ABSTRACT 
 
 
 
Title of Document: A MULTISCALE APPROACH TO 
PARAMETERIZATION OF BURNING 
MODELS FOR POLYMERIC MATERIALS.   
  
 Jing Li,  Ph.D. ,  2014 
  
Directed By: Assistant Professor, Stanislav I. Stoliarov, and 
Department of Fire Protection Engineering 
A quantitative understanding of the processes that occur in the condensed 
phase of burning materials is critical for the prediction of ignition and growth of fires.  
A number of models have been developed to simulate these condensed phase 
processes.  The main issue that remains to be resolved is the determination of 
parameters to be input into these models, which are formulated in terms of 
fundamental physical and chemical properties. 
This work is focused on developing and applying a systematic methodology 
for the characterization of polymeric materials based on milligram-scale and bench-
 
 
scale tests to isolate specific chemical and/or physical processes in each scale level. 
The entire study is divided into two parts corresponding to two different scale tests 
and analysis. The first part is concentrated on the measurement of kinetics and 
thermodynamics of the thermal degradation of polymeric materials at milligram-scale. 
It employs a simultaneous thermal analysis instrument capable of thermogravimetric 
analysis (TGA) and differential scanning calorimetry (DSC). A numerical model is 
utilized to fit TGA data and obtain thermal degradation kinetics to a continuum 
pyrolysis model. This model is subsequently employed to analyze DSC heat flow and 
extract sensible, melting and degradation reaction heats. The extracted set of kinetic 
and thermodynamic parameters is shown to simultaneously reproduce TGA and DSC 
curves for a set of 15 widely used commercial polymers.  
Then the first part of this study was extended to bench-scale gasification 
experiments that were carried out in a controlled atmosphere pyrolysis apparatus 
(CAPA) which has been recently developed in our group. The CAPA is used to 
measure material gravimetric and thermal changes during thermal decomposition in 
an anaerobic atmosphere with a capability of analyzing material thermal transport 
properties. These properties, combined with material kinetics and thermodynamics 
from the first part of this study, were used as inputs for a pyrolysis model to simulate 
one-dimensional polymer gasification under wide range of external heat fluxes. The 
predictive power of this model and validity of its parameters are verified against the 
results of gasification experiments. 7 out of 15 polymers were validated in bench-
scale and the parameterized simulations are in reasonable agreement with 
experimental data under wide range of conditions.  
 
 
 
 
 
 
 
 
 
A MULTISCALE APPROACH TO PARAMETERIZATION OF BURNING 
MODELS FOR POLYMERIC MATERIALS. 
 
 
 
By 
 
 
Jing Li 
 
 
 
 
 
Dissertation submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Doctor of philosophy 
2014 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Professor Stanislav I. Stoliarov, Chair 
Professor James G. Quintiere 
Professor Michael R. Zachariah, Dean's representative 
Professor Peter B. Sunderland 
Dr. Kevin B. McGrattan
  
 
 
 
 
© Copyright by 
Jing Li 
2014 
 
 
 
 
 
 
 
 
 
 
 
 
 
ii 
Dedication 
To my parents  
Jibang Li ( )，Huiling Liu ( ) 
and my dear Li Dabao ( ) 
 
 
 
 
 
 
 
 
 
 
 
 
iii 
Acknowledgements 
Firstly, I would like to thank my family in China for their unwavering 
supports, endless encouragements during my last 27 years. Every time I came back to 
my hometown -- Xi’an, China no matter where I had been from, I can feel the 
warmest love from them. This dissertation cannot be done without my love Li Dabao 
either. Her presence, patience and encouragements have always been essential 
flavorings during the most important period of my PhD training. 
I am indebted to my advisor, Professor Stoliarov, for leading me into a 
beautiful and exciting field and providing the opportunity to conduct this research and 
enrich my experience. His wealth of knowledge in the fields of polymeric material, 
chemistry and fire science have educated me to overcome many obstacles that I 
experienced in the last three years. He is also a good friend who provides me 
meticulous guidance, countless hours of discussion, and sustained encouragement. 
I thank my advisory committees, Professor James Quintiere, Professor Peter 
Sunderland, Professor Michael Zachariah, Professor Chunsheng Wang, Professor Bao 
Yang and Dr. Kevin B. McGrattan for their time, input, and help in reading and my 
proposal, dissertation and providing valuable comments. This work was supported by 
the National Institute of Standards and Technology (NIST) Grant #60NANB10D022. 
Special thanks go to this project grant monitor, Dr. Kevin B. McGrattan from NIST, 
for his important assistance and support over the years. 
I also want to thank all my group members for their helps, comments and 
discussions that make my work in real and enjoyable. My study and research have 
iv 
greatly benefited from discussions with many fellow graduate students from different 
departments in University of Maryland. Particularly I want to thank Xuan Liu, Xi 
Ding, Mark McKinnon, Isaac Leventon, Mollie Semmes, Ryan Fisher, Fernando 
Raffan, Kevin Korver from my group. And Dr. Guoqiang Jian, Yijing Liu, Jingyu 
Feng, Yihang Liu from chemistry and chemical engineering department for their 
useful discussions. I also want to thank my college classmate from USTC, Dr. Junhui 
Gong, who helped me a lot performing gasification experiments during his one-year 
guest visit in our group. I have to admit that my work could be delayed for at least a 
couple of months without his help. Last but not least, I want to thank Ms. Olga Zeller 
and Ms. Mary L. Holt for ordering all the parts that essential to finish my research 
and study. 
 
 
 
 
 
 
 
 
Jing Li ( ) 
v 
Table of Contents 
LIST OF TABLES .................................................................................................... IX 
LIST OF FIGURES .................................................................................................. XI 
CHAPTER 1 : INTRODUCTION ............................................................................. 1 
SECTION 1.1 POLYMER FLAMMABILITY ...................................................................... 1 
SECTION 1.2 MECHANISM OF POLYMER COMBUSTION ................................................ 2 
SECTION 1.3 NON-CHARRING AND CHARRING POLYMERS .......................................... 4 
CHAPTER 2 :  LITERATURE REVIEW ............................................................... 6 
SECTION 2.1 MATERIAL FLAMMABILITY TESTS .......................................................... 6 
SECTION 2.2 MATERIAL PYROLYSIS PROCESSES ....................................................... 16 
SECTION 2.3 RESEARCH MOTIVATION AND OVERVIEW ............................................. 23 
CHAPTER 3 EXPERIMENTAL ............................................................................ 29 
SECTION 3.1 MATERIALS AND SAMPLE PREPARATION .............................................. 29 
SECTION 3.2 MILLIGRAM-SCALE TESTING ................................................................ 31 
Section 3.2.1 Milligram-scale testing on non-charring polymers ....................... 31 
Section 3.2.2 Milligram-scale testing on charring polymers ............................... 34 
Section 3.2.3 Instrument calibration and data collection for milligram-scale 
testing .................................................................................................................. 34 
Section 3.2.4 Scanning Electron Microscopy (SEM) .......................................... 38 
SECTION 3.3 BENCH-SCALE TESTING ........................................................................ 38 
Section 3.3.1 Measurement of absorption coefficients........................................ 38 
vi 
Section 3.3.2 Gasification experiments part I ..................................................... 40 
Section 3.3.3 Gasification experiments part II .................................................... 45 
CHAPTER 4 : MODELING .................................................................................... 52 
SECTION 4.1 THERMAKIN FRAMEWORK ................................................................... 52 
SECTION 4.2 MILLIGRAM-SCALE MODELING ............................................................ 54 
SECTION 4.3 BENCH-SCALE MODELING .................................................................... 55 
Section 4.3.1 Modeling for gasification experiments part I ................................ 58 
Section 4.3.2 Gasification experiments part II .................................................... 59 
CHAPTER 5 : RESULTS- KINETICS AND THERMODYNAMICS FOR NON-
CHARRING POLYMERS ....................................................................................... 60 
SECTION 5.1 TGA OF POM ...................................................................................... 60 
SECTION 5.2 DSC OF POM ...................................................................................... 64 
SECTION 5.3 TGA OF PMMA, HIPS, PA 66, PP, PLA AND ABS ............................ 70 
SECTION 5.4 DSC OF PMMA, HIPS, PA 66, PP, PLA AND ABS ............................. 74 
CHAPTER 6 : RESULTS- KINETICS AND THERMODYNAMICS FOR 
CHARRING POLYMERS ....................................................................................... 80 
SECTION 6.1 TGA OF KYDEX ................................................................................... 80 
SECTION 6.2  DSC OF KYDEX................................................................................... 82 
SECTION 6.3 TGA OF DGEBA, PET, KEVLAR, BACY, PPS, PEI AND PEEK ......... 87 
SECTION 6.4 DSC OF DGEBA, PET, KEVLAR, BACY, PPS, PEI AND PEEK ......... 91 
SECTION 6.5 SEM OF CHARS ................................................................................... 98 
vii 
CHAPTER 7 : RESULTS-HEAT TRANSFER PARAMETERIZATION AND 
PYROLYSIS MODEL VALIDATION FOR NON-CHARRING POLYMERS
 .................................................................................................................................. 101 
SECTION 7.1 ABSORPTION COEFFICIENTS. .............................................................. 101 
SECTION 7.2 PMMA GASIFICATION EXPERIMENT AND VALIDATION PART I. .......... 101 
Section 7.2.1  PMMA pyrolysis model parameterization ................................. 101 
Section 7.2.2 Prediction of burning rate for PMMA with insulation on bottom.
 ........................................................................................................................... 103 
SECTION 7.3 GASIFICATION EXPERIMENT AND VALIDATION PART II FOR NON-
CHARRING POLYMERS ............................................................................................. 106 
Section 7.3.1 Uniformity of thermometry for non-charring polymers .............. 106 
Section 7.3.2 Thermal conductivity calibration and validation for non-charring 
polymers ............................................................................................................ 108 
Section 7.3.4 Prediction of burning rate for non-charring polymers ................. 115 
CHAPTER 8 : RESULTS-HEAT TRANSFER PARAMETERIZATION AND 
PYROLYSIS MODEL VALIDATION FOR CHARRING POLYMERS ........ 120 
SECTION 8.1 ABSORPTION COEFFICIENTS. .............................................................. 121 
SECTION 8.2 EXPERIMENTAL OBSERVATION........................................................... 121 
Section 8.2.1 ABS and PET .............................................................................. 121 
Section 8.2.2 Kydex and PEI ............................................................................. 125 
SECTION 8.3 MODELING ......................................................................................... 131 
Section 8.3.1 ABS and PET .............................................................................. 131 
Section 8.3.2 Kydex and PEI ............................................................................. 132 
viii 
SECTION 8.4 THERMAL CONDUCTIVITY CALIBRATION ............................................ 135 
Section 8.4.1 ABS and PET .............................................................................. 135 
Section 8.4.2 Kydex and PEI ............................................................................. 140 
SECTION 8.5 SAMPLE HEIGHT AND BURNING RATE PREDICTION ............................. 147 
Section 8.5.1 ABS and PET .............................................................................. 147 
Section 8.5.2 Kydex and PEI ............................................................................. 151 
SECTION 8.6 HRR CALCULATION ........................................................................... 157 
CHAPTER 9 : CONCLUDING REMARKS ....................................................... 159 
APPENDIX A FDS SIMULATION FOR NON-CHARRING POLYMERS .... 162 
APPENDIX B PARAMETERIZED MODELS FOR CHARRING POLYMERS
 .................................................................................................................................. 170 
BIBLIOGRAPHY ................................................................................................... 176 
  
ix 
List of Tables 
Table 2-1 Selective ASTM standards that relevant to solid material fire safety in 
different scenarios ......................................................................................................... 7 
Table 3-1 Source of materials analyzed in this study. ................................................ 30 
Table 5-1 Rules used to guide TGA curve fitting. ...................................................... 62 
Table 5-2 Kinetic parameters describing decomposition reactions for POM. ............ 63 
Table 5-3 Heat capacities of material components for POM. ..................................... 66 
Table 5-4 Kinetic parameters describing decomposition reactions and melting (Em 
and Am) for all non-charring polymers. ....................................................................... 71 
Table 5-5 Heat capacities of material components for non-charring polymers. ......... 75 
Table 5-6 Heats of melting and decomposition for non-charring polymers. .............. 75 
Table 5-7 Heats of gasification for non-charring polymers. ....................................... 79 
Table 6-1 Kinetic parameters describing decomposition reactions for Kydex. .......... 81 
Table 6-2  Heat capacities of material components for Kydex. .................................. 84 
Table 6-3 Kinetic parameters describing decomposition reactions and melting for 
charring polymers. ...................................................................................................... 88 
Table 6-4  Heat capacities of material components for charring polymers. ............... 92 
Table 6-5 Heats of decomposition reactions and melting (endo is positive) for 
charring polymers. ...................................................................................................... 93 
Table 6-6 Heats of gasification for charring polymers. .............................................. 98 
Table 7-1 Absorption coefficients for non-charring polymers ................................. 101 
Table 7-2. Thermal conductivities for HIPS and POM. ........................................... 112 
Table 8-1 Absorption coefficients for ABS and charring polymers ......................... 121 
x 
Table 8-2 Thermal transport properties for ABS. ..................................................... 137 
Table 8-3 Thermal transport properties for PET. ...................................................... 139 
Table 8-4 Thermal transport properties for Kydex. .................................................. 142 
Table 8-5 Thermal transport properties for PEI. ....................................................... 145 
 
Table A. 1 FDS Input Parameters for PMMA. ......................................................... 163 
Table A. 2 FDS Input Parameters for POM. ............................................................. 165 
Table A. 3 FDS Input Parameters for HIPS. ............................................................. 168 
 
Table B. 1 Parameters for ABS................................................................................. 170 
Table B. 2 Parameters for PET. ................................................................................ 171 
Table B. 3 Parameters for Kydex. ............................................................................. 172 
Table B. 4 Parameters for PEI. ................................................................................. 174 
  
xi 
List of Figures 
Figure 2.1 Experimental set-up for a cone calorimeter measurement [31]................... 9 
Figure 2.2 Fire Propagation Apparatus (FPA) [33]. ................................................... 10 
Figure 2.3 Schematic illustration of the gasification apparatus [37]. ......................... 12 
Figure 2.4 Illustration for pyrolysis-combustion flow calorimeter [47]. .................... 14 
Figure 2.5 The schematic diagram of FCC [48]. ........................................................ 15 
Figure 3.1 Sketch of heating furnace and sample carrier. ........................................... 32 
Figure 3.2  Heat capacity of sapphire. ........................................................................ 37 
Figure 3.3 Heat capacity of sapphire in the presence of degrading PMMA. .............. 38 
Figure 3.4 Radiation absorption coefficient measurement setup. ............................... 39 
Figure 3.5 Heat flux result from ABS absorption coefficient measurement experiment.
..................................................................................................................................... 40 
Figure 3.6. Schematic of the CAPA............................................................................ 42 
Figure 3.7  Top surface background temperature at different level of heat fluxes under 
cone heater. ................................................................................................................. 43 
Figure 3.8 Copper plate temperature measurements in CAPA and model simulation at 
external heat flux of 40 kW m-2. ................................................................................. 45 
Figure 3.9 Schematic of modified controlled atmosphere pyrolysis apparatus. ......... 46 
Figure 3.10 Comparison of temperature measurements using thermocouples and IR 
camera for blackened copper plate at radiative heat flux of 40kW m-2. ..................... 47 
Figure 3.11 Comparison of temperature measurements using thermocouples and IR 
camera for HIPS with blackened aluminum foil on its bottom at radiative heat flux of 
30kW m-2. ................................................................................................................... 48 
xii 
Figure 3.12 Copper plate bottom surface temperature measurements in CAPA using 
IR camera and model prediction at external heat flux of 20, 40 and 60 kW m-2. ....... 49 
Figure 3.13 Heat flux at various level of locations. .................................................... 51 
Figure 4.1 Schematic of virgin polymer sample defined in the model of bench-scale 
experiments when insulation is present. ..................................................................... 58 
Figure 4.2 Schematic of virgin polymer sample defined in the model of bench-scale 
experiments part II. ..................................................................................................... 59 
Figure 5.1 TGA of POM at 10 K min-1. ...................................................................... 60 
Figure 5.2 Experimental and simulated TGA of POM at 10 K min-1. ........................ 63 
Figure 5.3 Experimental and simulated TGA of POM at 30 K min-1. ........................ 64 
Figure 5.4 DSC of POM at 10 K min-1. ...................................................................... 65 
Figure 5.5 DSC of POM normalized by instantaneous heating rate.  Linear fits 
represent heat capacities of the condensed phase at various stages of heating. .......... 66 
Figure 5.6 Determination of melting and decomposition contributions to the POM 
DSC signal. ................................................................................................................. 67 
Figure 5.7 Experimental and simulated DSC of POM at 10 K min-1. ........................ 69 
Figure 5.8 Time integral of 10 K min-1 DSC of POM. ............................................... 70 
Figure 5.9 Experimental and simulated TGA of PMMA, HIPS and PA 66 at 10 K 
min-1 and 30 K min-1. .................................................................................................. 72 
Figure 5.10 Experimental and simulated TGA of PP, PLA and ABS at 10 K min-1 and 
30 K min-1. .................................................................................................................. 73 
Figure 5.11 Experimental and simulated DSC of PMMA, HIPS and PA 66 at 10 K 
min-1. ........................................................................................................................... 76 
xiii 
Figure 5.12 Experimental and simulated DSC of PP, PLA and ABS at 10K min-1. .. 77 
Figure 6.1 TGA of Kydex at 10 K min-1. .................................................................... 80 
Figure 6.2 Experimental and simulated TGA of Kydex at 10 K min-1. ...................... 81 
Figure 6.3 Experimental and simulated TGA of Kydex at 30 K min-1. ...................... 82 
Figure 6.4 DSC of Kydex at 10 K min-1. .................................................................... 83 
Figure 6.5 DSC of Kydex (left) and Kydex decomposition residue (right) normalized 
by instantaneous heating rate. ..................................................................................... 84 
Figure 6.6 Determination of decomposition reaction contributions to the Kydex DSC 
signal. .......................................................................................................................... 85 
Figure 6.7 Experimental and simulated DSC heat flow (left) and heat flow integral 
(right) for Kydex at 10 K min-1. .................................................................................. 86 
Figure 6.8 Experimental and simulated TGA of DGEBA, PET and Kevlar at 10 and 
30 K min-1. .................................................................................................................. 89 
Figure 6.9 Experimental and simulated TGA of BACY, PEI and PEEK at 10 and 30 
K min-1. ....................................................................................................................... 90 
Figure 6.10 Experimental and simulated TGA of PPS at 10 K min-1. ........................ 91 
Figure 6.11 Experimental and simulated DSC of DGEBA, Kevlar and PET at 10 K 
min-1. ........................................................................................................................... 95 
Figure 6.12 Experimental and simulated DSC of BACY, PEI and PEEK at 10 K min-1.
..................................................................................................................................... 96 
Figure 6.13 Experimental and simulated DSC of PPS at 10 K min-1. ........................ 97 
Figure 6.14 SEM images of chars produced as a result of anaerobic thermal 
degradation of Kydex, DGEBA, PET and Kevlar. ..................................................... 99 
xiv 
Figure 6.15 SEM images of chars produced as a result of anaerobic thermal 
degradation of BACY, PPS, PEI and PEEK. ............................................................ 100 
Figure 7.1 Back temperature measurement using thermocouple and model prediction 
of anaerobic pyrolysis for PMMA at 20 and 60 kW m-2 (the error bars for both heat 
fluxes are not significantly shown because the temperature measurement differences 
from two thermocouples are small). ......................................................................... 103 
Figure 7.2 MLR measurements using CAPA and model prediction of PMMA 
anaerobic pyrolysis with insulation at 20 kW m-2. ................................................... 104 
Figure 7.3 MLR measurements using CAPA and model prediction of PMMA 
anaerobic pyrolysis with insulation at 40 kW m-2. ................................................... 105 
Figure 7.4 MLR measurements using CAPA and model prediction of PMMA 
anaerobic pyrolysis with insulation at 60 kW m-2. ................................................... 105 
Figure 7.5 Infrared images of bottom surfaces of the non-charring samples 
undergoing gasification. ............................................................................................ 107 
Figure 7.6 Spatial variation in bottom surface temperature histories. ...................... 108 
Figure 7.7 Experimental and simulated bottom surface temperature histories obtained 
for PMMA at 20 kW m-2. .......................................................................................... 109 
Figure 7.8 Experimental and simulated bottom surface temperature histories obtained 
for PMMA at 40 and 60 kW m-2. .............................................................................. 110 
Figure 7.9 Experimental and simulated bottom surface temperature histories obtained 
for HIPS at 30 kW m-2. ............................................................................................. 111 
Figure 7.10 Experimental and simulated bottom surface temperature histories 
obtained for HIPS at 50 and 70 kW m-2. ................................................................... 111 
xv 
Figure 7.11 Experimental and simulated bottom surface temperature histories 
obtained for POM at 30 kW m-2. .............................................................................. 112 
Figure 7.12 Experimental and simulated bottom surface temperature histories 
obtained for POM at 50 and 70 kW m-2. ................................................................... 112 
Figure 7.13 Thermal conductivity for PMMA. ......................................................... 113 
Figure 7.14 Thermal conductivity for HIPS. ............................................................ 114 
Figure 7.15 Thermal conductivity for POM. ............................................................ 115 
Figure 7.16 Experimental and simulated burning rate histories obtained for PMMA at 
20-60 kW m-2. ........................................................................................................... 117 
Figure 7.17 Experimental and simulated burning rate histories obtained for HIPS at 
30-70 kW m-2. ........................................................................................................... 118 
Figure 7.18 Experimental and simulated burning rate histories obtained for POM at 
30-70 kW m-2. ........................................................................................................... 119 
Figure 8.1 Char residues after gasification experiments for ABS at 50 kW m-2. ..... 122 
Figure 8.2 Infrared images of bottom surfaces of the ABS sample undergoing 
gasification at 50 kW m-2. ......................................................................................... 123 
Figure 8.3 Char residues after gasification experiments for PET at 50 kW m-2. ...... 124 
Figure 8.4 Infrared images of bottom surfaces of the PET sample undergoing 
gasification at 50 kW m-2. ......................................................................................... 125 
Figure 8.5 Char residues after gasification experiments for Kydex at 50 kW m-2. .. 126 
Figure 8.6 Side views and Infrared images of bottom surfaces of the Kydex sample 
undergoing gasification at 50 kW m-2. ...................................................................... 127 
Figure 8.7 Char residues after gasification experiments for PEI at 50 kW m-2. ....... 129 
xvi 
Figure 8.8 Side views and Infrared images of bottom surfaces of the PEI sample 
undergoing gasification at 50 kW m-2. ...................................................................... 130 
Figure 8.9 Experimental measurements and linear fits for the height to sample bottom 
vs time for Kydex and PEI at various heat fluxes. .................................................... 134 
Figure 8.10 Relation of incident radiative heat flux on top surface and time. .......... 135 
Figure 8.11 Experimental and simulated bottom surface temperature histories 
obtained for ABS at 30 kW m-2. ............................................................................... 136 
Figure 8.12 Experimental and simulated bottom surface temperature histories 
obtained for ABS at 50 kW m-2. ............................................................................... 137 
Figure 8.13 Experimental and simulated bottom surface temperature histories 
obtained for ABS at 70 kW m-2. ............................................................................... 138 
Figure 8.14 Experimental and simulated bottom surface temperature histories 
obtained for PET at 50 kW m-2. ................................................................................ 139 
Figure 8.15 Experimental and simulated bottom surface temperature histories 
obtained for PET at 70 kW m-2. ................................................................................ 140 
Figure 8.16 Experimental and simulated bottom surface temperature histories 
obtained for Kydex at 30 kW m-2 (fitted range). ....................................................... 141 
Figure 8.17 Experimental and simulated bottom surface temperature histories 
obtained for Kydex at 30 kW m-2. ............................................................................ 141 
Figure 8.18 Experimental and simulated bottom surface temperature histories 
obtained for Kydex at 50 kW m-2. ............................................................................ 142 
Figure 8.19 Experimental and simulated bottom surface temperature histories 
obtained for Kydex at 70 kW m-2. ............................................................................ 143 
xvii 
Figure 8.20 Experimental and simulated bottom surface temperature histories 
obtained for PEI at 50 kW m-2 (fitted range). ........................................................... 144 
Figure 8.21 Experimental and simulated bottom surface temperature histories 
obtained for PEI at 50 kW m-2. ................................................................................. 144 
Figure 8.22 Experimental and simulated bottom surface temperature histories 
obtained for PEI at 70 kW m-2. ................................................................................. 146 
Figure 8.23 Experimental and simulated bottom surface temperature histories 
obtained for PEI at 90 kW m-2. ................................................................................. 146 
Figure 8.24 Side view snapshots of PET at 50-90 kW m-2. ...................................... 147 
Figure 8.25 Experimental and simulated thickness histories obtained for ABS at 50 
kW m-2. ..................................................................................................................... 148 
Figure 8.26 Experimental and simulated burning rate histories obtained for ABS at 
30-70 kW m-2. ........................................................................................................... 149 
Figure 8.27 Experimental and simulated thickness histories obtained for PET at 50 
kW m-2. ..................................................................................................................... 150 
Figure 8.28 Experimental and simulated burning rate histories obtained for PET at 50 
and 70 kW m-2. .......................................................................................................... 151 
Figure 8.29 Experimental and simulated thickness histories obtained for Kydex at 50 
kW m-2. ..................................................................................................................... 152 
Figure 8.30 Experimental and simulated burning rate histories obtained for Kydex at 
30 and 70 kW m-2. ..................................................................................................... 153 
Figure 8.31 Experimental and simulated thickness histories obtained for PEI at 50 kW 
m-2. ............................................................................................................................ 154 
xviii 
Figure 8.32 Experimental and simulated burning rate histories obtained for PEI at 50 
and 90 kW m-2. .......................................................................................................... 156 
Figure 8.33 Maximum heat release rate verse heat flux for polymers (These 
maximum heat release rates were calculated by multiplying the maximum gasification 
experiment burning rate and effective HOC values obtained from this study). ....... 158 
 
