polymers Article
Development of a Semiglobal Reaction Mechanism for the Thermal Decomposition of a Polymer Containing Reactive Flame Retardants: Application to Glass-Fiber-Reinforced Polybutylene Terephthalate Blended with Aluminum Diethyl Phosphinate and Melamine Polyphosphate Yan Ding 1 , Stanislav I. Stoliarov 1, * and Roland H. Kraemer 2 1 2
*
Department of Fire Protection Engineering, University of Maryland, 3106 J.M. Patterson Building, College Park, MD 20742, USA;
[email protected] Flame Retardancy & Performance Polymers Research, BASF Advanced Chemicals Co., Ltd., No 300 Jiangxinsha Road, Pudong, Shanghai 200137, China;
[email protected] Correspondence:
[email protected]; Tel.: +301-405-0928
Received: 17 September 2018; Accepted: 10 October 2018; Published: 12 October 2018
Abstract: This work details a methodology for parameterization of the kinetics and thermodynamics of the thermal decomposition of polymers blended with reactive additives. This methodology employs Thermogravimetric Analysis, Differential Scanning Calorimetry, Microscale Combustion Calorimetry, and inverse numerical modeling of these experiments. Blends of glass-fiber-reinforced polybutylene terephthalate (PBT) with aluminum diethyl phosphinate and melamine polyphosphate were used to demonstrate this methodology. These additives represent a potent solution for imparting flame retardancy to PBT. The resulting lumped-species reaction model consisted of a set of first- and second-order (two-component) reactions that defined the rate of gaseous pyrolyzate production. The heats of reaction, heat capacities of the condensed-phase reactants and products, and heats of combustion of the gaseous products were also determined. The model was shown to reproduce all aforementioned experiments with a high degree of detail. The model also captured changes in the material behavior with changes in the additive concentrations. Second-order reactions between the material constituents were found to be necessary to reproduce these changes successfully. The development of such models is an essential milestone toward the intelligent design of flame retardant materials and solid fuels. Keywords: polymer combustion; pyrolysis; flame retardants; thermal analysis; inverse modeling; ThermaKin
1. Introduction The combustion of polymeric materials can be characterized as a coupling between gas-phase and condensed-phase phenomena. The condensed-phase phenomena, broadly referred to as pyrolysis, have been less understood due to their inherent complexity and a lack of experimental capabilities for direct monitoring of relevant chemical transformations [1,2]. The kinetics of thermal decomposition is, perhaps, the most important characteristic of the pyrolysis process [3]. This kinetics is usually derived from a global measurement, such as thermogravimetric analysis (TGA), which provides information on mass loss from a thermally thin sample exposed to a linear temperature ramp.
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provides information on mass loss from a thermally thin sample exposed to a linear temperature ramp. Polymers 2018, 10, 1137 2 of 14 Isoconversional methods [4–6], which require TGA data collected at multiple heating rates and/or temperatures, have been widely used to determine kinetic parameters of decomposition. Isoconversional which require TGA data at multiple heating These methods utilizemethods a single [4–6], (global) reaction to represent thecollected overall decomposition process.rates The and/or temperatures, have been widely used to determine kinetic parameters of decomposition. complexity of decomposition, which may include thousands of elementary steps, is captured via a These methods utilize aenergy single with (global) represent the decomposition variation of activation the reaction extent oftoconversion. Oneoverall significant drawback process. of these The complexity decomposition, which may include thousands of elementary is captured methods is thatof they do not naturally extend to multicomponent materials,steps, especially when via a variation of activation energy with the extent of conversion. One significant drawback of components chemically interact with each other at elevated temperature. theseIn methods is that do kinetic not naturally extend to multicomponent especially when addition to they global models, several highly detailedmaterials, mechanisms of thermal components chemically interact with each elevated temperature. decomposition have been developed for aother few at commodity plastics [7,8]. These mechanistic models In addition to global kinetic models, several detailed mechanisms of thermal decomposition include hundreds of species and thousands ofhighly elementary reactions and provide a molecular-level have been developed for a few commodity plastics [7,8].have These mechanistic models include hundreds insight into the decomposition process. These models also been demonstrated to capture crossof specieschemical and thousands of elementary reactions and provide a molecular-level insight into the polymer interactions in binary blends undergoing pyrolysis [9–11]. The main drawback of decomposition These models have alsofor been demonstrated capture cross-polymer chemical such models isprocess. the formidable effort required their constructiontoand validation. They also require interactions blends of undergoing pyrolysiswhich [9–11]. main drawback of directly. such models is estimation ofina binary large number kinetic parameters areThe impossible to measure Finally, the formidable effort required for their construction and validation. They also require estimation the high computational cost of these models precludes their use in simulations of large physical of a large number of kinetic parameters which are impossible to measure directly. Finally, the high systems. computational these models in simulations physical systems. Over the cost pastofseveral years, precludes our grouptheir hasuse been developing of anlarge approach where polymer Over the past severalusing years,a small our group has been developing approach where polymer decomposition is modeled number (1 to 15) of Arrheniusan reactions of the first or second decomposition is modeled small number to 15) ofAArrhenius of the first or second order [12–18]. This featureusing of oura approach is not(1unique. number ofreactions researchers constructed their order [12–18]. This feature models of our approach is not unique.ofAconsecutive number of or researchers constructed their solid fuels decomposition from a small number parallel reactions [1,19,20]. solid decomposition models from a small to number of consecutive parallel reactions [1,19,20]. The fuels resulting model is frequently referred as a semiglobal or or lumped-species model. The The resulting model is frequently referred toisasthat a semiglobal or lumped-species model. distinguishing feature of our approach it is not based on TGA data aloneThe butdistinguishing also relies on feature of our approach is that Scanning it is not based on TGA(DSC) data alone but also relies on fully quantitative fully quantitative Differential Calorimetry and Microscale Combustion Calorimetry Differential Scanning Calorimetry andprocess, Microscale Calorimetry measurements. (MCC) measurements. Using an(DSC) iterative theCombustion simplest reaction model(MCC) that simultaneously Using an iterative process, reaction modelisthat simultaneously captures model the results of all of captures the results of allthe ofsimplest these measurements constructed and multiple parameters these measurements is constructed and multiple model parameters including stoichiometric coefficients, including stoichiometric coefficients, activation energies, pre-exponential factors, heat capacities of activation energies, pre-exponential factors, heat capacities the condensed-phase reactants and the condensed-phase reactants and products, heats ofof melting and decomposition, andproducts, heats of heats of melting andgaseous decomposition, andare heats of combustion of the gaseous pyrolyzate are derived. combustion of the pyrolyzate derived. In In aa recent recent publication publication [18], [18], we we showed showed evidence evidence indicating indicating that that itit isis possible possible to to extend extend this this methodology methodologyto toaabinary binary mixture mixtureof of reactive reactive components componentsand andcreate createaa semiglobal semiglobal reaction reactionmechanism mechanism that that successfully successfully captures captures the the degradation degradation behavior behavior over over aabroad broadrange rangeof ofmixture mixturecompositions. compositions.In In the thecurrent currentstudy, study,we weprovide providefurther furthervalidation validationof ofthis thisassertion assertionby bydemonstrating demonstratingthat thatthis thisapproach approach can can be beextended extended to totertiary tertiaryreactive reactiveblends. blends. The The subject subject of ofthe thecurrent currentinvestigation investigationisispolybutylene polybutylene terephthalate terephthalate(PBT) (PBT)reinforced reinforcedwith withglass glassfiber fiber(GF) (GF)and andblended blendedwith withaluminum aluminumdiethyl diethyl phosphinate phosphinate (DEPAL) (DEPAL)and andmelamine melaminepolyphosphate polyphosphate(MPP). (MPP).The Thechemical chemical structures structures of of the thepolymer polymerand andthe thetwo two flame flameretardant retardantadditives additivesare areshown shownin inFigure Figure1.1.
