RWORK(NACT), RWORK(NSDEN), IWORK(NISK), 2 RWORK(NRSK), RWORK(NSDOT), RWORK(NSITDT)) C C Form the gas-phase mass conservation equation DO 300 K = 1, KK WDOT = RWORK(NWDOT + K - 1) WT = RWORK(NWT + K - 1) 135 SDOT = RWORK(NSDOT + K - 1) ZP(K) = (WDOT + AVRAT0*SDOT) * WT / RHO 300 CONTINUE C C Form the energy equation SUM = 0.0 DO 400 K = 1, KK WT = RWORK(NWT + K - 1) WDOT = RWORK(NWDOT + K - 1) SDOT = RWORK(NSDOT + K - 1) HMS = RWORK(NHMS + K - 1) SUM = SUM + HMS * (WDOT + AVRAT0*SDOT) * WT 400 CONTINUE C ZP(KKTOT+1) = - SUM / (RHO*CPB) CALL TTTT(Z(KKTOT+1),Z(KKTOT+2),ZP(KKTOT+2),ZP1) ZP(KKTOT+1) = ZP(KKTOT+1)*1.0 + ZP1 IF (TCONST) THEN ZP(KKTOT+1) = 0.0 ENDIF C C dRd/dt = (dRd/dx)*(dx/dt) ZP(KKTOT+3) = RD1*ZP(KKTOT+2) C IF (NNSURF .GT. 0) THEN C C Form the surface mass equations DO 440 N = NFSURF, NLSURF SDEN0 = RWORK(NSDEN + N - 1) KFIRST = IWORK(NIPKF + N - 1) KLAST = IWORK(NIPKL + N - 1) DO 430 K = KFIRST, KLAST SDOT = RWORK(NSDOT + K - 1) ZP(K) = SDOT/SDEN0 430 CONTINUE 440 CONTINUE ENDIF RETURN END C***********************************************************************C SUBROUTINE PRT1 (KK, KSYM, LOUT, X) C IMPLICIT DOUBLE PRECISION (A-H, O-Z), INTEGER (I-N) DIMENSION X(KK) CHARACTER*(*) KSYM(KK) C WRITE(LOUT,6005) (KSYM(K),K=1,KK) 6005 FORMAT (150(3X,A10)) C RETURN END C***********************************************************************C SUBROUTINE PRT2 (KK, KSYM, LOUT, X) C IMPLICIT DOUBLE PRECISION (A-H, O-Z), INTEGER (I-N) DIMENSION X(KK) CHARACTER*(*) KSYM(KK) C WRITE(LOUT,6010) (X(K),K=1,KK) 6010 FORMAT (150(1PE12.5,0P,1X)) 136 C RETURN END C***********************************************************************C subroutine TTTT(T, x, dxdt, dTdt) c***********************************************************************c implicit real*8 (a-h,o-z) common /furnace/ Tf, SLPM, area c-----------------------------------------------------------------------c dimension c(0:5,0:5) c c 5th polynomial coefficients c c(0,0) = 0.0000E+00 c(0,1) = 2.0640E+00 c(0,2) = -8.5320E-01 c(0,3) = 1.9925E-02 c(0,4) = -2.7651E-04 c(0,5) = 1.6583E-06 c(1,0) = -1.2151E-06 c(1,1) = 1.6622E+00 c(1,2) = 2.5097E-01 c(1,3) = -1.6959E-03 c(1,4) = -3.8912E-06 c(2,0) = 3.3606E+00 c(2,1) = -7.5710E-01 c(2,2) = -2.7336E-02 c(2,3) = 1.6831E-04 c(3,0) = -5.3576E-01 c(3,1) = 1.5047E-01 c(3,2) = 3.3223E-04 c(4,0) = 2.5543E-02 c(4,1) = -5.9539E-03 c(5,0) = 0.0000E+00 c dxdt = SLPM * 1000 / 60.0 / area / 298.2 * T c tt = Tf/100.0 xx = x dTdx = 0.0 c do i=0,5 sum = 0.0 do j = 1, 5-i sum = sum + float(j)*xx**(j-1)*c(i,j) end do dTdx = dTdx + sum * tt**i end do c dTdt = dTdx * dxdt c-----------------------------------------------------------------------c