Figure A. 1 Comparison of predicted and measured mass loss rates for PMMA. .... 165 
Figure A. 2 Comparison of predicted and measured mass loss rates for POM. ....... 167 
Figure A. 3 Comparison of predicted and measured mass loss rates for HIPS. ....... 169 
 
  
xix 
Nomenclature 
Abbreviation  
ABS poly(acrylonitrile butadiene styrene) 
ASTM  American Society for Testing Materials 
BACY polymerized bisphenol A cyanate ester 
CAPA Controlled Atmosphere pyrolysis Apparatus 
DGEBA polymerized diglycidylether of bisphenol A 
DSC differential scanning calorimetry 
FAA Federal Aviation Administration 
FPA Fire Propagation Apparatus 
HIPS high impact polystyrene 
Kevlar poly(paraphenylene terephthalamide) 
HOC heat of combustion 
Kydex poly(methyl methacrylate)-poly(vinyl chloride) alloy 
MCC Microscale Combustion Calorimetry 
MLR mass loss rate 
MPC Mass Pyrolysis Calorimetry 
NFPA National Fire Protection Association 
NIST National Institute of Standard Technology 
PA 66 polyamide 6,6 
PCFC Pyrolysis Combustion Flow Calorimetery 
PE polyethylene 
PEEK poly(ether ether ketone) 
PEI polyetherimide 
PET poly(ethylene terephthalate) 
PFCC or FCC Pyrolysis Flaming Combustion Calorimetery 
PLA poly(lactic acid) 
PMMA poly(methyl methacrylate) 
POM poly(oxymethylene) 
PP polypropylene 
PPS poly(phenylene sulfide) 
SEM Scanning Electron Microscopy 
TGA thermogravimetric analysis 
UL Underwriter’s Laboratories 
Equation symbols  
xx 
A Arrhenius pre-exponential factor 
 radiation absorption coefficients 
c heat capacity 
D cylindrical coordinates 
E Arrhenius activation energy 
e base of the natural logarithm 
f reflectivity 
h heat of reaction 
I radiation heat flux 
J mass flux 
k thermal conductivity 
 gas transfer coefficients 
m mass 
q stoichiometric coefficient 
 density 
r reaction rate 
R gas constant 
 Stefan-Boltzmann constant 
t time 
T temperature 
x cartesian coordinate 
 concentration 
Subscript  
0 or init initial stage 
base baseline 
d decomposition 
e final simulation 
ex external 
g gasification 
j,k,l component  
max maximum stage 
Melt or m molten polymer 
Res1 residue of polymer decomposition stage 1 
Res2 residue of polymer decomposition stage 2 
v vaporization 
  
1 
Chapter 1 : Introduction 
Section 1.1 Polymer flammability  
Polymeric materials or plastics are generally defined as materials that contain 
essential ingredients such as polymers. Polymers are organic substances with 
extremely high molecular mass. Most of this class of materials is synthetized or semi-
synthetized from petrochemicals with other substances for special purpose. Polymers 
are ubiquitous in both high technology and routine household applications. 
Thousands of polymers were created and widely used in the last century and endless 
types of new polymers are continually being produced around the world. An 
attractive combination of customizable mechanical properties, low weight, and easy 
processability makes them an irreplaceable part of today’s modern society [1].  
One of the main disadvantages associated with a widespread use of these 
materials is their inherent flammability [2] because of a large fraction of carbon and 
hydrogen atoms in these organic substances that make their compositions very similar 
to that of fossil fuels. Combustion can occur easily under sufficiently heat and oxygen 
for some polymers. For example, most early credit cards and Ping-Pong balls were 
made of highly flammable and hazardous celluloid plastic. Therefore most polymer-
containing end products (i.e. electrical cables, furniture and home or office decorating 
materials and carpets) that exist everywhere in our daily lives must pass certain fire 
safety requirements (for example, UL 94) to assure personal and public safety [3]. 
Researchers are examining and exploring hundreds of ways to reduce the 
polymer flammability in application, transportation and storage while keeping their 
other advantages. The burning of solid polymeric material is a complex process that 
2 
involves multiple chemical and physical phenomena such as pyrolysis at the 
condensed phases including phase transitions, chemical reactions, heat transfer, mass 
diffusion and flame or flameless combustion that occurs at the gaseous phase [4]. It is 
important to quantitatively understand the fundamental principles behind polymer 
ignition and burning. From this aspect, chemists and material scientists can 
understand how to best modify existing polymers to reduce their flammability in 
order to pass such tests without significantly increasing the cost of end products. 
Section 1.2 Mechanism of polymer combustion  
When most polymers or solid materials burn in presence of a flame, they burn 
similarly to other liquids and gaseous fuels. The flame is usually termed a diffusion 
flame. In diffusion flame, combustion occurs at the interface where the oxidizer meets 
the combustible gaseous fuel which is generated from the thermal degradation of the 
condensed phase fuel and the gaseous fuel is transported by diffusion and controls 
convection. Gas phase combustion provides the continual sources of heat, which can 
be categorized into two groups: radiative and convective, over the boundaries of 
condensed phase thermal degradation. The gas phase combustion phenomena, 
including chemical reactions, turbulence, soot generation and oxidization, species 
concentration distribution etc. were intensively studied for years and are reasonably 
well understood. For example, scientists in the last century have been able to 
understand the combustion of gaseous fuels and chemical processes, in terms of 
elementary chemical reactions with defined chemical kinetic parameters [5]. 
Commercial computational software, such as CHEMKIN [6], is available in the 
market for basic chemical kinetic simulations. 
3 
The condensed phase thermal degradation reaction mechanisms, which 
dominate the overall burning rate play an important role in the delivery of  gaseous 
combustibles for the gas phase combustion [3]. There are several kinds of chemical 
and physical processes that occur in the condensed phase and some of them are key 
factors that affect overall material flammability and combustion. The mechanisms of 
how these phenomena interact and give rise to gaseous fuel generation that defines 
material flammability [3] have been studied by many researchers [7-13] for various 
types of polymers. For example, thermal degradation dynamics of polymers were 
studied for various of polymers (Polyethylene(PE) [14], Polypropylene (PP) [15], 
poly(methyl methacrylate) (PMMA) [16], and poly(isobutylene) (PIB) [17]) at an 
atomistic and molecular level to find the factors that governs the overall thermal 
degradation kinetics.  
However, the process that governs the polymer combustion at the condensed 
phase is not only governed only at the molecular level, though it can affect 
ignitability and overall combustion process. When polymers thermally degrade and 
burn, a number of physical and chemical processes occur simultaneously and it is 
hard to separate them individually. Previous evidence and studies lead to the 
conclusion that without clearing an understanding of macro-scale morphology and 
heat transfer within condensed phase, especially for some charring polymers, no 
quantitative connection can be made between molecular-level phenomena and 
polymer flammability performance. Therefore in this study, special attention has been 
focused on thermal degradation process at milligram scale and bench scale of 
polymeric materials at the condensed phase.  
4 
Section 1.3 Non-charring and charring polymers 
In most cases, solid polymer long chains break down into a number of smaller 
fragments, which can either be monomers or groups of chemical species, under 
thermal decomposition. Some polymers break down completely in the condensed 
phase leaving no significant amount of residue. Those polymers that usually remain 
within 5 wt.% of the initial mass are categorized into non-charring polymers. 
However, some polymer chains break in a different manner. Those heavier molecule 
fragments crosslink, and instead of further chain scission, they remain in the 
condensed phase and forms as carbonaceous residues. Those polymers are named 
charring polymers. The charring processes for polymer thermal degradation in the 
condensed phase are complicated and they can be affected by many factors such as 
naturally chemical composition, incorporation of flame retardants [18] and surface 
treatment ( i.e intumescent coating). Other than the polymeric materials themselves, 
ambient conditions are also important factors to lead the charring processes. For 
example, Martel’s research [19] in late 1980s disclosed that oxygen has a decisive 
effect on the charring process for some polymers without containing aromatic rings in 
their main chain. There is no standard criterion to regularize the minimum amount of 
residue for charring polymer. In this work, we choose 10 wt.% as the minimum value 
to determine this group of polymers by studying their thermal degradation residues 
upon heating up to 1223 K from room temperature in a thermally thin condition at 
purely inert condition.  
It was found that charring polymers during bench-scale burning have lower 
ignitability [1] and lower heat release rate than non-charring polymer because of the 
following reasons: lower amount of volatile fuel is produced by burning charring 
5 
polymer and a formation of insulation layer which reduce heat and mass transfer at 
the condensed phase. However, production cost of charring polymer is usually more 
expensive than cost of non-charring polymer. Therefore in the engineering market, 
one of the ways for chemists and material scientists to reduce the polymer 
flammability in order to pass material fire safety tests is by adding the flame retardant 
additives [20, 21]. A conventional solution to the problem is to use halogenated 
flame-retardant additives. However, with more and more concerns on the use of 
halogenated flame-retardant additives for its tendency to bioaccumulate and potential 
toxicity [22], researchers are seeking halogen-free fire additives for inducing char 
formation. The current state of the art approaches [23] to improve polymer flame 
retardancy are blending with some charring polymers to non-charring polymers, using 
of nontraditional charring agent, using of nanoparticles and improving intumescence. 
The polymer nanocomposite [24-26] is one of the most promising improvements to 
replace the conventional formulations in the area of flame retardancy. For instance, 
Zanetti et al. [27] reported that the use of nanoclays in the polymer nanocomposites 
can led to the reduction of oxygen permeability to improve its thermo-oxidative 
stability and thermal stability in some cases [28]. Kashiwagi et al.[29] found that 
nanoparticle fillers such as carbon nanotubes can surpass nanoclays to simultaneously 
improve both mechanical and flammability properties. Intumescent materials are 
called “Intumescent” because their surfaces begin to swell and then expand when 
heated to critical temperature. As a result, a foamed cellular layer is formed and 
shields the unpyrolyzed material from the action of the heat flux or the flame [30]. 
  
6 
Chapter 2 :  Literature review 
This chapter focuses on providing an overview of previous studies that 
address material flammability and in particular polymeric material flammability. 
Other similar solid materials are also discussed, such as wood - a natural composite 
polymer made of cellulose, hemicelluloses and lignin. Cellulose (≈ 42 wt.% in wood) 
and lignin (≈ 28 wt.%) are organic compounds and corresponding approximately to 
the formula (C6H10O5)n and (C31H34O11)n respectively. The physical and chemical 
processes that occur at the condense phase, and which control the material 
flammability and ignitability and are discussed in detail here. In addition, key 
parameters that dominate the overall burning of material are discussed and research 
works of the measurement for these parameters are reviewed. Pyrolysis numerical 
pyrolysis models that are capable of simulating the process of thermal degradation, 
material ignition and combustion are also reviewed and existing impediments and 
challenges to accurate model prediction are addressed. Last but not least, the 
motivation and primary contribution of this dissertation is emphasized.  
Section 2.1 Material flammability tests 
As mentioned in the chapter 1, material flammability especially for polymeric 
material is generally a big concern for fire protection for material manufactures. The 
way to judge whether a particular polymer is more flammable than the other one 
really depends on the scenarios in which the polymers are placed. Therefore, the fire 
behavior when polymeric materials are exposed to fire is generally evaluated as a 
quantitative measurement through a number of flammability tests that resemble 
certain types of fire scenarios. There are numbers of organizations around the world 
7 
which proposes such standard tests such as American Society for Testing Materials 
(ASTM), which is mostly adopted in the United State, and Underwriter’s 
Laboratories (UL), National Fire Protection Association (NFPA) and International 
Conference of Building officials (ICBO). Most of the material flammability testing 
standards are similar despite that they are issued and adopted in different areas. Table 
2-1 lists selective ASTM standards that are relevant to solid material fire safety in 
different scenarios. 
Table 2-1 Selective ASTM standards that relevant to solid material fire safety in 
different scenarios 
Standard number Standard description 
ASTM C209 Insulating board 
ASTM D568 Plastics, vertical 
ASTM D635 Plastics, horizontal 
ASTM D757 Plastics, horizontal, incandescence, Globar 
ASTM D1433 Plastics, 45 degree angle 
ASTM D1692 Cellular plastics, horizontal 
ASTM D1929 Plastics, ignition, Setchkin furnace 
ASTM D2863 Measuring the Minimum Oxygen Concentration to Support 
Candle-Like Combustion of Plastics 
ASTM D3014 Cellular plastics, vertical , Butler chimney 
ASTM D3713 Plastics, ignition, small flame 
ASTM D4100 Plastics, smoke, gravimetric, Arapahoe chamber 
ASTM D4151 Blankets, flammability 
ASTM D4205 Rubber, flammability and combustion 
ASTM D4986 Cellular polymers, horizontal, similar to ASTM D1692 
ASTM D7309 Determining Flammability Characteristics of Plastics Using 
Microscale Combustion Calorimetry 
ASTM E84 Building materials, surface burning, 25-foot tunnel 
8 
ASTM E119 Standard fire tests 
ASTM E136 Combustibility 
ASTM E162 Surface flammability, radiant panel 
ASTM E286 Surface flammability, 8-foot tunnel 
ASTM E1354 Heat and Visible Smoke Release Rates for Materials Using an 
Oxygen Consumption Calorimeter 
ASTM E2058 Standard Test Methods for Measurement of Material 
Flammability Using a Fire Propagation Apparatus 
ASTM E2254 Room Fire Test of Wall and Ceiling Materials 
ASTM E2257 Room Fire Test of Wall and Ceiling Materials 
ASTM F501 Aerospace material, vertical 
All these testing standards aim to resemble real fire scenarios, and are either 
primarily research tests or primarily acceptance tests, from micro scale to room scale.  
The complexity and costs for the fire tests increase dramatically as the scale 
increasing. Full scale tests are usually too expensive to afford for most users. 
However, larger scale of fire tests resembles the real fire scenarios closer. Therefore, 
one of the most widely used testing standards named ASTM 1354 in the United States 
is carried out at a bench scale, which places in the middle range among those scales. 
The instrument used in this type of test is named cone calorimeter, which is widely 
and effectively used in the field of fire safety engineering. It usually measures heat 
release rate of the solid materials which is difficult to perform in the full-scale tests. It 
was initially developed by National Institute of Standard Technology (NIST) 
researchers [31] about 30 years ago and relied on an empirical observation that 
releasing energy from burning material is directly proportional to the quantity of 
consumed oxygen [32]. There are several standard tests that are carried under this 
instrument, such as ASTM D 6113, ASTM E1474, ASTM E1740 and ASTM F1550. 
9 
As shown in Figure 2.1, a testing sample is heated underneath a conical radiant 
electrical heater, which delivers a uniform one-dimensional external radiative heat 
flux that simulates the burning surroundings in a room fire. The exhaust gases after 
combustion are collected from a hood with centrifugal fan on top and are then 
analyzed by a gas analyzer. Concentrations of O2, CO and CO2 are measured in the 
gas analyzer. Other key parameters (i.e., heat release rate, mass loss rate, smoke 
production, etc.) of material under external heat flux measuring up to 100 kW m-2 can 
be calculated. In addition, from these types of tests, the time to ignition, combustion 
time and total smoke released are also characterized.  
 
Figure 2.1 Experimental set-up for a cone calorimeter measurement [31]. 
Although cone calorimeter measures the heat release rate well for many 
materials, one of the major issues, which has existed for years, is the measurements 
that are taken near ambient air under well-controlled environments. Usually, this is 
not the same case that occurs at the real fire scenarios, especially in some 
compartment fires when the ventilations are limited. Therefore, researchers from FM 
10 
Global developed an apparatus that can control the testing environment by purging 
gases flow uniformly into an infrared-grade quartz tube, which shields the sample and 
gasification products from the ambient air. As shown in Figure 2.2, instead of using a 
conical radiant electrical heater, four high-power high-density infrared tungsten 
halogen heaters are used to generate a uniform external heat flux of up to 120 kW m-2.  
The exhaust system, which is similar to a cone calorimeter, is used to analyze the 
combustion production gas. Many important parameters are related to material 
flammability, such as critical heat flux for ignition, thermal response parameter, 
effective heat of combustion and smoke yield are then recorded.  
 
Figure 2.2 Fire Propagation Apparatus (FPA) [33]. 
11 
Because of its significant characteristics, FPA is designed and used to evaluate 
existing standards for fire propagation along cables and the flammability of clean 
room materials. However, one of the main issues related to this apparatus that limits 
its use is the spectral radiance from the radiative lamps. There are more than one 
evidences that disclose the fact that the radiative spectrum from the lamps used in 
FPA does not cover the entire range of radiative wavelengths is observed in the real 
fire scenario. There is a clear shift to the time to ignition using cone calorimeter and 
FPA for PMMA [34], especially for high heat flux [35]. In this case, experimental 
results directly from FPA need extra work to amend by applying the integration of 
entire radiative wavelength [36]. 
For a gasification test on a bench-scale, where flame is completely removed 
from the burning sample, FPA can produce good results except for a couple of issues. 
Besides the radiative spectral from lamps, the hot quartz during the gasification 
affects the boundary conditions that need to be well controlled. Kashiwagi et al. [37] 
from NIST built a well-controlled gasification apparatus that is somewhat similar in 
design to a cone calorimeter. The primary difference between their apparatus and 
cone calorimeter is that the sample is placed inside a sealed cylindrical chamber in 
which nitrogen is continuously purged at a prescribed rate rather than in the open air, 
as in the case of a cone calorimeter. As shown in Figure 2.3, the cylindrical chamber, 
which is made of stainless-steel and painted black internally, is designed to remain a 
constant temperature at 25oC by water cooling and minimize background radiation. 
Incident flux (20 kW m-2 to 70 kW m-2) is delivered by a cone heater on top of the 
testing samples. Mass loss rate, rather than calorimetry, is recorded during material 
12 
gasification. Visual observation and video are available to provide excellent 
documentation of the pyrolysis process. In general, this apparatus provides a well-
controlled gasification condition to study the material, mainly polymers, and 
pyrolysis under uniform heat fluxes and it has been used extensively after its 
invention [29, 38-46]. However, this apparatus has two main drawbacks that limit its 
use in gasification experiments: cost and limited diagnostics. During the tests, this 
instrument require significant power from the heater and exhaust system and 
extremely large amounts of nitrogen flow (approximately 1200 SLPM). Besides mass 
loss rate, only video data is taken from the top side view during the gasification. No 
other diagnostics are applied in the test, such as temperature measurement. 
 
Figure 2.3 Schematic illustration of the gasification apparatus [37]. 
13 
All these tests require a gram-scale of the samples to examine the material 
flammability which is fairly expensive, especially for manufacturers that design and 
make new polymeric materials with flame retardants. Therefore, a number of 
researchers have made considerable efforts in developing laboratory instruments to 
measure the heat release rate of milligram-scale samples.  
One of the successful inventions in recent years for material flammability 
study on the milligram-scale is the Microscale Combustion Calorimetery (MCC), 
which was initially developed by Lyon et al. [47] from the Federal Aviation 
Administration (FAA). MCC, also is named Pyrolysis Combustion Flow Calorimetry 
(PCFC), which measures the complete combustion of the given material in milligram 
scale. According to ASTM D7309, MCC is used to screen research materials at the 
milligram level for a fireproof aircraft cabin. The principle of MCC is shown in 
Figure 2.4. The milligram sample is placed inside the pyrolyzer at a prescribed 
heating rate. The gaseous volatiles meet with oxidizer (typically O2) inside the 
combustor. This combustor is preheated to 900oC for complete combustion and 
oxygen consumption is recorded in real time by an oxygen analyzer that sits close to a 
mass flow meter. The heat release rate is then calculated, similarly to cone 
calorimeter and FPA, using oxygen depletion technique [32]. 
14 
 
Figure 2.4 Illustration for pyrolysis-combustion flow calorimeter [47]. 
Although ASTM D7309 or MCC is widely used by chemists and material 
scientists to screen new material at the milligram level and measure the complete 
combustion of polymer. However, the major concerns raised by fire protection 
engineers in the past, is the comparison of combustion efficiency with the real 
material burning, like the flaming and soot generation observed in the cone 
calorimeter or FPA. A new instrument that aims at measuring the flaming combustion 
at the milligram scale, which shares the advantages between MCC and the cone 
calorimeter named Pyrolysis Flaming Combustion Calorimetery (PFCC or FCC), is 
recently developed by Stoliarov et. al [48]. The schematic diagram for FCC is shown 
in Figure 2.5. In this figure, the FCC in essence consisted of four parts: the pyrolyzer, 
15 
the base, the combustion chamber and the gas analyzing system. In FCC, a sample of 
approximately 30 mg was being heated in the pyrolyzer. Instead of forcing pyrolysis 
volatiles in the combustor in MCC, FCC has an igniter to generate flaming 
combustion at the gas phase where oxygen consumption is recorded similarly with 
MCC and heat release rate is calculated using oxygen depletion technique [32]. The 
actual flaming combustion took place in the combustion chamber which was made of 
quartz tube that had extremely low thermal expansion coefficient. The flame height, 
combustion time, time to ignition information can also be measured since quartz tube 
is transparent.  
 
Figure 2.5 The schematic diagram of FCC [48]. 
All these laboratory scale testing methods hold their own advantages and 
represent in well-controlled behavior in different levels of scale. However, each of the 
16 
above method has its own disadvantages, obviously. Besides the drawback of being 
expensive, the bench-scale cone calorimeter test is a complex process and it is hard to 
separate the effect of gas-phase combustion and condensed-phase pyrolysis. Although 
MCC is capable of separating the aforementioned effect, it fails to capture gas phase 
effects because of forced combustion. FCC decoupled the gas-phase combustion and 
condensed phase pyrolysis and measures the effective heat of combustion in a 
reasonable manner with combustion efficiency result within the cone calorimeter 
results. However, the FCC was not fully capturing the effect that bromine acts as gas 
phase combustion inhibitor to the extent that cone calorimeter was capturing [48]. 
Section 2.2 Material pyrolysis processes  
From the material flammability aspect, there are two processes that dominate 
the polymeric material burning rate under condensed phase: thermal and chemical 
processes. 
The thermal process always occurs at the initial state when polymeric 
materials are subjected to external heat, such as from visible flame or fires. 
Researchers were using Fourier’s law to represent the heat conduction inside the solid 
phase. One of the early examples was a research paper by Tinney [49] who modeled 
the pyrolysis of one small wooden dowel under external heat using a one-dimensional 
assumption, before polymer flammability issue draws public attention widely. He 
descripted the conduction equation in cylindrical coordinates in Equation 2.1 to 
describe the temperature distribution in the solid state       . T, D, t represent 
temperature of the wood, radial distance from the center of the wooden dowel and 
17 
time respectively. A number of researchers focused on different geometries [9, 50-56] 
following the methodology of Tinney [49].  
   
  
  
  (
   
   
 
 
 
  
  
)                                                                                (2.1) 
Where   represents the thermal conductivity of material, which is the key 
parameter of this equation.   is assumed temperature-independent for simplicity.   is 
the density of wood.    denotes the wood heat capacity. A solution of Equation 2.1 
can be obtained either numerically or by analytically providing an initial condition 
and two boundary conditions are specified. There are a number of scientific papers 
that have stepped into the study of inclusion of char formation [8, 57-61] and used 
temperature-dependent properties during solid material combustion and pyrolysis, 
which makes the problems more realistic. Properties other than thermal conductivity 
such as specific heat capacity, emissivity, surface absorptivity and density were 
obtained accurately from experiments and coupled into modeling [62-68]. Other 
terms affecting heat transfer such as convection and radiation were also considered 
and added into the thermal model to calculate the temperature distribution in the later 
models [9, 56, 64, 65, 68]. The physical process also involves a series of phase 
transformations such as glass-liquid transition for some amorphous materials (or in 
amorphous regions within semicrystalline materials) and melting. 
The chemical process of material pyrolysis includes chemical decomposition 
and volatilization. For most solid polymeric material, the decomposition process to 
produce a gaseous fuel can be idealized by an Arrhenius type of reaction. As 
18 
described in a thermal analysis handbook [69], the reaction rate of thermally activated 
process can be described:  
  
  
   
   
                                                                                                             (2.2) 
where   is the extent of conversion and can be defined as  
  
     
     
                                                                                                                 (2.3) 
Where mT is the mass at temperature T and mi and mf are respectively the 
initial and final masses for a given step of mass change. Pre-exponential factor (A) 
and activation energy (E) are two Arrhenius parameters. T is the temperature and t is 
the time. The reaction model is defined as 
                                                                                                                  (2.4) 
n is the reaction order. Many researchers frequently found that the first order 
reaction assumption in their models predicts the experiments well for most of 
common solid materials such as wood [58, 66, 70], non-charring polymers [71-77] 
and charring polymers [76, 78, 79]. The other two key parameters, A and E, are 
intensively studied almost by every material flammability scientist for different types 
of solid materials for decades. The determination of kinetic characteristics and 
parameters including Arrhenius parameters and reaction model can be obtained from 
experiments in several methods. Isothermal and non-isothermal methods are two 
frequently used methods. In isothermal method, yield-time measurements are made 
while the reactant is maintained at a constant known temperature, while in 
nonisothermal method, the sample is subjected to a controlled rising temperature. 
19 
Many researchers used the isothermal [70, 73, 80, 81] method to calculate these 
kinetic parameters while some chose the  non-isothermal method [82, 83]. One of 
great advantages of the isothermal method is that changes in the apparent order of the 
reaction and the apparent activation energy in the reaction mechanisms are easily 
detectable [84]. In practically, a sample requires some time to reach experimental set 
temperature which experiences non-isothermal heating period. During this period, the 
sample undergoes unknown transformations that are likely affecting the final results. 
Non-isothermal method mitigates this problem that restricts the use of isothermal 
method at high temperature. The main drawback for non-isothermal conditions, as 
described in the literature for various analysis methods, such as differential ones (
  
  
 
values need conveniently obtain data of Derivative Thermogravimetric Analysis) [85], 
integral (equation 2.2 is integrated without an analytical solution to handle TGA data) 
[86], the kinetic parameters were found to be slightly different from method to 
method for the same polymer under the same conditions [87].  
A model-free approach based on the principle of reaction rate at a constant 
extent of conversion is only a function of temperature is called isoconversional 
methods. It requires multiple experiments conducted at different heating rates [88, 89]. 
From this method, if the reaction rate is not too high, activation energy, which 
obviously corresponds to a given extent of conversion can be estimated model-
independently by assuming that the extent of conversion does not vary during the 
temperature jump. These are multiple issues using isoconversional methods and one 
of those, as Agrawal [90] pointed, is no identical effective conversion value could be 
estimated due to the fact that no unique overall conversion for the individual reactions 
20 
exists in some complex multi-step reactions at various of heating rates. In fact, it was 
called “model-free” because E could be estimated independent of the reaction order. 
However, to get the complete set of Arrhenius parameters, A cannot be estimated if 
no value is assigned for the reaction order. Therefore, Arrhenius parameters cannot 
thus be used for elucidation of the reaction mechanism, nor for predicting the thermal 
behaviour of the polymer in both isothermic and other non-isothermic conditions [91, 
92]. 
When polymers undergo thermal decomposition, it also involves obvious 
energy absorption or release in addition to gaseous volatiles generation. The total 
energy that gasifies the solid material per unit mass from room temperature is 
quantified by a value termed as heat of gasification (  ).    can be defined: 
   ∫       
  