Figure Figure1. 1. Chemical Chemical structures structuresof of polymer polymer (polybutylene (polybutylene terephthalate terephthalate(PBT)) (PBT))and andtwo twoflame flameretardant retardant additives additives(aluminum (aluminumdiethyl diethylphosphinate phosphinate(DEPAL) (DEPAL)and andmelamine melaminepolyphosphate polyphosphate(MPP)). (MPP)).
PBT widely used usedin inelectrical electricalsystems, systems,including including lamp holders, switches, circuit breakers, PBT is is widely lamp holders, switches, circuit breakers, and and motor casings. It has high heat resistance, mechanical strength, and water resistance, and motor casings. It has high heat resistance, mechanical strength, and water resistance, and excellent excellent electrical insulating properties [21]. However, pure PBT is flammable. GF is added to PBT to prevent dripping and to help maintain integrity upon burning. Phosphorus-based compounds are added to
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PBT to improve fire resistance [22–24]. Melamine derivatives (such as MPP) have been shown to act as a synergist to phosphorus flame retardants to further enhance the fire resistance of the blends [24–26]. Several studies have been conducted to understand the pyrolysis and fire behavior of flame retardant PBT/GF [22,24]. Braun et al. [22] found that an addition of 13–20 wt % of DEPAL in combination with melamine cyanurate improves the fire retardancy of PBT/GF significantly (UL-94 rating of V0 and limiting oxygen index above 42% were achieved). DEPAL was hypothesized to act primarily through a release of phosphinate compounds that inhibited the chemistry of the gas-phase combustion. It was also noted that DEPAL increases carbonaceous residue (char) production and thus creates an additional thermal barrier and further improves mechanical stability of the material exposed to flame. None of the studies provided a quantitative relation between the thermal decomposition behavior of PBT/GF blends and flame retardant content. Knowledge of this relation is critical for the design of materials with the optimum combination of flame resistance and mechanical properties tailored for specific applications [27]. 2. Materials and Methods 2.1. Materials The materials studied in this work were provided by BASF (Ludwigshafen am Rhein, Rhineland-Palatinate, Germany). Compounds were produced in a twin-screw extruder and subsequently injection-molded [28] into 3.8 mm thick plates. Their compositions are shown in Table 1. The top five blends were used to build the reaction mechanism; the last three were employed to demonstrate the mechanism’s ability to extrapolate beyond the compositions used in the building process. Additional experiments were conducted on pure MPP (not listed in Table 1) supplied in the form of powder. The results of these experiments were also used in the mechanism construction. Table 1. Composition of tested materials. Formulation Name
PBT (wt %) Ultradur B4500
GF (wt %) Glassfiber PPG 3786
DEPAL (wt %) Exolit OP 1240
MPP (wt %) Melapur 200
Model Development
PBT/GF25 PBT/GF25-DEPAL8 PBT/GF25-DEPAL16 PBT/GF25-MPP4 PBT/GF25-MPP8
75 67 59 71 67
25 25 25 25 25
0 8 16 0 0
0 0 0 4 8
Model Validation
PBT PBT/GF25-DEPAL8-MPP4 PBT/GF25-DEPAL16-MPP8
100 63 51
0 25 25
0 8 16
0 4 8
The samples for TGA, DSC, and MCC tests were prepared by either cutting or grinding the plates into 3–7 mg specimens. Each test was repeated multiple times using varying sample mass and shape to verify that the test results were not sensitive to these factors and thus ensure thermally thin behavior (i.e., no significant temperature or composition gradients within the sample). All samples were conditioned in a desiccator in the presence of Drierite for a minimum of 48 h prior to testing to obtain measurements with negligible contribution from moisture. 2.2. Simultaneous Thermal Analysis (STA) 449 F3 Jupiter Simultaneous Thermal Analyzer (Netzsch Geratebau GmbH, Selb, Bavaria, Germany) was employed to conduct TGA and DSC tests simultaneously. All STA tests followed a carefully prescribed temperature program. The temperature program for these tests had a conditioning period in which the sample was maintained at 313 K for 25 min, followed by a linear heating up to 873 K. The majority of the tests were conducted at a nominal heating rate of 10 K·min−1 to ensure that the heating rate was sufficiently low to decouple the chemical reactions from the mass and thermal transport. The furnace was continuously purged with nitrogen at a flow rate of 50 mL·min−1
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to guarantee an anaerobic environment. Platinum–Rhodium crucibles with lids containing a small opening were utilized to maximize heat flow sensitivity and temperature uniformity. The sample mass and heat flow data were collected as a function of time and pyrolyzing sample temperature. An empty crucible baseline was collected prior to every test and subtracted from the corresponding data obtained with a sample. A detailed description of the instrument calibration and testing protocol can be found in an earlier publication [12]. The STA tests of the five blends used in the reaction model development (see Table 1) were conducted at 10 K·min−1 and were repeated ten times to ensure reproducibility and accumulate the necessary statistics. Additional tests of these blends were performed at 5 and 20 K·min−1 . These tests were repeated three times and were used to verify that the developed reaction model correctly extrapolates the material’s behavior to alternate thermal conditions. Only TGA data were collected in these additional tests because of their significantly higher reproducibility. The STA tests on the remaining three (model validation) blends were conducted at 10 K·min−1 and repeated five times. Finally, the TGA tests of MPP were performed at 10 K·min−1 in triplicate. 2.3. Microscale Combustion Calorimetry MCC is a standardized test method used to measure the heat release rate (HRR) from complete combustion of gaseous products evolved from a pyrolyzing solid. The MCC tests were performed at the same prescribed heating rate of 10 K·min−1 as used in the STA tests to enable a direct comparison with the STA measurements. A slightly higher temperature of 348 K was set as the initial temperature. All the samples were pyrolyzed in a ceramic crucible without a lid. The gaseous pyrolyzate was purged by nitrogen at a flow rate of 80 mL·min−1 into the combustor, where the pyrolyzate was mixed with excess oxygen, supplied at a flow rate of 20 mL·min−1 , and oxidized. The temperature of the combustor was set at 1173 K to ensure completeness of the combustion process. The heat released from the combustion process was measured using the principle of oxygen consumption [29]. The HRR was measured as a function of time and pyrolyzing sample temperature. The MCC apparatus was carefully calibrated following the recommended procedures [29]. The MCC tests were performed on the materials used in the reaction model development. Each test was repeated three times to ensure reproducibility. 