return end c***********************************************************************c double precision function TFLOW(x) c***********************************************************************c implicit real*8 (a-h,o-z) common /furnace/ Tf, SLPM, area c-----------------------------------------------------------------------c dimension c(0:5,0:5) 137 c c(0,0) = 0.0000E+00 c(0,1) = 2.0640E+00 c(0,2) = -8.5320E-01 c(0,3) = 1.9925E-02 c(0,4) = -2.7651E-04 c(0,5) = 1.6583E-06 c(1,0) = -1.2151E-06 c(1,1) = 1.6622E+00 c(1,2) = 2.5097E-01 c(1,3) = -1.6959E-03 c(1,4) = -3.8912E-06 c(2,0) = 3.3606E+00 c(2,1) = -7.5710E-01 c(2,2) = -2.7336E-02 c(2,3) = 1.6831E-04 c(3,0) = -5.3576E-01 c(3,1) = 1.5047E-01 c(3,2) = 3.3223E-04 c(4,0) = 2.5543E-02 c(4,1) = -5.9539E-03 c(5,0) = 0.0000E+00 c tt = Tf/100.0 xx = x T = 0.0 c do i=0,5 sum = 0.0 do j = 0, 5-i sum = sum+xx**j*c(i,j) end do T = T + sum*tt**i end do c TFLOW = T+273.2 c-----------------------------------------------------------------------c return end c***********************************************************************c 138 Appendix B Ignition Delay Time Simulation Code C PROGRAM SKIGN C**********************************************************************C C This is the user's Fortran code that models nanoparticle-dispersed C gas mixture and computes ignition delay time. C By T. Shimizu, University of Southern California 2012 C**********************************************************************C IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER(I-N) C PARAMETER (LENIWK=60000, LENRWK=1200000, LENCWK=800, 1 ITOL=1, IOPT=0, LIN=15, LOUT=16, LOUTG=17, LOUTS=18, 2 LINKCK=25, LINKSK=27, KMAX=800, 3 RTOL=1.0E-3, ITASK=1, ATOL=1.0E-15) C DIMENSION IWORK(LENIWK), RWORK(LENRWK), X(KMAX), Z(KMAX) C C COMMON /RCONS/ P, AVRAT, RD, RU COMMON /SURFACE/ RD, AVRAT0 COMMON /RCONS/ P, RU COMMON /ICONS/ KK, KKS, KKB, KKTOT, NFSURF, NLSURF, NFBULK, 1 NLBULK, NISK, NIPKK, NIPKF, NIPKL, NRSK, NSDEN, 2 NRCOV, NX, NZ, NWDOT, NWT, NACT, NHMS, NSDOT, 3 NSITDT, NNSURF, NNBULK COMMON /PV/ DTDT, TCONST CHARACTER*16 CWORK(LENCWK), KSYM(KMAX) DATA IWORK/LENIWK*0/, RWORK/LENRWK*0.0/, CWORK/LENCWK*' '/ CHARACTER*80 LINE C LOGICAL KERR, IERR, TCONST EXTERNAL FUN DATA KERR/.FALSE./, X/KMAX*0.0/, KSYM/KMAX*' '/ C----------------------------------------------------------------------C open(unit=25,file='cklink',form='unformatted') open(unit=27,file='sklink',form='unformatted') open(unit=15,file='input',form='formatted') open(unit=16,file='output',form='formatted') open(unit=17,file='outputg',form='formatted') open(unit=18,file='outputs',form='formatted') open(unit=26,file='save',form='unformatted') C----------------------------------------------------------------------C