  
                                                                                (2.5) 
The four terms on the right-hand side of Equation 2.5 represent the four 
thermal and chemical processes that occur for a solid material gasification as the 
temperature rises: sensible enthalpy changes [     is temperature-dependent heat 
capacity], heat of melting for material that melts at Tmelting (T0 < Tmelting <Tp), heat of 
decomposition and heat of vaporization. Usually for most polymeric materials,     
accounts for the energy that is required by the polymer molecule to break into smaller 
fragments during thermal decomposition process and equals to the chemical bonds 
dissociation energy.     is the amount of heat required to  subsequently vaporize the 
decomposition products from the condensed phase to the gas phase. For material 
flammability research,    is an important parameter that affects the material burning 
21 
rate and it has been measured and tabulated for a number of materials [33, 93]. More 
than one reasons have been found that the    for the same material is not technically 
constant from many researchers’ measurements. The first parameter that affects the 
   calculation is Tp, the pyrolysis temperature where the volatilization occurs. Most 
solid materials do not instantaneously volatilize completely at a fixed Tp, but are finite 
temperature ranges near Tp. In principle, the heating rate does affect the   because 
the temperature range at which the degradation takes place shifts to higher values 
with an increasing rate of heating. As a consequence, the solid (or molten) polymer is 
heated to a higher temperature before it degrades. The details discussed for the 
heating rate effect can be found in Chapter 5. 
Besides A, E and cp, there is a list of parameters that affect the material 
flammability and heat and mass transfer, such as density, emissivity, absorption 
coefficient and thermal conductivity. Usually measurements for those properties are 
carried out and the values are tabulated at room temperature [94]. Most of these 
properties are temperature-dependent properties but the knowledge of the data from 
the room temperature to the material pyrolysis temperature is limited. With the 
development of science and technology in polymer research, researchers are able to 
measure these temperature-dependent properties for polymers.  For example, most 
polymer properties handbooks such as the one recently updated [1] list the volumetric 
changes during heating, and this value can be up to 20 % from room temperature and 
ignition temperature. Temperature-dependent values for polymer specific heat 
capacities were also studied by a number of researchers [71, 95-99]. For example, 
22 
Henderson [99] measured specific heat of virgin and decomposed polymer 
composites between temperatures of 333 to 1003 K.  
Thermal conductivities for polymers were measured by groups of researchers 
but they are still scattered throughout the literature and little to no information is 
available for various polymers at different temperatures. Most studies were focused 
on PMMA measurements at room temperature [100-102] and seldom go beyond 300 
K and up to 600 K [71, 77, 103]. Zhang and his coworkers [104, 105] made careful 
thermal conductivity measurements for a number of common polymers such as PE, 
Polystyrene (PS), PP and PC (Polycarbonate). Due to the lack of experimental data 
and difficulties associated with accurate measurements of polymer thermal 
conductivity at higher temperatures when melting or decomposition in present, crude 
approximations were often used in the past for many polymers that including 
composites.  
Changes in above parameters will affect the material heat release rate or 
burning rate curve, which is an important output of the fire models that used in the 
research and engineering applications. While the fundamental physical and chemical 
processes can be well explained and calculated by the mass and energy conservation 
equations in the state of art fire modeling tools, for instance NIST Fire Dynamics 
Simulator (FDS), accurate prediction of the heat release rate or mass lose rate requires 
good input data with physical-meaningful parameters. It is hard to measure or obtain 
all the properties precisely; however, knowing which parameters dominate the overall 
process of solid material burning is the key to improve prediction. Researchers in the 
past few years examined the effect of variations in the polymer properties on the 
23 
polymer burning behaviors [106-109] to gain better knowledge about the importance 
of each property. The key finding from these sensitivity analysis studies leads the 
conclusion that the knowledge of the kinetics (defined by the Arrhenius pre-
exponential factor and activation energy to resemble the rate of decomposition), heat 
of decomposition and char yield is crucial for predicting the peak and average heat 
release rate. Other properties such as density, heat capacity, thermal conductivity and 
optical properties are less important and can be estimated from the mean of various 
literature.  
Section 2.3 Research motivation and overview 
To better understand how chemical and physical phenomena such as phase 
transitions, chemical reactions, heat transfer and mass diffusion interact to give rise to 
gaseous fuel generation, a number of numerical pyrolysis models have been 
developed. The solid phase submodel in the FDS [65], ThermaKin [110], Gpyro [68] 
and Pyropolis [67] are pyrolysis modeling computer codes that were developed 
during the last few years. These models require property values that describe the 
aforementioned chemical and physical phenomena as input and compute the rates of 
gaseous fuel generation by solid material objects exposed to external heat.   
While some progress has been made in the development of experimental 
procedures for the measurement of these properties [11, 39, 40, 71, 98, 111-114], the 
accuracy, generality and robustness of these procedures clearly require further 
refinement. For example, several approaches to the property determination have been 
developed. Lautenberger and Fernandez-Pello [115] proposed using data from bench-
scale fire tests as a target for property value optimization. They employed a genetic 
24 
algorithm to solve a multi-parameter optimization problem. Subsequently, Chaos and 
co-authors[116] advanced this methodology by using controlled pyrolysis 
experiments in a fire propagation apparatus [117] and performed property calculation 
using a more efficient, shuffled complex evolution optimization algorithm. 
One of the main advantages of the optimization-based property evaluation is 
that a complete set of properties can be obtained from a relatively small number of 
standard bench-scale tests. The main drawback, according to Ghorbani et al. [118], is 
that the derived values may not represent true material properties. As a consequence, 
the parameterized model does not provide reliable predictions outside the range of 
conditions realized in the calibration experiments. Bal and Rein [119] argued that 
maintaining a consistent level of complexity for all modeled processes is highly 
important for minimization of uncertainties arising in the parameterization process. 
Besides estimating these properties from the experiments with parameter 
optimization algorithms, an alternate way to access these fundamental properties is 
measuring the individual parameters with separate experimental devices and it was 
performed by a number of researchers [71, 111, 120-124]. The fact that many of the 
newly synthetic polymer fundamental properties are frequently unknown, it prevent 
us from using these models in fire safety applications. Besides, most of these material 
properties measurement methods dissimilated for a wide range of polymeric materials. 
The purpose of this work was to develop a systematic experimental procedure for the 
measurement and validation of the core subset of these properties including mass loss 
kinetics parameters, heat capacities, heats of melting, heats of decomposition 
reactions and heat transfer properties. This procedure is based on milligram-scale and 
25 
bench-scale approaches to isolate specific chemical and/or physical processes in each 
test so that each property can be systematically measured or calculated from the data 
analysis and interpretation. The wide range of scales and conditions in the modeling 
are validated against pyrolysis experiments to ensure that the property values reflect 
the fundamental aspects of material behavior. While inverse modeling is still 
employed for some property evaluations, the resulting optimization problems are 
always well-defined and the optimum values can be obtained in a few iterations. 
To obtain polymer kinetics and thermodynamics at the milligram scale, 
thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) are 
among the most frequently used techniques employed for these types of 
measurements. The main advantage of these techniques is associated with the use of 
small material samples (3-10 mg) and relatively slow and steady heating rates (3-30 
K min-1) [125]. These heating conditions minimize the effects of heat and mass 
transport inside the sample on mass loss (in the case of TGA) and heat flow (in the 
case of DSC), which makes it possible to exclude the transport from data analysis and 
interpretation. In this study, both of these techniques were utilized to determine the 
aforementioned properties. 
TGA experiments performed in an inert atmosphere were used to develop a 
reaction mechanism describing material volatilization upon heating. The mass loss 
data analysis was based on the assumption that a polymer degrades through 
consecutive first-order reactions. The parameters of these reactions were obtained by 
fitting a TGA curve with a numerical model capable of solving kinetic equations for 
an arbitrary user-defined reaction mechanism under linear heating conditions. This 
26 
approach differs significantly from that traditionally employed in the field of thermal 
analysis.  In the traditional approach, as described in the section 2.2.2, solid 
degradation is described by a single n-th order reaction, whose activation energy may 
depend on the degree of conversion [126].  
DSC is used routinely to measure heat capacities and heats of melting of 
polymeric solids [125]. In this dissertation, this technique was extended to anaerobic 
thermal degradation reactions for non-charring and charring polymers. Measurement 
of the heats of degradation is a challenging task because of instrumental baseline 
instabilities caused by volatile products [98] and the fact that both sensible and 
reaction heats contribute to the heat flow as the material’s temperature is raised 
through degradation. Several research groups have attempted to perform these 
measurements with some degree of success [98, 114, 127].  The main distinguishing 
features of the current approach are that it employs a simultaneous thermal analysis 
(STA) instrument calibrated using the melting of organic and inorganic compounds 
(the advantages of this instrument and its calibration procedure are discussed below) 
and a unique DSC data analysis methodology. This methodology utilizes a TGA-
derived kinetic mechanism to generate a sensible heat baseline for the reaction region 
of the DSC curve and yields a complete thermo-kinetic model (including heat 
capacity of the condensed-phase constituents, heat of melting and heats of 
decomposition) that reproduces both TGA and DSC experiments.   
Then our approach is extended to a larger (bench) scale to measure material 
gravimetric and thermal changes during thermal decomposition in an anaerobic 
atmosphere with a capability of analyzing material thermal transport properties. In 
27 
this work, standard cone calorimetry tests [128] (without the part of analyzing 
exhaust gas) were modified to enable inert atmosphere, radiation-driven gasification 
under thoroughly controlled, near-one-dimensional heating conditions similar to those 
realized in a fire propagation apparatus [117] or a NIST gasification device [37]. Heat 
transfer through a solid was monitored in two different methods: placing 
thermocouples and focusing an infrared camera on the bottom surface of a 
horizontally-mounted sample, of which the top surface faced the cone heater. The 
advantage of using the non-contact nature of infrared camera measurement made it 
possible to collect both sample mass and temperature data simultaneously, which 
reduced the number of bench-scale experiments by a factor of two. Spatial resolution 
of the temperature data (collected only using the infrared camera) made it possible to 
assess the validity of the one-dimensional thermal transport assumption always 
invoked during analysis of this type of experiments. Therefore, the thermal transport 
properties of materials can be calculated. These properties, combing with material 
kinetics and thermodynamics obtained from the milligram scale, serve as inputs for 
the parameterized model with simulating one-dimensional pyrolysis. The resulting 
models were employed to predict the gasification burning rate histories at 20-90 kW 
m-2 of external radiant heat flux, which almost cover the most frequently conditions 
that are used in the general room fire modeling. The simulation results are then 
validated against the experimental burning rate histories at various levels of heat 
fluxes. 
This overall parameterization methodology is expected to minimize possible 
compensation errors and extend the scope of the model validity; however as a trade-
28 
off, it requires a notably larger number and broader range of experimental 
measurements with respect to other standalone tests such as NIST gasification and 
FPA tests.  
This main achievement for dissertation is the development of a systematic 
methodology for parameterization of continuum pyrolysis models for polymeric 
material at multi-scale levels. The accurate measurements of material kinetics, 
thermodynamics and thermal transfer properties at wide range of scales and 
conditions ensure that the property values reflect the fundamental aspects of material 
behavior. Validation work was also performed against other numerical modeling 
solvers to guarantee the measurements are not model-specific either. This 
methodology covers the most promising (from the fire safety prospective) and most 
complex class of combustible materials–charring and intumescing polymers and even 
potentially for composites materials in the market.   
29 
Chapter 3  Experimental 
Section 3.1 Materials and sample preparation 
The polymers examined in this study are seven representative non-charring 
materials: poly(oxymethylene) (POM), poly(methyl methacrylate) (PMMA), high-
impact polystyrene (HIPS), polyamide 6,6 (PA 66), polypropylene (PP), poly(lactic 
acid) (PLA), and poly(acrylonitrile butadiene styrene) (ABS) and eight charring 
polymeric materials which produce a significant amount of carbon rich residues 
during their thermal degradation process: poly(methyl methacrylate)-poly(vinyl 
chloride) alloy (Kydex), polymerized diglycidylether of bisphenol A (DGEBA), 
poly(ethylene terephthalate) (PET), poly(paraphenylene terephthalamide) (Kevlar), 
polymerized bisphenol A cyanate ester (BACY), poly(phenylene sulfide) (PPS), 
polyetherimide (PEI) and poly(ether ether ketone) (PEEK). The materials were 
classified as non-charring because the residual mass obtained as a result of heating 
milligram-sized samples from room temperature to 873 K in an anaerobic 
environment was found to be below 10 wt.%. The char yield produced by charring 
polymers anaerobic pyrolysis heated from room temperature to 1223 K varied 
between 11 and 51 wt.%. 
With the exception of PLA, all non-charring polymers were supplied in the 
form of large (approximately 1220610mm), extruded sheets, which were about 6 
mm thick. PLA sheets were 0.7 mm thick. Detailed information on the material 
origins is summarized in Table 3-1. For charring polymers, Kydex, PET, PPS, PEI 
and PEEK were purchased in large, extruded sheets (approximately 
12206106.4mm in size). Kevlar was purchased in the form of woven fabric 
30 
samples (1500.2 mm). DGEBA and BACY were prepared in our laboratory by 
curing manufacturer supplied resins in a square mold (8080 mm). 1-2 wt.% of 
2-ethyl-4-methylimidazole was added to DGEBA resin to promote curing. No curing 
agent was used for BACY. DGEBA and BACY specimens were cured in a 
convection oven. In the case of DGEBA, the oven temperature was increased from 
293 to 393 K in 50 K increments and was held constant for 4 hours after each 
increase. In the case of BACY, the oven temperature was increased from 293 to 523 
K using the same incremental approach. Detailed information on the source of 
purchased materials is provided in Table 3-1. 
Table 3-1 Source of materials analyzed in this study. 
Polymer Manufacturer Trade Name Distributor 
Poly(oxymethylene) (POM) Ensinger Acetal Curbell Plastics,Inc. 
Poly(methyl methacrylate) (PMMA) 
CYRO 
Industries 
Acrylic Evonik Industries 
High Impact Polystyrene (HIPS) 
Spartech 
Plastics 
HIPS 
Professional 
Plastics 
Polyamide 6,6 (PA 66) Quadrant EPP Nylon 101 Modern Plastics 
Polypropylene (PP) 
Compression 
Polymers Corp. 
Protec HPP U.S. Plastic Corp. 
Poly(lactic acid) (PLA) NatureWorks PLA Rejuven8 Plus Spartech 
Poly(acrylonitrile butadiene styrene) 
(ABS) 
Westlake 
Plastics 
Absylux Modern Plastics 
Poly(methyl methacrylate)-poly(vinyl 
chloride) alloy (Kydex) 
Kydex, LLC Kydex® T 
Professional 
Plastics 
Diglycidylether of bisphenol A Sigma 
Bisphenol A 
diglycidyl ether 
Sigma-Aldrich 
31 
Poly(ethylene terephthalate) (PET) Ensinger PET Curbell Plastics 
Poly(paraphenylene terephthalamide) 
(Kevlar) 
DuPont 
Kevlar® Plain 
Weave Fabric 
Fibre Glast 
Developments 
Bisphenol A cyanate ester Lonza 
Primaset Cyanate 
Esters 
Lonza 
Poly(phenylene sulfide) (PPS) Ensinger PPS Curbell Plastics 
Polyetherimide (PEI) GE Plastics Ultem 1000 Curbell Plastics 
Poly(ether ether ketone) (PEEK) Victrex plc PEEK grade 450G Victrex plc 
 
Thermal analysis samples for milligram-scale test were prepared by cutting 
polymer specimens into thin, flat squares, less than 0.5 mm in thickness and 4 to 7 mg 
in mass. Bench-scale samples were prepared by cutting squares (80×80 mm) (the 
thickness and density for different polymers varies, and they were measured using a 
caliper and a balance at the room temperature the details are discussed in the Chapter 
7 and Chapter 8) from the supplied sheets. The sample mass is about 40 to 60 g for a 
single square. These samples were conditioned in a desiccator in the presence of 
Drierite for a minimum of 48 hours prior to testing to minimize their moisture. 
Section 3.2 Milligram-scale testing 
Section 3.2.1 Milligram-scale testing on non-charring polymers 
A Netzsch F3 Jupiter STA was employed in this study. This apparatus 
combines a TGA instrument equipped with 1 µg-resolution microbalance and a heat 
flux DSC implemented using a Netzsch TGA-DSC sample carrier. Stoliarov’s [98] 
previous DSC-based decomposition heat measurements indicated that significant heat 
flow errors may result from a relatively low temperature of the enclosure containing 
32 
sample and reference containers (due to deposition of volatiles on the cold walls and 
consequent changes in the heat transfer characteristics of the enclosure). In the current 
apparatus, which was selected to mitigate this problem, the containers were 
positioned in the middle of a long (26 cm), vertical, uniformly heated furnace (as 
shown in Figure 3.1), which wall temperature exceeded that of the containers 
throughout the heating process. More information on the design of the F3 Jupiter STA 
can be found elsewhere [129]. 
 
Figure 3.1 Sketch of heating furnace and sample carrier. 
An anaerobic environment was created inside the furnace by continuously 
purging it with nitrogen at a rate of 50 cm3 min-1. Most TGA and DSC experiments 
were conducted using the same heating program. A sample was first heated to 313 K 
and maintained at this temperature for 25 min. This period was included to ensure 
that the system is initially in thermal equilibrium and free of oxygen.  Subsequently, 
the sample was heated to 873 K at a heating rate of 10 K min-1. The mass and heat 
33 
flow data were collected only during the second, linear heating phase of the test.  The 
selection of the heating rate was based on a recent theoretical analysis [130] that 
indicated that using 10 K min-1 for <10 mg samples insures a uniform temperature 
inside the sample even when the heat associated with decomposition processes is 
significant. The experiments carried on this heating rate were repeated 7 times and 
averaged prior to analysis (details are explained in the section 3.2.3). Additional TGA 
experiments were performed at 30 K min-1. These experiments were used to evaluate 
how well the kinetic model developed using 10 K min-1 data performs at higher 
heating rates. The high (30 K min-1) heating rate TGA experiments were only 
repeated 3 times (and averaged prior to analysis). 
Each material test was preceded by a baseline test, where empty sample and 
reference containers were subjected to the same heating program. The baseline mass 
(in the case of TGA) or heat flow history (in the case of DSC) was subtracted from 
the corresponding data obtained from the sample test. All TGA and DSC data 
presented below have been baseline corrected. 
While the instrument used in this study is capable of simultaneous TGA and 
DSC, these experiments were conducted separately only for non-charring polymers. It 
was initially assumed that accurate TGA readings require a well-ventilated sample 
container. Therefore, all TGA tests for non-charring polymers were performed using 
open ceramic pans. DSC tests were performed using Platinum-Rhodium pans with 
lids. The lids had small (0.25mm in diameter) orifice for ventilation. This container 
configuration was used to maximize the thermal contact between a degrading sample 
and heat flow sensing thermocouple located underneath the container. Subsequent 
34 
comparison of the mass loss data collected with both configurations showed that the 
presence of a lid had no significant impact on the mass loss. 
Section 3.2.2 Milligram-scale testing on charring polymers 
Same anaerobic environment was created inside the furnace by continuously 
purging it with nitrogen at a rate of 50 cm3 min-1 as stated in non-charring polymer 
milligram-scale testing. TGA and DSC experiments were conducted simultaneously 
using a somewhat different heating program compared to the program used for the 
non-charring polymer. One significant difference of the thermal treatment to the non-
charring polymer is the sample was heated to higher temperature up to 1223 K at the 
same heating rate. Additional TGA experiments were also performed at 30 K min-1.  
All thermal analysis experiments for charring polymers were performed using 
Platinum-Rhodium crucibles with lids. TGA and DSC experiments on PPS were 
conducted only at 10 K min-1 and only 3 times because the gases evolved during the 
decomposition were found to be damaging to the STA’s sample carrier. Additional 
DSC experiments were performed on char residue produced in the polymer thermal 
analysis experiments. These experiments were performed on 3-5 mg samples at 10 K 
min-1 and were repeated 3 times for char produced from each material. The char was 
compacted in the crucible prior to DSC to ensure a good thermal contact with crucible 
bottom. 
Section 3.2.3 Instrument calibration and data collection for milligram-scale 
testing 
The STA apparatus requires two types of calibration: temperature and 
sensitivity. The temperature calibration provides a relation between measured and 
35 
actual sample temperature. The sensitivity calibration provides a conversion between 
the difference in voltage generated by sample and reference thermocouples (P-type 
thermocouples were employed in this study, see Figure 3.1) and sample heat flow. 
For open ceramic pans (used in TGA experiments), temperature calibration was 
performed using known melting points of pure metals including indium, tin, bismuth, 
zinc and aluminum. These melting points span the temperature range between 430 K 
and 933 K. No sensitivity calibration was performed for these sample containers. For 
Platinum-Rhodium pans with lids (used in DSC experiments), temperature and 
sensitivity calibrations were performed using a set of organic and inorganic 
compounds with known melting points and heats of melting. This set included 
biphenyl, benzoic acid, RbNO3, KClO4, CsCl, AgSO4, K2CrO4 and BaCO3. The 
melting points of these compounds span the temperature range between 343 K and 
1081 K. The calibrations were carried out following the STA manual 
recommendations [131, 132]. All calibration materials were supplied by Netzsch. 10 
K min-1 heating rate and 50 cm3 min-1 nitrogen purge flow were used in all calibration 
runs. The temperature and sensitivity calibrations were checked (by collecting data on 
2-3 calibration substances) once a month. The instrument was completely recalibrated 
every six months. 
The rationale behind choosing heat-of-melting-based sensitivity calibration 
was that the heat flow profile produced by the melting processes (a peak in time or 
temperature coordinate) was similar in shape to that of polymer decomposition. It was 
unclear, however, whether such calibration could be used to measure sensible heat 
(associated with heat capacity of a given polymer). To examine the ability of the 
36 
calibrated instrument to measure heat capacity, three DSC tests were performed on a 
disk (6 mm in diameter and 0.25 mm in thickness) of sapphire, which has a well-
known heat capacity temperature dependence [133]. These measurements were 
carried out within 313-1000 K temperature range, where sapphire does not experience 
any physical or chemical transitions. The heat capacity was computed by dividing 
measured heat flow (in W) by sapphire mass (in g) and instantaneous heating rate (in 
K s-1). The instantaneous heating rate was used instead of nominal (or set point) 
because it had a tendency to deviate notably from the set point (10 K min-1) during 
the first 100 K of heating. 
The resulting heat capacities are compared with the literature data [133] in 
Figure 3.2. The individual measurements show notable deviations. However, these 
deviations are not systematic. Averaging these measurements produces a heat 
capacity temperature dependence (also shown in Figure 3.2) that closely follows the 
literature curve (within 350-1000 K temperature range, the difference never exceeds 
8%).  From this analysis, it was concluded that it is possible to measure heat capacity 
using the current approach. However, multiple experiments were needed to obtain 
reliable information on sensible heat flow. Therefore, each material (except for PPS) 
heat flow curve analyzed below was obtained by averaging 7 DSC experiments. The 
same methodology was applied to mass loss data. In addition to improving accuracy, 
multiple experiments provided the data necessary for the calculation of uncertainties 
in the extracted properties.   
37 
 
Figure 3.2  Heat capacity of sapphire. 
Another important question related to calibration is whether the sensitivity 
remains stable in the presence of volatiles produced during decomposition. To 
examine this issue, three sapphire heat capacity measurements were performed in the 
presence of degrading PMMA. Each measurement consisted of two DSC tests. In the 
first test, a sample of PMMA was placed in the sample pan, while a sapphire disk was 
placed in the reference pan. In the second test, PMMA was placed in the sample pan, 
while the reference pan was kept empty. The heat flow obtained in the first test was 
normalized by the initial mass of PMMA and subtracted from the heat flow observed 
in the second test, which was also normalized by PMMA mass. The resulting 
difference was re-normalized by the mass of sapphire and divided by the nominal 
heating rate (10 K min-1) to compute heat capacity. A comparison of the experimental 
results and literature data is shown in Figure 3.3. The heat capacity data obtained 
within PMMA degradation temperature range, 580-720 K, do show significant 
fluctuations. However, these fluctuations appear to be caused by instabilities in the 
38 
heating rate (no instantaneous heating rate normalization was performed for this data). 
On average, the sapphire heat capacity measured in the PMMA decomposition region 
falls within 3% of the literature data, which clearly indicates that the sensitivity 
calibration was not affected by the volatile decomposition products. 
.  
Figure 3.3 Heat capacity of sapphire in the presence of degrading PMMA. 
Section 3.2.4 Scanning Electron Microscopy (SEM) 
Char samples produced in the thermal analysis experiments were further 
examined with a Hitachi S3400 scanning electron microscope. The imaging was 
performed using 3 and 10 kV electrons. The purpose of this exercise was to determine 
whether there exist significant differences in the microscale topology of chars 
produced from different charring polymers. 
Section 3.3 Bench-scale testing 
Section 3.3.1 Measurement of absorption coefficients 
A schematic of the experimental setup employed to estimate polymer 
broadband radiation absorption coefficients is shown in Figure 3.4. The experimental 
39 
procedure was similar to that outlined by Linteris et al. [134]. A slab of Kaowool PM 
with a cylindrical opening was used to collimate the radiation from the cone heater. 
The collimated radiation was sent through a polymer sample, which was milled 
locally down to thin polymer film. The thickness of the film is chosen 2 mm for non-
charring polymers, while 1.5 mm for charring polymers. A water-cooled Schmidt-
Boelter heat flux gauge located below the sample was used to detect the transmitted 
radiation. The film was exposed to about 35 kW m-2 of incident radiant heat. The data 
on transmitted radiation were collected for the first 20 s (for non-charring polymers) 
and 5 s (for charring polymers) after the beginning of exposure (to avoid 
contributions associated with conduction through the sample). Subsequently, the 
polymer sample was quickly removed after about 30 s of exposure and then the exact 
incident radiation was measured. An example of the heat flux measurement for this 
type of experiments is demonstrated in Figure 3.5. 
 
Figure 3.4 Radiation absorption coefficient measurement setup. 
The radiative transport was assumed to be one-dimensional and insensitive to 
the variation in the spectral characteristics of the cone heater with heat flux.  A Beer-
Lambert-law-based expression (as shown in equation 3.1) taking into account 
40 
radiation reflection at the polymer-air interfaces, which was previously utilized by 
Tsilingiris [135], was used to compute the absorption coefficients.  Where l is the 
polymer film thickness, f is reflection loss coefficient, and    is spectral normal 
transmission. Broadband surface reflectivity of all polymers was estimated to be 0.05. 
The reflectivity value was computed from the index of refraction, which shows little 
variation among thermoplastics [134]. Only one transmission measurement for non-
charring polymers and two transmission measurements for each charring materials 
were performed and the results were presented in Chapters 7 and 8. 
  
