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Flammability : An attempt to understand it by computational thermochemistry
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Content
FLAMMABILITY: AN ATTEM PT TO UNDERSTAND IT BY
COMPUTATIONAL THERMOCHEMISTRY
b y
Jianfen Cai
A Thesis Presented to the
FACULTY OF THE SCHOOL OF ENGINEERING
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
( Chemical Engineering)
May 1994
Copyright 1994 Jianfen Cai
UMI Number: EP41843
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a com plete m anuscript
and there are missing pages, th e se will be noted. Also, if material had to be removed,
a note will indicate the deletion.
Dissertation Publishing
UMI EP41843
Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author.
Microform Edition © ProQuest LLC.
All rights reserved. This work is protected against
unauthorized copying under Title 17, United S tates C ode
ProQ uest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, Ml 4 8 1 0 6 -1 3 4 6
Ch
G 1 3 3
This thesis, written by
Jianfen Cai
under the guidance of Faculty Committee
and approved by all its members, has been
presented to and accepted by the School of
Engineering in partial fulfillment of the re
quirements for the degree of
Mast e r of Science
Chemical Engineering
April 15, 1994
Date .........................................................
airman,
Acknowledgements
I acknowledge the guidance of my advisor, professor W.V.Chang for his support
over the years. Thanks are also due to the faculty of the Chemical Engineering
Departm ent, University of Southern California, whose help is greatly appreciated.
Contents
A cknow ledgem ents
v
List of Tables
List of Figures v*
A bstract
1 Introduction 1
2 C om putational therm ochem istry 3
2.1 C om puter P r o g r a m s.............................................................................. 3
2.2 T h erm odynam ic P rop erty of S p e c i e s .......................................... 4
3 R esu lts and discussion 5
3.1 Selection of M odel C om pound . ................................................. 5
3.2 P yrolysis O f C8H1 S ................................................................................. 6
3.3 P yrolysis O f C % H uC U ........................................................................... 7
3.4 O xidation R e a c tio n s .............................................................................. 9
3.5 R eaction Pathw ay And Inhibition M echanism ........................ 10
3.6 Conclusion.................................................... .................................................... 14
iii
A p p e n d ix A
Generali Aspects of Polymer C om bustion........................................................... 18
A ppendix B
Thermodynamic Properties of Species In R eaction.......................................... 22
iv
List of Tables
Table 1. Heat of reaction as a function of temperature
from 300K to 1500K for some typical reactions
in pyrolysis and oxidation stages............................................................. 23
Table 2. Heat of reaction for random C-C bond scission from
a PE model chain by radical mechanism.......................................................24
Table 3. Calculated heat of reaction for elimination of Cl from
a PVC model compound and of the subsequent formation
of a double bond and a HC1............................................................................25
Table 4. Pyrolysis mechanism of C8H18.................................................................... 26
Table 5. Molecular dynamics simulation on pyrolysis of model
polymers as a function of molecular structure and
simulation temperatures.................................................................................. 27
Table 6. Reaction mechanism of C8C 14H14 pyrolysis................................................ 28
Table 7. Oxidation mechanism of C8H18 pyrolysis products....................................29
Table 8. Oxidation mechanism of C8C 14H14 pyrolysis products.............................. 31
Table 9. Frontier orbital energy of the species from AMI
quantum mechanical calculation.....................................................................33
Table 10. Frontier molecular orbital energy of species and
their reaction pathway in the radical reactions........................................... 34
v
List of Figures
Figure 1. The flammability process..........................................................................35
Figure 2. Heat of reaction as a function of chain length in
pyrolysis reactions.................................................................................... 36
Figure 3. Molecular dynamic simulation of C8H18 at 3500K, 0.5 ps..................37
Figure 4. Molecular dynamic simulation of C8H18 at 3500K, 0.5 ps...................38
Figure 5. Molecular dynamic simulation of C8H18 at 1500K, 5.0 ps................. 39
Figure 6. Molecular dynamic simulation of C12H26 at 3500K, 0.5 ps................ 40
Figure 7. Molecular dynamic simulation of C8 H17 at 3500K, 0.5 ps.................. 41
Figure 8. Molecular dynamic simulation of CsH^Clj at 3500K, 0.5 ps............ 42
Figure 9. Molecular dynamic simulation of C8C 14H14 at 3000K, 0.5 ps............ 43
Figure 10. Molecular dynamic simulation of C8C 14H14 at 3500K, 0.5 ps.........44
Figure 11. The interaction of the singly occupied molecular orbitals................ 45
Figure 12. Frontier orbital interactions for an electrophilic
and a nucleophilic radical.......................................................................46
Figure A l. Schematic representation of polymer combustion............................ 47
Abstract
Computer simulations based on molecular dynamics were carried out to investi
gate the flammability of model polymers. The pyrolysis of polyethylene(PE) and
polyvinyl chloride(PVC) model compounds was simulated as a function of tempera
ture and molecular structure. It was shown, from the simulation results and the cal
culated heat of reaction based on the proposed pyrolysis and oxidation mechanism,
that the PVC model compound was more susceptible to therm al decomposition but
less flammable than the PE model compound. The proposed flame-resistant mech
anism for the chlorinated compound was then evaluated by calculating molecular
orbital energies for the species involved in the oxidation reactions.
vii
Chapter 1
Introduction
It is important to understand polymer flammability so th at fire retardants materials
can be developed effectively. The flammability of polymers can be changed to achieve
fire-retardancy by modifying the polymer structure chemically through incorporating
atoms like halogens in the main structure[l] There have been a number of studies on
pyrolysis and combustion of chlorinated hydrocarbons researching the reaction and
inhibition mechanism involved in hydrocarbon combustion[2, 3, 4]. However, few of
them addressed the problem from the energetic point of view involved in halogenated
inhibition of combustion. Flammability of polymers and the related mechanism of
fire-retardancy remain to be understood.
The flammability cycle of polymers can be visualized as taking place in several
distinct stages[5, 6, 7, 8] as shown in figure 1. The general aspects of polymer
combustion are stated in Appendix A. The polymer m aterial is first converted by
pyrolysis into gaseous products, which requires heat (Q i). The combustible gaseous
products then enter the flame zone, there they undergo oxidation reaction in the gas
phase leading to the formation of combustion products and the liberation of heat
(Q2)• Finally this heat of combustion is transferred back to support the pyrolysis.