C Initialize CHEMKIN and SURFACE CALL CKLEN (LINKCK, LOUT, LENI, LENR, LENC) CALL SKLEN (LINKSK, LOUT, LENIS, LENRS, LENCS) C LITOT = LENI + LENIS LRTOT = LENR + LENRS LCTOT = MAX(LENC, LENCS) C CALL CKINIT (LENI, LENR, LENC, LINKCK, LOUT, IWORK, RWORK, 1 CWORK) 139 CALL CKINDX (IWORK, RWORK, MM, KK, II, NFIT) C NISK = LENI + 1 NRSK = LENR + 1 CALL SKINIT (LENIS, LENRS, LENCS, LINKSK, LOUT, IWORK(NISK), 1 RWORK(NRSK), CWORK) CALL SKINDX (IWORK(NISK), NELEM, KK, KKS, KKB, 1 KKTOT, NNPHAS, NNSURF, NFSURF, NLSURF, 2 NNBULK, NFBULK, NLBULK, IISUR) C IKSYM = LCTOT + 1 IPSYM = IKSYM + KKTOT LCTOT = IPSYM + NNPHAS - 1 C NIPKK = NISK + LENIS NIPKF = NIPKK + NNPHAS NIPKL = NIPKF + NNPHAS NICOV = NIPKL + NNPHAS NEQ = KKTOT + 1 + NNSURF NIODE = NICOV + KKTOT LIW = 30 + NEQ ITOT = NIODE + LIW - 1 C NSDEN = NRSK + LENRS NRCOV = NSDEN + NNPHAS NX = NRCOV + KKTOT NZ = NX + KKTOT NWDOT = NZ + KKTOT + 1 + NNSURF NWT = NWDOT + KK NACT = NWT + KKTOT NHMS = NACT + KKTOT NSDOT = NHMS + KKTOT NSITDT= NSDOT + KKTOT NRODE = NSITDT + NNPHAS LRW = 22 + 9*NEQ + 2*NEQ**2 NTOT = NRODE + LRW - 1 C IF (LENIWK.LT.ITOT .OR. LENRWK.LT.NTOT .OR. LENCWK.LT.LCTOT 1 .OR. KMAX.LT.KKTOT) THEN IF (LENIWK .LT. ITOT) WRITE (LOUT, *) 1 ' ERROR: LENIWK must be at least ', ITOT IF (LENRWK .LT. NTOT) WRITE (LOUT, *) 1 ' ERROR: LENRWK must be at least ', NTOT IF (LENCWK .LT. LCTOT) WRITE (LOUT,*) 1 ' ERROR: LENCWK must be at least ', LCTOT IF (KMAX .LT. KKTOT) WRITE (LOUT, *) 1 ' ERROR: KMAX must be at least ', KKTOT GO TO 1111 ENDIF C CALL SKPKK (IWORK(NISK), IWORK(NIPKK), IWORK(NIPKF), 1 IWORK(NIPKL)) CALL SKSDEN (IWORK(NISK), RWORK(NRSK), RWORK(NSDEN)) CALL SKCOV (IWORK(NISK), IWORK(NICOV)) C DO 30 K = 1, KKTOT RWORK(NRCOV + K - 1) = IWORK(NICOV + K - 1) RWORK(NX + K - 1) = 0.0 30 CONTINUE C 140 CALL SKSYMS (IWORK(NISK), CWORK, LOUT, CWORK(IKSYM), IERR) KERR = KERR.OR.IERR CALL SKSYMP (IWORK(NISK), CWORK, LOUT, CWORK(IPSYM), IERR) KERR = KERR.OR.IERR C CALL SKWT (IWORK(NISK), RWORK(NRSK), RWORK(NWT)) CALL SKRP (IWORK(NISK), RWORK(NRSK), RU, RUC, PATM) IF (KERR) THEN WRITE (LOUT, *) 1 'STOP...ERROR INITIALIZING CONSTANTS...' GO TO 1111 ENDIF C C Pressure and temperature WRITE (LOUT, '(/A)') 1 ' INPUT INITIAL PRESSURE(ATM) AND TEMPERATURE(K)' READ (LIN, *) PA, T WRITE (LOUT,7105) PA, T P = PA*PATM C C Initial non-zero moles WRITE (LOUT, '(/A)') 1 ' INPUT INITIAL ACTIVITY OF NEXT SPECIES' 40 CONTINUE LINE = ' ' READ (LIN, '(A)', END=45) LINE WRITE (LOUT, '(1X,A)') LINE ILEN = INDEX (LINE, '!') IF (ILEN .EQ. 1) GO TO 