DOT/FAA/AR-05/32 

Office of Aviation Research 

Washington, D.C. 20591

Molecular Modeling of the Thermal 

Decomposition of Polymers 

October 2005 

Final Report 

This document is available to the U.S. public 

through the National Technical Information 

Service (NTIS), Springfield, Virginia 22161. 

U.S. Department of Transportation 

Federal Aviation Administration
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 Technical Report Documentation Page

1. Report No.

DOT/FAA/AR-05/32

2. Government Accession No. 3. Recipient's Catalog No.

5. Report Date 

October 2005

 4. Title and Subtitle 

MOLECULAR MODELING OF THE THERMAL DECOMPOSITION OF 

POLYMERS 6. Performing Organization Code

7. Author(s)

Stanislav I. Stoliarov1

, Phillip R. Westmoreland2, Huiqing Zhang2, Richard E. Lyon3, 

and Marc R. Nyuden4

8. Performing Organization Report No. 

10. Work Unit No. (TRAIS) 

 

9. Performing Organization Name and Address

1

SRA International, Inc. 

3120 Fire Road 

Egg Harbor Twp., NJ 08234 

2

University of Massachusetts Amherst 

Chemical Engineering Department 

Amherst, MA 01003 

3

Federal Aviation Administration 

William J. Hughes Technical Center 

Fire Safety Branch 

Atlantic City International Airport, NJ 

08405 

4

National Institute of Standards and 

Technology 

Building and Fire Research Laboratory 

Gaithersburg, MD 20899

11. Contract or Grant No.

 

13. Type of Report and Period Covered

 Final Report

12. Sponsoring Agency Name and Address

U.S. Department of Transportation 

Federal Aviation Administration

Office of Aviation Research 

Washington, DC 20591

14. Sponsoring Agency Code

 ANM-110

15. Supplementary Notes 

16. Abstract 

The applications presented here demonstrate the potential for using quantum chemical methods and molecular simulations to 

determine the mechanisms and rates of the thermal decomposition of polymers. The expectation is that these capabilities can be

used to predict the flammability of materials and develop strategies to improve fire resistance. The thermal decompositions of

poly(dihydroxybiphenylisophthalamide) and bisphenol C polycarbonate are investigated by performing density-functional 

calculations of potential energy surfaces of model compounds representing the polymers. Reactive molecular dynamics, a 

relatively new technique that extends conventional molecular dynamics to modeling chemical reactions, was used to simulate the 

thermal decomposition of polyisobutylene. The advantages and limitations of both computational approaches are discussed. 

17. Key Words 

Molecular modeling, Thermal degradation, Polymer, Plastic, 

Flammability, Fire 

18. Distribution Statement 

This document is available to the public through the National 

Technical Information Service (NTIS) Springfield, Virginia 

22161.

19. Security Classif. (of this report) 

 Unclassified

20. Security Classif. (of this page) 

 Unclassified

21. No. of Pages 

 17 

22. Price

Form DOT F1700.7 (8-72) Reproduction of completed page authorized
TABLE OF CONTENTS 

Page 

EXECUTIVE SUMMARY vii 

INTRODUCTION 1 

QUANTUM CHEMICAL CALCULATIONS OF REACTION PATHS 1 

Poly(dihydroxybiphenylisophthalamide) 2 

Bisphenol C 3 

REACTIVE MOLECULAR DYNAMICS 5 

CONCLUDING REMARKS 8 

REFERENCES 9 

iii
LIST OF FIGURES 

Figure Page 

1 Thermal Decomposition of PHA 2 

2 Keto-Enol Rearrangements 2 

3 Cyclizations 3 

4 Thermal Decomposition of BPC 4 

5 Cl-Atom Shift 4 

6 Abstractions of Hydrogen Atoms by Cl Atoms 5 

7 Mechanism of the Thermal Decomposition of PIB 6 

8 The 150-Unit Model of PIB After 10 ps of Reactive Dynamics at 1525 K 7 

iv
LIST OF ACRONYMS 

BDC Bond-dissociation criterion 

BPC Bisphenol C 

EN Enol 

HA Hydroxyamide 

PHA Poly(dihydroxybiphenylisophthalamide) 