It has been proposed that to be flame-resistant a m aterial should have a high Q 1
value, a low Q 2 value[5](cf., Fig. 1).
1
Based on the above proposed flammability mechanism of organic polymers this
research was initiated to develop a fundamental understanding of pyrolysis and com
bustion characteristics of model polymer chain aiming to explore the flame-inhibition
mechanism resulting from chlorinated polymers. A semi-empirical AMI quantum
mechanics method[9] was used to simulate the initiation of pyrolysis process of PE
and PVC model compounds in order to evaluate the proposed pyrolysis mechanism.
Then the heat of reaction for each of the steps in pyrolysis stage as well as the
heat of combustion was calculated for both model polymers. The flammability for
both model polymers could then be evaluated quantitatively. Finally the inhibition
mechanism for the chlorinated compound in combustion was investigated based on
the calculated frontier orbital energies of the reacting species.
2
Chapter 2
Computational thermochemistry
2.1 Computer Programs
All calculations were carried out using HyperChem version 2.0 program package[10]
which contains AMI method for quantum mechanical calculation. AMI is an im
provement of the MNDO method. Useful for organic molecules containing elements
from long rows 1 and 2 of the periodic table. It can calculate electronic properties,
optimized geometries, total energy, and heat of form ation[9]. The set of programs
was implemented on PC 486 unit. All calculations involved model molecular struc
ture building and geometry optimization. All single point calculation (including heat
of formation at standard state) and molecular dynamics simulation were based on the
full optimized geometry. “HyperChem” is a computational chemistry package with
many types of molecular and quantum mechanics calculations. Its functions include:
(1) Building and displaying molecules: HyperChem can draw a two-dimentional(2D)
representation of a molecule, and then use the ModelBuilder to generate a three-
dimentional(3D) structure; (2) Optimizing the structure of molecules. (3) Investi
gating the reactivity of molecules and their functional groups; (4) Generating and
viewing orbitals and electronic plots: HyperChem can plot orbital wave functions,
3
the electrostatic potential, the total charge density and the total spin density result
ing from semi-empirical, single point calculations; (5) Evaluating chemical reaction
pathways and mechanism; (6) Studying the dynamic behavior of molecules both
qualitatively and quantitatively.
2.2 Thermodynamic Property of Species
All chemical reactions are accompanied either by an absorption or evolution of en
ergy, which usually manifests itself as heat. It is possible to determine this amount
of heat from basic thermodynamic principles. The heat of formation at 298K was
calculated by AMI method for both compound molecules and radicals (cf., Ap
pendix B). AMI reports heat of formation accurate to within a few kilocalories per
mole[10]. The heat of reaction at 298K was first calculated from the calculated heat
of formation(298K, 1 atmosphere). Based on the heat capacity of species obtained
from estimation technique of group additivity[11] (errors are estimated to within 2
kcal/mol)(cf., Appendix B), the heat of reaction as a function of tem perature was
also examined at tem peratures ranging from 500K to 1500K which covered the typ
ical tem perature range of pyrolysis and oxidation stages for hydrocarbons (cf., Table
1) (pyrolytic decomposition tem perature range is generally from 500K to 1000K[5]
and the moderate tem perature in the flame region is around 1500K[12]). The heat
of reaction was found to have a negligible dependence on temperature. Therefore,
the heat of reaction at 298K could be considered to represent those at tem peratures
ranging from 298K to 1500K.
4
Chapter 3
Results and discussion
3.1 Selection of Model Compound
Due to the difficulties such as computational capacity in carrying out geometry
optimization and molecular dynamic simulation, it is preferred to work with model
compounds in order to understand the thermal decomposition as well as oxidation
mechanism of polymers.
Taking into account the computation time to run a set of dynamic simulation, a
simulation time of 0.5 (ps) was selected for all of the molecular dynamic simulation.
On the basis of molecular dynamic simulation and the AMI calculated heat of
formation, the heat of reaction as a function of chain length was plotted in Figure
2 (cf., Table 2, Table 3). For PE model compounds with the number of carbons
being more than 6, The minimum average decomposition tem perature(up to the
tem perature causing the first bond dissociation) was found to be constant at around
3500K (bond dissociation could be observed during the process of molecular dynamic
simulation, see also reference[10]). The heat of reaction for the first C-C bond
dissociation was actually independent of chain length (cf., Fig. 2).
Similarly, for chlorinated compounds, we performed calculations on the loss of
HC1 as it occurs in PVC degradation by assuming a two-step process with the first
5
step being the evolution of the labile chlorine species in a radical mechanism. It was
observed that the heat of reaction for the first endothermic step as well as the overall
heat of reaction for the formation of a double bond and a accompanying formation
of HC1 was practically independent of chain length with carbon number being larger
than 8 (cf.,fig.2). A similar result of quantum chemical calculation was report ed for
long chain P VC-like compounds [13].
It was therefore demonstrated that model compounds with carbon number larger
than 8 could be sufficiently long enough to simulate the therm al decomposition pro
cess for polymer chains. Thus G8 H \ 8 and C&H1 4CU were chosen as model com
pounds to represent PE and PVC long chain polymers respectively. These model
compounds will yield results that are closely comparable with long polymer chains,
both qualitatively and quantitatively.
3.2 Pyrolysis Of C g H \g
It was proposed that, when polyethylene decomposes in an inert atmosphere, fol
lowing initial random chain scission, successive intramolecular and intermolecular
hydrogen abstractions occur along the chain resulting in the formation of new rad
icals followed by isomerization or /3-scission reactions, thus a complex m ixture is
formed of alkanes and alkenes of varying chain length[14]. Based on the proposed
pyrolysis mechanism of polyethylene, the pyrolysis reactions of C$Hl 8 were estab
lished. The initiation step was chosen to be the random scission of C-C bond on
any possible site of the main chain resulting in radicals of varying length. Follow
ing the initial degradation, intermoleculax hydrogen transfer of methyl and ethyl
radical attack on the parent chain was included in the model. The different decom
position of alkyl radicals was included in the mechanism: the radicals produced by
random initiation decomposed by /3-scission or rapidly isomerized, splitting off an
olefin and producing a new radical by intramolecular hydrogen transfer. Prim ary
radicals decompose essentially by splitting off C2H 4 and producing a lower radical.