40 C ILEN = ILEN - 1 IF (ILEN .LE. 0) ILEN = LEN(LINE) IF (INDEX(LINE(:ILEN), 'END') .EQ. 0) THEN IF (LINE(:ILEN) .NE. ' ') THEN CALL SKSNUM (LINE(1:ILEN), 1, LOUT, CWORK(IKSYM), 1 KKTOT, CWORK(IPSYM), NPHASE, IWORK(NIPKK), 2 KNUM, NKF, NVAL, VAL, IERR) IF (IERR) THEN WRITE (LOUT,*) ' Error reading moles...' KERR = .TRUE. ELSE RWORK(NX + KNUM - 1) = VAL ENDIF ENDIF GO TO 40 ENDIF C 45 CONTINUE C C Read if it is a constant temperature. TCONST=.FALSE. READ(LIN, *) 46 READ(LIN,7000) LINE IF(LINE(1:1).EQ.'*') GOTO 47 IF(LINE(1:1).EQ.'T') TCONST=.TRUE. GOTO 46 47 CONTINUE C C Surface area to volume ratio WRITE (LOUT, '(/A)') ' INPUT SURFACE AREA TO VOLUME RATIO' 141 READ (LIN, *) AVRAT0 WRITE (LOUT,7105) AVRAT0 C C Particle radius WRITE (LOUT, '(/A)') ' INPUT PARTICLE RADIUS' READ (LIN, *) RD WRITE (LOUT,7105) RD RD=RD/1.0E7 C C Final time and print interval (in microseconds) WRITE (LOUT, '(/A)') ' INPUT FINAL TIME AND DT' READ (LIN, *) T2, DT WRITE (LOUT,7105) T2, DT T2=T2/1.0E6 DT=DT/1.0E6 C C Normalize the mole fractions for each phase DO 60 N = 1, NNPHAS XTOT = 0.0 KFIRST = IWORK(NIPKF + N - 1) KLAST = IWORK(NIPKL + N - 1) DO 50 K = KFIRST, KLAST XTOT = XTOT + RWORK(NX + K - 1) 50 CONTINUE IF (XTOT .NE. 0.0) THEN DO 55 K = KFIRST, KLAST RWORK(NX + K - 1) = RWORK(NX + K - 1) / XTOT 55 CONTINUE ELSE WRITE (LOUT, *) 1 ' ERROR...NO SPECIES WERE INPUT FOR PHASE ', 2 CWORK(IPSYM+N-1) KERR = .TRUE. ENDIF 60 CONTINUE C IF (KERR) THEN WRITE (LOUT, *) 'STOP...ERROR INITIALIZING SOLUTION...' GO TO 1111 ENDIF C C Initial conditions and mass fractions TT1 = 0.0 RWORK(NZ+KKTOT) = T CALL CKXTY (RWORK(NX), IWORK, RWORK, RWORK(NZ)) C IF (NNSURF .GT. 0) THEN C Initial surface site fractions KFIRST = IWORK(NIPKF + NFSURF - 1) KLAST = IWORK(NIPKL + NLSURF - 1) DO 110 K = KFIRST, KLAST RWORK(NZ+K-1) = RWORK(NX + K - 1) 110 CONTINUE ENDIF IF (NNBULK .GT. 0) THEN C Initial bulk deposit amounts KFIRST = IWORK(NIPKF + NFBULK - 1) KLAST = IWORK(NIPKL + NLBULK - 1) DO 120 K = KFIRST, KLAST RWORK(NZ+K-1) = 0.0 142 120 CONTINUE ENDIF C Initila gas-phase mass density CALL CKRHOY (P, RWORK(NZ+KKTOT), RWORK(NZ), IWORK, RWORK, RHO) C IF (NNSURF .GT. 0) THEN DO 130 N = NFSURF, NLSURF IZ = NZ + KKTOT + 1 + N - NFSURF RWORK(IZ) = RWORK(NSDEN + N - 1) 130 CONTINUE ENDIF C C Integration control parameters for VODE TT2 = TT1 MF = 22 ISTATE= 1 C C Print page heading C WRITE (LOUT,*) ' ' WRITE (LOUT,7050) CALL PRT1 (KK, CWORK(IKSYM), LOUTG, RWORK(NX)) C IF (NNSURF .GT. 0) THEN KKPHAS = IWORK(NIPKK + NFSURF - 1) KFIRST = IWORK(NIPKF + NFSURF - 1) CALL PRT1 (KKPHAS, CWORK(IKSYM+KFIRST-1), LOUTS, 1 RWORK(NZ+KFIRST-1)) ENDIF C DTDTX = 