            
 
                                                                          (3.1) 
 
Figure 3.5 Heat flux result from ABS absorption coefficient measurement experiment. 
Section 3.3.2 Gasification experiments part I 
The goal of this section is aim to measure PMMA sample (80806 mm) back 
surface temperature under gasification experiments using traditional method-
thermocouple. The sample was gasified using controlled radiant heating. These 
41 
experiments were performed in a Govmark CC-1 cone calorimeter [136] equipped 
with the Controlled Atmosphere pyrolysis Apparatus (CAPA) [137] that was newly 
designed in our group. The cone calorimeter radiant heater was used to deliver a 
uniform and steady heat flux to the top surface of a horizontally mounted sample, 
while the calorimeter’s precision balance system monitored sample mass loss. The 
CAPA (Figure 3.6) was used to provide a controlled gaseous environment in the 
immediate vicinity of the sample. The functionality of CAPA and NIST Gasification 
Device is comparable [37] but the size of CAPA is much smaller. As shown in this 
figure, CAPA consists of two concentric square metal ducts connected at the bottom 
and sits on top of the calorimeter’s precision balance. Gas is introduced into the space 
between the ducts from the gas inlets in each of the four sides.  The space above the 
gas inlets between the two ducts is filled with small (4.5 mm diameter) glass beads to 
ensure a uniform gas velocity.  The upper edge of the inner duct is 10 mm below the 
top surface of the sample; the upper edge of the outer duct is 10 mm above the 
surface. The interior volume of the inner duct and sample holder each has a square 
cross section with sides measured 120 mm and 115 mm, respectively. The gap 
between these two is blocked by a lip installed on the sample holder (see Figure 3.6).  
The lip is located 1 mm above the upper edge of the inner duct, ensuring that the 
sample holder is suspended on the balance and does not make contact with the CAPA 
ducts to prevent mass measurement interference. 
PMMA sample was mounted on a 25.4 mm thick layer of Kaowool PM 
thermal insulation, which has well-known thermophysical properties [138]. A 0.03 
mm thick layer of aluminum foil was used to separate the bottom of the sample from 
42 
the insulation. The sample perimeter was wrapped with a 0.1 mm thick paper tape and 
thermally insulated with a 5 mm wide strip of Kaowool PM. This sample mounting 
procedure was found to maximize horizontal uniformity of the heating process while 
preserving the sample shape throughout gasification. 
 
Figure 3.6. Schematic of the CAPA. 
Mass loss rate measurements were repeated 3 times for each (20, 40, and 60 
kW m-2) radiant heat flux setting. In separate experiments, back surface temperature 
histories were measured three times each with samples exposed to 20 and 60 kW m-2 
of radiant heat flux. Temperature measured at heat flux of 20 kW m-2 was used as a 
calibration target for PMMA thermal conductivity and temperature measured at heat 
flux of 60 kW m-2 was a reference for model validation. The temperature 
measurements were taken at three positions: at the sample’s center and 28 mm 
diagonally inwards from two opposite corners.  These measurements were performed 
using 0.25 mm diameter shielded type K thermocouples, which were placed beneath 
the aluminum foil and bonded to the foil with the Omega high temperature cement. 
Please note that, for this form of setup, only PMMA samples were tested.  
43 
In the experiments, the CAPA was operated at 225 L min-1 of nitrogen 
(measured at the standard ambient pressure of 100 kPa and temperature of 298 K) 
using ALICAT MCR series mass flow controller. The cone calorimeter exhaust flow 
rate was maintained at 1440 L min-1. Under these conditions, oxygen concentration, 
measured 1 mm above the top sample surface using a Servomex 4100 gas analyzer, 
was found to hold steady at 2.2 ± 0.4 vol.%. Thus an effectively anaerobic 
environment was used in both thermal analysis and gasification experiments to 
simulate the pyrolysis conditions experienced by PMMA covered by a continuous 
diffusion flame. 
The top surface background gas temperature was measured as an average of 
temperatures at four locations that near the level of sample top surface in the middle 
between the ducts by using a thin (0.13 mm diameter) type K thermocouple. The 
background gas temperature was found to be changed linearly from 330 to 390 K as 
the radiant heat flux under the cone heater increased from 20 to 80 kW m-2, as shown 
in Figure 3.7 (x is the heat flux value in kW m-2).  
 
Figure 3.7  Top surface background temperature at different level of heat fluxes under 
cone heater.  
44 
The radiant heat flux was set using a water-cooled Schmidt-Boelter heat flux 
gauge, which was positioned at a location corresponding to the geometric center of 
the top sample surface. The variation of the heat flux across the surface was examined 
in an earlier study [139] and found to be within 3% of the center set point for the 
overwhelming majority of the surface area with the exception of the corners, which 
were within 10%. To quantify convective heat losses from the sample top surface in 
the CAPA, a 3 mm thick blackened (emissivity ≈ 0.95) copper plate of same sample 
dimensions was placed into CAPA instead of a sample. The plate was equipped with 
two imbedded type K thermocouples (0.25 mm in diameter). Insulation 
(808025.4mm) was placed underneath the copper plate to provide same boundary 
conditions that applied to the PMMA gasification tests. Temperature measurements 
of the copper plate were conducted at incident radiant heat flux of 40 kW m-2 and the  
mean of the two thermocouples’ readings is shown in Figure 3.8. A one dimensional 
pyrolysis model named ThermaKin (details can be found in Chapter 4) was utilized 
for reverse modeling to determine the convection coefficient, which was the only 
unclear parameter in this simulation. The convection coefficient on the top boundary 
was varied until the temperature of copper in the simulation result fits the 
experimental result. As the results shown in Figure 3.8, it was found that by setting a 
convection coefficient of 5 W m-2 K-1 the model fits the experimental results well. It 
was expected that the copper temperature model prediction is slight above 
experimental results. Because the copper top surface black paint was observed 
starting decomposing at high temperature (> 600 K) and then the copper plate surface 
emissivity is likely below 0.95, while this value keeps constant in the simulation. 
45 
 
Figure 3.8 Copper plate temperature measurements in CAPA and model simulation at 
external heat flux of 40 kW m-2. 
Section 3.3.3 Gasification experiments part II 
The CAPA sample holder, which detailed description is given in the earlier 
section 3.3.2, was modified to make it possible to focus an infrared camera on the 
bottom sample surface. A schematic of the modified CAPA is shown in Figure 3.9. 
The sample was placed on a 0.03 mm thick sheet of aluminum foil supported by a 0.8 
mm thick aluminum mesh. The aluminum foil and mesh were coated with a high 
emissivity (≈0.95) paint.  
A gold-coated, flat mirror (0.97 reflectivity in 0.8-10 m range) was mounted 
about 10 cm below the sample to provide optical access for an infrared camera. The 
camera, FLIR E40, was mounted outside of the CAPA and focused on the aluminum 
foil supporting the sample bottom. The temperature readings were taken through the 
spacing in the aluminum mesh, which covered about 20% of the bottom sample 
surface. The camera was set for the paint emissivity. This novel solution to measure 
46 
the sample bottom temperature is aim to provide non-contact, spatially-resolved 
thermometry. The advantages of this solution combined with CAPA in polymer 
gasification experiments are the followings. As mentioned in the section 3.3.2, 
bottom temperature using thermocouples and mass loss rate are taken separately 
because of the sensitivity of the balance is greatly affectedly by the thermocouple 
wires. In the modified setup, this issue is solved because of using non-contact 
measurement by IR camera which reduced the number of bench-scale experiments by 
a factor two. In the meanwhile, since material gravimetric and thermal changes during 
gasification were recorded simultaneously, this type of experimental setup provides 
more reliable data because two types of measurements (temperature and mass) are 
obtained from exactly same experiments. 
 
Figure 3.9 Schematic of modified controlled atmosphere pyrolysis apparatus. 
To ensure that the camera provides accurate measurements, two steps of 
validation experiments were conducted. Firstly, a sample was replaced with a 3.0 mm 
thick copper plate coated with the high emissivity paint and equipped with 2 type K 
thermocouple probes (0.25 mm in diameter), which were embedded into the plate. 
47 
The plate was placed on the aluminum mesh and subjected to 40 kW m-2 of radiant 
heat flux. As shown in Figure 3.10 , the IR camera temperatures were found to be 
within 5 K of those measured by the thermocouples up to the point where the plate 
temperature rose to 650 K. Above 650 K, a lager systematic difference of about 10 K 
was observed. This difference was attributed to a reduction in the emissivity of the 
paint (due to its partial degradation). In the second step, this experiment was repeated 
at 30 kW m-2 and the copper plate was replaced by a HIPS sample (80806.0 mm) 
which bottom surface was wrapped with the blackened aluminum foil. Two 0.25 mm 
diameter shielded type K thermocouples (0.13 mm in diameter), which were placed 
between the aluminum foil and HIPS bottom surface (at the sample’s center and 28 
mm diagonally inwards from one arbitrary corner) bonded to the foil with the Omega 
high temperature cement. The comparison of temperature measurements results using 
these two different methods shown on Figure 3.11 suggests that this experimental 
setup produces essentially identical results to the method using thermocouples. 
 
Figure 3.10 Comparison of temperature measurements using thermocouples and IR 
camera for blackened copper plate at radiative heat flux of 40kW m-2. 
48 
 
Figure 3.11 Comparison of temperature measurements using thermocouples and IR 
camera for HIPS with blackened aluminum foil on its bottom at radiative heat flux of 
30kW m-2. 
As described in the section 3.3.2, convective heat losses from the top sample 
surface corresponding to the current flow conditions were determined using an 
inverse modeling of copper plate heating experiments. These losses were found to be 
well represented by a convection coefficient of 5 W m-2 K-1 and background gas 
temperature that changed linearly from 330 to 390 K as the radiant heat flux increased 
from 20 to 80 kW m-2. Convective loss from the bottom surface was characterized 
using a similar procedure as described in the section 3.3.2. One major change to the 
previous procedure is that, instead of using thermocouple to measure the copper plate 
temperature, IR camera was utilized to provide non-contact measurements. Both top 
and bottom surfaces of the copper plate were painted black with an emissivity of 0.95. 
Background temperature for the sample bottom surface was measured by a  type K 
thermocouple(0.13 mm in diameter) at four locations near the bottom part of the 
CAPA inner duct wall and the mean value was found to be kept constant at 310 K at 
49 
various levels of heat fluxes. This background temperature is considered to provide 
approximate additional 0.5 kW m-2 radiation toward the bottom surface radiation at 
background temperature of 310 K. Provided the top surface convective loss is well 
defined in the section 3.3.2, the only unknown parameter is the bottom surface 
convection coefficient. The copper temperature measurements were performed under 
20, 40 and 60 kW m-2 of incident radiant heat flux and the experimental and modeling 
results were shown in Figure 3.12. In all the simulations shown in Figure 3.12, the 
convective loss was found to be well represented by a convection coefficient of 4 W 
m-2 K-1. 
 
Figure 3.12 Copper plate bottom surface temperature measurements in CAPA using 
IR camera and model prediction at external heat flux of 20, 40 and 60 kW m-2. 
7 out of 15 non-charring and charring polymers were studied at this bench-
level experiment. They are PMMA, POM, HIPS, ABS, PET, Kydex and PEI. Only 
for Kydex and PEI, since no dripping and melting occur, blackened aluminum foil 
was not used. However, the back of the samples were paint black (emissivity ≈0.95) 
50 
to obtain correct temperature measurements from IR camera. Most polymer 
gasification experiments were performed either at radiant heat fluxes of 20, 40, and 
60 kW m-2 or 30, 50 and 70 kW m-2 (for PET, radiant heat fluxes were set to 50 and 
70 kW m-2 ; for PEI, radiant heat fluxes were set to 50, 70 and 90 kW m-2). Each 
experiment was repeated 3 times to accumulate statistics. 
As mentioned earlier in the Chapter 1, besides thermal decomposition, some 
charring solid polymers experience morphological changes including formation of 
residue layer (char), bubbles and fissures and melt flow that affect the thermal 
transport during polymer burning. Sometimes, the charred layer generated during 
thermal decomposition formed into mushroom-like intumescent structure. This 
intumescent structure was only observed obviously for Kydex and PEI in this study 
which needs analyzing specially. A video camera that intends to record the 
morphological visible change during the polymer gasification through a 6 mm thick 
quartz plate is placed at one side of the CAPA. The overall thicknesses of ABS, PET, 
Kydex and PEI samples at 50 kW m-2 were measured from the video data by 
comparing an inert reference. The overall thicknesses for those polymers were 
determined from the top surface maximum level to their bottom.  
For additional information, the incident radiative heat fluxes at various level 
of locations above the sample top surface were measured using a water-cooled 
Schmidt-Boelter heat flux gauge. The heat fluxes at the locations where sample top 
surface locates in the CAPA were initially set from 30 to 90 kW m-2, and then the 
heat flux gauge was used to measure the heat flux at the elevated levels to resemble 
the phenomenon that the polymers’ (such as Kydex and PEI) top surfaces were 
51 
observed swelling and expanding during gasification experiments. Five locations 
were randomly selected to cover the entire area size of 8080 mm in each horizontal 
level. The mean value (dot) from this measurement against the distance (height) from 
the elevated location to the bottom of the sample surface is plotted in Figure 3.13. In 
this figure, linear fits (lines) for all conditions are also provided. The overall thickness 
changes of the polymers were recorded in time and the heat flux changes on top of the 
sample surface in time could be estimated by using the results in Figure 3.13. 
 
Figure 3.13 Heat flux at various level of locations. 
  
52 
Chapter 4 : Modeling 
This chapter aims to provide a brief introduction for a flexible computational 
numerical solver named ThermaKin which is utilized in this study for the data 
analysis, interpretation and validation. ThermaKin computes the transient rate of 
gaseous fuel production from a pyrolyzing solid subjected to external (convective 
and/or radiative) heat. ThermaKin is capable to handle one- or two- dimensional 
object but in this study, only one one-dimensional mode was used. In this model, 
materials or computational objects are physically defined as a homogenous object or 
composites which consisting of layers of varying thickness. The material of the object 
is represented by a mixture of components, which may interact chemically and 
physically. The components are assigned individual temperature-dependent properties 
and categorized as solids or gases. The reaction mechanism in ThermaKin can be 
defined as in parallel or series of up to 30 zeroth to second order reactions. The model 
framework and model setup are also explained in this chapter. The detail description 
of ThermaKin can be found in FAA technical note [110]. ThermaKin has been 
validated by a number of researchers at various levels of scales in the last few years 
including myself  [39, 71, 77, 79, 107, 109, 111, 140, 141]. 
Section 4.1 ThermaKin framework 
In this study, ThermaKin (thermally thin mode) was employed to analyze 
TGA and DSC experiments and obtain a parametric description of the kinetics and 
thermodynamics of polymer degradation. Besides, ThermaKin (thermally thick mode) 
was also used to validate the final parameterized model against the gasification 
experiments. The key governing equations are summarized as follows: 
53 
1 0
1xNrj jj
i i j
i
Jr dxt x x t
   
             
                                                               (4.1)
1 1 1 0
1gN xN Nr ex rr
j j i i g g
j i g
T q I I T Tc h r c J c dxt x x x x x t
    
                 
               (4.2)
exp ii i k lEr A RT  
    
                                                                                             (4.3)
 /g g
g gJ x
     
                                                                                                (4.4)
Tq k x
  
                                                                                                                 (4.5) 
1
N
ex
ex j j
j
I Ix  
   
                                                                                                       (4.6)
4
0
rr ex
ex
I T I
x I x
  
                                                                                                           (4.7) 
Equation 4.1 is component j mass conservation statement formulated in terms 
of this component’s concentration, j. This statement accounts for component 
consumption/production in chemical reactions, the rate of which is defined by 
Equation 4.3, gas flow within the solid, the flux of which is defined by Equation 4.4 
(only gaseous components are considered to be mobile), and mass transfer associated 
with contraction/expansion of the material object (the last term in Equation 4.1).  
Equation 4.2 is the energy balance formulated in terms of temperature, T. This 
balance includes heat produced in chemical reactions, heat transfer due to conduction, 
the flux of which is given by Equation 4.5, radiative heat from an external source, the 
absorption of which is defined by Equation 4.6, re-radiation of energy to the 
environment defined by Equation 4.7, and convection associated with gaseous 
54 
component flow (the fifth right-hand-side term in Equation 4.2) and overall material 
expansion/contraction (the last term in Equation 4.2). 
The symbols in Equations 4.1-4.7 are defined as follows. t is time; is a 
stoichiometric coefficient, which is negative when the corresponding component is a 
reactant and positive when it is a product; x is the Cartesian coordinate.  and c are 
density and heat capacity. h is the heat of reaction; A and E are the Arrhenius 
parameters; and R is the molar gas constant. , k and  are gas transfer, thermal 
conductivity, and radiation absorption coefficients.  is the Stefan-Boltzmann 
constant; and 0exI  is the external radiation incident onto the object boundary. Properties 
without a subscript indicate the property of mixture (rather than that of an individual 
component). The density of mixture is defined as one over the sum of component 
mass fractions divided by the corresponding component densities. The volumetric 
contribution of gaseous components can be scaled by a user defined factor related to 
the local composition. A detailed description of ThermaKin can be found elsewhere 
[64, 110]  
Section 4.2 Milligram-scale modeling 
To model TGA and DSC experiments, one boundary of the one-dimensional 
object (representing a sample) was prescribed as external temperature history 
mimicking the experimental temperature program. The heat flux into the object was 
defined by the product of the convection coefficient and the difference between 
external and object surface temperatures. The value of the convection coefficient was 
set sufficiently high (1105 W m-2 K-1) for the object surface to follow the external 
55 
temperature closely (within  0.1 K). The other boundary was defined to be 
impenetrable to heat flow. All polymers and its condensed-phase decomposition 
products were assumed to have the same density of 1 g cm-3 and thermal conductivity 
of 0.3 W m-1 K-1. This setup was used only in the milligram scale modeling to allow 
ThermaKin calculating the physical and chemical equations functionally (with no 
strange outputs) and minimize the temperature gradient inside the condensed phase 
object. The initial thickness of the object was selected to be 0.01 mm (thermally thin 
mode). This thickness selection insured that, throughout the heating process, the 
object temperature was uniform and defined by the external temperature program. 
Gaseous decomposition products were specified to leave the condensed phase upon 
formation. In essence, this model was set up to represent idealized TGA and DSC 
experiments where heat and mass transport were infinitely fast. 
For simplicity, all considered reaction mechanisms were limited to a series of 
consecutive first order reactions (the concentration of the second, l’s, component in 
Equation 4.3 was always set to unity). All calculations for milligram-scale were 
performed using 0.001 mm element size and 0.005 s time step. Increasing or reducing 
these integration parameters by a factor of 2 did not produce significant changes in 
the results. 
Section 4.3 Bench-scale modeling  
The models of bench-scale tests included transient heat transfer inside the 
material. Heat was transferred to the material with a radiation boundary condition set 
to the external heat flux of the cone calorimeter tests. The gas transfer coefficient λ 
was set sufficiently high, 2× 10-5 m2 s-1, for all material components and all 
56 
simulations to ensure that the fluxes of gases out of a material object were always 
equal to the rates of their production inside the object. This value corresponds to a 
reasonable upper bound, the average diffusivities of CO2 and H2O into air at 25°C 
[142]. In other words, the mass transport was assumed to be infinite fast and the 
gaseous decomposition products were specified to leave the condensed phase upon 
formation. All calculations on bench-scale were performed using 0.025 mm spatial 
discretization and 0.005 s time step. It was also examined that increasing or 
decreasing these integration parameters by a factor of 2 did not produce any 
significant changes in the results of the simulations indicating convergence of the 
numerical solutions. 
Literature data [143] indicate that the densities of the thermoplastics have a 
weak temperature dependence. Densities and emissivities of all condensed-phase 
components (include intermediates and char) are assumed to be temperature-
independent. For all the materials, those condensed-phase components properties 
were assumed to be equal to the corresponding polymer properties that measured at 
room temperature except for the intermediate components of PET, Kydex and PEI, 
residue of ABS, PET, Kydex and PEI. PET intermediate density is assumed to be the 
mean density value of the virgin material and its char residue. For Kydex and PEI, 
which produce significant amount of residues, their intermediate components 
densities for those two polymers are assigned to be equal to the corresponding 
polymer residues’ densities. The densities calculation for those residues was 
explained in Chapter 8. Emissivity for those 4 polymers residues is estimated as 0.86, 
which is the value of the emissivity of graphite in the same temperature range when 
57 
char is formed [144], based on apparent high carbon content of degraded residues.  
All other condensed-phase components are assigned value of 0.95 from a recent work 
[134] that shows the little variation of reflectivity were found among thermoplastics. 
The reflectivity value was computed from the index of refraction [134] and assigned 
value of 0.05 for all the polymers in this dissertation for simplify. 
Absorption coefficient (assumed temperature-independent also in m-1) for of 
all condensed-phase components are assumed to be the same as it was measured in 
the experiment ( section 3.3.1) to the corresponding virgin polymer properties except 
for the PEI and residue of HIPS, ABS , PET and Kydex. All the condensed-phase 
components in PEI pyrolysis were assumed to be optical opaque and non-transparent 
because from the experimental observation, PEI top blackened due to chemical 
decomposition and it varies by radiation intensity. For HIPS’s residue, it is considered 
optical opaque too and absorption coefficient is defined infinitely high. For the other 
polymers that also produce char during bench-scale gasification experiments such as 
ABS, PET, Kydex and PEI, their char absorption coefficients are optimized with the 
char thermal conductivity during the inverse modeling process and summarized in 
Chapter 8. In general, less information on char absorption can be found, however, 
from the visual observation (details in Chapter 8), char is a semitransparent black 
pours object within absorption coefficient assumed to be in a range of 2500 to 10000 
m-1 because of following reasons: for a normal semitransparent polymeric material, 
its absorption coefficient is usually around 2500 m-1. If the value of absorption 
coefficient for an object is near 10000 m-1, it is considered to be purely non-
transparent. All these coefficients are expected to carry significant uncertainty (at 
58 
least 30%) and are dependent on the thickness of a sample used in the measurement 
[134]. However, as long as the measured values indicate that most of the radiation is 
absorbed within a relatively small (1 mm) thickness, as is the case here, the impact 
of these uncertainties on the overall heat transfer is negligible.  
The heat capacity of all gaseous decomposition products was assumed to be 
equal to 1.8 kJ kg-1 K-1, which was the mean heat capacity of a series of C1-C8 
hydrocarbons at 400-500 K [145]. The value of heat capacity had a minor impact on 
the simulation results because of the fast transport assumption implemented in the 
model. 
Section 4.3.1 Modeling for gasification experiments part I 
This part of experiment was simulated in transient heat transfer through 
PMMA samples with object dimensions defined as per Figure 4.1 and external 
boundary conditions matching those observed experimentally as discussed in section 
3.3.2.  
 
Figure 4.1 Schematic of virgin polymer sample defined in the model of bench-scale 
experiments when insulation is present. 
59 
The thermophysical properties for Kaowool and aluminum foil are well 
reported [146, 147] and summarized in Chapter 7.   
Section 4.3.2 Gasification experiments part II 
As explained in the section 3.3.3, gasification experiments part II has 
employed the IR camera to measure the sample bottom temperature instead of using 
thermocouples. Here the object schematic diagram dimensions and heat transfer used 
in the modeling is different from that used in the gasification experiments part I and is  
shown in Figure 4.2. The external top and bottom boundary conditions are set equal 
to which have been characterized in the section 3.3.3. 
 
Figure 4.2 Schematic of virgin polymer sample defined in the model of bench-scale 
experiments part II. 
  
60 
Chapter 5 : Results- kinetics and thermodynamics for non-
charring polymers 
Section 5.1 TGA of POM 
The results of 10 K min-1 TGA experiments performed on POM are shown in 
Figure 5.1. In this figure, sample mass (m) and mass loss rate (MLR) normalized by 
the initial mass (m0) are plotted with respect to sample temperature. The MLR curve 
contains two major peaks indicating that at least two reactions, 
 POM     1 POM_int;     POM_Res1    2 POM_char                           (5.1) 
are required to capture this polymer’s decomposition behavior. POM_int and 
POM_char denote condensed-phase decomposition products. Gas-phase products are 
not shown because, as stated in Chapter 4, they are assumed to leave the condensed 
phase and sample container instantaneously. Note that these reactions describe a 
semi-global decomposition mechanism formulated to capture key features of the 
polymer mass loss dynamics. Each reaction corresponds to tens or, perhaps, hundreds 
of elementary chemical processes occurring in the corresponding temperature range. 
 
Figure 5.1 TGA of POM at 10 K min-1. 
61 
The kinetic parameters describing these reactions were obtained as follows. 
The values of stoichiometric coefficients (or condensed-phase product yields) were 
determined directly from the TGA data. 1 was set to m/m0 at the temperature of the 
MLR minimum located between the two peaks. 2 was set to m/(1*m0) at the end of 
the mass loss process (at T  750 K). An initial guess for the Arrhenius parameters of 
each reaction was computed using an approximate solution for the first order 
decomposition under linear heating conditions [148]: 
2 MLR
(1 )
max
max
init
eRT
m
E
dT
dt



                                                                                                 (5.2)
MLR maxERTmax
init
eA em
                                                                                                                          (5.3) 
Here, the subscript max designates the values taken at the maximum of the 
corresponding MLR peak. minit is the initial reactant mass (for the first reaction, minit = 
m0; for the second reaction, minit = 1m0).  e is the base of the natural logarithm. 
Subsequent refinement of the Arrhenius parameters was performed using 
ThermaKin. A and E of each reaction were changed in small increments; the results of 
the simulations were compared with the experimental TGA curves. The changes that 
lead to an improvement in the quality of the agreement were retained. The fitting 
process continued until the coefficient of determination of the model for the 
experimental MLR exceeded 0.9 (note this valued is different for charring polymers; 
details can be found in Chapter 6). Desired changes in the temperature or height of 
62 
each MLR peak were accomplished by augmenting the corresponding Arrhenius 
parameters in accordance with the rules summarized in Table 5-1.  
Table 5-1 Rules used to guide TGA curve fitting. 
Desired change in MLR peak Procedure 
Shift peak to higher 
temperature 
Increase Tmax and re-compute A and E using Equations 5.2 
and 5.3 and mass, MLR and heating rate information from 
the corresponding experiment  
Shift peak to lower 
temperature 
Decrease Tmax and re-compute A and E using Equations 5.2 
and 5.3 and mass, MLR and heating rate information from 
the corresponding experiment 
Increase peak height  
Increase E and re-compute A using Equation 5.3 and mass 
and MLR information from the corresponding experiment 
Decrease peak height 
Decrease E and re-compute A using Equation 5.3 and mass 
and MLR information from the corresponding experiment 
The results of this process are shown in Figure 5.2. The optimized kinetic 
parameters are given in Table 5-2. The model captures both POM mass and MLR 
behaviors accurately. To assess uncertainties in the fitted Arrhenius parameters, the 
simulations were compared with the TGA data obtained from individual experiments 
(Figure 5.1 and Figure 5.2 display only the average of seven experimental runs to 
avoid congestion). The Arrhenius parameters were varied, one at a time. The 
maximum variation in each parameter that corresponded to a shift in the simulation 
results that was still within the scatter of the experimental data was used to define this 
parameter’s uncertainty. The computed uncertainty values are listed in Table 5-2.  
63 
 
Figure 5.2 Experimental and simulated TGA of POM at 10 K min-1. 
Table 5-2 Kinetic parameters describing decomposition reactions for POM. 
Polymer 
 
A1 
(s-1) 
E1 
(kJ mol-1) 
1 
 
A2 
(s-1) 
E2 
(kJ mol-1) 
2 
 
POM 3.841014 ± 50% 200 ± 5% 0.400 4.761044 ± 20% 590 ± 2% 0.018 
As a final test, the parameterized kinetic models’ ability to reproduce 
experimental data at a higher heating rate was examined. A comparison of 30 K min-1 
experiments with a simulation (performed at the same heating rate) is shown in 
Figure 5.3. The agreement is reasonable, although not perfect. There is a clear shift 
toward higher temperature in the experimental data. Deviations of similar nature were 
observed for all non-charring polymers analyzed in this work (these results are 
discussed in the section 5.3). However, POM’s 30 K min-1 model and experiment 
disagreement was found to be by far the largest. This disagreement was attributed to 
inability of the sample to keep up with the set heating rate during the experiments. 
This inability is most pronounced in the case of POM because, as shown below, this 
polymer was found to have the highest heat of endothermic decomposition (see 
details in the section 5.4). A recent theoretical analysis [130] indicates that a 
64 
temperature gradient within a TGA sample caused by fast heating manifests itself as a 
high temperature shift of the MLR peak and that the magnitude of this shift increases 
with increasing decomposition endothermicity. 
 