As a result, the principal pyrolytic products were ethylene, methane, propene,
ethane and propane. This distribution was similar to the reported results of study on
octane pyrolysis[15]. The detailed pyrolysis mechanism is given with the calculated
heat of reaction in Table 4.
Molecular dynamics simulation showed that the first C-C bond scission occured
at different positions along the main chain when the number of carbons equals 6, 8,
and 12 (cf, Table 5, structures 5-9; Figures 3-6). The C-C bond dissociation occured
at different position even for the same molecular structure under same simulation
conditions(cf., Table 5, structures 6,7; Figures 3 and 4). This is reasonable from our
AMI calculation that the activation energy required to break C-C bond along the
main chain was almost independent of the position on the main chain (cf., Table 4,
reaction number 2-4). Besides, our molecular dynamic simulation on radical chain
showed that /3-scission did take place prior to C-C bond scission at other positions
(cf.,Table 5, structure 4; Figure 7). At longer simulation tim e (5ps, 1500K), bond
dissociation occured randomly at any position in the molecule (cf., Table 5, structure
8; Figure 8).
It was shown that the thermal decomposition of PE model was initiated in a
mode of random chain scission. It is also feasible to simulate therm al decomposition
at a reasonable tem perature if long enough simulation tim e is allowed.
3.3 Pyrolysis Of C % H u C U
The pyrolysis reaction of CgHuCh was based on PVC decomposition mechanism.
The step by step reactions for pyrolysis of PVC model are listed in Table 6. It
is generally accepted that PVC undergoes thermal decomposition in the following
7
way[16]: first, the stripping of HC1 from the main chain resulting in the formation
of double bonds on the main chain. The free radical mechanism is proposed for the
therm al dehydrochlorination. Initiation involves liberation of a chlorine atom from
a labile centre, the chlorine atom is the chain carrier. Subsequent elimination of
HC1 from adjacent positions along the polymer chain causes the formation of longer
polyenes . Then the secondary reactions proceed by intramolecular cyclisation and
intermolecular combinations of the polyenes leading to the formation of benzene and
other compounds.
Our molecular dynamic simulation indicated that the chlorine radical was first
split off from the parent chain at a constant tem perature of 3000k without C-C bond
scission(cf., Table 5, structures 1-2; Figures 8, 9). At a higher tem perature of 3500K
at which PE model compounds decompose, it was observed that in addition to the
removal of HC1 group from the main chain, the C-C bond breaking occured (cf.,
Table 5, structure 3; Figure 10).
The calculated heat of reaction for the formation of HC1 (around 30 kj/m ol)
from CzHu CIa pyrolysis(cf., fig. 2) was much lower than that of any pyrolytic steps
involved in pyrolysis of C%Hi& (over 100 kj/mol)(cf. figure 2, Table 4). The heat of
reaction for initial elimination of chlorine (around 253 kj/m ol) was also lower than
that for the initial C-C bond scission in pyrolysis of PE model compound(261-296
kj/m ol) (cf., fig. 2, Tables 4, 6). It therefore can be inferred that the overall heat
(Qi) required to complete the pyrolytic process for PVC model should be lower than
th at of PE model. It therefore can be concluded that PVC model compound is more
likely to decompose into volatile fragments under therm al condition.
8
3.4 Oxidation Reactions
The general aspects of polymer combustions are described in Appendix A. The
oxidation mechanism of G^Hg,, CzHg, C3 H 6 , C2# 6, C2 H 4 , CH 4 which are the major
pyrolytic products of CgHis (cf., Table 7) as well as that of benzene and C 2H 2 which
are the main pyrolytic products of CgH^CU (cf., Table 8) has been established[17,
18]. It is known that the combustion of hydrocarbon compounds consists primarily
of the sequential fragmentation of the initial combustible molecules into smaller
intermediate species which are ultim ately converted to H 2 O and CO 2 from which
large amount of heat is released, each step of the reactions consists of oxidation
reaction of the organic species with the radical pool produced among 0 , H, OH
and other species. Carbon monoxide(CO) and "hydrogen are common species which
are observed during the oxidation of all hydrocarbon combustion. In hydrocarbon
combustion, the radical species pool is evolved among OH, O, and H by following
reactions:
H + 0 2 — >0 + 0 H (3.1)
0 + H2 —+ H + 0 H (3.2)
H 2 + OH — ► H20 + H (3.3)
H + O 2 + M — » H 0 2 + M (3.4)
H + H 0 2 — vO H + OH (3.5)
Where M refers to any available third body species, required to conserve both
momentum and energy. The H atom initiates the main chain branching reaction
by producing OH radicals through the above reactions. It was reported that in the
combustion of hydrogen and hydrocarbons, the first reaction (reaction (3.1)) is the
most im portant chain branching reaction consuming one H atom and producing two
radical species, O and OH. In addition, due to its large activation energy caused
by the endothermicity , it is one of the rate-controlling elementary reactions [2].
Therefore any processes which reduce the H atom population and reactions which
compete with reaction (3.1) for H atoms will tend to inhibit the combustion process.
3.5 Reaction Pathway And Inhibition Mechanism
The general conclusion based on modelling and experimental study of the inhibition
of hydrocarbon oxidation by halogens is that the effect of halogens such as HC1 is to
inhibit the overall reaction of hydrogen-oxygen radical pool. Inhibition of hydrocar
bon flame by chlorine and chlorinated compounds was extensively studied[2, 3, 12].
HC1 was one of the main intermediate products in burning of PVC compound as
was shown in pyrolysis stage. Thus the inhibition mechanism of oxidation reactions
for PVC model compound is primarily attrubuted to the HC1 inhibited reaction of
hydrocarbon oxidation reactions.
First, it is reported that HC1 inhibition appears to be in one way due to the
following set of H radical scavenging reactions:
H + HCl — ► H 2 + Cl (3.6)
H + Cl 2 — ► HCl + Cl (3.7)
Cl + Cl + M — >Cl 2 + M (3.8)
10
with a net result of being H + H — > H2. This “catalyzed” recombination of H
atom offers a lower activation energy path for H consumption and competes with
the key chain branching reaction (3.1): H + 0 2 —> OH + O.
The hydrogen atom preferentially reacts with HCl and C72 species (which will be
shown below). This inhibition mechamism has been demonstrated for hydrocarbon
combustion[12].