0.0 TPREV = 0.0 C+++++++++++++++++++++++++Integration loop+++++++++++++++++++++++++++++C 250 CONTINUE C C========Print the solution============================================C CALL CKRHOY (P, RWORK(NZ+KKTOT), RWORK(NZ), IWORK, RWORK, RHO) T = RWORK(NZ+KKTOT) AVRAT = AVRAT0*298.5/RWORK(NZ+KKTOT) PA = P / PATM WRITE (LOUT,7100) TT2*1.0E+6, PA, T, RHO, AVRAT C CALL CKYTX (RWORK(NZ), IWORK, RWORK, RWORK(NX)) CALL PRT2 (KK, CWORK(IKSYM), LOUTG, RWORK(NX)) C IF (NNSURF .GT. 0) THEN KKPHAS = IWORK(NIPKK + NFSURF - 1) KFIRST = IWORK(NIPKF + NFSURF - 1) CALL PRT2 (KKPHAS, CWORK(IKSYM+KFIRST-1), LOUTS, 1 RWORK(NZ+KFIRST-1)) ENDIF C======================================================================C C Finds ignition delay C IF(DTDT .GT. 1.0E6) THEN DTDTX = MAX(DTDTX,DTDT) IF(DTDTX .GT. DTDT) THEN TIG = TPREV GOTO 1111 ENDIF 143 TPREV = TT1 ENDIF C IF (TT2 .GE. T2) GO TO 1111 TT2 = MIN(TT2 + DT, T2) C-------Call the differential equation solver--------------------------C 350 CONTINUE CALL DVODE(FUN, NEQ, RWORK(NZ), TT1, TT2, ITOL, RTOL, ATOL, 1 ITASK, ISTATE, IOPT, RWORK(NRODE), LRW, 2 IWORK(NIODE), LIW, JAC, MF, RWORK, IWORK) C IF (ISTATE .LE. -2) THEN IF (ISTATE .EQ. -1) THEN ISTATE = 2 GO TO 350 ELSE WRITE (LOUT,*) ' ISTATE=',ISTATE GO TO 1111 ENDIF ENDIF GO TO 250 C 1111 CONTINUE C WRITE(*,7200) TIG*1.E6 C++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++C C FORMATS C----------------------------------------------------------------------C 7000 FORMAT (A) 7050 FORMAT (1X,'t(us)',9X,'P(atm)',9X,'T(K)',8X,'RHO(g/cc)' 1,3X,'AVRAT(1/cm)') 7100 FORMAT (5(1PE12.5,0P,1X)) 7105 FORMAT (1X,12E10.3) 7200 FORMAT ('Ignition delay = ', F14.3,1X,'(microseconds)') C----------------------------------------------------------------------C END C----------------------------------------------------------------------C SUBROUTINE PRT1 (KK, KSYM, LOUT, X) C IMPLICIT DOUBLE PRECISION (A-H, O-Z), INTEGER (I-N) DIMENSION X(KK) CHARACTER*(*) KSYM(KK) C WRITE(LOUT,6005) (KSYM(K),K=1,KK) 6005 FORMAT (150(3X,A10)) C RETURN END C----------------------------------------------------------------------C SUBROUTINE PRT2 (KK, KSYM, LOUT, X) C IMPLICIT DOUBLE PRECISION (A-H, O-Z), INTEGER (I-N) DIMENSION X(KK) CHARACTER*(*) KSYM(KK) C WRITE(LOUT,6010) (X(K),K=1,KK) 6010 FORMAT (150(1PE12.5,0P,1X)) C RETURN END 144 C***********************************************************************C SUBROUTINE FUN (NEQ, TIME, Z, ZP, RWORK, IWORK) C IMPLICIT DOUBLE PRECISION(A-H,O-Z), INTEGER(I-N) C DIMENSION Z(NEQ), ZP(NEQ), RWORK(*), IWORK(*) C C COMMON /RCONS/P, AVRAT, RD, RU C COMMON /SURFACE/ RD, AVRAT0 COMMON /RCONS/ P, RU C COMMON /ICONS/KK, KKS, KKB, KKTOT, NFSURF, NLSURF, NFBULK, 1 NLBULK, NISK, NIPKK, NIPKF, NIPKL, NRSK, NSDEN, 2 NRCOV, NX, NZ, NWDOT, NWT, NACT, NHMS, NSDOT, 3 NSITDT, NNSURF, NNBULK COMMON /PV/ DTDT, TCONST LOGICAL TCONST C ----------------------------------------------------------------------C C Variables in Z are: Z(K) = Y(K), K=1,KK C Z(K) = SURFACE SITE FRACTIONS, C K=KFIRST(NFSURF), KLAST(NLSURF) C Z(K) = BULK SPECIES MASS, C K=KFIRST(NFBULK), KLAST(NLBULK) C Z(K) = TEMPERATURE, K=KKTOT+1 C Z(K) = SURFACE SITE MOLAR DENSITIES, C K=KKTOT+2, KKTOT+1+NNSURF C ----------------------------------------------------------------------C C Call CHEMKIN and SURFACE CHEMKIN subroutines C ----------------------------------------------------------------------C RWORK(NZ+KKTOT) = Z(KKTOT+1) C CALL CKRHOY (P, Z(KKTOT+1), Z(1), IWORK, RWORK, RHO) CALL CKCPBS (Z(KKTOT+1), Z(1), IWORK, RWORK, CPB) CALL CKWYP (P, Z(KKTOT+1), Z(1), IWORK, RWORK, RWORK(NWDOT)) CALL CKYTX (Z(1), IWORK, RWORK, RWORK(NACT)) C AVRAT = AVRAT0*298.5/RWORK(NZ+KKTOT) C IF (NNSURF .GT. 0) THEN KFIRST = IWORK(NIPKF + NFSURF - 1) KLAST = IWORK(NIPKL + NLSURF - 1) DO 100 K = KFIRST, KLAST RWORK(NACT + K - 1) = Z(K) 100 CONTINUE ENDIF C IF (NNBULK .GT. 0) THEN KFIRST = IWORK(NIPKF + NFBULK - 1) KLAST = IWORK(NIPKL + NLBULK - 1) DO 150 K = KFIRST, KLAST RWORK(NACT + K - 1) = RWORK(NX + K - 1) 150 CONTINUE ENDIF C IF (NNSURF .GT. 0) THEN DO 160 N = NFSURF, NLSURF RWORK(NSDEN + N - 1) = Z(KKTOT+2+N-NFSURF) 160 CONTINUE ENDIF 145 C CALL SKHMS (RWORK(NZ+KKTOT), IWORK(NISK), RWORK(NRSK), 1 RWORK(NHMS)) CALL SKRAT (P, RWORK(NZ+KKTOT), RWORK(NACT), 1 RWORK(NSDEN), IWORK(NISK), 2 RWORK(NRSK), RWORK(NSDOT), RWORK(NSITDT)) C C Form the gas-phase mass conservation equation DO 300 K = 1, KK WDOT = RWORK(NWDOT + K - 1) WT = RWORK(NWT + K - 1) SDOT = RWORK(NSDOT + K - 1) ZP(K) = (WDOT + AVRAT*SDOT) * WT / RHO 300 CONTINUE C C Form the energy equation SUM = 0.0 DO 400 K = 1, KK WT = RWORK(NWT + K - 1) WDOT = RWORK(NWDOT + K - 1) SDOT = RWORK(NSDOT + K - 1) HMS = RWORK(NHMS + K - 1) SUM = SUM + HMS * (WDOT + AVRAT*SDOT) * WT 400 CONTINUE C IF (TCONST) THEN ZP(KKTOT+1) = 0.0 ELSE ZP(KKTOT+1) = - SUM / (RHO*CPB) ENDIF C DTDT = ZP(KKTOT+1) C IF (NNSURF .GT. 0) THEN C C Form the surface mass equations DO 420 N = NFSURF, NLSURF SDEN0 = RWORK(NSDEN + N - 1) KFIRST = IWORK(NIPKF + N - 1) KLAST = IWORK(NIPKL + N - 1) DO 410 K = KFIRST, KLAST SDOT = RWORK(NSDOT + K - 1) ZP(K) = SDOT / SDEN0 410 CONTINUE 420 CONTINUE ENDIF RETURN C-----------------------------------------------------------------------C END C***********************************************************************C