2.4. Modeling ThermaKin [30,31] is a numerical modeling environment that was developed to compute the transient rate of gaseous fuel production by a pyrolyzing solid. Non-steady mass and energy conservation equations are solved by ThermaKin to account for the fundamental physical and chemical processes occurring in the condensed phase during pyrolysis. First- and second-order (two-component) chemical reactions are represented in ThermaKin using the Arrhenius expression for the reaction rate constants. ThermaKin was employed in this study to inversely model the TGA, DSC, and MCC data to determine the kinetics and thermodynamics of the thermal decomposition as well as the heats of combustion of the gaseous decomposition products. In the current model setup, all samples were treated as thermally thin and simulated using a single element (i.e., no temperature or composition gradients inside the samples). The convection coefficient at the element boundary was defined as sufficiently high (1 × 105 W·m−2 ·K−1 ) to ensure that the element’s temperature follows the corresponding mean experimental temperature profile. This profile was approximated by expressing the heating rate as an exponentially decaying sinusoidal function. This function was used to correctly account for deviations of the instantaneous experimental heating rate from the nominal (or set) rate with time, as explained in detail in earlier publications [15,17]. The mass flow boundary condition was defined such that all gaseous decomposition products escaped the element instantaneously.
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3. Results and Discussion 3.1. Overall Approach to Reaction Model Development The development of a generalized reaction model for the PBT/GF/DEPAL/MPP blends consisted of five steps. In the first step, a PBT decomposition model was derived from the TGA and DSC data obtained for the PBT/GF25 blend. The GF component was assumed to be nonvolatile and chemically inert. In the second step, an attempt was made to simulate the TGA and DSC data obtained for the PBT/GF/DEPAL blends using a combination of the PBT decomposition model and DEPAL decomposition model, which was based on information available in the literature [32]. Significant differences between these simulations and experimental data were identified. These differences were interpreted as evidence of a chemical interaction between the polymer matrix and DEPAL. The reaction parameters of this interaction were initially estimated through a fitting of the TGA and DSC data obtained for PBT/GF25-DEPAL8 (a blend with a low concentration of DEPAL) and further adjusted by fitting of the data collected for PBT/GF25-DEPAL16 (a blend with a high concentration of DEPAL) until the best compromise in representing both datasets was achieved. In the third step, the same procedure was used to develop a reaction mechanism for the PBT/GF/MPP blends. In the fourth step, the combined reaction model (including PBT, DEPAL, and MPP decomposition, as well as PBT–DEPAL and PBT–MPP interactions) was employed to simulate experimental MCC data for all blends used for the reaction model development (see Table 1). Heats of combustion of all gaseous products were derived from these simulations. In the final step, the combined reaction model was validated by testing its ability to predict TGA and DSC data at heating rates and for material compositions not used in the model development process. 3.2. Inverse Modeling of TGA and DSC Data for PBT/GF25 The mean experimental results of TGA and DSC tests conducted on the PBT/GF25 material are shown as symbols in Figure 2. Figure 2a shows the dependence of sample mass, m, and mass loss rate, MLR, normalized by the initial mass, m0 , on temperature, T. Figure 2b contains the initial-sample-mass normalized heat flow and integral heat flow as a function of temperature. The error bars were calculated from the scatter of the experimental data as two standard deviations of the mean (some error bars are comparable in size to the data symbols and, therefore, not shown). The experimental MLR profile contains a single peak at 680 K corresponding to the thermal decomposition process. The decomposition produced 31.5 wt % of residue including 25 wt % of GF. The heat flow curve contains two distinct maxima. The first (500 K) and second (680 K) maxima represent the melting and decomposition processes, respectively. Inverse modeling of the TGA and DSC data was performed using the approach described in detail in earlier publications [15–18]. Only a brief description is provided here. A single first-order reaction was initially employed to model the TGA data. The mass-based stoichiometric coefficients of this reaction were initially set to capture the residue yield observed in the TGA experiments. The Arrhenius parameters of this reaction were initially estimated using analytical expressions [33] relating these parameters to the temperature and height of the targeted MLR peak. Subsequently, these parameters were refined through a manually iterative process using ThermaKin until the modeling results were found to be in agreement with the experimental data. The reaction parameter manipulation was based on the following observations: an increase in the activation energy (E) shifted the MLR curve to a higher temperature and reduced the height of the peak; an increase in the pre-exponential factor (A) shifted the MLR curve to a lower temperature and increased the height of the peak. The agreement was declared to be satisfactory when the differences between the average experimental and modeled final mass residues and the temperatures and magnitudes of the MLR maxima were found to be within 3%, 5 K, and 8%, respectively. If it was impossible to achieve such agreement, an additional
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reaction was added to the reaction scheme and its parameters were adjusted iteratively to achieve further Polymers improvement. 2018, 10, x FOR PEER REVIEW 6 of 14
−1−1.. Figure2. 2. Experimental Experimentaland andsimulated simulated(a) (a)TGA TGAand and(b) (b)DSC DSCdata dataobtained obtained PBT/GF25atat1010KK min Figure forfor PBT/GF25 ·min