Another inhibition pathway is that the radicals, most im portantly OH radical,
are removed by the following mechanism:
HCl + OH — y H20 + Cl (3.9)
Cl + OH —y HCl + O (3.10)
which compete with the following m ajor heat producing reaction:
CO + OH —y C 0 2 + H (3.11)
The oxidation mechanism of carbon monoxide consists of
CO + O + M C 0 2 + M (3.12)
CO + 0 2 — y C 0 2 -b O (3.13)
The rate of both reaction (3.12) and reaction (3.13) are small at combustion tem
peratures in hydrogen-free environments[17]. W ith the presence of hydrogen, the
oxidation of CO was strongly coupled by reaction (3.11): CO + OH — y C 0 2 + H .
11
It has been reported that during the oxidation of hydrocarbons, carbon monox
ide (CO) is produced in substantial amounts, but the subsequent oxidation of CO
into CO 2 is usually retarded until after the original hydrocarbon species have been
consumed[17]. All hydrocarbon oxidation eventually involves CO oxidation, and
most of the CO 2 produced results from reaction (3.11) which consumes almost all of
the CO, it plays a dominant role in the combustion of all hydrocarbon fuels[2, 17].
Therefore, the rate of CO oxidation depends heavily on the availability of OH radi
cals.
12
In order to quantify the heat of combustion released from the oxidation reactions
a stoichiometric overall oxidation model was proposed for Cgifis and CsHi 4 Cl 4 as
follows:
C8 H 1 4Cl 4 + 21/20 2 — ■ > 8 0 0 2 + 4HCl + 5H20 + 17.7(kj/g) (3.14)
CsHis + 25/202 — > 8 0 0 2 + 9H20 + 45.1 (kj/g) (3.15)
The calculated heat of combustion was 45.1 kj/g for PE model and 17.7 kj/g
for PVC model compound (here the experimental heat of formation for CO and
0 0 2 was used in the calculation). The calculated value was close to that of exper
imentally reported hea t of combustion( 46.5 kj/g and 19.9 kj/g for PE and PVC
respectively[6]). Obviously, much more heat was released from combustion of PE
model than that from PVC model.
Molecular orbital theory is able to study the effect of the electronic stucture as
well as orbital energies of reacting species on chemical reaction pathway. In a radical
reaction, electrons must leave one molecular orbitals and fill others. The orbitals
of colliding species interact in forming new molecular orbitals. The energetically
most significant interaction is between the frontier orbitals the highest occupied
orbital(HOMO) of one molecule and the lowest unoccupied orbital(LUMO) of the
other molecule[19]. Plainly, the frontier orbital of the radicals is the singly occupied
one (SOMO). This SOMO orbital will react with both the HOMO and the LUMO
of the molecule it is reacting with (cf., Figure 11). However the reaction favors
interactions where the frontier orbitals can overlap m ost favorably, two orbitals must
have net overlap. Thus it is conculuded that radicals with a high-energy SOMO will
react fast with molecules having a low-energy LUMO, and radicals with a low-energy
SOMO will react fast with molecules having a high-engergy HOMO[19](cf. figure
13
12). In molecular orbital plots, the region which has the highest density (which is
the atom with the largest orbital coefficient) is generally the site of reaction.
The frontier orbital energies for the reacting species were calculated by AMI
quantum mechanical method (cf., Table 9). On the one hand, the radical, H atom
with an unpaired electron, has a high energy SOMO. it shows nucleophilic properties.
It will react faster with the molecules having the lower energy LUMO. Therefore H
atom will react with HCl, and CI 2 preferentially compared with O 2 which has a
higher LUMO energy. While on the other hand, The OH radical with a low energy
SOMO will react faster with HCl and Cl2 molecules than with CO molecule, because
HCl has a higher HOMO energy than HOMO energy of CO molecule.
The main reaction pathway is summarized in Table 10 with the solid line showing
faster reactions.
3.6 Conclusion
The molecular dynamic simulation on the therm al decomposition of model com
pounds showed that initiation of thermal decomposit ion of PE model compound
proceeded by random chain scission while that of the chlorinated compound by elim
ination of the labile chlorine atom at a lower tem perature. Based on the calculated
heat of reaction for the proposed mechanism, it was found that PVC model com
pound required less heat both in initiation of thermal decomposition and in overall
pyrolysis stage than PE model. It follows that PVC model is less resistant to therm al
decomposition.
However, much less heat was released from combustion of PVC model than from
PE model compound. The exothermic oxidation reaction in combustion of chlori
nated compound was inhibited by HCl and Cl species which were evolved in the
pyrolysis stage; calculations on the molecular orbital energetic state of the reacting
14
species supported the proposed inhibition mechanism. It can be concluded that
PVC model compound is less flammable than PE model.
It should be pointed out that as the PE compound having a high heat of combus
tion decomposed, in fact, at relatively higher tem peratures and higher heat require
m ent than PVC model, simple correlations do not appear to exist between polymer
flammability and the parameters (such as Qi and Q2) governing the separate stages
of the flammability process.
15
Reference List
[1] K.Kishore and R. Nagarajan, J. of Polymer Engineering, Vol.7, No.4, 1987,
p.319
[2] J.F. Roesler, R.A. Yetter and F.L. Dryer, Combust. Sci. and Tech., 85, 1, 1992.
[3] W.D. Chang, S.M. Senkan, Combust. Sci. and Tech., 43, 49, 1985.
[4] B W. Ho, Q.R. Yu, and J.W , Bozzelli, Combust. Sci. and Tech. 85, 23, 1992.
[5] D.W. Van Krevelen, Polymer, 16, 615, 1975.
[6] M. Elomaa, Physico-Mathematicae, the Finnish Society of Sciences and Letters,
1991, pp.2, 8.
[7] G.L. Nelson, Intern. J. Polym. Mater., 7, 140, 1979.
[8] N. Grassie, and G. Scott, Polymer Degradation and Stablisation, 1985, Cam
bridge Univ. Press.
[9] M.J.S. Dewar, E.G. Zoebisch etc., J. Am. Chem. Soc., 107, 3902, 1985.
[10] Autodesk, Inc., HyperChem Computational Chemistry, Publication 100033-02,
1992.
[11] S.W. Benson, Thermo chemical kinetics, John Wiley and Son, 1976.