Figure 5.3 Experimental and simulated TGA of POM at 30 K min-1. 
Section 5.2 DSC of POM 
Figure 5.4 shows the result of DSC experiments performed on POM. The heat 
flow normalized by the initial mass is plotted as a function of sample temperature. 
There are three distinct peaks in this heat flow curve. The lowest temperature peak, at 
about 455 K, is not accompanied by mass loss (according to the TGA data in Figure 
5.1) and is assumed to correspond to melting process. The positions of the other two 
peaks approximately match the mass loss peaks and, therefore, are associated with the 
decomposition reactions. 
65 
 
Figure 5.4 DSC of POM at 10 K min-1.    
At the first stage of analysis, the DSC curve was normalized by instantaneous 
heating rate. The parts of this curve that do not contain melting or decomposition 
peaks were fit with straight lines. The results of this process are shown in Figure 5.5. 
These linear temperature dependencies were associated with the heat capacities of 
solid POM (designated as POM) and molten POM (designated as POM_melt). These 
heat capacities are reported in Table 5-3. The amount of POM_char produced during 
the decomposition was too small (< 1% of the initial mass) to resolve its heat capacity. 
Therefore, it was assumed to be equal to 1 J g-1 K-1 (note that, due to a small yield, 
this assumption has little impact on the decomposition thermodynamics). The heat 
capacity POM_int also could not be resolved because of the overlap between two 
reaction peaks. Therefore, POM_int heat capacity was assumed to be equal to that of 
POM_melt. The uncertainties in the heat capacities reported in Table 5-3 were 
obtained from individual heat flow curves (only the average of seven experiments is 
66 
shown in Figure 5.5) by calculating two standard deviations of the mean at several 
temperatures within the fitted temperature range and averaging these uncertainty 
values. 
 
Figure 5.5 DSC of POM normalized by instantaneous heating rate.  Linear fits 
represent heat capacities of the condensed phase at various stages of heating. 
Table 5-3 Heat capacities of material components for POM. 
Component 
c 
(J g-1 K-1) 
POM (-1.86+0.0099T ) ± 14% 
POM_melt 
(1.65+0.0012T ) ± 40% 
At the second stage of analysis, the heat capacities were used to compute a 
sensible heat flow baseline. This baseline (Hbase, measured in W g
-1) was calculated as 
follows: 
10
1( ) ( ) ( )
N
base j j
j
dTH t c T m tm dt 
                                                                                 (5.4) 
67 
Here the temperature derivative versus time is the instantaneous heating rate. 
The summation is performed over all condensed-phase components (POM, 
POM_melt, POM_int, and POM_char). The baseline is resolved in terms of time. The 
temperature history comes directly from the experiments (average of seven 
experimental temperature histories was used in the calculations). Component masses 
were computed by assuming that POM converts to POM_melt instantaneously at the 
melting temperature, which was assumed to correspond to the maximum of the 
melting peak. In the decomposition region, component masses were resolved using 
the results of numerical modeling of TGA experiments (described in the section 5.1). 
 
Figure 5.6 Determination of melting and decomposition contributions to the POM 
DSC signal. 
This baseline is plotted together with the total DSC heat flow in Figure 5.6. 
Note that both data are presented as a function of time. Subtraction of this baseline 
from the total heat flow and subsequent integration of the difference in the melting 
region produced the value for the heat of melting (hm) which is 192 ± 6% J g
-1. The 
68 
difference integration in the decomposition region produced the value of the total heat 
of decomposition, h1+1*h2 (the h value subscripts indicate references to the 
corresponding reactions, which kinetic parameters are reported in Table 5-2). This 
integration process is illustrated in Figure 5.6. The heat values for h1 and h2 were 
calculated to be 1192 ± 5% and 1352 ± 5% J g-1 respectively. Only in the cases of 
POM and Kydex (details can be found in Chapter 6), the heats of individual reactions 
(h1 and h2) were obtained directly from the integration of experimental heat flow. For 
other polymers analyzed in this study, the reaction heat flow peaks were not clearly 
separated in time. Therefore, the last stage of analysis was also utilized to distribute 
the total heat of decomposition (h1+1*h2) obtained from the integration among 
individual reactions through fitting of the heat flow history in the reaction region.  
These uncertainties for values of hm , h1 and h2 were calculated as two 
standard deviations of the mean by performing this procedure for individual 
experiments (using the same average baseline) produced a set of hm and total 
decomposition heats that were used to compute uncertainties.  
It should be noted that what is referred to here as the heat of decomposition 
reaction is actually a sum of heats of two processes: chemical decomposition process, 
which involves braking and formation of covalent chemical bonds and vaporization 
of the decomposition products, which involves braking of the Van der Waals bonds. 
Both of these processes change the system’s enthalpy and cannot be separated within 
the framework of the current experiments. 
69 
At the last stage of analysis, the heat capacities and heats of melting and 
decomposition were added to the ThermaKin model of POM. This model was used to 
simulate DSC. The reaction mechanism was augmented to include melting: 
 POM  POM_melt;  POM_melt    1 POM_int;  POM_int    2 POM_char  (5.5) 
The heat of reaction representing melting was set to be equal to hm. The 
reaction rate was defined by activation energy, Em, and pre-exponential factor, Am.  
The values of Em (382 kJ mol
-1) and Am (2.710
42 s-1) were fitted to reproduce the 
shape of the melting peak observed in the experiments. The heat flow profile 
matching was also used to distribute the total heat of decomposition (h1+1*h2) 
among the two reactions. 
 
Figure 5.7 Experimental and simulated DSC of POM at 10 K min-1. 
70 
 
Figure 5.8 Time integral of 10 K min-1 DSC of POM. 
A comparison of the resulting POM model with the experimental DSC heat 
flow history is shown in Figure 5.7. The agreement is good; however, it is not perfect. 
The small differences are primarily due to the fact that the instant experimental 
heating rate deviates somewhat from its set value (while in the simulation, no 
deviations take place). A comparison of the experimental and simulated integral DSC 
heat flows shown in Figure 5.8 further illustrates how well the model reproduces the 
experiment. At the end of the decomposition process (t  2250 s), the experimental 
and simulated integral heats converge within 3% of each other. 
Section 5.3 TGA of PMMA, HIPS, PA 66, PP, PLA and ABS 
The experimental and simulated TGA results obtained for the rest of the 
studied materials are shown in Figure 5.9 and Figure 5.10. For each polymer, the 
normalized mass (left plot) and MLR (right plot) measured at 10 and 30 K min-1 are 
compared with the corresponding modeling outcomes. The model parameters were 
71 
derived from 10 K min-1 experiments by following the procedure described in the 
section 5.1. These parameters for all non-charring polymers are summarized in Table 
5-4. PLA was the only material mentioned in this chapter, in addition to POM, that 
required two reactions to reproduce experimental mass loss. Decomposition of the 
rest of the polymers was represented by a single reaction. All models capture 10 K 
min-1 experiments accurately. These models also reproduce 30 K min-1 data. The 
worst agreement is observed for PLA at 30 K min-1. Similar to POM (see discussion 
in the section 5.1), this disagreement was attributed to inability of the sample to keep 
up with the set heating rate during experiments. 
Table 5-4 Kinetic parameters describing decomposition reactions and melting 
(Em and Am) for all non-charring polymers. 
Polymer 
 
A1 
(s-1) 
E1 
(kJ mol-1) 
1 
 
A2 
(s-1) 
E2 
(kJ mol-1) 
2 
 
Am 
(s-1) 
Em 
(kJ mol-1) 
POM 3.841014 ± 50% 200 ± 5% 0.400 4.761044 ± 20% 590 ± 2% 0.018 2.71042 382 
PMMA 8.601012 ± 40% 188 ± 2% 0.015 N/A N/A N/A N/A N/A 
HIPS 1.701020 ± 40% 301 ± 5% 0.043 N/A N/A N/A N/A N/A 
PA 66 3.861012 ± 50% 200 ± 2% 0.026 N/A N/A N/A 2.01039 420 
PP 9.601022 ± 50% 350 ± 2% 0.018 N/A N/A N/A 2.51035 308 
PLA 1.681018 ± 50% 245 ± 3% 0.100 4.58106 ± 30% 126 ± 5% 0.400 6.01040 355 
ABS 1.001014 ± 40% 219 ± 2% 0.023 N/A N/A N/A N/A N/A 
 
72 
 
Figure 5.9 Experimental and simulated TGA of PMMA, HIPS and PA 66 at 10 K 
min-1 and 30 K min-1. 
73 
 
Figure 5.10 Experimental and simulated TGA of PP, PLA and ABS at 10 K min-1 and 
30 K min-1. 
74 
Section 5.4 DSC of PMMA, HIPS, PA 66, PP, PLA and ABS 
The experimental and simulated DSC results obtained for the rest of the 
studied materials are shown in Figure 5.11 and Figure 5.12. These data are presented 
as m0-normalized heat flow plotted with respect to time and temperature (left plot) 
and the heat flow integral plotted with respect to time (right plot). The 
thermodynamic model parameters were derived from the experiments by following 
the procedure described in the section 5.2. These parameters are listed in Table 5-5 
and Table 5-6. Melting was observed for PA66, PP and PLA at about 535, 435 and 
425 K, respectively. The kinetic parameters for all the non-charring polymers 
describing these processes are given in Table 5-4. Overall, the models fit 
experimental heat flow data well. The discrepancies observed in the low temperature 
region (313-450 K) are attributed to heating rate deviations detected in the 
experiments (and discussed above). The decomposition region (550-750 K) 
disagreements are most notable in the cases of ABS and PLA.  These disagreements 
are speculated to be a result of a temporary loss of thermal contact between the 
sample and the pan due to bubble formation at the onset of decomposition. The 
modeled integral heat at the end of decomposition was found to be within 5% of the 
corresponding experimental values for all polymers. 
 
 
 
 
 
75 
Table 5-5 Heat capacities of material components for non-charring polymers. 
Component 
c 
(J g-1 K-1) 
Component 
c 
(J g-1 K-1) 
POM 
(-1.86+0.0099T ) ± 14% POM_melt 
(1.65+0.0012T ) ± 40% 
PMMA 
(0.60+0.0036T ) ± 11% N/A 
N/A 
HIPS 
(0.59+0.0034T ) ± 13% N/A 
N/A 
PA 66 
(-1.18+0.0087T ) ± 20% PA_melt 
(1.71+0.0023T ) ± 30% 
PP 
(-2.05+0.0123T ) ± 10% PP_melt 
(1.45+0.0033T ) ± 35% 
PLA 
(1.09+0.0012T ) ± 25% PLA_melt 
(1.93+0.0004T ) ± 45% 
ABS 
(1.58+0.0013T ) ± 22% N/A 
N/A 
 
  
 
Table 5-6 Heats of melting and decomposition for non-charring polymers. 
Polymer 
hm 
(J g-1) 
h1+1*h2 
(J g-1) 
h1 
(J g-1) 
h2 
(J g-1) 
POM 192 ± 6% 1733 ± 5% 1192 ± 5% 1352 ± 5% 
PMMA N/A 846 ± 5% 846 ± 5% N/A 
HIPS N/A 689 ± 8% 689 ± 8% N/A 
PA 66 65 ± 24%  625 ± 11% 625 ± 11% N/A 
PP 90 ± 10% 412 ± 8% 412 ± 8% N/A 
PLA 30 ± 30% 656 ± 6% 655 ± 6% 8 ± 6% 
ABS N/A 460 ± 5% 460  ± 5% N/A 
 
76 
 
Figure 5.11 Experimental and simulated DSC of PMMA, HIPS and PA 66 at 10 K 
min-1.  
77 
 
Figure 5.12 Experimental and simulated DSC of PP, PLA and ABS at 10K min-1. 
It is difficult to compare kinetic parameters obtained in this work with those 
determined in other studies of polymer degradation because of model-specific nature 
78 
of these parameters and their partial interdependence [149]. The thermodynamic 
parameters measured in this work are also model-specific. However, it should still be 
possible to compare the integral values of heat required to degrade a given material. 
This heat is frequently referred to as the heat of gasification (Hg). It can be defined as 
the amount of energy required to completely degrade and volatilize a unit mass of 
material that is initially at room temperature (298 K). In principle, this quantity 
depends on heating rate. This is the case because the temperature range at which the 
degradation takes place shifts to higher values with increasing rate of heating (see 
Figure 5.9 and Figure 5.10). As a consequence, the solid (or molten) polymer is 
heated to a higher temperature before it degrades (in this analysis, it is assumed that 
gaseous degradation products leave instantaneously and do not contribute to the heat 
capacity of the system). In addition, the heat of decomposition is a temperature 
dependent quantity. The former dependence is captured by the current material 
models. The latter dependence is considered to be minor and is ignored.  Ignoring this 
dependence is equivalent to assuming that the integral of the difference in the heat 
capacities of the polymer and gaseous decomposition products over a decomposition 
temperature shift (induced by a change in the heating rate) is negligibly small with 
respect to the overall heat of gasification value [150]. 
The heats of gasification calculated by simulating material heating and 
decomposition at 10 and 100 K min-1 are shown in Table 5-7. This table also gives 
the final simulation temperatures (Te), which correspond to the earliest point at which 
the decomposition process is complete. For most polymers, the higher heating rate Hg 
values are within uncertainties of the lower heating rate Hg values. These 
79 
uncertainties were calculated by propagating errors [151] in the thermodynamic 
parameters. Table 5-7 also contains the heats of gasification measured by means of 
mass pyrolysis calorimetry (MPC) [152]. In MPC, a thermally thick sample is heated 
by a constant radiant heat flux. While the heating rate observed in these experiments 
is highly variable and depends on the set heat flux value, time and position inside the 
sample, it may still be appropriate to compare MPC heats of gasification with those 
calculated using constant heating rates because, as shown above, Hg dependence on 
heating rate is weak. For all polymers for which MPC values are available (POM, 
PMMA, HIPS, and PP), this comparison shows a very good agreement.  The heats of 
gasification obtained by numerical integration the material models developed in this 
study converge within 1-11% of the MPC heats. 
Table 5-7 Heats of gasification for non-charring polymers. 
Polymer 
  
         
10 K min-1  
(J g-1) 
Te, 
10 K min-1 
 (K) 
  
         
100 K min-1 
(J g-1) 
Te, 
100 K min-1 
(K) 
  
    
[152] 
(J g-1) 
POM 2700 ± 7% 730 2700 760 2400 
PMMA 1660 ± 5% 730 1780 760 1600 
HIPS 1620 ± 7% 780 1710 800 1700 
PA 66 1830 ± 11% 780 1980 800 N/A 
PP 1870 ± 12% 815 2010 830 2000 
PLA 1310 ± 12% 730 1370 740 N/A 
ABS 1370 ± 12% 815 1450 815 N/A 
  
80 
Chapter 6 : Results- kinetics and thermodynamics for charring 
polymers 
Section 6.1 TGA of Kydex 
The results of 10 K min-1 TGA experiments performed on Kydex are shown in 
Figure 6.1.  In this figure, sample mass (m) and mass loss rate (MLR) normalized by 
the initial mass (m0) are plotted with respect to sample temperature. The MLR curve 
shows two well resolved peaks, which is probably a consequence of the fact that 
Kydex is an alloy of two chemically distinct polymers, poly(methyl methacrylate) and 
poly(vinyl chloride). These two peaks can be represented by two reactions: 
Kydex     1 Kydex_int;     Kydex_int    2 Kydex_char                                   (6.1) 
where Kydex_int and Kydex_char denote condensed-phase decomposition 
products from the first and second reaction, respectively. Gas-phase products are not 
shown because, as stated in Chapter 4, they are assumed to leave the condensed phase 
and sample container instantaneously.  
 
Figure 6.1 TGA of Kydex at 10 K min-1. 
81 
The kinetic parameters describing these reactions were obtained by following 
the procedure that explained in the section 5.1. Compared to the procedure for 
analyzing the TGA data for non-charring polymers, there are two major differences to 
the kinetics analysis for charring polymers. Firstly, 2 was set to m/(1*m0) when T  
1000 K for charring polymers (750 K for non-charring polymers). Secondly, because 
of the complexity due to the char formation during thermal degradation, the iterations 
stop earlier when R2 of the model for the experimental MLR reached 0.85. 
 
Figure 6.2 Experimental and simulated TGA of Kydex at 10 K min-1. 
The results of this fitting process are shown in Figure 6.2. The optimized 
kinetic parameters and the computed uncertainty values are given in Table 6-1. The 
model captures both Kydex mass and MLR behaviors with a reasonable accuracy (R2 
= 0.86).  
Table 6-1 Kinetic parameters describing decomposition reactions for Kydex. 
Polymer 
 
A1 
(s-1) 
E1 
(kJ mol-1) 
1 
 
A2 
(s-1) 
E2 
(kJ mol-1) 
2 
 
Kydex 6.03 1010 ± 50% 141 ± 3% 0.45 1.36 1010 ± 40% 174 ± 5% 0.31 
82 
A comparison of 30 K min-1 experiments with a simulation (performed at the 
same heating rate) is shown in Figure 6.3 to examine the parameterized kinetic 
models’ ability to reproduce experimental data at a higher heating rate. The quality of 
agreement indicates that the developed kinetic model is still valid at higher heating 
rates. 
 
Figure 6.3 Experimental and simulated TGA of Kydex at 30 K min-1. 
Section 6.2  DSC of Kydex 
Figure 6.4 shows the result of DSC experiments performed on Kydex. The 
heat flow normalized by the initial mass is plotted as a function of sample 
temperature. There are two distinct peaks in this heat flow curve, which 
approximately match the temperatures of Kydex decomposition reactions.  
83 
 
Figure 6.4 DSC of Kydex at 10 K min-1. 
Then DSC curve was normalized by instantaneous heating rate, as shown in 
the left graph of Figure 6.5. The pre-decomposition part of this curve was fit with a 
straight line. The parameters of this line describe temperature dependence of heat 
capacity of non-degraded Kydex and are reported in Table 6-2. In a similar manner, 
the post-decomposition part of this curve could theoretically be used to obtain heat 
capacity of the final char (represented by component Kydex_char in the reaction 
model). However, an in-depth analysis revealed that the post-decomposition heat flow 
was a subject to large random and systematic errors. The random errors were a 
consequence of a significant decrease in the sensitivity of the heat flow sensor with 
increasing temperature. The systematic errors were probably caused by heat transfer 
effects brought about by the formation of char, which had a porous structure. 
84 
 
Figure 6.5 DSC of Kydex (left) and Kydex decomposition residue (right) normalized 
by instantaneous heating rate. 
Table 6-2  Heat capacities of material components for Kydex. 
Component c (J g
-1 K-1) Component c (J g
-1 K-1) 
Kydex (-0.624+5.93×10-3T ) ± 8% N/A N/A 
Kydex_int (0.265+3.01×10-3T ) ± 12% Kydex_char (1.15+9.56×10-5T ) ± 15% 
To elucidate Kydex_char heat capacity, separate DSC experiments were 
performed on the polymer decomposition residue. As stated in the section 3.2.2, the 
residue, collected from several polymer tests, was compacted in a crucible to improve 
the thermal contact with the heat flow sensor. The results of these experiments are 
shown in the right graph of Figure 6.5. The normalized heat flow data collected 
between 450 to 1000 K were fitted with a straight line to obtain Kydex_char heat 
capacity. The heat capacity of the intermediate component, Kydex_int, could not be 
resolved because of the proximity of two reaction peaks. Therefore, the heat capacity 
of this component was assumed to be the mean of the heat capacity of Kydex and 
Kydex_char components. Heat capacity parameters for Kydex_int and Kydex_char 
are also listed in Table 6-2. The uncertainties in the heat capacities reported in this 
table were obtained from individual heat flow curves (only the average curves are 
85 
shown in Figure 6.4 and Figure 6.5) by calculating two standard deviations of the 
mean at several temperatures within the fitted temperature range and averaging these 
uncertainty values. 
 
Figure 6.6 Determination of decomposition reaction contributions to the Kydex DSC 
signal. 
The sensible heat flow baseline was calculated by following the procedure 
described in the section 5.2 and equation 5.4. This calculated baseline is plotted 
together with the total DSC heat flow as a function of time in Figure 6.6. Note that 
the deepening of the heat flow curve below the baseline between the reaction peaks is 
ignored during the integration because it is assumed to be associated with a temporary 
loss of thermal contact between the sample and crucible. The difference integration in 
the decomposition region produced the value of the total heat of decomposition, 
h1+1*h2. The after decomposition heat flow (at 2750-3000 s) is notably higher than 
what is predicted on the basis of the char heat capacity measurement. This 
discrepancy is a manifestation of the systematic errors mentioned above. To minimize 
86 
the impact of these errors on the results of the integration, this integration was bound 
by the point in time where the second decomposition reaction was 95% complete.  
Performing this integration procedure for individual experiments (using the same 
average baseline) produced a set of the heat of decomposition values that were used to 
compute uncertainties.  The values of h1 and h2 were calculated to be 180 ± 10% and 
125 ± 12% J g-1 respectively.  
The thermodynamics of the parameterized reaction model was verified by 
comparing ThermaKin calculated heat flow with that observed in the experiments. 
This comparison is presented using time resolved heat flow as well as heat flow 
integral, which are depicted in left and right graph of Figure 6.7, respectively. The 
experimental and simulated heat flow integrals match very well. The heat flow 
comparison is not as favorable. The most notable deviations occur in the pre-
decomposition region. These deviations are primarily due to the fact that, as 
mentioned earlier in Chapter 5, the instant experimental heating rate deviates from its 
set value, while, in the simulations, no deviation takes place. 
 
Figure 6.7 Experimental and simulated DSC heat flow (left) and heat flow integral 
(right) for Kydex at 10 K min-1. 
87 
Section 6.3 TGA of DGEBA, PET, Kevlar, BACY, PPS, PEI and PEEK 
The experimental and simulated TGA results obtained for the rest of the 
studied charring materials are shown in Figure 6.8, Figure 6.9 and Figure 6.10. Figure 
6.8 shows the results for charring polymers with relatively low char yields, while 
Figure 6.9 contains results for highly charring polymers. PPS results are presented in 
a separate figure, Figure 6.10, because of the limited amount of data obtained for this 
material (see explanation in the section 3.2.2). For each charring polymer with the 
exception of PPS, the normalized mass (left plot) and MLR (right plot) measured at 
10 and 30 K min-1 are compared with the corresponding modeling outcomes. The PPS 
comparison contains only 10 K min-1 data. 
All charring polymer mass loss processes were represented in the model by 
two consecutive reactions. The parameters describing kinetics of these reactions were 
obtained from 10 K min-1 experiments by following the procedure described in the 
sections 5.1 and 6.1. These parameters are summarized in Table 6-3. Note that the 
amount of PPS data was insufficient for uncertainty calculation. Therefore, these 
uncertainties were estimated as the mean of uncertainties calculated for the other 
materials. 
All charring polymer models represent 10 K min-1 TGA experiments with a 
good accuracy.  However, notable discrepancies are observed for 30 K min-1 heating 
rate. These discrepancies are the highest for PEI and PEEK and are hypothesized to 
be caused by deviations of the experimental conditions from spatial isothermality.  
 