PIB Polyisobutylene 

RMD Reactive molecular dynamics 

v/vi
EXECUTIVE SUMMARY

The applications presented here demonstrate the potential for using quantum chemical methods 

and molecular simulations to determine the mechanisms and rates of the thermal decomposition 

of polymers. The expectation is that these capabilities can be used to predict the flammability of 

materials and develop strategies to improve fire resistance. The thermal decompositions of 

poly(dihydroxybiphenylisophthalamide) and bisphenol C polycarbonate are investigated by 

performing density-functional calculations of potential energy surfaces of model compounds 

representing the polymers. Reactive molecular dynamics, a relatively new technique that 

extends conventional molecular dynamics to modeling chemical reactions, was used to simulate 

the thermal decomposition of polyisobutylene. The advantages and limitations of both 

computational approaches are discussed. 

vii/viii
INTRODUCTION

Computational chemistry, which embraces the application of methods of quantum, classical, and 

statistical mechanics to molecules and molecular assemblies, offers new possibilities for the 

investigation of materials flammability. In principle, these methods can be used to determine the 

mechanisms and calculate the rates of thermal decomposition reactions, thereby providing 

guidance for the development of new and more fire-resistant materials. The ability of these 

methods to predict thermodynamics and kinetics of chemical reactions involving small gas-phase 

molecules is well established [1 and 2]. Unfortunately, the extension of the methods to large 

molecules, such as polymers, in the condensed phase introduces many conceptual and 

computational challenges. Nevertheless, the results from recent studies [3-6] demonstrate that it 

is possible to obtain valuable information about the mechanism and kinetics of polymer 

decomposition by means of computational chemistry. 

Here, an overview of the studies of the thermal decompositions of 

poly(dihydroxybiphenylisophthalamide) (PHA) [3], bisphenol C (BPC) polycarbonate [4], and 

polyisobutylene (PIB) [6] are presented. PHA and BPC polycarbonate are among the most fireresistant polymers ever tested. Their thermal degradation results in the formation of a large 

amount of char (about 50% by weight) and the release of nearly noncombustible gasses [7 and 

8]. In an effort to determine the source of this exceptional fire performance, the decomposition 

chemistries of both PHA and BPC were investigated by performing quantum chemical 

calculations to determine the most probable reaction paths. Based on the results of these 

calculations, the chemical mechanisms responsible for the unusually high-temperature behavior 

of these materials were proposed. A relatively new method, called reactive molecular dynamics 

(RMD), was employed to study the thermal decomposition of PIB. The results of the RMD 

calculations provided a detailed, dynamic picture of the decomposition process and led to 

important observations about the kinetics of key elementary reactions. 

QUANTUM CHEMICAL CALCULATIONS OF REACTION PATHS

The B3LYP density-functional method [9] was used in combination with the 6-31G(d) and 6-

31G(d,p) basis sets [10] to calculate potential energies of model compounds representing the 

molecular structures of PHA and BPC. The model compounds contained up to 19 multielectron 

(nonhydrogen) atoms. This method was chosen to achieve the maximum accuracy within a 

reasonable computational time. A basis set with additional functions on the hydrogen atoms (the 

6-31G(d,p) basis set) was used for the PHA calculations because of the expectation that these 

atoms play an important role in the decomposition process. 

Potential energy surfaces of the model compounds (i.e., dependencies of potential energies of the 

compounds on internal atomic coordinates) were carefully examined to identify transition states 

leading to chemical transformations. Intrinsic reaction coordinate reaction-path-following 

calculations [11] were performed for the transition states to establish the connected reactants and 

products. The structures of the reactants, products, and transition states were optimized. The 

energies of the optimized structures were corrected for zero-point energy contributions. No 

corrections were made for the basis set superposition errors. These energies were subsequently 

used in the analyses of chemical mechanisms. During the analyses of competing reactions, it 

1
was usually assumed that the most probable reaction channel was the one with the lowest energy 

barrier. However, only differences in energy larger than 40 kJ/mol, which is about twice the 

average error of the method [4], were considered as conclusive evidence of the domination of 

one reaction channel over the other. All quantum chemical calculations were carried out using 

the Gaussian 98 package of programs [12]. 

POLY(DIHYDROXYBIPHENYLISOPHTHALAMIDE). 