[12] C.K. Westbrook, Combustion Science and Technology, 23 191, 1980.
16
13] R.J. Meier and B.J. Kip, Polymer Degradation and Stability J., 38, 1, 1992.
14] S.A., Liebman and E.J. Levy, Pyrolysis and GC in Polymer Analysis, Marcel
Dekker, INC., New York, 1985.
15] K.R. Doolan and J.C. Mackie, Combustion and Flame, 50, pp. 29, 39, 1983.
16] E.D. Owen, Degradation and Stabilisation of PVC, EAS publishers, New York,
1984, pp. 1, 58.
17] C.K.Westbrook and F.L. Dryer, Prog. Energy Combust. Sci., 10, pp.l, 57, 1984.
18] W.C. Gardiner, Combustion Chemistry, Springer-Verlag, New York, 1984,
pp.198, 360.
19] I. Fleming, Frontier Orbitals and Organic Chemical Reactions, JWS publishers,
New York, 1977, p.183.
20] C.F. Cullis and M.M. Hirschler, The Combustion of Organic Polymers, Claren
don Press, Oxford, 1981.
17
Appendix A
Generali Aspects of Polymer Combustion
Combustion is the name given to overall exothermic reactions, usually of an oxidative
character, which have the ability to propagate throughout the phase concerned.
When the combustion process becomes uncontrolled it is often described by the
term fire. Combustion process usually involves a fuel and an oxidant, and in the
case of a fire these reactants are generally a condensed phase fuel and a gaseous
oxidant such as air. Flames are light-emitting combustion reactions in which both
the fuel and the oxidant are present in the gas phase, in the case of organic polymers,
the polymers first break down to produce gaseous products. A m aterial is said to be
flammable if it is susceptible to easy ignition and rapid flaming combustion. Many
organic polymers if subjected to some suitable ignition source, undergo self-sustained
combustion in air or oxygen. Ignition is the autoacceleration of an oxidation reaction,
leading to glow, flame, or explosion[20]. The chemistry of polymer combustion is the
study of the reactions taking place in the various regions of a polymer flame. Figure
A l shows the elementary structure of the polymer flame. Combustion of polymers
and related mechanisms of fire-retardancy are very complex processes. Two basic
models are generally assumed for the multi-stage cyclic process of combustion of
organic polymers. The first model is represented by the solid lines in Figure Al.
Once the flame is established the therm al degradation of the polymer supplies the
18
combustible products to the flames, which in turn provides the heat necessary for
sustaining the pyrolysis. In this model, heat is derived from oxidation of volatile
products in the flame ( gas-phase oxidation). The second model is represented by
dashed lines in Figure A l. This involves the therm al oxidation of the polymer
(condensed phase oxidation). In both models, the m ajor source of combustible
products is the thermal degradation process of polymers. The validity of this two
models depends on the chemical structure of the polymer and on the conditions or
stage of the overall combustion process.
The reaction regions can be brought under two zones: the “condensed phase”
and the “gas phase”. The condensed phase consists of the region below the burning
surface and the gas phase the three zones above the burning surface. The three
zones above the burning surface are the gaseous preflame zone, the flame zone, and
the combustion products zone, in the gaseous preflame zone, the gases and tars
produced in the degradation zone mix with oxygen from surroundings, Evantually,
sufficient oxygen mixes with these gases and tars that they ignite, producing large
quantities of energy in the form of heat and light. This occurs in the flame zone.
In the combustion products zone, the compounds produced during the preceding
processes begin to cool down and become the smoke and toxic gases associated with
combustion.
Condensed phase reactions
The condensed phase reactions are chiefly the rupture of various bonds in the
polymer, producing smaller fragments. Pure therm al degradation requires the rup
ture of a C-C bond or a C-X bond igtially, once initiated, these processes would
proceed rapidly due to the propagation reactions, giving the following results: (1)
degradation of the polymer giving gaseous products, and (2) crosslinking to produce
involatile char. The reactions occurring in the condensed phase can be classified into
19
two categories: Thermal degradation and Oxidative degradation. In therm al degra
dation, there are three modes of reaction for thermoplastic polymers: (1) depoly
merization: the unzipping of polymer chains leading to the evolution of flammable
monomer; (2) random scission: the process in which the breaking of bonds occurs at
random throughout the length of the chain; and (3) substituent reactions: the sub
stituents attached to the polymer backbone are modified or eliminated partially or
totally. The degradation reactoin occurring in therm osetting polymers differs very
much. Thermosetting polymers undergo complicated modes of reaction producing
a variety of products, depending on the curing cycle, curing agent, and chemical
structures, etc.
20
Gas phase reactions
In gas phase flame reactions, the majority of common polymers are hydrocarbon-
based, the flames above burning polymers are usually in essence hydrocarbon flames.
The chemical reaction takes place in two regions and in two stages: (1) primary
reaction zone: the initial hydrocarbon is converted to CO, hydrogen, and water plus
interm ediate products, (2) secondary zone: oxidation of CO into CO2.
21
Appendix B
Thermodynamic Properties of Species In
Reaction
The following tables list the thermodynamic properties for some of the species in
reaction. The heat of formation at 298 K calulated by Hyperchem AMI is listed.
The experimentally established heat of formation and the specific heat capacity
estim ated by group additivity are also listed.
22
Table 1 Heat of reaction as a function of temperature from 300K to 1500K
for some typical reactions in pyrolysis and oxidation stages, KJ/mol
Reactions
A H
298 A //500 A / / 1000 A / / 1500
C7 H 15--->C31^+C4 7H9 112.2 110.7 106.3 102.9
CH3 +C8H18—>C8H17+CH4 -20.1 - 20.6 -21.3 -22.7
c 8 h 1 8- > c 7h 15+c h 3 296.1 297.5 298.5 298.0
C7 H1 5- > C 5H11+C2H4 122.7 123.0 124.7 114.8
C8 C 1 4 H 1 4—>C6H6 4C2H4+4HC1 92.8 91.8 87.3 88.6
OH+CO—>C02+H -98.1 -97.6 -94.3 -91.7
HC1+OH—>H20 + Q -63.1 -63.7 -63.5 -67.4
C8H18+25/2 0 2—>8C02+9H20 5136.8 5216.7 5410.0 5613.4
C8C1 4H14+ 21/2 0 2—>
8C02+ 4HC1+5H20 4464.41 4505.21 4463.43 4485.45
23
Table 2 Heat of reaction for random C-C bond scission from a PE model chain by
radical mechanism. The reactions are represented in Table 4 No.(l)-(4).