88 
Table 6-3 Kinetic parameters describing decomposition reactions and melting for 
charring polymers. 
Polymer 
 
A1 
(s-1) 
E1 
(kJ mol-1) 
1 
 
A2 
(s-1) 
E2 
(kJ mol-1) 
2 
 
Am 
(s-1) 
Em 
(kJ mol-1) 
Kydex 6.03 1010 ± 50% 141 ± 3% 0.45 1.36 1010 ± 40% 174 ± 5% 0.31 N/A N/A 
DGEBA 1.72 107 ± 50% 111 ± 8% 0.97 9.86 1016 ± 40% 259 ± 6% 0.12 N/A N/A 
PET 1.60 1015 ± 30% 235 ± 8% 0.18 3.53 104 ± 30% 96 ± 10% 0.72 1.5 1036 380 
Kevlar 6.68 1030 ± 30% 536 ± 4% 0.42 2.73 103 ± 50% 107 ± 8% 0.86 N/A N/A 
BACY 2.20 1030 ± 50% 442±10% 0.64 1.25 103 ± 50% 85 ± 5% 0.69 N/A N/A 
PPS 1.06 1011 ± 40% 205 ± 7% 0.5 3.70 10-1 ± 40% 36 ± 7% 0.88 1.5 1034 380 
PEI 7.66 1027 ± 50% 465 ± 7% 0.65 6.50 102 ± 50% 88 ± 10% 0.77 N/A N/A 
PEEK 4.30 1028 ± 20% 505 ± 6% 0.64 9.57 10-1 ± 20% 50 ± 8% 0.79 3.5 1033 415 
 
89 
 
Figure 6.8 Experimental and simulated TGA of DGEBA, PET and Kevlar at 10 and 
30 K min-1. 
90 
 
Figure 6.9 Experimental and simulated TGA of BACY, PEI and PEEK at 10 and 30 
K min-1. 
91 
 
Figure 6.10 Experimental and simulated TGA of PPS at 10 K min-1. 
Section 6.4 DSC of DGEBA, PET, Kevlar, BACY, PPS, PEI and PEEK 
The experimental and simulated DSC results obtained for the rest of the 
studied materials are shown in Figure 6.11, Figure 6.12 and Figure 6.13. These results 
are distributed among the figures in the same way as explained in the previous 
section. The DSC data are presented as m0-normalized heat flow plotted with respect 
to time and temperature (left plot) and the heat flow integral plotted with respect to 
time (right plot). The thermodynamic model parameters were derived from the 
experiments by following essentially the same procedure as described in the sections 
5.2 and 6.2. These parameters are listed in Table 6-4 and Table 6-5. 
Four of the seven charring polymers showed evidence of meting transition, 
which was not observed in Kydex. This transition was detected in PET, PEI, PEEK 
and PPS experiments at about 525, 500, 615 and 550 K, respectively. To take this 
transition into account during parameterization, additional components, PET_melt, 
PEI_melt, PEEK_melt and PPS_melt, were added to the corresponding material 
models. Then hm Am and Em were calculated and fitted to reproduce the shape of the 
92 
melting peak for each of the aforementioned charring polymer. The parameters 
describing melting kinetics are given in Table 6-3. The parameters describing melting 
thermodynamics are listed in Table 6-4 and Table 6-5. 
Table 6-4  Heat capacities of material components for charring polymers. 
Component c (J g
-1 K-1) Component c (J g
-1 K-1) 
Kydex (-0.624+5.93×10-3T ) ± 8% N/A N/A 
Kydex_int (0.265+3.01×10-3T ) ± 12% Kydex_char (1.15+9.56×10-5T ) ± 15% 
DGEBA (3.89-5.08×10-3T ) ± 20% N/A N/A 
DGEBA_int (2.04-8.05×10-4T ) ± 15% DGEBA_char (0.185+3.29×10-3T ) ± 10% 
PET (-0.269+4.64×10-3T ) ± 12% PET_melt (2.050-2.08×10-4T ) ± 15% 
PET_int (1.44-4.8×10-5T) ± 13% PET_char (0.820+1.12×10-4T ) ± 10% 
Kevlar (1.71-1.49×10-3T ) ± 15% N/A N/A 
Kevlar_int (1.15-3.43×10-4T ) ± 14% Kevlar_char (0.585+8.04×10-4T ) ± 12% 
BACY (-1.07+8.93×10-3T ) ± 18% N/A N/A 
BACY_int (0.305+4.36×10-3T) ± 19% BACY_char (1.68-2.04×10-4T ) ± 20% 
PPS 
(0.0687+2.73×10-3T ) ± 
14% 
PPS_melt (0.697+1.37×10-3T ) ± 18% 
PPS_int (-1.04+3.36×10-3T) ± 15% PPS_char (-2.77+5.34×10-3T) ± 14% 
PEI 
(-0.0357+4.11×10-3T ) ± 
16% 
PEI_melt (1.88+5.75×10-4T ) ± 20% 
PEI_int (1.59+3.08×10-4T ) ± 14% PEI_char (1.30+4.08×10-5T ) ± 8% 
PEEK (0.156+3.57×10-3T ) ± 10% PEEK_melt (1.27+1.45×10-3T ) ± 20% 
PEEK_int (0.859+1.36×10-3T ) ± 21% PEEK_char (0.447+1.26×10-3T ) ± 22% 
    
93 
    
Table 6-5 Heats of decomposition reactions and melting (endo is positive) for 
charring polymers. 
Polymer 
h1+1×h2 
(J g-1) 
h1 
(J g-1) 
h2 
(J g-1) 
hm 
(J g-1) 
Kydex 236 ± 10% 180 ± 10% 125 ± 12% N/A 
DGEBA 131 ± 17% 5 ± 200% 130 ± 10% N/A 
PET 265 ± 10% 220 ± 7% 250 ± 25% 30 ± 10% 
Kevlar 382 ± 10% 300 ± 6% 195 ± 25% N/A 
BACY -47 ± 3% -226 ± 10% 280 ± 12% N/A 
PPS -117 ± 38% -102 ± 37% -30 ± 40% 35 ± 9% 
PEI -83 ± 15% -80 ± 15% -5 ± 200% 1± 150% 
PEEK  -768 ± 11% -256 ± 10 % -800 ± 12% 34 ± 8% 
As evident from the right graphs of Figure 6.11, Figure 6.12 and Figure 6.13, 
the models reproduce experimental heat flow integral histories well. The modeled 
integral heat at the end of decomposition was found to be within 5% of the 
corresponding experimental values for the majority of the studied polymers 
(including Kydex). The exceptions were DGEBA and PEI, which models deviate 
from the experiments by 8 and 13%, respectively. As in the case of Kydex, 
discrepancies between the modeled and experimental heat flow (left graphs in Figure 
6.11, Figure 6.12 and Figure 6.13) are more notable especially in the beginning of the 
experiments. These discrepancies can be explained by the fluctuation in the 
experimental heating rate. 
Perhaps, the most significant outcome of the current heat flow analysis is an 
observation that all studied polymers with char yield exceeding 40 wt.%, which 
include BACY, PPS, PEI and PEEK, decompose exothermically, while the rest of the 
94 
polymers, including seven analyzed non-charring materials in Chapter 5 are 
characterized by an endothermic decomposition. Moreover, the most significant 
exothermicity is observed for PEEK, which also produces the highest char yield. The 
relationship between the char yield and decomposition exothermicity can be 
explained by noting that a polymer char, which molecular structure is likely to be 
similar to that of graphite or soot (i.e., multiple fused aromatic rings), is highly 
thermodynamically stable. When the char is produced in sufficient amount, its 
thermodynamic stability compensates an increase in enthalpy associated with the 
formation of small molecular mass volatiles. 
95 
 
Figure 6.11 Experimental and simulated DSC of DGEBA, Kevlar and PET at 10 K 
min-1. 
96 
 
Figure 6.12 Experimental and simulated DSC of BACY, PEI and PEEK at 10 K min-1. 
 
97 
 
Figure 6.13 Experimental and simulated DSC of PPS at 10 K min-1. 
While the heat of decomposition of highly charring polymers is exothermic, it 
does not mean that the degradation of these polymers occurs spontaneously. It still 
takes a considerable amount of energy to degrade these materials. The Hg calculated 
for the charring materials are given in Table 6-6. Hg values listed in Table 6-6 are 
provided for specific heating rates (10 and 100 K min-1) and specific Te. The values 
obtained for low and high char yield polymers are similar in magnitude indicating 
that decomposition exothermicity has a minor impact on the overall thermodynamics 
of polymer degradation. The uncertainties provided for the low heating rate Hg values 
were calculated by propagating errors [151] in the thermodynamic parameters. 
 
 
 
 
98 
Table 6-6 Heats of gasification for charring polymers. 
Polymer 
  
         
10 K min-1 
(J g-1) 
Te, 
10 K min-1 
(K) 
  
         
100 K min-1 
(J g-1) 
Te, 
100 K min-1 
(K) 
Kydex 900 ± 9% 785 905 850 
DGEBA 740 ± 18% 750 775 780 
PET 1010 ± 8% 790 1095 910 
Kevlar 905 ± 8% 1000 970 1175 
BACY 1620 ± 12% 900 2070 1030 
PPS 750 ± 10% 945 1050 1120 
PEI 1060 ± 10% 970 1270 1105 
PEEK 665 ± 21% 1100 1335 1540 
 
Section 6.5 SEM of Chars 
 Figure 6.14 and Figure 6.15 show SEM images of the charring polymer 
decomposition residues generated in the thermal analysis experiments. One 
interesting feature of these residues is that, with the exception of one produced by PEI, 
the chars have a relatively homogeneous, solid-like structure at micrometer scale. 
This structure is fundamentally different from that of an intumescent coating char 
[153], which shows a fractal-like void pattern with an extremely wide range of pore 
sizes (from several millimeters to below 5 μm). PEI char is somewhat porous at the 
microscale with clear signs of exfoliation of the char layers. 
99 
 
Figure 6.14 SEM images of chars produced as a result of anaerobic thermal 
degradation of Kydex, DGEBA, PET and Kevlar. 
100 
 
Figure 6.15 SEM images of chars produced as a result of anaerobic thermal 
degradation of BACY, PPS, PEI and PEEK. 
  
101 
Chapter 7 : Results-Heat transfer parameterization and pyrolysis 
model validation for non-charring polymers 
Section 7.1 Absorption coefficients. 
Table 7-1 summaries the absorption coefficients (in m-1) obtained from this 
study for selective non-charring polymers that were used in the gasification 
experiments. The detail measurement procedure and calculation can be found in the 
section 3.3.1. The polymer broadband absorption coefficients used in the ThermaKin 
model were computed from the infrared transmission experiments and normalized by 
density. Thus the coefficient values were found to be 1.94, 2.12 and 2.14 m2 kg-1 for 
PMMA, HIPS and POM, respectively. 
Table 7-1 Absorption coefficients for non-charring polymers 
Polymers Absorption coefficients  (m-1) 
PMMA 2240 
HIPS 2250 
POM 3040 
 
Section 7.2 PMMA gasification experiment and validation part I. 
Section 7.2.1  PMMA pyrolysis model parameterization 
 A one dimensional heat transfer scenario was produced where samples, 
insulated at their bottom surface, were subjected to a known radiative heat flux at 
their top. Bench scale gasification tests on PMMA provided requisite measurements 
needed to determine the material’s temperature dependent thermal conductivity, k, by 
an inverse modeling analysis. This analysis is based on by the following assumptions: 
the only undefined parameters remained in the PMMA pyrolysis models were 
102 
condensed-phase thermal conductivities for all components (since kinetics and 
thermodynamics were measured in the Chapter 5; boundary conditions are described 
in Chapter 4; absorption coefficient was measured in the section 7.1; the density and 
thickness for PMMA samples used in bench-scale tests were measured as 1160 kg m-3 
and 6.0 mm.). Then the thermal conductivities can be derived from average sample 
bottom temperatures measured in the gasification experiments. The thermal 
conductivity of most polymers shows a linear dependence on temperature with an 
abrupt change at the material’s glass transition temperature, Tg [1]. Then the thermal 
conductivity was optimized against modeling PMMA bottom surface temperature by 
assuming a piecewise linear function of temperature with a discontinuity at the glass 
transition temperature Tg ≈ 378 K [1]. Figure 7.1 shows the PMMA bottom surface 
temperature measurements using thermocouples at 20 and 60 kW m-2. In Figure 7.1 
for both heat fluxes, only average temperature ( dot ) from three experiments (each 
experiment includes 2 thermocouple measurements) are presented and the error bars 
indicate the uncertainties of these measurements, which are reported by calculating 
two standard deviations of the mean. Figure 7.1 also shows the optimization result for 
modeling PMMA bottom surface temperature under incident heat flux of 20 kW m-2. 
Note that only sample bottom temperature measurements taken under incident heat 
flux of 20 kW m-2 were used in the optimization (fitting) process. Because these tests 
are significant longer than those at 60 kW m-2 thus provided larger usable data set, as 
demonstrated in Figure 7.1. The values of k , which were determined from the 
optimization process at 20 kW m-2 , were used to compute the  PMMA bottom 
103 
surface temperature histories under incident heat flux 60 kW m-2, which were not 
used as an optimization target. And this validation result is shown in Figure 7.1 also. 
It was measured that the values of k for PMMA are: (0.45-3.810-4T) ± 10% 
(T <378 K) and (0.27-2.410-4T) ±13% (T  378K). The uncertainties are calculated 
as the following: k was varied, one at a time to assure its maximum variation that 
corresponded to a shift in the simulation results that was still within the scatter of the 
experimental data (which was not shown in this dissertation). The maximum variation 
was used to define this parameter’s uncertainty. 
 
Figure 7.1 Back temperature measurement using thermocouple and model prediction 
of anaerobic pyrolysis for PMMA at 20 and 60 kW m-2 (the error bars for both heat 
fluxes are not significantly shown because the temperature measurement differences 
from two thermocouples are small). 
Section 7.2.2 Prediction of burning rate for PMMA with insulation on bottom. 
Until here, all the PMMA fundamental properties including kinetics, 
thermodynamics, heat transfer and boundary conditions are measured. The 
104 
parameterized model for PMMA gasification at this setup of experiment was 
validated against the experimental burning rate at various heat fluxes. Figure 7.2, 
Figure 7.3 and Figure 7.4 show experimentally measured (discrete points) and model 
predicted (solid lines) sample mass loss rate collected at three incident heat flux 
settings (20, 40, and 60 kW m-2, respectively). The plots display data collected from 
the beginning of radiant exposure to the point of time when the PMMA sample was 
fully decomposed. Error bars in each figure indicate two standard deviations of the 
mean, calculated from three independent tests at each heat flux at each time step (1 s).  
The overall predictions at various heat fluxes are good with small discrepancies (< 6 % 
on average).   
   
Figure 7.2 MLR measurements using CAPA and model prediction of PMMA 
anaerobic pyrolysis with insulation at 20 kW m-2. 
105 
 
Figure 7.3 MLR measurements using CAPA and model prediction of PMMA 
anaerobic pyrolysis with insulation at 40 kW m-2. 
 
Figure 7.4 MLR measurements using CAPA and model prediction of PMMA 
anaerobic pyrolysis with insulation at 60 kW m-2. 
106 
Section 7.3 Gasification experiment and validation part II for non-charring polymers 
Section 7.3.1 Uniformity of thermometry for non-charring polymers 
One of the major assumptions in the gasification work that performed under 
CAPA is one-dimensional pyrolysis. Thus it is important to check the bottom surface 
temperature uniformity, which is hard to obtain using limited number of 
thermocouples as described in the section 3.3.2.  
An example of infrared images of the bottom sample surfaces at different 
stages of gasification for PMMA, POM and HIPS is shown in Figure 7.5. These 
images indicate that the surface temperature stays close to being spatially uniform 
with the largest difference (15 K) observed between the mesh and foil and attributed 
to the thermal resistance of the mesh-foil interface. 
 
107 
 
Figure 7.5 Infrared images of bottom surfaces of the non-charring samples 
undergoing gasification. 
A quantitative comparison of the temperature histories sampled from different 
areas of the bottom surface of PMMA subjected to 40 kW m-2 of radiant heat flux is 
shown in Figure 7.6. The temperature histories obtained by randomly sampling pixels 
at the center (area 1) and middle (area 2) of the surface are well within each other 
uncertainties. These uncertainties were calculated as two standard deviations of the 
mean. The temperature of the peripheral area (area 3) deviates slightly from that of 
the central areas towards the end of the experiment. This deviation was attributed to a 
108 
partial obscuration of camera view by gaseous decomposition products, small 
amounts of which had a tendency to accumulate in the space below and near the outer 
edge of the sample holder. 
 
Figure 7.6 Spatial variation in bottom surface temperature histories. 
Section 7.3.2 Thermal conductivity calibration and validation for non-charring 
polymers 
The average sample bottom temperature history obtained from IR camera for 
PMMA gasified at 20 kW m-2 of radiant heat flux is shown in Figure 7.7 (circles). In 
this figure, each temperature point is the average of 90 pixels (36 from area 1, 36 
from area 2, and 18 from area 3) which represents 10 randomly selected cursors 
( each cursor contains 9 pixels) further averaged over 3 gasification experiments. 
Error bars in Figure 7.7 show the uncertainties of the IR camera temperature 
measurements by computing the two times of standard deviation over the mean. The 
PMMA components thermal conductivities were calibrated from the section 7.2.1.  
The prediction of PMMA bottom surface temperature without insulation (using the 
109 
exactly same PMMA properties that used in the section 7.2.1) at 20 kW m-2 of radiant 
heat flux is also shown in Figure 7.7 (line). Besides, as it was demonstrated in Figure 
7.8 , the derived thermal conductivity parameters also provide a good description of 
40 and 60 kW m-2 bottom surface temperature histories. At all heat fluxes, the quality 
of agreement between the model and experiments tends to under predict somewhat to 
the IR measurements at different degrees. But the overall trends are close and the 
maximum discrepancy is found to be about 5%.  
 
Figure 7.7 Experimental and simulated bottom surface temperature histories obtained 
for PMMA at 20 kW m-2. 
110 
 
Figure 7.8 Experimental and simulated bottom surface temperature histories obtained 
for PMMA at 40 and 60 kW m-2. 
The HIPS and POM samples were 6.0 and 6.6 mm thick, respectively. Their 
densities were measured at room temperature and found to be 1060 and 1420 kg m-3, 
respectively. The thermal conductivities of the condensed-phase components 
representing HIPS and POM were determined using essentially the same approach. In 
all cases, the temperature data collected in the lowest heat flux gasification 
experiments were used as an optimization target because of the smallest uncertainties 
in the experimental conditions. Figure 7.9 (optimization target) and Figure 7.10 
(validation results) show the experimental and simulation results of HIPS sample 
bottom surface temperature for 30 kW m-2 and 50 and 70 kW m-2 respectively. 
Experimental and simulated results for the POM sample bottom surface tempertuare 
at 30 kW m-2 and 50 and 70 kW m-2 are shown in Figure 7.11 (optimization target) 
and Figure 7.12 (validation results) respectively. For most of the comparisons, the 
quality of agreement between the model and experiments tends to deteriorate somewhat 
at later times and higher temperatures, where experimental data become less reliable due 
to decomposition of the high emissivity paint, camera view obscuration by pyrolyzates 
111 
and increasing uncertainties in the sample thickness and incident radiant heat flux. The 
resulting thermal conductivity expressions are summarized in Table 7-2. For POM, 
separate linear temperature dependencies were assigned to the original polymer, 
POM_mlt and POM_int. 
 
Figure 7.9 Experimental and simulated bottom surface temperature histories obtained 
for HIPS at 30 kW m-2. 
 
Figure 7.10 Experimental and simulated bottom surface temperature histories 
obtained for HIPS at 50 and 70 kW m-2. 
112 
 
 
Figure 7.11 Experimental and simulated bottom surface temperature histories 
obtained for POM at 30 kW m-2. 
 
Figure 7.12 Experimental and simulated bottom surface temperature histories 
obtained for POM at 50 and 70 kW m-2. 
Table 7-2. Thermal conductivities for HIPS and POM. 
Polymer 
Thermal Conductivity 
(W m-1 K-1) 
113 
HIPS (0.10+1.010-4T) ±5% 
POM 
POM: (0.25+1.610-5T) ±10% 
POM_mlt: (0.21+810-6T) ±15% 
POM_int: (0.19-610-5T) ±20% 
To further investigate the k  for PMMA that obtained in section 7.2.1, its value 
was compared to a list of literature values [71, 100-102, 154-156] that shown in 
Figure 7.13. As the results shown in this figure, between 378 and 600 K, the 
measured conductivity values lie roughly in between those previously measured by 
Assael et al. [154] and Stoliarov et al. [71]. Below 378 K, our current values are over 
50% higher. This discrepancy is a consequence of the current presentation of the heat 
capacity as a linear temperature function, which ignores a discontinuity at the glass 
transition. While this presentation results in a significantly overestimated low 
temperature thermal conductivity, it has negligible impact on the overall heat 
transport and the heat of gasification [77]. 
 
Figure 7.13 Thermal conductivity for PMMA.  
114 
 As shown in Figure 7.14, the HIPS thermal conductivity is consistent with that 
reported by dos Santos [157]; however, it is about 25% lower than the values 
previously measured by Stoliarov et al. [71] in the same temperature range. The latter 
discrepancy is likely to be a consequence of the difference in the composition of 
HIPS, which is a manufacturer-specific copolymer/blend of polystyrene and 
polybutadiene.   
 
Figure 7.14 Thermal conductivity for HIPS. 
The thermal conductivity of POM obtained in this work is similar to that 
recently measured by Linteris et al.[40] as shown in Figure 7.15. Other literature data 
[158, 159] are only avaliable at room temperture and scattered in Figure 7.15.  
115 
 
Figure 7.15 Thermal conductivity for POM. 
Section 7.3.4 Prediction of burning rate for non-charring polymers 
A comparison of the burning rates computed using the fully parameterized 
PMMA model with the results of the gasification experiments is shown in Figure 7.16. 
The model predicts the burning rates at a range of radiant heat fluxes with the 
accuracy comparable with the experimental repeatability. 
The final comparison between the HIPS and POM models and the results of 
the corresponding gasification experiments is shown in Figure 7.17 and Figure 7.18. 
The model of HIPS demonstrates the quality of predictions similar to that observed 
for PMMA. POM burning rates are slightly (by average of about 13%) 
underpredicted by its model for all the heat fluxes, which suggests that the heats of 
POM decomposition are somewhat overestimated.  
The total mass loss of experiment data is found to be approximately 4.3 %, 
5.0 % and 1.4 % on average larger than the model predictions for PMMA, HIPS and 
116 
POM respectively because of the following reasons. The primary reason is due to two 
additional materials used in the experiments that were not mentioned in the model. 
They are glue which was used to stick Kaowool insulation layers and paper tape to 
prevent drippings during gasification experiment. When those two materials were 
placed together with the sample holder, they were partially or fully decomposed and 
the volatiles generated from those two material’s decomposition were hardly 
separately from the total mass loss that from the experimental reading. The 
contributions of those two material’s mass loss were estimated about 2.0 % and 0.5 % 
respectively. The other reason is probably caused by the errors of those materials’ 
sizes ( i.e size cutting error and thickness measurements error). It was found to be 
about 1-2 % on average.  
117 
 
Figure 7.16 Experimental and simulated burning rate histories obtained for PMMA at 
20-60 kW m-2. 
118 
 
Figure 7.17 Experimental and simulated burning rate histories obtained for HIPS at 
30-70 kW m-2. 
119 
 
Figure 7.18 Experimental and simulated burning rate histories obtained for POM at 
30-70 kW m-2.  
120 
Chapter 8 : Results-Heat transfer parameterization and pyrolysis 
model validation for charring polymers 
In this chapter, results of the bench-scale gasification results are presented 
including studying on ABS, PET, Kydex and PEI followed by the procedure 
described in the section 3.3.3. The reason why ABS is considered here is because, 
different from its TGA data, ABS produces different amount of char residue under 
various level of external heat fluxes, which has not been found in other non-charring 
polymers. For ABS at 30 kW m-2, residue near the end of experiments remains about 
35% (not decomposed completely) and this value is found to be about 4.5%, which is 
close to its TGA data (2.3%), under external radiative heat flux of 50 and 70 kW m-2. 
Therefore, ABS was included in this chapter and treated as a charring polymer. 
Gasification experiments for PET were only conducted at 50 kW m-2 and 70 kW m-2. 
Because PET melts during thermal decomposition and the molten PET, unlike other 
molten polymers, is low viscous fluid which drips from the edges of the sample 
holder and no good results can be obtained at the external heat flux of 30 kW m-2. PEI 
gasification experiments were not conducted at 30 kW m-2 because no obvious mass 
generation was recorded at this heat flux level. Therefore, external heat fluxes from 
50 to 90 kW m-2 were applied for PEI.  ABS and PET results are presented together 
because the char yields are significant smaller and the char size changes were 
observed significant different than the other two polymers. Kydex and PEI, who were 
found to produce relative large amount of intumescent char during their gasification 
experiments are presented together in each section (sections 8.2 to 8.5). 
121 
Section 8.1 Absorption coefficients. 
Table 8-1 summaries the absorption coefficients (in m-1) obtained from this 
study for the polymers that were studied in this chapter. The data in this table are the 
mean values from two independent measurements for each material. The mean 
variance of these two measurements is about 3 % to the mean values.  
Table 8-1 Absorption coefficients for ABS and charring polymers 
Polymers Absorption coefficients  (m-1) 
ABS 1800 
PET 1935 
Kydex 2145 
PEI 1745 
Section 8.2 Experimental observation 
Section 8.2.1 ABS and PET 
Figure 8.1 shows the char residues after gasification experiments for ABS at 
50 kW m-2. And Figure 8.2 displays the side video snapshots and bottom temperature 
for ABS under external heat flux of 50 kW m-2 at 0, 100, 200 and 400 s during 
gasification experiments. From the comparison at different stages of ABS pyrolysis at 
the heat flux of 50 kW m-2, the temperature uniformity is quantified by calculating the 
maximum average temperature variations among the three area regions (see how the 
areas are divided in the section 3.3.3; data are available in the section 8.4) and termed 
as uniformity variation. And the value of this variation is found to be small (about 25 
K) throughout the tests for ABS.  The possible reason to cause this variation could be 
122 
the deformation of ABS sample to generate a possible gap between the sample and 
the aluminum foil. 
 
Figure 8.1 Char residues after gasification experiments for ABS at 50 kW m-2. 
 
 
123 
 
Figure 8.2 Infrared images of bottom surfaces of the ABS sample undergoing 
gasification at 50 kW m-2. 
The PEI char residue after gasification at 50 kW m-2 forms a brittle and porous 
hollow carbon-based object, as illustrated in Figure 8.3. In this figure, the bulk 
volume of the residue does not change significantly respect to the virgin PEI sample 
volume. It is observed from Figure 8.4 that the top surface of the testing sample 
during gasification experiments is nearly flat. Therefore, this is still a one-
dimensional problem and the bottom surface temperature from the IR camera 
measurements indicates the temperature uniformity is not bad (the uncertainty 
variation is within 15 K). As it is presented in Figure 8.4, portion parts of the bottom 
124 
appear lower temperature nearby the edges of the testing sample near the end of the 
gasification, which is likely due to the dripping that discussed earlier in this Chapter. 
When dripping occurs, the dripping flow is accumulated near the edges of aluminum 
mesh and experiences natural cooling. The dripping is found significant severely at 
30 kW m-2 when the burning rate is low, thus no data was recorded for this heat flux 
level. 
 
Figure 8.3 Char residues after gasification experiments for PET at 50 kW m-2. 
 
125 
 
Figure 8.4 Infrared images of bottom surfaces of the PET sample undergoing 
gasification at 50 kW m-2. 
Section 8.2.2 Kydex and PEI 
One of the interesting phenomenon observed during Kydex gasification 
experiments is the growth of char. As shown in Figure 8.5, the height of char residue 
after Kydex complete decomposition at 50 kW m-2 is about 6 cm (please note that the 
char was laid down and the top surface is facing up in this figure). The growth of the 
126 
char can be further witnessed by the snapshots from the side video camera, as shown 
in Figure 8.6. Please note that the black semi-circles shown on some of the images at 
latter period of tests are corresponding to the appearance of cone heater reflected from 
the gold coated mirror when the base of the testing sample shrinks gradually. In the 
meanwhile, the height of the testing sample rises and the whole object forms like a 
mushroom. Clearly from visual observation, the shape of Kydex char differs 
significant from ABS and PET. This observation threatens the one-dimensional 
assumption. However as it demonstrated from Figure 8.6, until 200 s, the testing 
sample is fairly under a one-dimensional heat transfer scenario because of the top 
surface is nearly flat and bottom surface temperature is crudely uniform (with 
maximum uniformity variance of 25 K).  
 