It is well established [7] that, when heated, PHA converts to polybenzoxazole, which is an 

extremely thermally stable material. To a large degree, this explains the high fire resistance of 

PHA. However, the detailed mechanism of the decomposition reaction, which is shown in 

figure 1, is not known. To determine the mechanism, the potential energy surface of a model 

compound, hydroxyamide (HA), was analyzed as shown in figure 2. This compound represents 

a PHA fragment that undergoes the cyclodehydration reaction. The analysis led to the 

conclusion that this reaction is not a single-step process. Before HA cyclizes, it has to undergo a 

keto-enol rearrangement. Two possible mechanisms for this rearrangement are shown in figure 

2. The direct transfer of a hydrogen atom (top diagram) has a substantial energy barrier. 

However, this barrier is reduced by almost a factor of 3 when an external hydroxyl group 

participates in the rearrangement (bottom diagram). Presumably, the hydroxyl group comes 

from an adjacent PHA chain (which was represented by vinyl alcohol in the calculations) or a 

water molecule, which is an expected contaminant. 

FIGURE 1. THERMAL DECOMPOSITION OF PHA 

154

49

EN

HA O

57

39

O N

O N

O

O

FIGURE 2. KETO-ENOL REARRANGEMENTS 

(Energy values are in kJ/mol) 

2
Two conformations of the enol (EN) compound, which is formed as a result of the keto-enol 

rearrangement, were found to be capable of cyclization. These conformations are depicted in 

figure 3. Transformations between EN conformers require between 30 and 70 kJ/mol and are 

omitted here. A detailed description of these transformations can be found in reference 3. 

According to the mechanisms presented in figure 3, the cyclization of EN may proceed through a 

single transition state (top diagram) or through a sequence of two transition states separated by 

an intermediate state (bottom diagram). The latter reaction path is much more energetically 

accessible and, thus, more probable. Regardless of whether or not an external hydroxyl group is 

involved in the keto-enol rearrangement, the total energy required for the cyclodehydration of 

HA is about 170 kJ/mol. This is significantly less than 320 kJ/mol that is required to break the 

backbone of PHA [3]. On this basis, it was concluded that the polymer should convert to 

polybenzobisoxazole before any fragmentation of the chains takes place, which is consistent 

with experimental observations. 

267

126 122

28

127

42

EN

EN

O O

N

O O

N

FIGURE 3. CYCLIZATIONS 

(Energy values are in kJ/mol) 

BISPHENOL C.

As shown in figure 4, hydrogen chloride, carbon dioxide, and char are among the major products 

of the thermal decomposition of BPC [8]. The unusually high char yield suggests that 

cyclization and cross-linking dominate the decomposition process. To determine the mechanism 

of the process, a number of reactions that could potentially lead to cyclization or cross-linking of 

the polymer was examined. The reaction paths for Cl2 elimination, one-step HCl elimination, CCl bond dissociation, and Cl-atom shift were calculated. According to the calculations, the 

energy barriers of these reactions were 400, 380, 330, and 300 kJ/mol, respectively. The first 

two reactions were ruled out based on energetics. A detailed description of these reactions is 

given in reference 4. The last two reactions were found to be both energetically and 

mechanistically similar. The Cl-atom shift was identified as the key reaction that takes place at 

3
the initial stages of the thermal decomposition. However, the possibility that the C-Cl bond 

dissociation also plays a major role in the decomposition process could not be ruled out. 

FIGURE 4. THERMAL DECOMPOSITION OF BPC 

The Cl-atom shift is a reaction where a chlorine atom moves from its original position in BPC 

onto the adjacent phenyl ring. The reaction path, which was calculated using the 

β,β-dichlorostyrene model compound, is shown in figure 5. Once the shift occurs, the Cl atom 

can move freely around the ring structure. The fact that a Cl atom can bond with one as well as 

two phenyl rings [4] indicates that, in an environment with a high density of the rings, migration 

of the atom from one ring to another will also require little or no energy. Thus, the Cl-atom shift 

in BPC should be similar to the C-Cl bond dissociation, with the exception that the energy 

required for the former reaction is lower due to the stabilization provided by Cl-phenyl 

interactions. 

FIGURE 5. Cl-ATOM SHIFT 

(Energy values are in kJ/mol) 

Cl atoms migrating around and between the phenyl rings are likely to abstract hydrogens 

attached to the rings. According to the mechanisms shown in figure 6, these abstraction 

reactions have relatively low energy barriers. The reactions lead to cyclization and to the 

formation of phenyl radical sites. In the context of decomposing BPC structure, this results in 

internal cyclization of the polymer and the formation of highly reactive centers capable of 

establishing strong covalent cross-links between the chains. Chlorovinyl radical sites, which are 

formed as a result of the Cl-atom shifts, may also be involved in cross-linking. In addition, these 

radical sites may participate in phenyl-ring shifts followed by eliminations of the Cl atoms [4], 

which, in turn, lead to the formation of diphenylacetylene structural elements in the 

decomposing polymer. The cyclization and cross-linking reactions, which result in the 

formation of char, are expected to compete with the scissions of the O-C(O) backbone bonds (the 

weakest covalent bonds in BPC [4]), which result in fragmentation of the polymer chains and the 

subsequent elimination of CO2. 