In two consecutive consecutive reactions, Reaction 2 and 3, were required required to accurately In the the case case of of PBT/GF25, two accurately capture defined inin Table 2. capture the theinitial initialrise, rise,maximum, maximum,and andfinal finaldecay decayofofthe theMLR. MLR.These Thesereactions reactionsare are defined Table The component namesnames used inused the reaction are self-explanatory. The reaction contributions 2. The component in the definitions reaction definitions are self-explanatory. The reaction to MLR profiles depicted Figure 2; their areparameters summarized Table 3. contributions toare MLR profilesinare depicted in parameters Figure 2; their areinsummarized in Table 3. mechanism for all examined in this study. Thestudy. stoichiometric coefficients Table Table2.2.Reaction Reaction mechanism forthe allmaterials the materials examined in this The stoichiometric are mass-based. coefficients are mass-based. Reactive Blend Reactive Blend # Components Components 1 PBTPBT 2 3 4 PBT and DEPAL PBT and DEPAL 5 6 PBT and MPP PBT and MPP 7 8
#
ReactionEquation Equation Reaction
PBT→→PBT_Melt PBT_Melt PBT PBT_Melt 0.84PBT_Res1 PBT_Res1 ++ 0.16 0.16 PBT_Gas1 PBT_Melt →→ 0.84 PBT_Gas1 PBT_Res1 → 0.12 PBT_Res2 + 0.88 PBT_Gas2 PBT_Res1 → 0.12 PBT_Res2 + 0.88 PBT_Gas2 a DEPAL_Res1 + 0.93a DEPAL_Gas1 4 DEPAL → 0.07 + 0.93a DEPAL_Gas1 DEPAL → 0.07a DEPAL_Res1 5 PBT_Melt + 3.6 DEPAL → 2.0 PBT_DEPAL_Res1 + 2.6 PBT_DEPAL_Gas1 PBT_Melt + 3.6 DEPAL → 2.0 PBT_DEPAL_Res1 + 2.6 PBT_DEPAL_Gas1 6 MPP → 0.4 MPP_Res1 + 0.6 MPP_Gas1 MPP → 0.4 MPP_Res1 + 0.6 MPP_Gas1 7 PBT_Res1 + 0.04 MPP → 0.92 PBT_MPP_Res1 + 0.12 PBT_MPP_Gas1 + 0.04 MPP→ →0.07 0.92PBT_MPP_Res2 PBT_MPP_Res1 + 0.12 PBT_MPP_Gas1 8 PBT_Res1 PBT_MPP_Res1 + 0.93 PBT_MPP_Gas2 PBT_MPP_Res1 → 0.07 PBT_MPP_Res2 + 0.93 PBT_MPP_Gas2 a Stoichiometric coefficients obtained from literature [32]. 1 2 3
a
Stoichiometric coefficients obtained from literature [32].
Table Table3.3. Kinetics Kinetics and and thermodynamics thermodynamics of of melting melting and anddecomposition decomposition reactions. reactions. Positive Positive heats heats of of reaction, reaction, h, h, correspond correspondto toendothermic endothermicprocesses. processes. 3 ·kg 1 ·s−1 ) −1−1 −1 )−1 1 ) −1 −1 − −11 or (s−1m or3 m (J·mol−1−)1 ) hh(J (J·kg kg−−11 )) (s− or m ·s−s1−1) ) E kg− (s−1A or kg s−1 ) E (JE mol ## AA(s m3 ·3kgkg E(J(J·mol mol ) h h(J·(J kg ) 5 20 5 6 40 4 1 5 4.00 × 10 2.0 × 10 3.19 × 10 2.4 × 10 2.0 × 10 6.0 × 10 2.0 × 10 25 4.00 × 10 5 6.0 × 105 3.19 × 10 2.4 × 10 2.0 × 1020 5 2 6 2.0 × 10 3.41 × 10 1.4 × 10 2.5 × 10 2.88 × 105 6.9 × 105 5 2.0 ×2.4 10× 1020 3.412.90 ×× 10105 1.4 2.5 1020 2.88 6.9× × 67 3 3.1× × 10 105 2.0× × 10 2.70 ×× 1010 1.5 10510 5 20 5 12 4 2.5× × 10 2.87 ×× 1010 4.0 10510 2.4 ×1.0 10× 10 2.902.09 ×× 1010 3.1 ×0 10 2.0 10 2.70 1.5× × 78 1.0 × 10 0 2.5 × 10 4.0 × 10 2.09 × 10 2.87 × 10 8 The heat flow data were analyzed by first focusing on the regions not associated with melting or The heat flow were analyzedtoby firstregions focusing on divided the regions not associated with melting decomposition. The data corresponding these were by the instantaneous heating rate or decomposition. data corresponding to capacities, these regions divided by the instantaneous and fitted with linearThe functions representing heat c, ofwere the corresponding condensed-phase heating rate and fittedflow withdata linear functions representing capacities, c, of used the corresponding components. The heat between 313 and 460 K andheat 510 and 590 K were to determine condensed-phase components. The heat flow data between 313 and 460 K and 510 and 590 K from were the heat capacities of PBT and PBT_Melt, respectively. The heat capacity of GF was obtained used to determine [34]. the heat of PBTofand PBT_Melt, heat capacity was the manufacturer Thecapacities heat capacity PBT_Res2 wasrespectively. impossible The to resolve due toof itsGF small obtained from theits manufacturer [34]. heat capacity of PBT_Res2 was impossible to resolve due yield. Therefore, heat capacity wasThe assumed to be equal to the average heat capacity of chars − 1 − 1 to its smallbyyield. Therefore, heat capacity was to beThe equal to capacity the average heat capacity of produced several commonitspolymers—1700 J·kgassumed ·K [13]. heat of the intermediate chars produced by several common polymers—1700 J kg−1 K−1 [13]. The heat capacity of the intermediate condensed-phase product (PBT_Res1) was assumed to be equal to the average heat capacity of the PBT_Melt and PBT_Res2. All heat capacity values are listed in Table 4. The sensible heat flow baseline was subsequently calculated as a product of the mass fractions of condensed-phase components (whose temporal evolution was computed by ThermaKin), corresponding heat capacities, and instantaneous heating rate. The baseline obtained for the
# 1 2 3 4
#A
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condensed-phase product (PBT_Res1) was assumed to be equal to the average heat capacity of the PBT_Melt and PBT_Res2. All heat capacity values are listed in Table 4. The sensible heat flow baseline was subsequently calculated as a product of the mass fractions of condensed-phase components (whose temporal evolution was computed by ThermaKin), corresponding heat capacities, and instantaneous heating rate. The baseline obtained for the PBT/GF25 is shown as a green dotted line in Figure 2b. Subtraction of this baseline from the normalized experimental heat flow and subsequent integration of the differences yielded the values of the heat of melting and heats of decomposition, h. Reaction 1 (see Table 2) was added to the mechanism to simulate the melting process. The kinetics of this reaction and heats of melting and decomposition Polymers 2018, 10, x FOR PEER REVIEW 7 of 14 were refined until the overall heat flow curve simulated using ThermaKin was in agreement with the experimental Thisasagreement wasline defined by the heat maxima within 10%, PBT/GF25data. is shown a green dotted in Figure 2b. simulated Subtraction of thisflow baseline from the temperatures of theexperimental maxima within K, subsequent and the final integral flow yielded value the within normalized heat flow8and integration of theheat differences values5% of the of the experimental heat of melting and heats of results decomposition, Reaction are 1 (see Table 2) added to The the heats of corresponding data. The of thish.exercise shown inwas Figure 2b. mechanism to simulate the melting process. The kinetics of this reaction and heats of melting and melting and decomposition reactions are listed in Table 3. decomposition were refined until the overall heat flow curve simulated using ThermaKin was in agreement with the experimental data. This agreement was defined by the simulated heat flow Table 4. Heat capacities of condensed-phase components. maxima within 10%, temperatures of the maxima within 8 K, and the final integral heat flow value within 5% of the corresponding experimental data. The results of this exercise are shown in Figure Component Component (J·kg−1 ·K−1 )reactions are c (J·kg−1 ·K−1 ) 2b. The heats of melting andc decomposition listed in Table 3.