molecular chain scission » rr
structure steps
C2 H6 CH3 -CH 3 >CH 3 + CH3 324.57
C4 H10 CH3- CH2- CH2 - CH3
>CH 3 + CH 2 ~ CH2 - CH3 293.16
> CH2 - CH3 + CH2 - CH3 2 7 3 4 8
C 6 H14 terminal C- C bond 292.74
other steps 261.75-
266.78
C8H18 terminal C- C bond 292.74
other steps 261.75-
266.78
Ci2H2 6 terminal C- C bond 296.74
other steps 261.75-
268.45
C 16H3 4 terminal C-C bond 292.74
other steps 261.75-
268.45
24
Table 3 calculated heat of reaction for elimination of Cl from a PVC model
compound by radical mechanism, and of the subsequent formation
of a double bond and the accompanying formation of HC1
reaction reaction heat o f reaction
step 1 step 2 overall, kj/mol
9*2 ^ 3 _ - Q _ » ch2— ch3 - -H a » CH2= C H 2 75.80
a 302.37 -226.57
C H ,^ CH / / ^ C H 2 54.26
l 2 I - C h / CH _ CH, C H ^
I I ► C B r CH „ cjh2
Cl Cl 263-84 ^ -208.98 (L j
CH CH3
CHs T ^C H 47‘ 32
-216.52 l c i
CHo
C H / " - c h ^ 2 CH2 C H ^ . CH2
I C 1 1 S 3 T * CH^ ' ' c h * / * 2 ^ 5^ ''C H
c h 2 c h 2 ch2 , ch2 CH;, ^ c h2
31, 'CH ''C H , * * CH3 CH C H ------------ ► CH, 'C H " " c h ,
3 ^ ^ 3 263.84 3 3 -221.13 3 3
26.81
42.71
CH2 CH2 CH2 CH 3 C H 2 C H z CH 2 C H 3 c h 2 CH C H 2 CH3
3 l / 'CH/ 'CH/ N CHX — — ►CHg/ CH' € H ' CH^----------► CH 2^ CH^ "CH" CH 3 0 1 5
4 A 4 4 m 3 7 4 i i ' “ i 4 4 30'15
CH2 CH c h 2 CH3 CH2 c h CH2 c h 3 CH2 CH CH CH3
3 1 / 'CH ' c / W -c<;o> C H / " a / \ j / t 3 r ---------- ► CH2 / XH* CH* CH^ 26 38
4 4 4 4 4 - 189'30 4 4
c h 2 c h 2 c h 2 c h 2 c h 2 c h 3 c h 2 c h , c h 2 c h 2 c h 2 c h 3
^ Y Y Y Y Y - 1 2 — C H ,/ V W ' t / ' a / " t /
^ 4 4 4 4 4 ^ 4 4 4 4 4 25.7,
c h 2 c h 2 c h 2 c h 2 c h 2 c h 3
i S ? > . c h / xjf c h ' xY xY xY'
-222.34 I I I I I 25
a a a a a
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Table 4 Pyrolysis mechanism of CgH18
Reaction Heat of Reaction
@ 298 K, kj/mol
C8H 18—<-C7H15 + CH3 296.09
C8H18— ► C2H5 + Q H I3 267.19
C8H18— C3H7 + C5Hu 261.33
C8H18 — QH9 + C4H9 261.33
1-C7H15— C5H11 + C2H 4 122.71
2-C 7Hl5— ► C3H^ + C4H9 112.23
3-C7H15— -CtfLg + C3H7 110.45
1-C5H1 1 — C3H7 + C2H4 126.45
2 -C 5HH — C3H6 + C2H5 122.00
3-CsHn — ► C4H8 + CH3 147.75
1-CgHi7 — ► CgHi3 + C2H4 122.90
2- C8H17 — ► C5HU + C3H5 113.08
3-C8H17 — C4H9 + C4H8 113.90
1-C^Hi3 — ► C4H9 + C2H4 126.06
2-C6H13— CsHg + C3H7 115.59
3- Q H tf —^ + C2H5 120.78
1-C4H9 * * ■ C2H5 + G feH t 131.92
2-C4H9 — ► C3H5 + CH3 147.00
C3H7 — ► QH4 + CH3 156.58
CH3 + CH3 — C2H6 -323.73
CH3 + C2H5 — C3H8 -298.19
CH3 +C 8H18— ►C8H17 + CH4 -20.20
C2H5 + C8H18 **C 8Hi7 + C2Hg 1 -73.29
26
Table 5 molecular dynamic simulation on pyrolysis of model polymers as a
function of molecular structure and simulation temperature
molecular
structure
simulation
temp/time
( k / ps )
bond dissociation positions
C gH n C li 3000/0.5
C8 H1 4 CI4 3000 / 0.5
C8 H 1 4 C I4 3500/0.5
C8 H1 7 3500/0.5
H— C '
A
H
I
C h C H C h CH
A ( 4 )
7
C '
A
H
7
C
I
H
C6 H1 4 3500/0.5
C8 H i8 3500/0.5
C sH i 8 3500/0.5
CgHis
1 5 0 0 /5 .0
( 7 )
random scission of all bonds
( 8 )
Table 6 reaction m echanism o f Cg H1 4 C I 4 pyrolysis
heat o f
reaction steps reaction
( kj/m ol)
ch 2 ch 2 ch 2 ^
ch / sch/ 'eh''' "ch^
A A A A
- a
step 1
ch 2 ch 2 ch 2
CH/ 'CH/ 'CH/ '€H /
A A A
CH,
253.37
C H 2 CH, ch 2
C H 2/ CH' CH' C H / + . Cl
A A A
- H a
step 2
C H 2 C H CH, ,ch3
2 /
C H 2/ c h' >CH' -223.22
A A A
C H 2 C H 2 c h 2
ch-/ sc h / 'c h / > a r /
A A A A
C H 3
V
-4H Q
CH, CH, CH,
CH,
'C H // 172.71
C H 2 C H 2 CH, Q ,
C H /^ S € t / ' 'C H ^ N CH ^ intra-/inter- molecular cyclisation + ^ -87 28
secondary reaction by polyenes
C H 2 C H 2 C H 2 ^ 3 overall
ch / " G H '' 'CH/' ► + CH2==CH2 + 4HC1 85.43
A A A A
28
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Oxidation mechanism of C8Hj8 pyrolysis products
heat of reaction
reaction 298K, kj/mol