Figure 8.5 Char residues after gasification experiments for Kydex at 50 kW m-2. 
127 
 
Figure 8.6 Side views and Infrared images of bottom surfaces of the Kydex sample 
undergoing gasification at 50 kW m-2. 
128 
As mentioned earlier in this Chapter, PEI experiences similar features of char 
morphological changes as Kydex does during gasification experiments. However, PEI 
produces more char residues than Kydex does both in milligram TGA tests and 
bench-scale gasification tests. It was found that larger amount of char and pyrolyzing 
intermediacy formed in PEI gasification experiments generates heavier and bigger 
charring layers than in Kydex experiments, as shown in Figure 8.7. Please note that 
the top region part of the char residue shown in Figure 8.7 had to be removed to be 
taken out of the CAPA. 
Figure 8.8 illustrates the PEI top surface morphological and bottom surface 
temperature changes during gasification at 50 kW m-2. The temperature uniformity on 
the bottom surface is poor (about 35 K uniformity variations) and area 1 is clearly 
cooler than the area 2 and area 3 because of thicker char layer formed at the center. 
The aim of this work is developing a systemic methodology to measure the polymer 
including decomposition products properties that serves as inputs for CFD models at 
a modest experimental cost. However, to model some of the charring polymers like 
PEI need detail information about the progress changes of char structure and how it 
affects the heat transfer at the condensed phase which cannot be obtained from the 
current procedure.  
When the PEI sample is swelling until its top surface reaching the cone heater, 
the anaerobic assumption also fails. Our measurement of oxygen concentration based 
on current experimental setup is found to be about 2.2 vol. % near the initial top 
surface. However, when a testing polymer expands and grows into the cone heater, 
the pyrolyzing polymer is expected to experience partial oxidation or even burning 
129 
because the oxygen concentration possibly reaches above 10 vol. %.  Either from the 
side video or onsite experimental observation, visible flame was observed clearly at 
70 and 90 kW m-2 after the top surface reaching inside the cone heater. Therefore, the 
portion of the experimental data before the sample top surface reaches inside the cone 
heater at all conditions is considered valid for anaerobic assumption. 
 
Figure 8.7 Char residues after gasification experiments for PEI at 50 kW m-2. 
130 
 
Figure 8.8 Side views and Infrared images of bottom surfaces of the PEI sample 
undergoing gasification at 50 kW m-2. 
131 
Section 8.3 Modeling 
Section 8.3.1 ABS and PET 
ABS and PET virgin sample thicknesses were measured as 6.4 and 6.7 mm 
respectively at the room temperature. Then the density values for virgin ABS and 
PET are calculated as 1050 and 1385 kg m-3 respectively. The absorption coefficient 
values were found to be 1.71 and 1.40 m2 kg-1 for ABS and PET respectively. PET 
char was collected after completed decomposition at 50 kW m-2 ( experimental results 
show the sample is completely decomposed) and its bulk density was measured using 
a ruler and a balance at room temperature to measure its bulk volume and mass 
respectively. PET_melt density and absorption coefficient are assumed to be same as 
the values of PET. The PET char bulk density value is approximate to 80 kg m-3. As 
mentioned in the chapter 4, the density of PET_int is assumed to be the mean value of 
PET and PET_char. The absorption coefficient of PET_int is assumed same as the 
value of PET. The ABS char bulk density is assigned to be equal to the PET char bulk 
density value since the size of pure char produced at ABS gasification tests at 50 kW 
m-2 is fairly small, as demonstrated from Figure 8.1, therefore it is hardly to measure 
ABS char bulk volume using a ruler. The heat capacity of char produced by ABS 
thermal decomposition (was not measured in the milligram scale work) is assumed to 
be same as the PET char heat capacity which was measured and reported in Chapter 6.  
ABS and PET’s kinetic and thermodynamic properties were obtained from the 
milligram-scale study in the Chapter 5 and the Chapter 6, respectively. The mass 
transport coefficient and heat transfer boundary conditions were defined in the section 
4.3.  
132 
Section 8.3.2 Kydex and PEI 
Kydex and PEI virgin sample thicknesses were measured as 6.1 and 6.6 mm 
respectively at the room temperature. Then the density values for virgin Kydex and 
PEI are calculated as 1350 and 1285 kg m-3 respectively. The absorption coefficient 
values were found to be 1.58 and 1.36 m2 kg-1 for Kydex and PEI respectively. The 
PEI_melt density is assumed same as PEI. The char residues for both polymers were 
collected after gasification experiments at 50 kW m-2. This heat flux is chosen 
because it is considered as the most promising condition to obtain best char residue 
because of the following reasons. For Kydex, it was found that the char yield at this 
level of heat flux is close to the char yield value that obtained at TGA test, in which 
pyrolyzing sample is considered to be fully decomposed. In the case of PEI, 50 kW 
m-2 (the lowest heat flux used in PEI gasification experiments) is chosen because it 
was found that visible flame appears on top of pyrolyzing sample surface when the 
pyrolyzing sample swells into the cone heater only at 70 and 90 kW m-2. The flame is 
likely to destroy the PEI residue and brings less char yield compared to the non-
flaming situation at 50 kW m-2. The calculation of the residue density for Kydex and 
PEI was based on observation of the residue shape which is pyramid-like. The bulk 
volumes of the residue for both polymers were estimated carefully by measuring their 
lengths and heights with a ruler at room temperature. The entire mass of Kydex 
residue is considered to the mass of pure Kydex char and this char density is then 
calculated approximately to 100 kg m-3. Calculation on PEI char mass is somewhat 
different. At 50 kW m-2, PEI residue mass was found about 88 wt. % compared to its 
initial mass. This means about 12 wt. % of volatiles were escaped from the condensed 
phase and in the meanwhile, 12 wt. % of char was produced at the condensed phase 
133 
because, from the TGA result, PEI samples produces about 50 % char during thermal 
decomposition. Here the density of PEI char can be estimated by excluding the 
unpyrolyzed mass and volume from the entire residue mass and bulk volume and its 
value is found to about 80 kg m-3. As discussed in the chapter 4, the densities of 
intermediate component of those two polymers are assumed to be same as their char 
density.  
Kydex and PEI ’s kinetic and thermodynamic properties were obtained from 
the milligram-scale study in Chapter 6.  
Differently from boundaries characterization of the ABS and PET, the top 
surface of the Kydex and PEI samples rise significantly during the experiments and 
therefore, the prescribed heat flux that acting on the sample top surface is also 
increasing. ThermaKin allows linear external heat flux function in its one-
dimensional version. In addition to the bottom temperature and mass loss rate 
measurements for Kydex and PEI gasification experiments, the total heights from the 
sample top surface to its bottom were recorded by analyzing the video data obtained 
from the side camera. The Kydex pyrolyzing sample top surface is nearly flat during 
experiments (as demonstrated in Figure 8.6) and the top surface is considered as its 
maximum height. While PEI top surface experiences hill-like changes (as 
demonstrated in Figure 8.8), the value of the height for PEI (Figure 8.9 right part) is 
reported as 80% of its maximum height. The relation between the sample height and 
time for both polymers can be characterized at various heat fluxes by fitting them 
linearly, as illustrated in Figure 8.9. 
134 
      
Figure 8.9 Experimental measurements and linear fits for the height to sample bottom 
vs time for Kydex and PEI at various heat fluxes. 
Then these linear fits are used to calculate the relation of incident radiative 
heat flux on top surface and time, which are illustrated in Figure 8.10, since the heat 
flux at the elevated levels above sample initial surface level were already 
characterized in the section 4.3.3. In the ThermaKin model, the external heat flux for 
only these two polymers is set by a linear function and a constant value (dash line) 
from a transition point to the end of simulation as described in Figure 8.10. The 
transition point was chosen when the pyrolyzing sample top surface reaches nearly 
outside of the side camera visual field. After this point, the external radiative heat flux 
is assumed to be a constant value.  
135 
 
Figure 8.10 Relation of incident radiative heat flux on top surface and time. 
Section 8.4 Thermal conductivity calibration 
Section 8.4.1 ABS and PET 
When a polymer sample produces significant amount of char during thermal 
degradation and the char may form an intumescent structure, the sample’s 
temperature uniformity for this class of polymers fails. Therefore, instead of 
averaging 10 random selective cursors from three divided areas, the temperature 
profiles at the bottom part of charring samples are averaged by four random selective 
cursors which contain 36 pixels in individual area. In this way, the quality of its 
uniformity is displayed clearly by recognizing the differences among the three areas. 
The temperature differences among the three areas of sample bottom surface 
can be investigated by displaying average temperature within each area for charring 
polymers in this chapter [Section 7.3.2 presents the method for averaging over 3 
gasification experiments 90 pixels (36 from area 1, 36 from area 2, and 18 from area 
3) for non-charring polymers]. Only in this chapter, each area’s sample bottom 
surface temperature is displayed individually, as an example shown in Figure 8.11 
136 
(circles) for ABS bottom surface temperature histories at 30 kW m-2. Each data point 
in Figure 8.11 for all the areas were calculated by averaging pixels over 3 gasification 
experiments and 36 pixels were randomly selected within corresponding area in each 
experiment. 
The results of inverse modeling of this temperature are also presented in the 
Figure 8.11 (line). The thermal conductivities for ABS and ABS char and absorption 
coefficient for ABS char were adjusted (up to third order polynomial temperature-
dependent function) to fit the bottom surface temperature. Please note that the 
densities of all the components for all the polymers in this dissertation were not 
adjusted in the fitting. The thermal transport properties for all the components at 
condensed phase and their estimated uncertainties are reported in Table 8-2. The 
uncertainties were computed by propagating variation in the temperature 
measurements. 
 
Figure 8.11 Experimental and simulated bottom surface temperature histories 
obtained for ABS at 30 kW m-2. 
137 
Table 8-2 Thermal transport properties for ABS. 
Properties 
Density 
(kg m-3) 
Emissivity 
Absorption 
coefficient 
(m2 kg-1) 
Thermal conductivity 
(W m-1 K-1) 
ABS 1050 0.95 1.71 (0.30-2.810-4T ) ±10% 
ABS_char 80 0.86 31.25 (0.13-5.410-4T +4.810-9T 3) ±14% 
As demonstrated in Figure 8.12 and Figure 8.13, the derived thermal 
conductivity parameters also provide a good description of 50 and 70 kW m-2 bottom 
surface temperature histories in a reasonable degree of accuracy, which were not used 
as optimization targets.  
 
Figure 8.12 Experimental and simulated bottom surface temperature histories 
obtained for ABS at 50 kW m-2. 
138 
 
Figure 8.13 Experimental and simulated bottom surface temperature histories 
obtained for ABS at 70 kW m-2. 
For PET, back surface temperature measurements at 50 kW m-2 were 
considered as inverse modeling target. The thermal conductivities of all PET 
condensed phase components and PET char absorption coefficient were calibrated in 
the fitting process. The average sample bottom temperature history obtained for PET 
gasified at 50 kW m-2 of radiant heat flux is shown in Figure 8.14 (circles). This is the 
best fit obtained, although some discrepancies still exit. Table 8-3 lists all the heat 
transfer properties for PET. Then these properties are served as inputs for ThermaKin 
models to predict the sample bottom surface temperature at 70 kW m-2, provided all 
the other material properties are well measured and qualified in the previous chapters. 
Bottom temperature profile under 70 kW m-2, which is not served as the fitting target, 
is shown in Figure 8.15. From this figure, temperature differences among the three 
areas are clearly larger than the case at 50 kW m-2, especially when bottom 
temperature is above 500K. This is probably caused by the fast heating acting on the 
139 
pours char structure. Even though the model does not account this, the prediction is 
still within the uncertainties of the IR measurement up till about 600 K in a 
reasonable good degree. 
 
Figure 8.14 Experimental and simulated bottom surface temperature histories 
obtained for PET at 50 kW m-2. 
Table 8-3 Thermal transport properties for PET. 
Properties 
Density 
(kg m-3) 
Emissivity 
Absorption 
coefficient 
(m2 kg-1) 
Thermal conductivity 
(W m-1 K-1) 
PET 1385 0.95 1.4 (0.35-4.810-4T) ±8% 
PET_melt 1385 0.95 1.4 (0.33-210-5T) ±15% 
PET_int 730 0.95 1.4 (0.45+210-4T) ±20% 
PET_char 80 0.86 100 (0.45+3.810-5T +510-10T 3)±25% 
 
140 
 
Figure 8.15 Experimental and simulated bottom surface temperature histories 
obtained for PET at 70 kW m-2. 
Section 8.4.2 Kydex and PEI 
Kydex bottom surface temperatures for three different areas at 30 kW m-2 are 
plotted in Figure 8.16. As seen from this figure, the temperature uniformity appears 
good as least until 250 s which served as the thermal conductivity calibration 
optimization target (Figure 8.16). The thermal conductivities for condensed phase 
components are fitted and summarized in Table 8-4. Table 8-4 also provides 
Kydex_int and Kydex char absorption coefficients, which are also used in the 
optimization process. Cut-off time 250 s is chosen because, based on the observation 
from the side video camera, it is considered to be a critical point when Kydex sample 
is still under assumption of one-dimensional heat transfer. Beyond this point, the 
temperature data obtained from experiments is not used in the analysis. Figure 8.17 
illustrates the extend range of temperature measurements for three areas and model 
prediction. This one-dimensional model does not predict the measurements well due 
141 
to the reason of incorrect description of sample geometry. Please note that because 
the bottom surface areas shrink during the gasification tests, area 3 and area 2 
temperature measurements are only available partially. 
 
Figure 8.16 Experimental and simulated bottom surface temperature histories 
obtained for Kydex at 30 kW m-2 (fitted range). 
 
Figure 8.17 Experimental and simulated bottom surface temperature histories 
obtained for Kydex at 30 kW m-2. 
142 
Bottom temperature profiles under 50 and 70 kW m-2, which are not served as 
the fitting target, are shown in Figure 8.18 and Figure 8.19. Both of these predictions 
suggest the current model can predict the bottom in reasonable degree accuracy even 
though the entire Kydex pyrolysis is a complex non-one-dimensional problem.  
Table 8-4 Thermal transport properties for Kydex. 
Components 
Density 
(kg m-3) 
Emissivity 
Absorption 
coefficient 
(m2 kg-1) 
Thermal conductivity 
(W m-1 K-1) 
Kydex 1350 0.95 1.58 (0.28-2.910-4T) ±20% 
Kydex_int 100 0.95 30 (0.55+310-5T) ±15% 
Kydex_char 100 0.86 100 (0.28+8.410-5T +310-10T 3) ±25% 
 
 
Figure 8.18 Experimental and simulated bottom surface temperature histories 
obtained for Kydex at 50 kW m-2. 
143 
 
Figure 8.19 Experimental and simulated bottom surface temperature histories 
obtained for Kydex at 70 kW m-2. 
The thermal conductivities for all PEI condensed phase components were only 
optimized until 200 s when PEI sample is assumed to experience nearly one-
dimensional heat transfer by fitting with experimental measurements at lowest heat 
flux, which is 50 kW m-2. The absorption coefficients for the other condensed phase 
components were also optimized to improve the fit. And they are assumed to stay 
equal for simplicity. Table 8-5 summarizes the thermal transport properties that were 
measured and assumed for PEI. Figure 8.20 shows the experimental and fitted 
simulated data for PEI at this heat flux level for the fitted data range and Figure 8.21 
illustrates the extend temperature measurements and simulation.  
144 
 
Figure 8.20 Experimental and simulated bottom surface temperature histories 
obtained for PEI at 50 kW m-2 (fitted range). 
 
Figure 8.21 Experimental and simulated bottom surface temperature histories 
obtained for PEI at 50 kW m-2. 
The validations towards at higher external heat fluxes (70 and 90 kW m-2  are 
shown at Figure 8.22 and Figure 8.23. Unlike other polymers in this study, the 
145 
predictions are not good because of multiple reasons. The first and most important 
one is the thick char layers formed during gasification test at first 100 s (as can be 
demonstrated from Figure 8.24), which makes the PEI pyrolysis problem highly non-
one-dimensional. Secondly, one possible explanation is the inability to correct 
characterizes the top boundary condition in the model. As mentioned in the section 
8.3.2, the top surface radiation is assumed to be constant after a critical point in the 
model; however, this is not true as it observed in the experiments. When PEI samples 
top surface swelling and expanding into the cone heater, it receives much higher heat 
flux than it was set in the model. Thus the model underestimates the heat transferred 
into the PEI sample. The last but not least, in both cases, visible flame was observed 
on top of the sample and it brings additional heat loading towards the sample, which 
is not described in the model.  
Table 8-5 Thermal transport properties for PEI. 
Properties 
Density 
(kg m-3) 
Emissivity 
Absorption 
coefficient 
(m2 kg-1) 
Thermal conductivity 
(kJ kg-1 K-1) 
PEI 1285 0.95 1.36 (0.4-410-4T) ± 10% 
PEI_melt 1285 0.95 100 (0.32-3.310-4T) ± 14% 
PEI_int 80 0.95 100 (0.45+1.910-4T) ± 14% 
PEI_char 80 0.86 100 (0.5-3.410-5T +210-10T 3) ± 25% 
146 
 
Figure 8.22 Experimental and simulated bottom surface temperature histories 
obtained for PEI at 70 kW m-2. 
 
Figure 8.23 Experimental and simulated bottom surface temperature histories 
obtained for PEI at 90 kW m-2. 
147 
 
Figure 8.24 Side view snapshots of PET at 50-90 kW m-2. 
Section 8.5 Sample height and burning rate prediction 
Section 8.5.1 ABS and PET 
Figure 8.25 shows the experiment data (point) and model prediction (line) for 
the overall thickness of ABS at 50 kW m-2 (single test). For ABS, since no significant 
swelling or expanding was observed, thus the data shown in this figure only 
represents the maximum visible thickness direct from video and so does for PET 
(Figure 8.27). The total thickness was not seen clearly from the video data and it was 
observed to continue decreasing. 
148 
 
Figure 8.25 Experimental and simulated thickness histories obtained for ABS at 50 
kW m-2. 
A comparison of the burning rates computed using the fully parameterized 
ABS model with the results of the gasification experiments is shown in Figure 8.26. 
The model predicts the burning rates with the accuracy comparable with the 
experimental repeatability except at 30 kW m-2. At this heat flux level, as discussed 
earlier in this chapter, ABS produced extremely larger amount of residues at 30 kW 
m-2 , at which it was observed decomposed incompletely, than it did in 50 and 70 kW 
m-2. And this larger amount of residue forms thicker insulation layer on top of the 
virgin polymer and further affects the heat transfer inside the condensed phase. 
However, the model does not fully reflect the same amount of char residue in the 
ABS experiment. The effect of the char can be further demonstrated in the cases of 
external heat fluxes of 50 and 70 kW m-2, when ABS samples are nearly completed 
degradation. The largest discrepancy between experiment results and model 
prediction is found to be about 20 % on average at 30 kW m-2 from beginning up to 
149 
800 s. And these average values for 50 and 70 kW m-2 are computed less than 10 % 
up to 400 s and 250 s respectively.  
 
Figure 8.26 Experimental and simulated burning rate histories obtained for ABS at 
30-70 kW m-2. 
150 
The total thicknesses of PET for experiment (dot) and modeling (line) were 
shown in Figure 8.27. The dot data shows a single test data. The predication of model 
is good which demonstrates the volume consistency. 
 
Figure 8.27 Experimental and simulated thickness histories obtained for PET at 50 
kW m-2. 
A final comparison of the burning rates computed using the fully 
parameterized PET model with the results of the gasification experiments is shown in 
Figure 8.28. The model predicts the burning rates at two different stages of radiant 
heat fluxes with a notable improvement compared to an recent gasification 
experimental and modeling study on PET [40]. The mean discrepancies within 
experimental data and model prediction for 50 and 70 kW m-2 are calculated to be 
about 22 % ( up to 400 s) and 17 % (up to 350 s) respectively. 
151 
 
 
Figure 8.28 Experimental and simulated burning rate histories obtained for PET at 50 
and 70 kW m-2. 
Section 8.5.2 Kydex and PEI 
The heights of Kydex samples under thermal degradation of 50 kW m-2 with 
areas 1 and 3 range are plotted in Figure 8.29. In this figure, the top and bottom 
boundaries of the bars indicate the maximum and minimum heights of the sample 
measured from its bottom surface and represent the data of three independent tests 
within area 1 and area 3. The results are cut when the top surface of the sample 
reaches outside of the side camera vision. As expected, the simulated results do not 
152 
match the experimental data well because of reduction of the sample cross-section 
area (the model does not include this behavior). However, they match each other until 
100 s before the cross-section area changing significantly (as demonstrated in Figure 
8.29). 
A final comparison of the burning rates computed using the fully 
parameterized Kydex model with the results of the gasification experiments is shown 
in Figure 8.30. Although Kydex behaviors not purely one-dimensional pyrolysis, the 
model, which combines with previous knowledge on material kinetics and 
thermodynamics (Chapter 6), detail thermal transport properties and the enhanced top 
boundary characterization (this Chapter), predicts the burning rates with the mean 
discrepancies of experimental data and model prediction for 13 % (up to 950 s), 25% 
(up to 700 s) and 20 % (up to 600 s) for 30, 50 and 70 kW m-2 respectively. 
 
Figure 8.29 Experimental and simulated thickness histories obtained for Kydex at 50 
kW m-2. 
153 
 
Figure 8.30 Experimental and simulated burning rate histories obtained for Kydex at 
30 and 70 kW m-2. 
154 
The heights of PEI sample within the area 1 and area 3 were examined similar 
to the study of Kydex and the results at 50 kW m-2 are shown in Figure 8.31. The 
prediction is not good because the thermal expansion induced by density change was 
not characterized with a temperature-dependent variable in the model, which is 
indicative of the density temperature dependence needs further investigation.  
 
Figure 8.31 Experimental and simulated thickness histories obtained for PEI 
at 50 kW m-2. 
A final comparison of the burning rates computed using the fully 
parameterized PEI model with the results of the gasification experiments is shown in 
Figure 8.32. As one of the typical fire resistant polymers, the burning rate for PEI is 
extremely low, even at 90 kW m-2.  
From Figure 8.32, the predictions for all the conditions are relatively poor. 
The mean discrepancies of experimental data and model prediction for 27 % (up to 
700 s), 34% ( up to 600 s) and 44 % (up to 400 s) for 50, 70 and 90 kW m-2 
155 
respectively. There are several reasons that cause these uncertainties. The first one is 
the model external heat flux characterization, which is discussed in the section 8.3.2. 
The top surface external heat flux used in the model is underestimated for all heat 
fluxes because estimation for a constant external heat flux was made after a transition 
point (see details in the section 8.3.2). Therefore after this transition time the external 
heat flux in the model does not represent the actual external radiation. Secondly, the 
density characterization needs improvement. All the densities for the char estimation 
are crude estimation and assumed temperature-independent. But the changes of 
density in the experiment affect the total volume and further affect the heat transfer at 
the condensed phase. The last but not the least, which may contribute majorly to this 
uncertainly, is considered to be the oxidation effects during char swelling. As 
discussed in the section 8.2.2 clear visible flame were observed at 70 and 90 kW m-2 
when PEI sample top surface reaches into the cone heater, where oxygen 
concentration is considered to be much higher than the initial state. The increases on 
mass loss rate due to the effect of oxidation are demonstrated in Figure 8.32 for 70 
kW m-2 at about 350 s and 90 kW m-2 at about 300 s respectively, when visible flame 
appeared. 
 
156 
 
Figure 8.32 Experimental and simulated burning rate histories obtained for PEI at 50 
and 90 kW m-2. 
157 
Section 8.6 HRR calculation 
Standard cone calorimeter tests were also performed followed by the 
procedures described in [128] additionally for 3 non-charring polymer studied in 
Chapter 7 and 4 polymers parameterized in this chapter to obtain the effective heats 
of combustion (HOC) for those polymers. These tests were performed two times for 
each polymer and the average effective heat of combustion values are summarized in 
Appendix A-B. Note that the HOC values reported in this dissertation were obtained 
by the total heat release over the burning mass loss. Figure 8.33 displays maximum 
heat release rate verse heat flux for those seven polymers. The maximum heat release 
rate was calculated by multiplying the maximum gasification experiment (no flame) 
mass loss rate (time-averaged for 10 s to avoid unusual fluctuations) obtained from 
this study to the values of effective heat of combustion acquired from above 
discussion for the corresponding polymer. As demonstrated in Figure 8.33, the 
maximum heat release rate shows a linear tendency to the external heat flux. The fact 
that this linear tendency is indicative that the maximum heat release rate or burning 
rate at the bench-scale is primary defined by the process of heat transfer ( in the linear 
function to the external heat flux) at the condensed phase instead of the material 
kinetic decomposition, which is believed to highly non-linear to the external heat 
treatment. 
158 
 
Figure 8.33 Maximum heat release rate verse heat flux for polymers (These 
maximum heat release rates were calculated by multiplying the maximum gasification 
experiment burning rate and effective HOC values obtained from this study). 
  
159 
Chapter 9 : Concluding remarks 
This dissertation addressed the material flammability problem by developing 
and implementing a systematic methodology for parameterization and validation of 
continuum burning models over a number of representing polymeric materials 
including: widely used engineering plastics and promising high performance charring 
and intumescing polymers. The property values measured in this study form a 
foundation for a combustible material property database, which qualitatively improve 
the accuracy of fire growth simulations. The properties were measured and validated 
in the experiments performed at a wide range of scales and conditions. They are also 
validated against more than one numerical modeling solvers (see Appendix A), which 
further ensures that the property values reflect the fundamental aspects of material 
behavior and are neither test-specific nor model-specific. The modeling of this work 
helps reveal and close potential gaps in current understanding of polymer pyrolysis 
and clarify the roles and modes of heat and mass transport in the process of 
generation of gaseous fuels. 
The model developed for each material was shown to capture both mass loss 
and heat flow data. To the best of my knowledge, this is the first example of a 
systematic approach that yields a global reaction model that simultaneously 
reproduces both TGA and DSC measurements. In addition, this methodology has also 
been recently proved to be applied more complex composite materials such as 
corrugated cardboard [160] and demonstrates that it can be applied to a wide variety 
of combustible solids. Exothermicity of thermal degradation for some highly charring 
160 
polymers, which was not found for polymers by previous researches, were observed 
and reported in this dissertation. 
There are some novel methods in experimentally have been developed in this 
dissertation. In particular, temperature-dependent thermal conductivity of a solid 
material is extracted from material bottom surface temperature data in a 
computationally efficient way by an inverse modeling. Heat transfer through the solid 
was monitored by focusing an infrared camera on the bottom surface of a 
horizontally-mounted sample, which top surface faced the cone heater. The bottom 
surface of a testing material is designed expose to ambient air, which is significant 
differently from traditional experiments that are carried out in the cone calorimeter 
when the bottom surface is insulated. This new design allows possibility for the use 
of the non-contact nature of measurement. The use of an IR camera for the sample 
bottom surface thermometry with non-contact, spatially-resolved has been proved 
save time and effort in experiments and data analysis by at least factor of two prior to 
a previous design [137]. Spatial resolution of the temperature data (collected using 
the infrared camera) made it possible to assess the validity of the one-dimensional 
thermal transport assumption always invoked during analysis of this type of 
experiments. To the best of my knowledge, this is the first approach for monitoring 
both sample mass and temperature spatial data simultaneously applying an IR camera.  
A new method for recording material morphological in time change during a 
solid material gasification experiment has also been adopted to potentially allow 
further analyzing some intumescing polymers which representing overwhelming 
majority of the new generation of flame resistant materials. This part of work 
161 
provides possibility to detail study the char formation at different stage of gasification 
for this type of materials. 
The main distinguishing feature of our approach is that experimental burning 
rate histories, which serve as the main target for optimization-based methods, are not 
utilized in the property calculation. And this is completely different from many other 
material parameterization studies. Instead, they are employed to validate a fully 
parameterized model. This parameterization methodology minimizes possible 
compensation errors and extends the scope of the model validity. In essence, this 
combination of experiments and modeling represents a routine that generates 
complete property sets describing anaerobic pyrolysis of non-charring and charring 
polymers. The presented results clearly demonstrate that this routine produces 
consistent property values at a modest experimental cost. 
  
162 
Appendix A FDS simulation for non-charring polymers 
A completed investigation to check whether the data set obtained from this 
study is model-specific or not has been done by modeling the same scenario using a 
FDS pyrolysis model [65]. FDS is a fire-driven fluid flow computational fluid 
dynamics (CFD) 3D model which solves the Navier-Stokes equations numerically at 
low-speed (Ma < 0.3) velocity. This model is written with an emphasis on smoke and 
heat transport from fires. Besides the gas phase simulation, FDS’s pyrolysis model is 
also capable to predict the mass loss rate of a given material exposed to external heat 
flux at the condensed phase in a one-dimensional fashion, which is very similar to 
what ThermaKin does. The newest version is FDS 6.0.1 which was applied in this 
investigation. In this appendix results, all gas-phase reaction was essentially turned 
off by setting the mass fraction oxygen to 0.001 in the air to simulation the pyrolysis. 
Only a small domain was used in the simulation ((5510 rectangular cells, 0.05 
0.050.1m). The time step is set to 0.01s and it was found that increase or decrease 
this value by a factor of 10 does not affect the results. The boundary conditions were 
set same as the conditions used in ThermaKin.  
The difference between ThermaKin and FDS pyrolysis model is negligible at 
the condensed phase pyrolysis simulation [39, 107]. The major noticeable difference 
between those two models is the in-depth radiation absorption model selection. FDS 
treats the radiation transport within the condensed phase is a source term in the heat 
conservation equation while ThermaKin has two options:  The element that absorbs 
radiation is determined at every time step using either a maximum absorption or a 
random absorption algorithm [110]. While the maximum absorption algorithm is 
163 
employed, the element absorbs most of the radiation is assumed to absorb all of it, which 
is similar to the way FDS does. The FDS also does not consider the convection loss 
induced by the escape of volatiles, which is found to be small and the main reason of the 
difference between those two model results. Since FDS and ThermaKin use comparable 
physical descriptions of the fundamental physical and chemical phenomena, the choice of 
the model between those two models is less significant. Tables A. 1-3 summarized the 
properties of PMMA, POM and HIPS used in the FDS simulations, which are as same 
as the properties used in the ThermaKin simulations. The gasification tests were 
conducted CAPA [137], as described in the section 3.3.3.  
The reaction mechanism for PMMA is described as follows: 
                 (Reaction 1) 
                           (Reaction 2) 
Table A. 1 FDS Input Parameters for PMMA. 
Property Units Value Method Reference 
PMMA Density kg/m³ 1160 
Directly Determined through 
Volume and Mass Measurement [161] 
PMMA Conductivity W/m/K 
T < 378 K:  
0.45-3.810-4T 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
PMMA Specific Heat kJ/kg/K 0.60+0.0036T DSC [77] 
PMMA Emissivity   0.95 Literature [134] 
PMMA Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 1.94 (2240) Measured by Beer–Lambert law [161] 
PMMA_glass Density kg/m³ 1160 Assumed same as PMMA [161] 
PMMA_glass Conductivity W/m/K 
T  378 K:  
0.27-2.410-4T 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
PMMA_glass Specific Heat kJ/kg/K 0.60+0.0036T DSC [77] 
PMMA_glass Emissivity   0.95 Assumed same as PMMA [134] 
PMMA_glass Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 1.94 (2240) Assumed same as PMMA [161] 
PMMA_char Density kg/m³ 1160 Assumed same as PMMA [161] 
PMMA_char Conductivity W/m/K 0.27-2.410-4T Assumed same as PMMA_glass [161] 
PMMA_char Specific Heat kJ/kg/K 0.60+0.0036T Assumed same as PMMA_glass [77] 
164 
PMMA_char Emissivity   0.95 Assumed same as PMMA_glass [134] 
PMMA_char Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 1.94 (2240) Assumed same as PMMA [161] 
Reaction 1 Pre-Exponential 
Factor s‾¹ 1 
Assumed occur at 378 K 
instantaneously [77] 
Reaction 1 Activation 
Energy kJ/kmol 0 
Assumed occur at 378 K 
instantaneously [77] 
Reaction 1 Heat of Reaction 
per mass of Reactant kJ/kg 0 DSC [77] 
Reaction 1 Solid Residue   1 TGA [77] 
Reaction 2 Pre-Exponential 
Factor s‾¹ 8.60E+12 TGA [77] 
Reaction 2 Activation 
Energy kJ/kmol 1.88E+05 TGA [77] 
Reaction 2 Solid Residue   0.015 TGA [77] 
Reaction 2 Heat of Reaction 
per mass of Reactant kJ/kg 846 DSC [77] 
Effective HOC of volatiles kJ/kg 24450 ( 24800)* Standard cone calorimeter tests [162] 
Thickness mm 6.00 Directly measured [161] 
Top boundary temperature  K 
323 at 20 kW m-2 
348 at 40 kW m-2   
370 at 60 kW m-2 Directly measured [161] 
Top boundary convection 
coefficient W/m2/K 5 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
Bottom boundary 
temperature K 310 Directly measured [161] 
Bottom boundary 
convection coefficient W/m2/K 4 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
PMMA initial temperature K 305 Directly measured [161] 
* The value in the bracket is from literature and the value outside the bracket is from 
standard cone calorimeter measurement. 
The mass loss rates predicted by the simulations were used to validate the 
model against mass loss rate data collected in gasification tests. The parameters of the 
model were determined through analysis of material temperature data collected in 
gasification tests and the mass loss rate data was used only for blind validation of the 
model. The data collected in tests conducted with the CAPA at heat fluxes of 20, 40, 
and 60 kW m-2 and the results of simulations are provided in Figure A. 1. 
165 
 
 
  
Figure A. 1 Comparison of predicted and measured mass loss rates for PMMA. 
The reaction mechanism for POM is described as follows: 
              (Reaction 3) 
                                (Reaction 4) 
                                (Reaction 5) 
Table A. 2 FDS Input Parameters for POM. 
Property Units Value Method Reference 
POM Density kg/m³ 1424 
Directly Determined through 
Volume and Mass Measurement [161] 
POM Conductivity W/m/K 
0.25+1.610-5T 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
POM Specific Heat kJ/kg/K -1.86+0.0099T DSC [77] 
POM Emissivity   0.95 Literature [134] 
POM Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 2.12 (3050) Measured by Beer–Lambert law [161] 
POM_melt Density kg/m³ 1424 Assumed same as POM [161] 
166 
POM_melt Conductivity W/m/K 0.21+810-6T 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
POM_melt Specific Heat kJ/kg/K 1.65+0.0012T DSC [77] 
POM_melt Emissivity   0.95 Assumed same as POM [161] 
POM_melt Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 2.12 (3050) Assumed same as POM [161] 
POM_intermediate Density kg/m³ 1424 Assumed same as POM [161] 
POM_intermediate 
Conductivity W/m/K 0.19-610-5T 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
POM_intermediate Specific 
Heat kJ/kg/K 1.65+0.0012T Assumed same as POM_melt [77] 
POM_intermediate 
Emissivity   0.95 Assumed same as POM [134] 
POM_intermediate 
Absorption Coefficient 
m2 kg-1 
(m‾¹) 2.12 (3050) Assumed same as POM [161] 
POM_char Density kg/m³ 1424 
Assumed same as 
POM_intermediate [161] 
POM_char Conductivity W/m/K 0.19-610-5T 
Assumed same as 
POM_intermediate [161] 
POM_char Specific Heat kJ/kg/K 1.65+0.0012T 
Assumed same as 
POM_intermediate [77] 
POM_char Emissivity   0.95 
Assumed same as 
POM_intermediate [134] 
POM_char Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 2.12 (3050) Assumed same as POM [161] 
Reaction 3 Pre-Exponential 
Factor s‾¹ 2.69E+42 Fitted for melting process [77] 
Reaction 3 Activation 
Energy kJ/kmol 3.82E+05 Fitted for melting process [77] 
Reaction 3 Heat of Reaction 
per mass of Reactant kJ/kg 192.1 DSC [77] 
Reaction 3 Solid Residue   1 TGA [77] 
Reaction 4 Pre-Exponential 
Factor s‾¹ 3.84E+14 TGA [77] 
Reaction 4 Activation 
Energy kJ/kmol 2.00E+05 TGA [77] 
Reaction 4 Solid Residue   0.4 TGA [77] 
Reaction 4 Heat of Reaction 
per mass of Reactant kJ/kg 1192 DSC [77] 
Reaction 5 Pre-Exponential 
Factor s‾¹ 4.76E+44 TGA [77] 
Reaction 5 Activation 
Energy kJ/kmol 5.90E+05 TGA [77] 
Reaction 5 Solid Residue   0.018 TGA [77] 
Reaction 5 Heat of Reaction 
per mass of Reactant kJ/kg 1352 DSC [77] 
Effective HOC of volatiles kJ/kg 14350 (14400)* Standard cone calorimeter tests [162] 
Thickness mm 6.60 Directly measured [161] 
Top boundary temperature  K 
330 at 30 kW m-2 
360 at 50 kW m-2 
380 at 70 kW m-2 Directly measured [161] 
167 
Top boundary convection 
coefficient W/m2/K 5 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
Bottom boundary 
temperature K 310 Directly measured [161] 
Bottom boundary 
convection coefficient W/m2/K 4 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
POM initial temperature K 
305 at 30 kW m-2 
305 at 50 kW m-2 
310 at 70 kW m-2 Directly measured [161] 
* The value in the bracket is from literature and the value outside the bracket is from 
standard cone calorimeter measurement. 
The data collected in POM gasification tests conducted with the CAPA at heat 
fluxes of 30, 50, and 70 kW m-2 and the results of simulations are provided in Figure 
A. 2. 
  
 
 
 
Figure A. 2 Comparison of predicted and measured mass loss rates for POM. 
168 
The reaction mechanism for HIPS is described as follows: 
                    (Reaction 6) 
Table A. 3 FDS Input Parameters for HIPS. 
Property Units Value Method Reference 
HIPS Density kg/m³ 1060 
Directly Determined through 
Volume and Mass Measurement [161] 
HIPS Conductivity W/m/K 
0.1+1.010-4T 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
HIPS Specific Heat kJ/kg/K 0.59+0.0034T DSC [77] 
HIPS Emissivity   0.95 Literature [134] 
HIPS Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 2.14 (2250) Measured by Beer–Lambert law [161] 
HIPS_char Density kg/m³ 1424 Assumed same as HIPS [161] 
HIPS_char Conductivity W/m/K 0.21+810-6T Assumed same as HIPS [161] 
HIPS_char Specific Heat kJ/kg/K 1.65+0.0012T Assumed same as HIPS [77] 
HIPS_char Emissivity   0.95 Assumed same as HIPS [134] 
HIPS_char Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 1000 (106000) Assumed opaque [161] 
Reaction 6 Pre-
Exponential Factor s‾¹ 1.70E+20 TGA [77] 
Reaction 6 Activation 
Energy kJ/kmol 3.01E+05 TGA [77] 
Reaction 6 Heat of 
Reaction per mass of 
Reactant kJ/kg 689 DSC [77] 
Reaction 6 Solid Residue   0.043 TGA [77] 
Effective HOC of volatiles kJ/kg 29900 (29000)* Standard cone calorimeter tests [71] 
Thickness mm 6.00 Directly measured [161] 
Top boundary temperature  K 
330 at 30 kW m-2 
360 at 50 kW m-2 
380 at 70 kW m-2 Directly measured [161] 
Top boundary convection 
coefficient W/m2/K 5 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
Bottom boundary 
temperature K 310 Directly measured [161] 
Bottom boundary 
convection coefficient W/m2/K 4 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
HIPS initial temperature K 
305 at 30 kW m-2 
310 at 50 kW m-2 
310 at 70 kW m-2 Directly measured [161] 
* The value in the bracket is from literature and the value outside the bracket is from 
standard cone calorimeter measurement. 
169 
The data collected in HIPS gasification tests conducted with the CAPA at heat 
fluxes of 30, 50, and 70 kW m-2 and the results of simulations are provided in Figure 
A. 3. 
  
 
 
 
Figure A. 3 Comparison of predicted and measured mass loss rates for HIPS. 
  
170 
Appendix B Parameterized models for charring polymers 
In this appendix, the properties of the four polymers that studied in the Chapter 8 and 
the fully parameterized models are summarized. 
The reaction mechanism for ABS is described as follows: 
                   (Reaction 7) 
Table B. 1 Parameters for ABS. 
Property Units Value Method Reference 
ABS Density kg/m³ 1050 
Directly Determined through 
Volume and Mass Measurement 
 
ABS Conductivity W/m/K 
0.30-2.810-4T 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 ABS Specific Heat kJ/kg/K 1.58+0.0013T DSC [77] 
ABS Emissivity   0.95 Literature [134] 
ABS Absorption Coefficient 
m2 kg-1 
(m‾¹) 1.71 (1800) Measured by Beer–Lambert law 
 ABS_char Density kg/m³ 80 Assumed same as PET_char 
 
ABS_char Conductivity W/m/K 
0.13-5.410-
4T+4.810-9T3 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 ABS_char Specific Heat kJ/kg/K 0.82+1.1210-4T Assumed same as PET_char [79] 
ABS_char Emissivity   0.86 Literature [144] 
ABS_char Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 31.25 (2500) 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 Reaction 7 Pre-Exponential 
Factor s‾¹ 1.0E+14 Fitted for melting process [77] 
Reaction 7 Activation 
Energy kJ/kmol 2.19E+05 Fitted for melting process [77] 
Reaction 7 Heat of Reaction 
per mass of Reactant kJ/kg 460 DSC [77] 
Reaction 7 Solid Residue   0.023 TGA [77] 
Effective HOC of volatiles kJ/kg 28750 ( 29000)* Standard cone calorimeter tests [162] 
Thickness mm 6.40 Directly measured  
Top boundary temperature  K 
330 at 30 kW m-2 
360 at 50 kW m-2 
380 at 70 kW m-2 Directly measured [161] 
Top boundary convection 
coefficient W/m2/K 5 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
Bottom boundary 
temperature K 310 Directly measured [161] 
Bottom boundary 
convection coefficient W/m2/K 4 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
ABS initial temperature K 
305 at 30 kW m-2 
305 at 50 kW m-2 
310 at 70 kW m-2 Directly measured [161] 
171 
* The value in the bracket is from literature and the value outside the bracket is from 
standard cone calorimeter measurement. 
The reaction mechanism for PET is described as follows: 
              (Reaction 8) 
                                (Reaction 9) 
                                (Reaction 10) 
Table B. 2 Parameters for PET. 
Property Units Value Method Reference 
PET Density kg/m³ 1385 
Directly Determined through 
Volume and Mass Measurement 
 
PET Conductivity W/m/K 
0.35-4.810-4T 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 PET Specific Heat kJ/kg/K -0.269+0.00464T DSC [79] 
PET Emissivity   0.95 Literature [134] 
PET Absorption Coefficient 
m2 kg-1 
(m‾¹) 1.4 (1940) Measured by Beer–Lambert law 
 PET_melt Density kg/m³ 1385 Assume same as PET 
 
PET_melt Conductivity W/m/K 0.33-210-5T 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 PET_melt Specific Heat kJ/kg/K 2.05-2.0810-4T DSC [79] 
PET_melt Emissivity   0.95 Assumed same as PET 
 PET_melt Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 1.4 (1940) Assumed same as PET 
 
PET_intermediate Density kg/m³ 730 
Assumed to be average of PET 
and PET_char 
 PET_intermediate 
Conductivity W/m/K 0.45+210-4T 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 PET_intermediate Specific 
Heat kJ/kg/K 1.44-4.810-5T Assumed same as PET_melt [79] 
PET_intermediate 
Emissivity   0.95 Assumed same as PET [134] 
PET_intermediate 
Absorption Coefficient 
m2 kg-1 
(m‾¹) 1.4 (1025) Assumed same as PET  
PET_char Density kg/m³ 80 Directly measured   
PET_char Conductivity W/m/K 
0.45+3.810-
5T+510-10T3 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
PET_char Specific Heat kJ/kg/K 0.82+1.1210-4T DSC [79] 
PET_char Emissivity   0.86 Literature [144] 
PET_char Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 100 (8000) 
Inverse Analysis of Material 
Temperature in Gasification Exp.  
Reaction 8 Pre-Exponential 
Factor s‾¹ 1.5E+36 Fitted for melting process [79] 
172 
Reaction 8 Activation 
Energy kJ/kmol 3.80E+05 Fitted for melting process [79] 
Reaction 8 Heat of Reaction 
per mass of Reactant kJ/kg 30 DSC [79] 
Reaction 8 Solid Residue   1 TGA [79] 
Reaction 9 Pre-Exponential 
Factor s‾¹ 1.60E+15 TGA [79] 
Reaction 9 Activation 
Energy kJ/kmol 2.35E+05 TGA [79] 
Reaction 9 Solid Residue   0.18 TGA [79] 
Reaction 9 Heat of Reaction 
per mass of Reactant kJ/kg 220 DSC [79] 
Reaction 10 Pre-
Exponential Factor s‾¹ 3.53E+04 TGA [79] 
Reaction 10 Activation 
Energy kJ/kmol 9.6E+04 TGA [79] 
Reaction 10 Solid Residue   0.72 TGA [79] 
Reaction 10 Heat of 
Reaction per mass of 
Reactant kJ/kg 250 DSC [79] 
Effective HOC of volatiles kJ/kg 15950 (18000)* Standard cone calorimeter tests [162] 
Thickness mm 6.70 Directly measured  
Top boundary temperature  K 
360 at 50 kW m-2 
380 at 70 kW m-2 Directly measured [161] 
Top boundary convection 
coefficient W/m2/K 5 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
Bottom boundary 
temperature K 310 Directly measured [161] 
Bottom boundary 
convection coefficient W/m2/K 4 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
PET initial temperature K 
310 at 50 kW m-2 
310 at 70 kW m-2 Directly measured [161] 
* The value in the bracket is from literature and the value outside the bracket is from 
standard cone calorimeter measurement. 
The reaction mechanism for Kydex is described as follows: 
                              (Reaction 11) 
                                    (Reaction 12) 
Table B. 3 Parameters for Kydex. 
Property Units Value Method Reference 
Kydex Density kg/m³ 1350 
Directly Determined through 
Volume and Mass Measurement 
 
Kydex Conductivity W/m/K 
0.28-2.910-4T 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 
173 
Kydex Specific Heat kJ/kg/K -0.624+0.00593T DSC [79] 
Kydex Emissivity   0.95 Literature [134] 
Kydex Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 1.58 (2135) Measured by Beer–Lambert law 
 Kydex_intermediate  
Density kg/m³ 100 Assumed same as Kydex_char 
 Kydex_intermediate  
Conductivity W/m/K 0.55+310-5T 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 Kydex_intermediate  
Specific Heat kJ/kg/K 0.265+0.00301T DSC [79] 
Kydex_intermediate  
Emissivity   0.95 Assumed same as Kydex [134] 
Kydex_intermediate  
Absorption Coefficient 
m2 kg-1 
(m‾¹) 30 (3000) 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
Kydex_char Density kg/m³ 100 Directly measured  [161] 
Kydex_char Conductivity W/m/K 
0.28+8.410-
5T+310-10T3 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
Kydex_char Specific Heat kJ/kg/K 1.15+9.5610-5T DSC  [79] 
Kydex_char Emissivity   0.86 Literature [144] 
Kydex_char  Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 100 (10000) 
Inverse Analysis of Material 
Temperature in Gasification Exp.  
Reaction 11 Pre-
Exponential Factor s‾¹ 6.03E+10 TGA [79] 
Reaction 11 Activation 
Energy kJ/kmol 1.41E+05 TGA [79] 
Reaction 11 Heat of 
Reaction per mass of 
Reactant kJ/kg 180 DSC [79] 
Reaction 11 Solid Residue   0.45 TGA [79] 
Reaction 12 Pre-
Exponential Factor s‾¹ 1.36E+10 TGA [79] 
Reaction 12 Activation 
Energy kJ/kmol 1.74E+05 TGA [79] 
Reaction 12 Solid Residue   0.31 TGA [79] 
Reaction 12 Heat of 
Reaction per mass of 
Reactant kJ/kg 125 DSC [79] 
Effective HOC of volatiles kJ/kg 12650 Standard cone calorimeter tests  
Thickness mm 6.10 Directly measured  
Top boundary temperature  K 
330 at 30 kW m-2 
360 at 50 kW m-2 
380 at 70 kW m-2 Directly measured [161] 
Top boundary convection 
coefficient W/m2/K 5 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
Bottom boundary 
temperature K 310 Directly measured [161] 
Bottom boundary 
convection coefficient W/m2/K 4 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
Kydex initial temperature K 
300 at 30 kW m-2 
310 at 50 kW m-2 
310 at 70 kW m-2 Directly measured [161] 
 
174 
The reaction mechanism for PEI is described as follows: 
              (Reaction 13) 
                                (Reaction 14) 
                                (Reaction 15) 
Table B. 4 Parameters for PEI. 
Property Units Value Method Reference 
PEI Density kg/m³ 1285 
Directly Determined through 
Volume and Mass Measurement 
 
PEI Conductivity W/m/K 
0.4-4.010-4T 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 PEI Specific Heat kJ/kg/K -0.0357+0.0041T DSC [79] 
PEI Emissivity   0.95 Literature [134] 
PEI Absorption Coefficient 
m2 kg-1 
(m‾¹) 1.36 (1745) Measured by Beer–Lambert law 
 PEI_melt Density kg/m³ 1285 Assumed same as PEI 
 
PEI_melt Conductivity W/m/K 0.32-3.310-4T 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 PEI_melt Specific Heat kJ/kg/K 1.88+5.7510-4T DSC [79] 
PEI_melt Emissivity   0.95 Assumed same as PEI 
 PEI_melt Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 100 (128500) 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 PEI_intermediate Density kg/m³ 80 Assumed same as PEI_char 
 PEI_intermediate 
Conductivity W/m/K 0.45+1.910-4T 
Inverse Analysis of Material 
Temperature in Gasification Exp. 
 PEI_intermediate Specific 
Heat kJ/kg/K 1.59+3.0810-4T Assumed same as PEI_melt [79] 
PEI_intermediate 
Emissivity   0.95 Assumed same as PEI [134] 
PEI_intermediate 
Absorption Coefficient 
m2 kg-1 
(m‾¹) 100 (8000) Assumed same as PEI_melt  
PEI_char Density kg/m³ 80 
Directly Determined through 
Volume and Mass Measurement  
PEI_char Conductivity W/m/K 
0.5-3.410-
5T+210-10T3 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
PEI_char Specific Heat kJ/kg/K 1.30+4.0810-5T DSC [79] 
PEI_char Emissivity   0.86 Literature [144] 
PEI_char Absorption 
Coefficient 
m2 kg-1 
(m‾¹) 100 (80000) Assumed same as PEI_melt  
Reaction 13 Pre-
Exponential Factor s‾¹ 1 
Assumed occur at 496 K 
instantaneously [79] 
Reaction 13 Activation 
Energy kJ/kmol 0 
Assumed occur at 496 K 
instantaneously [79] 
Reaction 13 Heat of 
Reaction per mass of 
Reactant kJ/kg 1 DSC [79] 
175 
Reaction 13 Solid Residue   1 TGA [79] 
Reaction 14 Pre-
Exponential Factor s‾¹ 7.66E+27 TGA [79] 
Reaction 14 Activation 
Energy kJ/kmol 4.65E+05 TGA [79] 
Reaction 14 Solid Residue   0.65 TGA [79] 
Reaction 14 Heat of 
Reaction per mass of 
Reactant kJ/kg -80 DSC [79] 
Reaction 15 Pre-
Exponential Factor s‾¹ 6.5E+02 TGA [79] 
Reaction 15 Activation 
Energy kJ/kmol 8.8E+04 TGA [79] 
Reaction 15 Solid Residue   0.77 TGA [79] 
Reaction 15 Heat of 
Reaction per mass of 
Reactant kJ/kg -5 DSC [79] 
Effective HOC of volatiles kJ/kg 18050 (16700)* Standard cone calorimeter tests [162] 
Thickness mm 6.60 Directly measured  
Top boundary temperature  K 
360 at 50 kW m-2 
380 at 70 kW m-2 
400 at 90 kW m-2 Directly measured [161] 
Top boundary convection 
coefficient W/m2/K 5 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
Bottom boundary 
temperature K 310 Directly measured [161] 
Bottom boundary 
convection coefficient W/m2/K 4 
Inverse Analysis of Material 
Temperature in Gasification Exp. [161] 
PEI initial temperature K 
305 at 50 kW m-2 
315 at 70 kW m-2 
315 at 90 kW m-2 Directly measured [161] 
* The value in the bracket is from literature and the value outside the bracket is from 
standard cone calorimeter measurement. 
  
176 
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