PBT −524 + 5.60 × T DEPAL_Res1 1700 Table 4. Heat capacities of condensed-phase components. PBT_Melt 2100 + 0.20 × T PBT_DEPAL_Res1 1700 −1 K−1× −1 K PBT_Res1 1900 MPP 990 +−14.20 ×T Component c (J + kg0.10 ) T Component c (J−kg ) PBT_Res2 1700 MPP_Res1 −524 + 5.60 × T 1700 1700 PBT DEPAL_Res1 a GF (442 PBT_MPP_Res1 1900 2100++1.24 0.20× × T) T 1700+ 0.10 × T PBT_Melt PBT_DEPAL_Res1 DEPAL −1900 2750++0.10 11.8 PBT_MPP_Res2 1700 ×× T T −990 + 4.20 ×T PBT_Res1 MPP PBT_Res2 GF DEPAL
a Obtained 1700 from the manufacturer MPP_Res1[34]. (442 + 1.24 × T) a PBT_MPP_Res1 −2750 + 11.8 × T PBT_MPP_Res2 a
1700 1900 + 0.10 × T 1700
Obtained from the manufacturer [34].
3.3. Inverse Modeling of TGA and DSC Data for PBT/GF/DEPAL
3.3. Inverse Modeling of TGA and DSC Data for PBT/GF/DEPAL Figure 3 displays the mean experimental results of TGA and DSC tests on PBT/GF25-DEPAL8 Figure 3 displays the meansystems. experimental results TGA and DSCof tests on PBT/GF25-DEPAL8 and PBT/GF25-DEPAL16 material With the of introduction DEPAL, the MLR profiles gain and PBT/GF25-DEPAL16 material systems. With the introduction of DEPAL, the MLR profiles gain an additional, barely discernable peak at 765 K. This peak becomes somewhat more evident as the an additional, barely discernable peak at 765 K. This peak becomes somewhat more evident as the concentration of DEPAL increases to 16 %.%. concentration of DEPAL increases to wt 16 wt
Figure 3. Experimental and simulated TGA andDSC DSC data for (a,b) PBT/GF25-DEPAL8 and Figure 3. Experimental and simulated TGA and dataobtained obtained for (a,b) PBT/GF25-DEPAL8 and −1. (c,d) PBT/GF25-DEPAL16 at 10 K min − 1 (c,d) PBT/GF25-DEPAL16 at 10 K·min .
Duquesne et al. [32] investigated the decomposition of pure DEPAL using TGA which was
Duquesne et al. [32] investigated the decomposition of pure DEPAL using TGA which was conducted in nitrogen at a heating rate of 10 K min−1. They found that DEPAL decomposed at about − 1 through at a single step and produced wt % of. final residue. similarity between the at about conducted750 in K nitrogen a heating rate of 10 K7·min They foundGiven that aDEPAL decomposed position of the second MLR peak observed in this study and that of pure DEPAL, this second peak was attributed to DEPAL decomposition. Reaction 4 (see Table 2) was added to the mechanism to
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750 K through a single step and produced 7 wt % of final residue. Given a similarity between the position of the second MLR peak observed in this study and that of pure DEPAL, this second peak was attributed to DEPAL decomposition. Reaction 4 (see Table 2) was added to the mechanism to represent this process. The stoichiometric coefficients of this reaction were determined from the results obtained by Duquesne et al. The kinetic parameters of Reaction 4 were estimated using the position of the second MLR peak (765 K) observed in the current experiments. The results of the addition of Reaction 4 to the mechanism are shown as green dashed lines in Figure 3a,c. These simulations significantly overestimate the size of the second MLR peak for both blends, indicating that some DEPAL is consumed in a reaction with the polymer matrix prior to reaching its decomposition temperature. In addition, the experimental residue yields of the DEPAL-containing blends are notably higher than the values calculated based on the individual PBT and DEPAL contributions. The increased residue yields further support the existence of an interaction between the polymer matrix and DEPAL. The existence of this interaction was also noted in previous studies, which indicated that aluminum phosphinate terephthalate is formed due to a condensed-phase interaction between the polymer matrix and DEPAL [24,35]. To account for this interaction, a reaction between PBT_Melt and DEPAL—Reaction 5 (see Table 2)—was added to the mechanism. The stoichiometry and kinetics of this reaction were adjusted to correctly reproduce the experimental MLR peaks observed for the PBT/GF25-DEPAL8 and PBT/GF25-DEPAL16 blends. The final inverse modeling results using Reactions 1–5 are shown in Figure 3a,c as red solid lines; the reaction parameters are summarized in Table 3. The first simulated MLR peak is still primarily associated with the decomposition of PBT_Melt, only a relatively small fraction of which is consumed in the reaction with DEPAL. The second simulated peak is associated with the decomposition of the portion of DEPAL that did not react with PBT_Melt. The experimental heat flow data obtained for PBT/GF25-DEPAL8 and PBT/GF25-DEPAL16 in the temperature range between 313 and 460 K were used to determine the heat capacity of DEPAL. The sensible heat contributions of PBT and GF were subtracted from the heat flow data to determine DEPAL’s contribution. The heat capacities of DEPAL_Res1 and PBT_DEPAL_Res1 components could not be determined from the heat flow data due to their small yields and were therefore assumed to be equal to the average heat capacity of chars produced by several common polymers—1700 J·kg−1 ·K−1 [13]. The heats of Reaction 4 and 5 were subsequently determined by fitting the heat flow data for both blends. These final heat flow modeling results are shown in Figure 3b,d. The values of heat capacities and heats of reaction are reported in Tables 3 and 4, respectively. 3.4. Inverse Modeling of TGA and DSC Data for PBT/GF/MPP The mean experimental results of TGA and DSC tests of PBT/GF25-MPP4 and PBT/GF25-MPP8 blends are shown as symbols in Figure 4. With the incorporation of MPP into the GF-reinforced PBT, the main MLR peak increases in height (by 20% upon addition of 4 wt % of MPP) and becomes considerably more narrow in temperature. An attempt was made to capture this behavior by adding a reaction of decomposition of MPP, Reaction 6 (see Table 2), to the mechanism. This reaction was parameterized by matching the final residue yield and temperature of the main MLR peak observed in the TGA experiments conducted in this work on pure MPP. However, as indicated by green dashed lines in Figure 4a,c, the resulting model (no interaction) significantly underestimated the heights of the main MLR peaks; the initial rise and final decay of the MLR curves were not captured. Also, the final residue yields were underestimated by about 5%. It was further deduced that it is the reaction of decomposition of PBT_Res1 (Reaction 3) that was primarily responsible for the observed discrepancies. Therefore, a reaction between PBT_Res1 and MPP—Reaction 7 (see Table 2)—was added to the model to compete with Reaction 3. Finally, one more consecutive reaction, Reaction 8, was added to accurately capture the final decay of the MLR peaks observed for both blends. These inverse modeling results using Reactions 1–3 and 6–8 are shown in Figure 4a,c as red lines. The kinetic parameters of these additional reactions are summarized in Table 3.