C4 H8 + 0 ---- > C 3 H7 +HCO -170.7
C4 H8 + H ----- > C4 H7 +H 2 -64.5
C3 H7 ------> C2 H4 + CH3 157.5
C4 H7 > C2 H4 + C2 H3 198.5
C3 H8 ------ > CH3 + C2 H5 298.2
C3 H8 + O H >C 3 H7 + H20 -148.9
C3 H8 ----- > CH3 + C2 H4 157.9
C3 H $----- > C2 H3 + CH3 380.7
C3 H6 ------> C3 H5 + H 356.0
C 3H 6 + 0 ------> C2 H5 +H CO -164.2
C3 H5 + 0 2 ------ > C 3 H4 + H 0 2 147.4
C3 H4 + O H > C2 H4 + HCO -223.6
C2 H6 -------- >C H 3 + CH3 323.7
C2 H6 + CH3 ------> C 2 H 5 + CH4 -18.0
C2Hg + H -----------> C2 H5 + H2 -74.1
Q H g + O H -------> C2 H5 + H20 -143.4
C2 H5 (+M )-----> C2 H4 +H (+M) -216.1
C2 H5 + 0 2 -----> C 2 H4 + H 0 2 16.3
C2 H4 + M ------> C2 H2 + H2 + M 158.3
C2 H4 + M ------> C2 H3 + H +M 437.6
29
Table 7 Oxidation mechanism of C8H18 pyrolysis products(continued)
reaction
number reaction
heat of reaction
298K, kj/mol
2 1 C2H4 + H ------> c 2h 3 + h 2 -5.4
2 2 C2H4 + OH —— > c 2h 3 + h 2o -71.4
23 C2H3 + M —- -> c 2h 2 + h + m 160.0
24 C2H3 + H — - > c 2h 2 + h 2 -275.6
25 C2H2 + H + M ------> C2H + h 2 86.7
26 c 2h 2 + 0 - - — > c h 2 + CO -2 0 0 . 0
27 C2H2 + OH -— > c h 3 +CO 251.7
28 CH4 + M ------> c h 3 + h + m 397.4
29 CH4 + H ------> c h 3 + h 2 -54.9
30 CH4 + OH —— > c h 3 + h 2o -125.4
31 CH3 + CH3- — > C 2K s -323.7
32 c h 3 + o — —> CH20 + H 214.5
33
CH2 + 0 2 - —-> c o +h 2o -745.5
34 c 2h + 0 2 ~ — > HCO + CO -598.9
35 c h2o + OH — > h c o + h 2o -615.0
36 c h 2o + 0 - — > h c o + o h -539.0
37 h c o + o 2 — > c o + h o 2 -135.7
38 CO + OH ~ — > C 0 2 + H -104.2
overall
CgHlg + 25/2 0 2 -----------------► 8 C 0 2 + 9H20 + 5136.75 (kj/mol)
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Table 8 Oxidation mechanism o f CgHl 4 Cl4 pyrolysis products
heat of reaction
reaction 298K, kj/mol
C6 H6 + 0 - —> C6 H5 + OH 103.4
QjHg + OH -— > c 6h 5 + h 2o 25.8
Q H 5 + 0 — -> C5 H5 + CO -318.98
c 5h 5 + 0 —
--> C5 H50
-421.7
C5 H5 + 20H ------> c 5h 5 + h 2o -499.5
C5HsO ------> C4 H5 + CO 2.9
c 4 h 5 ------> c 2h 3 + c 2h 2 89.2
c 2 h 3 + h ——> c 2h 2 + h 2 -275.6
c 2h 3 ------> c 2h 2 + h 160.0
c 2h 3 + o 2 - —-> c 2h 2 + h o 2 -39.4
c 2h 2 ------> c2h + h 523.5
c 2h 2 + h + m — > c 2h + h 2 86.7
c 2 h 2 + o h - — > c h 3 +CO 251.7
c 2h 2 + 0 — -> c h 2 +C O 2 0 0 . 0
c h 2 + 0 2 — ■ ■ —> c o + h 2o -745.5
c 2h + 0 2 - --> HCO + CO -598.9
h c o + o 2 - — > CO + h o 2 -135.7
31
Table 8 O xidation m echanism o f C8 H1 4CI4 pyrolysis products(continued)
reaction heat of reaction
number reaction 298K, kj/mol
18 H + HC1 - - --> Cl + h 2 6 . 2
19 H + Cl2 - - --> HCI + Cl -199.8
2 0 H + 0 2 - - -> O + OH 70.7
2 1
h + h o 2 - — > OH + OH -157.8
2 2 H2 + OH — — > H 20 + H -63.2
23 HCI + O — --> Cl + OH 3.2
24 HC1 + OH - ---- > H20 + Cl -63.2
25 Cl + OH —---> HCI + O -14.3
26 h o 2 + C 1 -— -> HCI + 0 2 -242.8
27 OH + CO - —-> C 0 2 +H -98.1
C8 H14 Cl4
overall
8 C 0 2 + 4HCI + 5 H20 + 4464.41
32
Table 9 Frontier orbital energy of the species from AMI
quantum mechanical calculation, unit (ev)
Species SOMO LUMO HOMO
H -4.9724
Cl2 -1.1296 -11.5910
CO 0.9405 -13.3081
H 0 2 -5.7171 2.4866
O -8.1974
0 2 6.4908 -5.5043
OH -7.6514 4.6262
Cl -8.5401
HQ 1.8663 -12.3331
33
Table 10 Frontier Molecular Orbital Energy of Species and Their Reaction Pathway
In the Radical Oxidation Reactions(numbers refer to energies in unit of ev)
00
0.9405
LUMO
Q z
6.4908
HQ
1.8663
LUMO
LUMO
-1.1296
H
-4.9724
SOMO
02
- 5.5043
OR
•7.6514
SOMO
-11.5910
ha
-12.3331
-HOMO
O O
-13.3081
HOMO
LUMO
HOMO
34
COMBUSTION
PRODUCTS
-Q 2
combustion products
flame
heat
OXIDATION
REACTION
HEAT
FEEDBACK
THERMAL
DEGRADATION
PRODUCTS
- flammable gases
- nonflammable gases
- char
+ Q1 ------------------------- PYROLYSIS
POLYMER
Figure 1 The flammability process: when polymer material is subjected to heat it
undergoes decomposition producing volatile fragments at surface.