4
FIGURE 6. ABSTRACTIONS OF HYDROGEN ATOMS BY Cl ATOMS 

(Energy values are in kJ/mol) 

REACTIVE MOLECULAR DYNAMICS

The RMD method is based on conventional molecular dynamics, which makes use of analytical 

expressions (force field) that define the interactions between atoms. The atomic trajectories, 

obtained by numerical integration of the classical equations of motion, provide a time-resolved 

description of the system under study. The feature that distinguishes RMD from other force 

field-based implementations of molecular dynamics is that it is capable of modeling chemical 

reactions. 

The current implementation of RMD, a detailed description of which is given in reference 6, uses 

a version of the consistent valence force field [13], which was modified and calibrated to 

accommodate some general features of reactive potential energy surfaces. In this force field, the 

energy of a molecular system is represented as a sum of contributions from covalent bonds 

(defined by Morse potentials), bond angles (including torsions), and nonbonded interactions. To 

model chemical transformations, the RMD employs the following algorithm: after every time 

step of molecular dynamics, fractional bond orders, which are defined as 1-V/D, where V/D is 

the ratio of the bond energy to the bond dissociation energy, are computed for every covalent 

bond. The bond orders are then compared to a predefined bond-dissociation criterion (BDC). If 

a fractional bond order is less than or equal to BDC, the bond is eliminated and the atoms that 

had been connected are labeled as chemically active (if the bond order is higher than BDC, no 

action is taken with respect to that bond). Next, a set of new bonds is generated, consisting of all 

possible covalent interactions between the chemically active atoms. The most energetically 

favorable subset of the new bonds that complies with the rules of atomic valence is selected. If 

the total number of bonds to an atom is equal to its valence and the fractional bond order of each 

of its bonds is higher than BDC, then the chemically active label is removed from the atom. 

Otherwise, if an atom retains its chemically active status, it is allowed to form one additional 

bond, provided that the sum of the bond orders associated with the valence + 1 bonds to that 

atom does not exceed its valence. This feature is used to describe chemical reactions that occur 

via so-called hypervalent transition states, such as abstraction or radical disproportionation 

reactions. Once the bond analysis is complete and the structural information is updated, the next 

time step of molecular dynamics is executed. 

5
It should be noted that, as the result of the procedure described above, the bonds between atoms 

are not formally removed unless they are replaced by new, more energetically favorable bonds. 

For the purpose of quantifying chemical events, a covalent bond between atoms is considered to 

be broken when its energy is within 0.25RT (R is the ideal gas constant and T is the simulation 

temperature) of the dissociation energy. The BDC determines whether covalently bonded atoms 

are eligible to participate in chemical reactions. In the simulations described below, BDC was 

set to 0.8, which means that an atom was labeled as chemically active when at least one of its 

stretched covalent bonds reached the energy that was equal to or higher than 20% of the bond 

dissociation energy. The RMD is implemented as a Fortran/C computer code, MD_REACT 

program, interfaced with Discover 95, which is commercially available molecular dynamics 

software offered by Accelrys Inc*. The function of the MD_REACT is to compute the reactive 

force field, while Discover 95 updates the molecular geometry based on the solution of the 

equations of motion. 

The thermal decomposition of PIB has been studied experimentally by a number of investigators 

[14-16]. According to these studies, the mechanism of the decomposition can be summarized by 

the set of reactions shown in figure 7. 

FIGURE 7. MECHANISM OF THE THERMAL DECOMPOSITION OF PIB 

In all studies, homolytic scissions of the backbone and depolymerization reactions (reactions 1 

and 3 in figure 7) are considered to be important. There are, however, notable disagreements 

between investigators regarding the roles and mechanisms of reactions involving transfer of a 

hydrogen atom (reactions 2 and 4 in figure 7). 

Four single-chain models of PIB consisting of 4, 14, 50, and 150 isobutylene units were used in 

the RMD simulations of the decomposition process. Periodic boundary conditions were 

employed in the simulations involving the 14-, 50-, and 150-unit models to account for the 

condensed-phase environment. The 4-unit model, however, was treated as a single gas-phase 

molecule. Simulations were performed at a series of temperatures between 1300 and 1750 K. 