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Figure Figure 4.4. Experimental Experimental and and simulated simulated TGA TGA and andDSC DSCdata dataobtained obtainedfor for(a,b) (a,b)PBT/GF25-MPP4 PBT/GF25-MPP4 and and −.1 . (c,d) (c,d)PBT/GF25-MPP8 PBT/GF25-MPP8 at 10 K ·min−1
The capacity of of MPP MPPwas wasobtained obtainedininthethe same way as the capacity of DEPAL The heat heat capacity same way as the heatheat capacity of DEPAL (see (see Section 3.3). The heat capacities of MPP_Res1 and PBT_MPP_Res2 could not be resolved Section 3.3). The heat capacities of MPP_Res1 and PBT_MPP_Res2 could not be resolved and were and were to assumed equal to the average heat of charsby produced by several common assumed be equaltotobethe average heat capacity ofcapacity chars produced several common polymers— −1 ·K−1 [13]. The heat capacity of PBT_MPP_Res1 was taken as the average polymers—1700 J·kgThe 1700 J kg−1 K−1 [13]. heat capacity of PBT_MPP_Res1 was taken as the average heat capacity of heat capacity PBT_Melt and PBT_MPP_Res2. The heats Reaction 7, and 8 weredetermined subsequently PBT_Melt andofPBT_MPP_Res2. The heats of Reaction 6, 7,ofand 8 were6,subsequently by determined by fitting the for heatboth flowblends. data for both Themodeling final heatresults flow modeling are fitting the heat flow data The finalblends. heat flow are shownresults in Figure shown in values Figure of 4b,d. values and of heat capacities and of reaction are3reported in Tables 3 4b,d. The heatThe capacities heats of reaction areheats reported in Tables and 4, respectively. and 4, respectively. 3.5. Inverse Modeling of MCC Data 3.5. Inverse Modeling of MCC Data The mean experimental HRR normalized by the initial sample mass and the integral HRR for The mean experimental HRR normalized by the initial sample mass and the integralblends HRR PBT/GF25, PBT/GF25-DEPAL8, PBT/GF25-DEPAL16, PBT/GF25-MPP4, and PBT/GF25-MPP8 for PBT/GF25-DEPAL8, PBT/GF25-DEPAL16, PBT/GF25-MPP4, andHRR PBT/GF25-MPP8 arePBT/GF25, shown as symbols in Figure 5. Initial comparisons between the experimental and modeled blends are shown as symbols in Figure 5. Initial comparisons between the experimental HRR MLR profiles generated using the heating rate temporal profiles specific to the MCC experiments and modeled MLR profiles generated using the heating rate temporal profiles specific to the revealed minor discrepancies that were attributed to sample/sensor temperature nonuniformities MCC experiments revealed minor discrepancies thatofwere attributed sample/sensor temperature present in the MCC and associated with the use open ceramic to crucibles. To correct for these nonuniformities present in the MCC and associated with the use of open ceramic crucibles. ToKcorrect nonuniformities, the experimental HRR curves were shifted to a higher temperature by 5–10 using for nonuniformities, theany experimental HRR release curves were shifted to a higher temperature by the these guiding principle that detected heat required a concurrent mass loss. The 5–10 K using the principle that anythe detected required concurrent mass loss. experimental dataguiding presented in Figure 5 are shiftedheat data;release the original dataaare not shown because The experimental data presented in Figure 5 are the shifted data; the original data are not shown they are nearly indistinguishable from the shifted results. because they are nearly indistinguishable from the shifted results.
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Figure 5. Experimental Experimentaland andsimulated simulatedMicroscale Microscale Combustion Calorimetry (MCC) data obtained Combustion Calorimetry (MCC) data obtained for for (a) PBT/GF25, (b) PBT/GF25-DEPAL8, (c) PBT/GF25-DEPAL16, (d) PBT/GF25-MPP4, and (a) PBT/GF25, (b) PBT/GF25-DEPAL8, (c) PBT/GF25-DEPAL16, (d) PBT/GF25-MPP4, and (e) −1. −1 . (e) PBT/GF25-MPP8 K·min PBT/GF25-MPP8 at 10atK10min
The were first setset to atosingle value thatthat yielded the The heats heats of ofcombustion combustion(h(hc )c)ofofall allgaseous gaseousproducts products were first a single value yielded final integral HRR equal to that observed in the experiments. Subsequently, individual h values were c the final integral HRR equal to that observed in the experiments. Subsequently, individual hc values adjusted up or up down to capture the shapes of the experimental HRR peaks. in the of inverse were adjusted or down to capture the shapes of the experimental HRR As peaks. Ascase in the case of modeling of TGA and DSCand experiments, the iterative process continued until the until differences between inverse modeling of TGA DSC experiments, the iterative process continued the differences the modeled and experimental data satisfied criteria. These criteria were defined as differences between the modeled and experimental dataspecific satisfied specific criteria. These criteria were defined as of less than 8% between the values of HRR maxima, less than 10 K between the temperatures of the differences of less than 8% between the values of HRR maxima, less than 10 K between the maxima, and less thanmaxima, 8% between HRR values. The resulting heats of combustion that temperatures of the and the lessfinal thanintegral 8% between the final integral HRR values. The resulting −1 , satisfy these criteria are given in Table 5. criteria All hc values are within the range 107 –3.8 × within 107 J·kgthe heats of combustion that satisfy these are given in Table 5. All0.7 hc × values are consistent of these [36]. The finalnature simulated MCC results shown range 0.7 ×with 10 –the 3.8hydrocarbon × 10 J kg−1,nature consistent withgases the hydrocarbon of these gases [36].are The final in Figure 5. simulated MCC results are shown in Figure 5. Table 5. Table 5. Heats Heats of of combustion combustion of of gaseous gaseous decomposition decomposition products. products. Component Component
PBT_Gas1 PBT_Gas1 PBT_Gas2 PBT_Gas2 DEPAL_Gas1 DEPAL_Gas1
−1
hc (J (J·kg kg −1) ) h 2.1 2.1× ×10 107 2.5 × 107 2.5 × 10 0.7× ×10 107 0.7
Component Component
−1 −1 hc h(Jc·(J kgkg ))
Component Component
−1−1) hch(J ·kgkg c (J )
PBT_DEPAL_Gas1 PBT_DEPAL_Gas1 MPP_Gas1 MPP_Gas1
7 2.8 2.8 ×× 1010 7 1.8 × 10 1.8 × 10
PBT_MPP_Gas1 PBT_MPP_Gas1 PBT_MPP_Gas2 PBT_MPP_Gas2
7 3.8××1010 3.8 7 2.5 × 10 2.5 × 10
3.6. Model Performance at Different Heating Rates The reaction mechanism shown shown in in Table Table22and andcorresponding correspondingparameters parametersreported reportedininTables Tables3–5 3– − 1 −1 reproduce TGA, DSC, and MCC data collected atat a nominal heating rate ofof 1010KK ·min 5 reproduce TGA, DSC, and MCC data collected a nominal heating rate min for for PBT/GF25, PBT/GF25-DEPAL8, PBT/GF25-DEPAL16, PBT/GF25-MPP4, PBT/GF25-MPP4,and and PBT/GF25-MPP8 PBT/GF25-MPP8blends blends with with the PBT/GF25-DEPAL8, PBT/GF25-DEPAL16, accuracy defined by the criteria discussed in Sections 3.2 and 3.2. To further validate this reaction 3.5. − 1 −1 model, the ·min the mean mean experimental experimentalTGA TGAdata dataobtained obtainedatatlower lower(5(5KK min−1)) as as well wellas ashigher higher(20 (20KK·min min−1) heating rates thethe same blends were compared with thewith corresponding predictions.predictions. This comparison ratesonon same blends were compared the corresponding This is summarized in Figure 6; no MLR data are shown on this figure to avoid congestion. Overall, comparison is summarized in Figure 6; no MLR data are shown on this figure to avoid congestion. good predictions were obtained for all blends heating conditions. The model (by 5–8(by K) Overall, good predictions were obtained for alland blends and heating conditions. The slightly model slightly −1 for −1 underestimates the temperatures of the onset of the experimental mass loss at 20 K · min all 5–8 K) underestimates the temperatures of the onset of the experimental mass loss at 20 K min for blends, perhaps duedue to some minor nonuniformities in the temperature arising at this all blends, perhaps to some minor nonuniformities in sample/sensor the sample/sensor temperature arising at
this heating rate (and not corrected for by the STA temperature sensor calibration, which was carried out at 10 K min−1).
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Figure 6. Experimental and simulated TGA data obtained for (a) PBT/GF25, (b) PBT/GF25-DEPAL8, Figure 6. Experimental and simulated TGA data obtained obtained for for (a) (a) PBT/GF25, PBT/GF25, (b) PBT/GF25-DEPAL8, PBT/GF25-DEPAL8, K (c) PBT/GF25-DEPAL16, (d) PBT/GF25-MPP4, and (e) PBT/GF25-MPP8 blends at 5 K min−1−1 and −1 20 PBT/GF25-DEPAL16,(d) (d)PBT/GF25-MPP4, PBT/GF25-MPP4, and PBT/GF25-MPP8 blends K·min and and 20 K (c) PBT/GF25-DEPAL16, and (e)(e) PBT/GF25-MPP8 blends at 5atK 5min −1. min − 1 20 K−1·min . . min
3.7. Modeling of Different Material Compositions 3.7. Modeling of Different Material Compositions To To validate validate the the model model assumption assumption that that GF GF acts acts as as an an inert inert additive, additive, TGA TGA and and DSC DSC experiments experiments To validate the model assumption that GF acts as an inert additive, TGA and DSC experiments were performed performed on onpure purePBT PBTsamples. samples. results of these experiments are compared with the TheThe results of these experiments are compared with the model were performed on pure PBT samples. The results of these experiments are compared with the model model predictions in Figure 7. The experimental TGA data are in nearly perfect agreement with the predictions in Figure 7. The experimental TGA data are in nearly perfect agreement with the model. predictions in Figure 7. The experimental TGA data are in nearly perfect agreement with the model. model. The experimental heat is flow is slightly underpredicted toward endofofthe the experiment. experiment. This The experimental heat flow slightly underpredicted toward thethe end The experimental heat flow is slightly underpredicted toward the end of the experiment. This discrepancy is likely to be be associated associated with the the uncertainties uncertainties in the the high-temperature high-temperature portion of the discrepancy is likely to be associated with the uncertainties in the high-temperature portion of the experimental heat flow baseline, which may not have been completely resolved in the five STA runs experimental heat flow baseline, which may not have been completely resolved in the five STA runs from which these data were derived (ten STA STA runs runs were were used used to to generate generate all all model model calibration calibration data). data). from which these data were derived (ten STA runs were used to generate all model calibration data).
−−1 1. and simulated simulated(a) (a)TGA TGAand and(b) (b)DSC DSCdata dataobtained obtainedfor forpure purePBT PBTatat1010KK min Figure 7. Experimental Experimental and ·min Figure 7. Experimental and simulated (a) TGA and (b) DSC data obtained for pure PBT at 10 K min−1.
Finally, Finally, the the predictions predictions of of the the reaction reaction model model were were compared compared with with the the experimental experimental results results Finally, the predictions of the reaction model were compared with the experimental results obtained obtained for for material material blends blends containing containing both both flame flameretardants: retardants: PBT/GF25-DEPAL8-MPP4 PBT/GF25-DEPAL8-MPP4 and and obtained for material blends containing both flame retardants: PBT/GF25-DEPAL8-MPP4 and PBT/GF25-DEPAL16-MPP8. This comparison is shown in Figure 8. The model captures all TGA and PBT/GF25-DEPAL16-MPP8. This comparison is shown in Figure 8. The model captures all TGA and PBT/GF25-DEPAL16-MPP8. This comparison is shown in Figure 8. The model captures all TGA and DSC the exception exception of of aa slight slight overprediction overprediction of of the the maximum maximum heat heat flows. flows. DSC experimental experimental data data well, well, with with the DSC experimental data well, with the exception of a slight overprediction of the maximum heat flows. In In addition addition to to validating validating the the model, model, this this comparison comparison indicates indicates the the absence absence of of significant significant chemical chemical In addition to validating the model, this comparison indicates the absence of significant chemical interactions between DEPAL and MPP additives. The same conclusion was reached by Samyn interactions between DEPAL and MPP additives. The same conclusion was reached by Samyn and and interactions between DEPAL and MPP additives. The same conclusion was reached by Samyn and Bourbigot, Bourbigot, who who studied studied the the thermal thermal decomposition decomposition of of DEPAL DEPAL and and MPP MPP [37]. [37]. In In the the study study by by Samyn Samyn Bourbigot, who studied the thermal decomposition of DEPAL and MPP [37]. In the study by Samyn and and Bourbigot, Bourbigot, the the thermal thermal decompositions decompositions of of DEPAL DEPAL and and MPP MPP were were characterized characterized individually individually and and and Bourbigot, the thermal decompositions of DEPAL and MPP were characterized individually and the mass loss curve for a DEPAL–MPP blend was calculated based on the individual DEPAL and the mass loss curve for a DEPAL–MPP blend was calculated based on the individual DEPAL and MPP contributions. The calculated mass loss curve agreed with the experimental data on the blend, MPP contributions. The calculated mass loss curve agreed with the experimental data on the blend, which indicated the absence of chemical interactions between these additives in the condensed phase. which indicated the absence of chemical interactions between these additives in the condensed phase.
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the mass loss curve for a DEPAL–MPP blend was calculated based on the individual DEPAL and MPP contributions. The calculated mass loss curve agreed with the experimental data on the blend, 12 which Polymers 2018, 10, x FOR PEER REVIEW of 14 indicated the absence of chemical interactions between these additives in the condensed phase. It should should be be noted noted that that both both the the current did not not It current work work and and the the study study by by Samyn Samyn and and Bourbigot Bourbigot did account for the potential impact of DEPAL and/or MPP on the transport processes in the condensed account for the potential impact of DEPAL and/or MPP on the transport processes in the condensed phase. Analysis Analysis of of this this impact impact will will be be aa subject subject of of future future work. work. Both Both DEPAL DEPAL and and MPP MPP also also affect affect the the phase. kinetics of the gas-phase combustion, which may explain a synergy between these additives observed kinetics of the gas-phase combustion, which may explain a synergy between these additives observed in cone cone calorimetry calorimetry tests in tests [38]. [38].
TGA andand DSC datadata obtained for (a,b) Figure 8. 8. Experimental Experimentaland andsimulated simulated TGA DSC obtained for PBT/GF25-DEPAL8-MPP4 (a,b) PBT/GF25-DEPAL8−1min and (c,d) at 10 Kat ·min . −1. MPP4 andPBT/GF25-DEPAL16-MPP8 (c,d) PBT/GF25-DEPAL16-MPP8 10 K
4. Conclusions Conclusions 4. A methodology methodology for for development development of of aa quantitative quantitative reaction reaction mechanism mechanism for for aa blend blend of of reactive A reactive solids has been presented and demonstrated using a material system containing a GF-reinforced solids has been presented and demonstrated using a material system containing a GF-reinforced PBT PBT compounded with retardants flame retardants andThis MPP. This methodology is based on TGA, compounded with flame DEPALDEPAL and MPP. methodology is based on TGA, DSC, and DSC, and MCC experiments that are analyzed using inverse numerical modeling. The developed MCC experiments that are analyzed using inverse numerical modeling. The developed model was model was shown to simultaneously all measurement for containing mixtures containing a full shown to simultaneously reproduce reproduce all measurement results forresults mixtures a full range of range of relevant flame retardant concentrations with a high degree of accuracy. While this model relevant flame retardant concentrations with a high degree of accuracy. While this model was based was based onspecies a lumped species approach thus did not explicitly resolve individual chemical on a lumped approach (and thus did(and not explicitly resolve individual chemical species), it did species), it did capture all essential aspects of the thermal decomposition behavior relevant to the capture all essential aspects of the thermal decomposition behavior relevant to the flammability of flammability of studied materials. Moreover, through analysis, the presented analysis, key binarybetween interactions studied materials. Moreover, through the presented key binary interactions the between the material constituents were and identified and implemented in the using modelsecond-order using second-order material constituents were identified implemented in the model (two(two-component) reactions. component) reactions. A combination combination of of the the current current reaction reaction mechanism mechanism development development methodology methodology with with aa bench-scale bench-scale A heat and analysis described in detail elsewhere [15,16,39–41] will bewill required to develop heat andmass masstransport transport analysis described in detail elsewhere [15,16,39–41] be required to comprehensive pyrolysis models for such reactive systems. This expansion of the current approach develop comprehensive pyrolysis models for such reactive systems. This expansion of the current will be a subject Provided such pyrolysis canmodels be successfully developed, approach will beofa future subjectwork. of future work.that Provided that suchmodels pyrolysis can be successfully they will provide a quantitative relation between material composition and its reaction to thermal developed, they will provide a quantitative relation between material composition and its reaction to insult. Development of such relations will enable optimization of passive fire protection of a built thermal insult. Development of such relations will enable optimization of passive fire protection of a environment as well maximization of useful energy output from composite solid fuels. built environment as as well as maximization of useful energy output from composite solid fuels. Author Contributions: Conceptualization, S.I.S.; Methodology, Y.D. and S.I.S.; Formal Analysis, Y.D.; Resources, R.H.K.; Writing-Original Draft Preparation, Y.D.; Writing-Review & Editing, S.I.S.; Supervision, S.I.S.; Project Administration, S.I.S. and R.H.K; Funding Acquisition, S.I.S. and R.H.K. Funding: This research was funded by BASF and the U.S. National Science Foundation CAREER Award #1347196 under the grant monitor Song-Charng Kong. The APC was funded by the authors and University of Maryland.
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Author Contributions: Conceptualization, S.I.S.; Methodology, Y.D. and S.I.S.; Formal Analysis, Y.D.; Resources, R.H.K.; Writing-Original Draft Preparation, Y.D.; Writing-Review & Editing, S.I.S.; Supervision, S.I.S.; Project Administration, S.I.S. and R.H.K; Funding Acquisition, S.I.S. and R.H.K. Funding: This research was funded by BASF and the U.S. National Science Foundation CAREER Award #1347196 under the grant monitor Song-Charng Kong. The APC was funded by the authors and University of Maryland. Conflicts of Interest: The authors declare no conflict of interest.
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