The fuel thus produced diffuses to die flame front mixing with oxygen.
Heat is produced there which in turn causes more polymer decomposition.
35
heat o f reaction,kj/mol
Fig. 2, heat of reaction as a function of chain length in pyrolysis reactions
3 5 0
3 0 0
2 5 0
o: C-C bond scission for PE model
200
x: formation of a double bond and HCI
150
+: elimination of Cl from PVC m odel com pound
100
50
number of carbon atoms
36
Figure 3 molecular dynamics simulation of CgH^g, 3500K, 0.5ps
bond breaking is indicated by the sphere structure.
H
H
H
H
Figure 4 molecular dynamics simulation of CgHig, 3500K, 0.5ps
bond breaking is indicated by the sphere structure.
Figure 5 molecular dynamics simulation of C8H18,1500K, 5.0ps
bond breaking is indicated by the sphere structure.
Figure 6 molecular dynamics simulation of Ci2H2$, 3500K, 0.5ps
bond breaking is indicated by the sphere structure.
H
H / 9
H \
H
\
Vh
H H
Figure 7 molecular dynamics simulation o f CgHi7 ,3 5 0 0 K , O.Sps
bond breaking is indicated by the sphere structure.
1 C
’ H
H
Figure 8 molecular dynamics simulation o f C gH ^C lj, 3000K , 0.5ps
bond breaking is indicated by the sphere structure.
Figure 9 molecular dynamics simulation o f CgH14Cl4 ,3000K , 0.5ps
bond breaking is indicated by the sphere structure.
43
Figure 10 molecular dynamics simulation of CgH^Cl^ 3500K, 0.5ps
bond breaking is indicated by the sphere structure.
LU M O
/a
SOM O
4 /
44 \
E3 SOMO
44
\ H /
4 4 " '
>44
14
44
HOMO
/ /
A f ‘
1 / f
- j —>
E4 /
'4 f /
» ^ 44
44
44
44
(a) SOMO-HOMO
(b)SOMO-LUMO
The interaction of die singly occupied molecular orbital(SOMO) of
a radical with (a) the HOMO and (b) LUMO of a molecule
LUM O
LUMO
weak
strong
SOMO-
4t
SOMO-
x
strong
weak
X .
HOMO
HOMO
Figure 12 Frontier orbital interactions for an electrophilic and a nucleophilic radical
GAS PHASE
CONDENSED
PHASE
/
THERMAL
OX IDATION
I -------- <_--------1
1
I
r
V
\
HEAT HEAT
DEGRADATION
THERMAL
VOLATILE
PRODUCTS
CHARRED RESIDUE
Fi gu re A1 Schematic representation of polymer combustion.
Appendix B Therm odynam ic properties for som e species in reaction
Hf298 CP
(AMX ) (EXP) 298 500 1000 1500
kcal/mol cal/mol K
C6 H6
21.9 19.81 19.9 33.3 51.1 58.3
c h 3. 29.9 34.0 8 .8 1 0 .6 14.5 16.8
c 2 h 5. 16.9 26.0 1 1 .1 16.3 25.7 30.4
C3 H7 8.7 16.8 17.1 25.2 38.1 44.7
c 4 h 9 1 .8 4.5 22.7 33.8 50.6 59.1
C5H 11 -5.1 1 1 .0 28.0 42.44 63.26 73.47
c 6 h 13
-11.9 5.94 34.5 50.6 75.0 87.5
c 7 h 15 -18.0 0.99 39.2 58.9 87.94 1 0 2 . 0
CgHiT
-24.9 -3.96 45.17 67.19 100.28 116.22
c h 4 -8 .8 -17.9 8.5 1 1 .1 17.2 20.7
C2H6 -17.5 -2 0 . 2 12.7 18.7 29.3 34.9
C 3* k
7.0 4.9 15.3 2 2 . 6 34.5 40.4
c 4 h 8 0.28 0 . 0 1 20.57 31.04 46.97 54.75
c 2h 4 16.4 12.5 10.3 14.9 22.4 26.3
c 3h 8 -24.4 -25.11 17.88 27.05 41.88 49.41
C8H18
-58.8 45.38 68.3 103.58 1 2 0 . 6 6
c 2 h 2 54.2 10.5 13.1 16.3 18.3
c h 2
92.35 8.28 8.99 1 0 .8 8 1 2 . 2 2
C8 C14H 14 -80.5 58.59 77.95 106.29 122.13
48
Appendix B Therm odynam ic properties for som e species in reaction(continued)
Hf298
(AM^ (EXP)
kcal/mol
298
Cp
500 1000
cal/mol K
1500
H 2 (g)
0 . 0 6.90 6.99 7.21 7.72
0 2 (g)
0 . 0 7.0 7.4 8.3 8.7
H 52.09 52.10 4.97 4.97 4.97 4.97
O 59.57 59.6 5.2 5.1 5.0 5.0
h 2o -59.26 -57.8 8 . 0 8.4 9.9 1 1 .2
OH 1.4 9.4 7.2 7.1 7.2 7.1
h 2 o 2 -32.6 10.3 1 2 . 6 15.0 16.3
h o 2 4.4 3.5 8.3 9.5 11.4 12.4
CO -5.68 -26.4 7.0 7.1 7.9 8.4
C 02 -79.8 -94.0 8.9 10.7 13.0 14.0
h c i -24.6 -2 2 . 1 6.96 6.99 7.21 8 . 1 0
Cl 28.98 28.9 5.2 5.4 5.35 5.24
Reference sources:
BSN: S.W. Benson, Thermochemical Kinetics, John Wiley and Son, (1976)
JANAF: JANAF Thermochemical Tables, 3rd Edition, NSRDS-NBS 37, (1987)
UCK: H.E. O’neai, International J. of Chemical Kinetics, Vol.l, pp. 221-243, (1969)
49
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Cai, Jianfen (author)
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Flammability : An attempt to understand it by computational thermochemistry
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Chemical Engineering
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