 

*

Certain commercial equipment, instruments, materials, or companies are identified in this paper to adequately 

specify the procedure. This in no way implies endorsement or recommendation by the National Institute of 

Standards and Technology. 

6
The lowest temperature was dictated by the necessity to observe reactive events within 

computationally feasible simulation times. The thermal motion was initiated by assigning each 

atom a velocity with Cartesian components chosen at random from a Maxwell-Boltzmann 

velocity distribution. The reactive dynamics were run for 5-100 ps (longer times were used at 

lower temperatures and with smaller models). To accumulate statistics on chemical reactions, 

between 11 and 70 RMD simulations were done for each model at every temperature. 

A still frame from an RMD trajectory of the 150-unit model of PIB is shown in figure 8. 

According to the results of the simulations, homolytic backbone scission and subsequent 

depolymerization of the resulting radicals (reactions 1 and 3 in figure 7) are the dominant 

decomposition reactions for all models within the examined range of temperatures. The only 

hydrogen transfer reactions observed in the simulations were hydrogen abstractions involving 

small molecules (smaller than the dimer). Aside from occasional terminations of the 

depolymerization process, these reactions had little effect on the decomposition of the polymer 

chains. 

FIGURE 8. THE 150-UNIT MODEL OF PIB AFTER 10 ps OF REACTIVE 

DYNAMICS AT 1525 K 

(The black dots are chemically active atoms.) 

The times to the first backbone scission determined from the simulations were used to calculate 

the rate constants of the initiation reaction. The rate constants were normalized by the initial 

number of backbone bonds in the PIB models to provide a common basis for comparing the 

results from models having different chain lengths. Arrhenius fits of the temperature 

dependence of the rate constants revealed that the pre-exponential factors and activation energies 

decrease systematically with increasing size of the model. The Arrhenius parameters change 

from a pre-exponential factor of 2×1017 s

-1 and an activation energy of 240 kJ/mol, obtained for 

the 4-unit model (gas-phase tetramer), to a pre-exponential factor of 1×1015 s

-1 and an activation 

7
energy of 170 kJ/mol, obtained for the 150-unit model. Based on the observation of these trends, 

it was concluded that the kinetics of the backbone scission reaction is affected by the density and 

by the degree of polymerization of the decomposing polymer. This means that the conventional 

approach to the kinetic modeling of polymer decomposition, in which the chain scission rate 

constants are assigned values obtained from the measurements performed on small gas-phase 

molecules, is not generally valid. This approach should be modified to account for the potential 

effects of the macromolecular environment on the rate of the scission reactions. For a complete 

description of the RMD simulations and comparison of the simulation results with experimental 

observations, see reference 6. 

Each of the computational approaches discussed in this report has its own advantages and 

limitations. The quantum chemical approach is an effective tool for mapping complex chemical 

transformations that are localized on a small segment of a polymer structure. The information 

obtained from the quantum chemical calculations can be used in combination with statistical 

reaction rate theories [17] to determine rate constants of the model reactions. However, it is not 

clear whether the calculated rate constants would represent the kinetics of the corresponding 

reactions in the polymer melt because the presence of the surrounding molecular structure (the 

condensed-phase) is ignored in the calculations. 

CONCLUDING REMARKS 

The application of reactive molecular dynamics (RMD) makes it possible to capture the effects 

of the condensed-phase environment. Unlike the case of the quantum chemical approach, RMD 

simulations do not require a priori assumptions about reaction mechanisms. However, despite 

these advantages, RMD does have several drawbacks. Currently, the computationally accessible 

time scales of these calculations are several orders of magnitude shorter than what is needed to 

make direct comparisons with experimental measurements on burning polymers. Even more 

important is the issue of force field accuracy. For RMD to produce reliable quantitative results, 

the force field should be able to reproduce reactive potential energy surfaces with chemical 

accuracy (be accurate within about 5 kJ/mol). The development and validation of a force field 

that is capable of this level of accuracy, even for a small number of chemical elements, is a grand 

challenge. Further complications arise from the fact that RMD uses classical mechanics to 

simulate quantum mechanical systems. That is, there is no accounting for the discrete nature of 

molecular vibrations or tunneling. It is apparent that, to a large degree, RMD and the quantum 

chemical approach (combined with statistical reaction rate theories) are complementary. The 

development of methodologies that combine best features of both approaches are actively being 

pursued. 

8
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9
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10