Abstract (if available)

Abstract Methane ignition catalyzed by palladium (Pd) nanoparticles (NPs) finely dispersed in a CH₄-O₂-N₂ mixture was examined both experimentally and numerically. The ignition experiments were carried out using a temperature-programmed aerosol flow reactor wherein a catalyst precursor was injected into the flow reactor in a form of aerosol generated through a miniature nebulizer. The kinetics of nanoparticle formation was examined using time-resolved microprobe-sampling measurements along with mobility sizing. The morphology and the chemical composition of the NPs were identified by the transmission electron microscopy and the x-ray photoelectron spectroscopy analyses. A microkinetic gas-surface model of methane oxidation over Pd surface was developed ensuring thermodynamic consistency. The proposed model was validated against the aerosol flow reactor experiment as well as the literature stagnation flow reactor experiments for H₂-O₂ mixtures. Adiabatic-isobaric ignition delay time calculations performed using the proposed gas-surface model suggests that fuel ignition occurs through a two-stage process of heat release due to catalysis followed by gas-phase reactions. Guidelines toward optimum atomistic design of nanocatalyst are discussed.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Shimizu, Tsutomu (author)

Core Title Catalytic methane ignition over freely-suspended palladium nanoparticles

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Mechanical Engineering

Publication Date 04/26/2012

Defense Date 03/27/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag catalytic combustion,flow reactor,ignition delay times,methane ignition,nanoparticles,OAI-PMH Harvest,palladium,surface reactions

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Wang, Hai (committee chair), Campbell, Charles S. (committee member), Ronney, Paul D. (committee member), Tsotsis, Theodore T. (committee member)

Creator Email tsutomu.shimizu@gmail.com,tsutomus@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-14900

Unique identifier UC11289504

Identifier usctheses-c3-14900 (legacy record id)

Legacy Identifier etd-ShimizuTsu-656.pdf

Dmrecord 14900

Document Type Dissertation

Rights Shimizu, Tsutomu

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA