Pyrolysis Modeling and Kinetic Study of Typical Insulation Materials for Building Exterior Envelopes

Abstract

Thermal insulation materials are important for building energy conservation, but the inherent combustibility of these materials increases the fire risk of building facades. To better understand the fire behaviors of these materials, the study of the kinetics of thermal insulation pyrolysis is particularly important because it is the initial step in ignition and combustion during fire. In this paper, the pyrolysis behavior of expanded polystyrene (EPS), a typical non-charring insulation polymer, has been investigated by thermogravimetric analysis at five different heating rates. The model-free kinetic analysis showed that the obtained average values for E and lnA were 151.23 kJ/mol and 21.29 ln/s, respectively. Model-fitting CR and masterplot methods indicated that f(α) = [2(1-α)[-ln(1-α)]]^1/2 is considered the pyrolysis reaction mechanism of EPS degradation. Based on these results, the equation of the kinetic compensation effect was further developed as lnA = −3.1955 + 0.1736 E_α. Finally, the reaction model was reconstructed with the result of the expression f(α) = 3.95335α^0.24174 (1-α) [-ln(1-α)]^1.64712. In addition, PY-GC-MS experiments were conducted to analyze the composition of EPS pyrolysis volatiles. The results showed that the products were mainly compounds of benzene, naphthalene, and biphenyl. The analysis of EPS pyrolysis behavior and evolved gas provides numerical guidance for the future treatment and fire protection of insulation materials.

1. Introduction

The innovation of materials drives the development of the industry [1]. People have a long history of using natural polymers, but it was in the 19th century that man-made chemical improvements began to be implemented. Today, polymer is an important science, and polymers are important materials in various fields because of their good physical and chemical properties [2,3,4].

Thermal insulation materials are important for building energy conservation, but the inherent combustibility of these materials increases the fire risk of building facades and affects safety performance under fire conditions. Expandable polystyrene (EPS) is widely accepted as an insulation material because of its low price and good insulation performance [5]. At the same time, its low density produces lightweight and its expandability leads to better moisture resistance, so EPS, invented in 1949, has grown to tens of millions of tons per year in global demand today [6,7].

However, the widespread use of polymers in construction also brings some problems. EPS and other polymers are used as insulation materials for buildings; however, their thermal conductivity is very low, so their combustibility is one of the serious hazards of buildings [8,9]. Once ignited, fires will quickly occur and release a huge amount of heat while generating high levels of toxic gas, the flame will quickly spread from the source of the fire to the entire building, and the consequences are unimaginable. Throughout the investigation of reports of building fires in recent years, it is not surprising to find that fires resulting from insulation materials are common.

Pyrolysis technology is popular in engineering and technology sciences such as thermodynamics, materials science, and chemistry, especially when it comes to designing environmental issues in materials. Pyrolysis is also the first step in fire, producing pyrolysis gas. When the gas concentration reaches a certain amount, the temperature reaches the ignition point and combustion occurs [10]. Thermal insulation materials are important for building energy conservation, but the inherent combustibility of these materials increases the fire risk of building facades and affects safety performance under fire conditions. As a matter of fact, pyrolysis is generally an endothermic process that occurs in the absence of oxygen. To better understand the fire behaviors of these materials, the study of the kinetics of EPS pyrolysis is particularly important because it is the initial step in ignition and combustion during fire. A large number of studies have been conducted on the pyrolysis of insulation materials, and their properties are influenced by heat transfer and the reaction rate, which can lead to differences and distinctions in the results. EPS pyrolysis has also been partially studied by many researchers. Jun et al. [11] studied EPS with several methods and analyzed the effects at different oxygen concentrations. They found that the differential method using multiple heating rates was more suitable for the analysis of EPS pyrolysis kinetics and that the activation energy was reduced in the presence of oxygen. Kannan et al. [12] studied the effect of heating rate and gas environment on the kinetics of EPS foam decomposition. The rate of temperature increase was found to have a remarkable influence on EPS pyrolysis, and the pyrolysis temperature in air was discovered to be lower than that in the non-oxidizing environment, as was the activation energy. Jiao et al. [13] concluded that the pyrolysis process of EPS can be approximated as a reaction step in a nitrogen environment with the average value of E being approximately 245 kJ mol-1. Ni et al. [14] investigated the EPS pyrolysis processes in nitrogen and air environments, respectively. The kinetic parameters were calculated by coupling the Flynn–Wall–Ozawa model-free method with the Coats–Redfern model fitting method, and finally the parameters were optimized by the particle swarm optimization algorithm. Although previous studies have yielded meaningful results, no coupled model-free and model-fitting methods have yet been derived to characterize specific reaction model functions for pyrolysis in a nitrogen atmosphere. Therefore, in this paper, the kinetic parameters were re-derived for comparison with previous research results. The kinetic pyrolysis reaction function that accurately reflects the whole process of EPS pyrolysis was finally calculated.

In the present study, pyrolysis experiments were performed under selected experimental conditions to obtain mass loss data, which were analyzed by using thermogravimetric analysis (TG) and derivative thermogravimetric analysis (DTG). To describe the pyrolysis behavior, kinetic parameters are acquired by model-free and model-fitting method analysis, while compensation effects are added to obtain the determined kinetic parameters. Finally, model reconstruction is performed to complete the whole analysis. In addition, cracking gas analysis experiments were performed to obtain the analysis of the gas composition generated by pyrolysis, which helped us to further understand the pyrolysis of EPS. The results of this study can provide effective numerical guidance for fire prevention, the control of EPS insulation materials, and waste environmental protection treatment.

2. Materials and Methods

2.1. Sample Preparation

The experimental materials were produced by a plastic chemical factory in Dongguan City, Guangdong Province. The state of EPS was powder and had a particle size of 40 mesh. Samples were dried in an electric blast dryer (Tianjin, China) for 48 h and then loaded into centrifuge tubes for TGA experiments.

2.2. TGA Experiments

The EPS samples were subjected to mass loss experiments employing a thermogravimetric analyzer Pyris 1 TGA. The experiments were conducted under a nitrogen atmosphere of 80 mL/min. For each test, about 2 mg of the dry sample was placed in the alumina crucible and heated from room temperature to 900 °C. In order to provide more experimental data for non-isothermal kinetic analysis, the International Confederation for Thermal Analysis and Calorimetry (ICTAC) [15,16] recommended four or more heating rates ranging from 5 to 80 K/min in TGA experiments. And for our study, to calculate the kinetic parameters from the FWO, KAS, advanced Vyazovkin, and Senum–Yang-based analyses, we finally adopted heating rates ranging from 5 to 40 K/min for the current TGA experiments.

2.3. Reaction Kinetics

TGA experiments are the recording of the change in mass of a sample with the temperature at a constant rate of temperature increase. Normally we use the conversion rate to express the mass loss of a material, and the conversion rate α can be expressed as

α = (m₀ − m_t)/(m₀ − m_∞)

(1)

where m₀, m_t, and m_∞ represent the initial sample mass, the sample mass at time t, and the final sample mass, respectively.

Thermal analysis kinetic studies consider the rate as a function of two variables depending on the conversion rate α and the temperature T:

dα/dt = k(T)f(α)

(2)

where $\mathrm{k}\left(\mathrm{T}\right) \mathrm{i}\mathrm{s}$ the chemical reaction rate constant, which can be expressed by the Arrhenius equation, and f(α$)$ is the reaction mechanism function model. By introducing the Arrhenius formula, the equation can be expressed as

dα/dt = A exp(−E/RT)f(α)

(3)

where $\mathrm{T}$ refers to the absolute temperature, R is the gas constant, $\mathrm{A}$ is the pre-exponential factor, $\mathrm{E}$ is the activation energy, and $\mathrm{f}\left(\mathsf{\alpha }\right)$ is the reaction model. Among the above parameters, A, $\mathrm{E}$, and $\mathrm{f}\left(\mathsf{\alpha }\right)$ are called the kinetic triplets.

In the analysis of non-isothermal data, the heating rate is calculated as $\mathsf{\beta }=\mathrm{d}\mathrm{T}/\mathrm{d}\mathrm{t}$, and the final equation can be expressed as

dα/dt = A/ꞵ exp(−E/RT)f(α)

(4)

In order to calculate the kinetic triplets, the above equation can be integrated, and then the integral function $\mathrm{g}\left(\mathsf{\alpha }\right)$ is represented as

$$\mathrm{g}(\mathsf{\alpha })={\int }_0^{\mathsf{\alpha }}{\displaystyle \frac{\mathrm{d}\mathsf{\alpha }}{\mathrm{f}\left(\mathsf{\alpha }\right)}}={\displaystyle \frac{\mathrm{A}}{\mathsf{\beta }}}{\int }_{{\mathrm{T}}_0}^{\mathrm{T}}\exp ({\displaystyle \frac{-\mathrm{E}}{\mathrm{R}\mathrm{T}}})\mathrm{d}\mathrm{T}\approx {\displaystyle \frac{\mathrm{A}}{\mathsf{\beta }}}{\int }_0^{\mathrm{T}}\exp ({\displaystyle \frac{-\mathrm{E}}{\mathrm{R}\mathrm{T}}})\mathrm{d}\mathrm{T}={\displaystyle \frac{\mathrm{A}\mathrm{E}}{\mathsf{\beta }\mathrm{R}}}{\int }_0^{\mathrm{x}}{\displaystyle \frac{\exp (\mathrm{x})}{{\mathrm{x}}^2}}\mathrm{d}\mathrm{x}={\displaystyle \frac{\mathrm{A}\mathrm{E}}{\mathsf{\beta }\mathrm{R}}}\mathrm{p}(\mathrm{x})$$

(5)

$$\mathrm{p}(\mathrm{x})={\int }_0^{\mathrm{x}}{\displaystyle \frac{\exp (\mathrm{x})}{{\mathrm{x}}^2}}\mathrm{d}\mathrm{x}$$

(6)

where T₀ is the initial temperature and $\mathrm{x}=\mathrm{E}/\mathrm{R}\mathrm{T}$. $\mathrm{p}\left(\mathrm{x}\right)$ is the temperature integral, which is difficult to solve by numerical methods, so various methods use different approximation algorithms.

In the present work, multiple methods were adopted to calculate kinetics parameters. For non-isothermal experiments, the kinetic analysis methods are divided into two different ways: the model-free method and the model-fitting method [17].The model-free method, also known as the isoconversional method, is a method for analyzing the kinetic triplets by using thermogravimetric curves at different heating rates [18].

2.3.1. Flynn–Wall–Ozawa (FWO)

FWO [19,20] method is expressed as

lgꞵ = lg{AEα/Rg(α)} − 2.315 − 0.4567 (Eα/RT)

(7)

Plotting the relationship for different $\lg \mathsf{\beta }$ at different $1/\mathrm{T}$ with determined $\mathsf{\alpha }$, the slope is −0.4567 E_α/R. This can be calculated as the value of E_α.

2.3.2. Kissinger–Akahira–Sunose Method (KAS)

KAS [21] method is expressed as

ln(ꞵ/T²) = ln(AR/E_αg(α))- E_α/RT

(8)

Similarly, drawing relations between $\ln (\mathsf{\beta }/{\mathrm{T}}^2)$ and $1/\mathrm{T}$, convert ${\mathrm{E}}_{\mathsf{\alpha }}$ through the slope E_α/R.

2.3.3. Senum–Yang Method

Senum and Yang [22]. proposed an approximation algorithm for $\mathrm{p}\left(\mathrm{x}\right)$, and the formula is expressed as

ln(ꞵ/T²h(x)) = ln(AE_α/Rg(α))- E_α/RT

(9)

p(x) = exp(-x)/x²h(x)

(10)

Note this method requires iterative computation. To facilitate the calculation, we take ${\mathrm{E}}_{\mathsf{\alpha }}$ in KAS as the initial value and substitute it into $\mathrm{h}\left(\mathrm{x}\right)$ to calculate it, and then calculate the new ${\mathrm{E}}_{\mathsf{\alpha }}$ by working out the slopes of $\ln (\mathsf{\beta }/{\mathrm{T}}^2\mathrm{h}\left(\mathrm{x}\right))$ and $1/\mathrm{T}$ as in the above method. Next, the new ${\mathrm{E}}_{\mathsf{\alpha }}$ is then substituted into $\mathrm{h}\left(\mathrm{x}\right)$ again and the above process was repeated until $\left|{{\mathrm{E}}_{\mathsf{\alpha }}}_{\mathrm{i}}-{{\mathrm{E}}_{\mathsf{\alpha }}}_{\mathrm{i}-1}\right|/{{\mathrm{E}}_{\mathsf{\alpha }}}_{\mathrm{i}}\le 1\mathrm{\%}$, and the final ${\mathrm{E}}_{\mathsf{\alpha }}$ is taken as the [23].

2.3.4. Advanced Vyazovkin Method

Vyazovkin [15,16] proposed an advanced method, and its equation is as follows:

$$\mathsf{\Omega }({\mathrm{E}}_{\mathsf{\alpha }})={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum }_{\mathrm{j}\ne \mathrm{i}}^{\mathrm{n}}{\displaystyle \frac{\mathrm{I}({\mathrm{E}}_{\mathsf{\alpha }},{\mathrm{T}}_{\mathsf{\alpha },\mathrm{i}}){\mathsf{\beta }}_{\mathrm{j}}}{\mathrm{I}({\mathrm{E}}_{\mathsf{\alpha }},{\mathrm{T}}_{\mathsf{\alpha },\mathrm{j}}){\mathsf{\beta }}_{\mathrm{i}}}}$$

(11)

$$\mathrm{I}({\mathrm{E}}_{\mathsf{\alpha }},{\mathrm{T}}_{\mathsf{\alpha }})={\int }_0^{{\mathrm{T}}_{\mathsf{\alpha }}}\exp ({\displaystyle \frac{-{\mathrm{E}}_{\mathsf{\alpha }}}{\mathrm{R}\mathrm{T}}})\mathrm{d}\mathrm{T}={\mathrm{E}}_{\mathsf{\alpha }}\mathrm{p}(\mathrm{x})/\mathrm{R}$$

(12)

$$\mathrm{p}(\mathrm{x})={\displaystyle \frac{\exp (-\mathrm{x})}{\mathrm{x}}}\times {\displaystyle \frac{{\mathrm{x}}^5+40{\mathrm{x}}^4+552{\mathrm{x}}^3+3186{\mathrm{x}}^2+7092\mathrm{x}+4320}{{\mathrm{x}}^6+42{\mathrm{x}}^5+630{\mathrm{x}}^4+4200{\mathrm{x}}^3+\mathrm{12,600}{\mathrm{x}}^2+\mathrm{15,120}\mathrm{x}+5040}}$$

(13)

where the temperature integral $\mathrm{p}\left(\mathrm{x}\right)$ value is used as the result of Farjas and Roura. The value of activation energy ${\mathrm{E}}_{\mathsf{\alpha }}$ is obtained by a self-written program, and ${\mathrm{E}}_{\mathsf{\alpha }}$ is the result obtained when $\mathsf{\Omega }\left({\mathrm{E}}_{\mathsf{\alpha }}\right)$ is the minimum value.

2.3.5. Coats–Redfern Method

In addition to the above four model-free methods, this paper also uses the model-fitting method. The Coats–Redfern [24]. method is the more common calculation method, and its expression is as follows:

ln(g(α)/T²) = ln(AR/ꞵE_α)-E_α/RT

(14)

Similarly, activation energy ${\mathrm{E}}_{\mathsf{\alpha }}$ is obtained by the slope relationship between $\ln \left[\mathrm{g}\right(\mathsf{\alpha })/{\mathrm{T}}^2]$ and $1/\mathrm{T}$, while $\mathrm{lnA}$ is obtained by the intercept. As for $\mathrm{g}\left(\mathsf{\alpha }\right)$, 19 common reaction models are listed in

Table 1. Nineteen commonly used reaction models for describing the pyrolysis of substances.

Symbol Reaction Method	f(α)	g(α)
Power law	$4{\mathsf{\alpha }}^{3/4}$	${\mathsf{\alpha }}^{1/4}$
Power law	$3{\mathsf{\alpha }}^{2/3}$	${\mathsf{\alpha }}^{1/3}$
Power law	$2{\mathsf{\alpha }}^{1/2}$	${\mathsf{\alpha }}^{1/2}$
Power law	$2/3{\mathsf{\alpha }}^{-1/2}$	${\mathsf{\alpha }}^{3/2}$
Zero-order (Polany–Winger equation)	$1$	$\mathsf{\alpha }$
Phase-boundary controlled reaction	$2{(1-\mathsf{\alpha })}^{1/2}$	$\left[1-{(1-\mathsf{\alpha })}^{1/2}\right]$
Phase-boundary controlled reaction	$3{(1-\mathsf{\alpha })}^{2/3}$	$\left[1-{(1-\mathsf{\alpha })}^{1/3}\right]$
First-order	$(1-\mathsf{\alpha })$	$-\ln (1-\mathsf{\alpha })$
Three-halves order	${(1-\mathsf{\alpha })}^{3/2}$	$2\left[{\left(1-\mathsf{\alpha }\right)}^{-1/2}-1\right]$
Second-order	${(1-\mathsf{\alpha })}^2$	${(1-\mathsf{\alpha })}^{-1}-1$
Third-order	${(1-\mathsf{\alpha })}^3$	$(1/2)\left[{\left(1-\mathsf{\alpha }\right)}^{-2}-1\right]$
Avrami–Eroféev (n = 1.5)	${(3/2)(1-\mathsf{\alpha })\left[-\ln (1-\mathsf{\alpha })\right]}^{1/3}$	${\left[-\ln (1-\mathsf{\alpha })\right]}^{2/3}$
Avrami–Eroféev (n = 2)	${2(1-\mathsf{\alpha })\left[-\ln (1-\mathsf{\alpha })\right]}^{1/2}$	${\left[-\ln (1-\mathsf{\alpha })\right]}^{1/2}$
Avrami–Eroféev (n = 3)	${3(1-\mathsf{\alpha })\left[-\ln (1-\mathsf{\alpha })\right]}^{2/3}$	${\left[-\ln (1-\mathsf{\alpha })\right]}^{1/3}$
Avrami–Eroféev (n = 4)	${4(1-\mathsf{\alpha })\left[-\ln (1-\mathsf{\alpha })\right]}^{3/4}$	${\left[-\ln (1-\mathsf{\alpha })\right]}^{1/4}$
One-dimensional diffusion	$1/2\mathsf{\alpha }$	${\mathsf{\alpha }}^2$
Two-dimensional diffusion	$1/[-\ln (1-\mathsf{\alpha }\left)\right]$	$\left(1-\mathsf{\alpha }\right)\ln \left(1-\mathsf{\alpha }\right)+\mathsf{\alpha }$
Three-dimensional diffusion	$3{\left(1-\mathsf{\alpha }\right)}^{1/3}/2[{\left(1-\mathsf{\alpha }\right)}^{-1/3}-1]$	${\left[{1-\left(1-\mathsf{\alpha }\right)}^{-1/3}\right]}^2$
Three-dimensional diffusion	$3/2[{\left(1-\mathsf{\alpha }\right)}^{-1/3}-1]$	$\left(1-2\mathsf{\alpha }/3\right)-{(1-\mathsf{\alpha })}^{2/3}$

.

2.3.6. Masterplot Method

In addition to the Coats–Redfern method, masterplot method was also chosen to reconstruct the reaction model. For single-step reaction processes, the masterplot method allows for the explicit selection of an appropriate kinetic model [25]. In single-step reactions, the activation energy $\mathrm{E}$, pre-exponential factor $\mathrm{A}$, and the kinetic model are constant. Substituting the conversion rate $\mathsf{\alpha }=0$.5 as the reference point in Equation (5), one receives

g(0.5) = AR/ꞵR p(X_0.5)

(15)

where ${\mathrm{x}}_{0.5}=\mathrm{E}/\mathrm{R}{\mathrm{T}}_{0.5}$ and ${\mathrm{T}}_{0.5}$ is the temperature corresponding to $\mathsf{\alpha }=0$.5. By dividing Equation (5) by Equation (15), one receives

g(α)/g(0.5) = p(x)/p(x_0.5)

(16)

The $\mathrm{g}\left(\mathsf{\alpha }\right)$ function in the theoretical masterplots $\mathrm{g}\left(\mathsf{\alpha }\right)/\mathrm{g}\left(0.5\right)$ is still listed in Table 1. As for the experimental masterplots $\mathrm{p}\left(\mathrm{x}\right)/\mathrm{p}\left({\mathrm{x}}_{0.5}\right)$, they are plotted by experimental data corresponding to $\mathsf{\alpha }$ at different heating rates. Equation (16) shows that for a given $\mathsf{\alpha }$, the calculated values $\mathrm{p}\left(\mathrm{x}\right)/\mathrm{p}\left({\mathrm{x}}_{0.5}\right)$ and the theoretical values $\mathrm{g}\left(\mathsf{\alpha }\right)/\mathrm{g}\left(0.5\right)$ should be equal when a suitable reaction model is used. Therefore, we can determine the kinetic model of the pyrolysis reaction by substituting the most optimal $\mathrm{g}\left(\mathsf{\alpha }\right)$. The methods adopted in the present study follows the flow chart as shown in Figure 1.

2.4. PY-GC-MS Analysis

The products of sample pyrolysis were analyzed by PY-GC-MS. Samples were first passed through the pyrolysis (PY) analyzer and then coupled to a gas chromatograph/mass (GC-MS) spectrometer system for analysis. During PY-GC-MS test, about 10 mg EPS sample was degraded at target temperature of 680 K. The volatile products generated during the process were identified by the online GC-MS system. The mass spectrometer scan range was from 40 to 500 mass units, a chromatographic column (30 m × 250 μm) was used, and helium was adopted as carrier gas with flow rate of 100 mL/min. Finally, the products were qualitatively analyzed by software.

3. Results

3.1. Analysis of Thermal Decomposition

The TG and DTG curves of EPS at different heating rates (5, 10, 20, 40, and 80 °C/min) are illustrated in Figure 2. Both graphs show that the curve shifts to the right as the heating rate increases. The temperature at which the sample undergoes pyrolysis increases with the increase in the heating rate. The mass loss of EPS can be seen from the thermogravimetric curve and occurs mainly between 620 K and 780 K. The curve of DTG also shows that there is only one main peak at each heating rate under a nitrogen atmosphere, and the peak is mainly between 600 K and 840 K, which indicates that EPS pyrolysis is a rapid one-step reaction process. In addition, Zhang et al. [26] and Ha et al. [27] also reported a single-stage establishment for EPS pyrolysis. Generally, for the mass loss profiles, the whole temperature range at which EPS thermal decomposition occurs is around 600 K. The peak values in the mass loss rate curves become larger as the heating rate rises. This phenomenon is also observed by Roussi et al. [28] and Liu et al. [29]. As indicated by Wu et al. [30], this could be generally explained by the fact that with the increase in heating rate, the time required for the same temperature increment dT decreases. In addition, all reaction rate dα/dT curves have similar shapes except for the peak values that increased with the heating rate. This phenomenon is also observed by Chen et al. [31] and Kaur et al. [32].

3.2. Kinetic Analysis

The kinetics of the samples were researched and analyzed by two types of methods, model-free and model-fitting, to obtain kinetic triples.

3.2.1. Model-Free Methods

Four methods, FWO, KAS, Senum–Yang, and Advanced Vyazovkin, were used to obtain the activation energy Eα values at different conversion rates, and the results are shown in Figure 3. As can be seen from the figure, the activation energy Eα values calculated under different methods deviate slightly, but the overall trend is still consistent, showing a slow increase. This illustrates the accuracy of the isoconversional method in calculating kinetics. The calculation result of FWO is the largest, and the other three calculations are closer. The values of the activation energy E_α do not fluctuate much and are within 10% above and below their average values (FWO: 154.40 kJ/mol, KAS: 150.85 kJ/mol, Senum–Yang: 151.22 kJ/mol, Advanced Vyazovkin: 151.23 kJ/mol), which means that a single kinetic description of the EPS pyrolysis process is feasible. We take the average of Senum–Yang and Advanced Vyazovkin as the result of the model-free method. The calculated activation energy results in the present study were found to be very close to some previous studies. For example, Ren et al. [33] reported the activation energy of 123.8 kJ/mol, Zhang et al. [26] obtained Eα values of 158.82 kJ/mol, and Ni et al. [14] found the activation energy to be 163.23 kJ/mol. The slight deviations maybe attributed to the fact that the sample materials were obtained in different ways and handled differently after the acquisition, coupled with distinctions in how the materials were produced and the processing.

3.2.2. Model-Fitting Methods

The model-free method does not rely on the reaction model for the calculation, so the reaction model cannot be determined, which requires the adoption of the model-fitting method. Among the model-fitting methods, the most common method is the Coats–Redfern method. For each heating rate, the sample data can be subjected to the Coats–Redfern method once. The results for the five heating rates are displayed in Figure 4, where the different g(α) are listed in Table 1. By fitting the obtained data points, the Eα and lnA can be calculated under different response models based on Equation (8).

The activation energy E_α calculated under different models according to the Coats–Redfern method at different heating rates are listed in

Table 2. The Ea values were calculated by the Coats–Redfern method for different heating rates.

Model	5 °C min−1	10 °C min−1	20 °C min−1	40 °C min−1	80 °C min−1
P1	42.96	45.86	46.62	48.55	49.83
P2	60.89	64.83	65.94	68.61	70.42
P3	96.75	102.77	104.57	108.73	111.60
P4	311.89	330.42	336.35	349.45	358.70
R1	204.32	216.60	220.46	229.09	235.15
R2	234.67	248.54	253.52	263.43	270.65
R3	246.53	261.01	266.44	276.87	284.54
F1	273.18	289.03	295.50	307.09	315.80
F3/2	320.64	338.90	347.29	361.00	371.54
F2	376.26	397.33	408.00	424.24	436.93
F3	505.10	532.65	548.67	570.82	588.51
A3/2	178.51	189.00	193.23	200.85	206.55
A2	131.18	138.99	142.09	147.73	151.92
A3	83.84	88.97	90.95	94.61	97.30
A4	60.17	63.97	65.39	68.05	69.99
D1	419.46	444.24	452.24	469.82	482.25
D2	455.76	482.46	491.76	510.84	524.65
D3	503.88	533.08	544.21	565.36	581.04
D4	471.45	498.97	508.85	528.61	543.03

. As shown in Table 2, the obtained E_α was more dependent on the reaction model, while the effect of the heating rates was not significant. Based on Section 3.2.1, the comparison between the results of the model-free calculation and the Coats–Redfern method shows that the results under the A2 (Avrami–Eroféev model) are the closest. The pyrolysis of EPS contains multiple reactions of various substances and is a complex process. We substitute one model for the whole reaction process to simplify the whole process [34]. Although the deviation of A2 is minimized, it was still not certain that the function corresponding to A2 is the reaction function of the sample pyrolysis, so the masterplot method was further introduced to determine the reaction function.

The predetermined value of activation energy Eα and the temperature corresponding to α were both substituted into Equation (13) to calculate the value of p(x), from which the p(x) at different α was divided by p(x_0.5) at α = 0.5 to obtain the experimental masterplots p(x)/p(x_0.5) at different heating rates. The results from the theoretical masterplots g(α)/g(0.5) are compared. The theoretical masterplots g(α)/g(0.5) for 19 models are plotted in Figure 5, and the best-fit model data plots for the experimental masterplots are drawn in Figure 6. The A2 (Avrami–Eroféev model) model had the highest matching degree, which also reached an agreement with the calculation results of the Coats–Redfern method. Therefore, f(α) = [2(1-α)[-ln1-α]]^(1/2) was considered the pyrolysis reaction function of EPS in nitrogen. It should be noted that this does not mean that the A2 model was the actual response model, but only the closest mathematical numerical model, and if this model was chosen to reconstruct the experimental data, it may still not be well adapted to the experimental results [35].

3.3. Compensation Effects

There is a linear relationship between the activation energy and the pre-exponential factor, called the compensation effect, which is expressed as follows:

lnA = a + bE

(17)

where a = lnk_iso, and b = 1/RT_iso, both of which are constant. k_iso and T_iso are the artificial isokinetic rate constant and the artificial isokinetic temperature, respectively. The E and lnA calculated by the Coats–Redfern method at different heating rates under different models were linearly fitted to achieve the compensation effect plot, as shown in Figure 7. At each heating rate, a corresponding pair of E and lnA was obtained by each model, and a linear fit of these 19 sets of data yielded a fitted straight line at each heating rate, which is the compensation effect. The fitting results are illustrated in

Table 3. Fitting results at different heating rates.

Heating Rate	$\mathit{a}$	$\mathit{b}$	${\mathit{k}}_{\mathit{i}\mathit{s}\mathit{o}}$	${\mathit{T}}_{\mathit{i}\mathit{s}\mathit{o}}$
5 °C min−1	−6.53385	0.18291	0.001453	657.586
10 °C min−1	−5.81719	0.17909	0.002976	671.6123
20 °C min−1	−5.16082	0.17514	0.005737	686.7594
40 °C min−1	−4.48485	0.17037	0.011279	705.9872
80 °C min−1	−3.82186	0.16592	0.021887	724.9219
Total	−4.9783	0.17373	0.006886	692.3332

, indicating that the artificial kinetic temperature rises with an increase in the heating rate. If the reaction model is not selected suitably, the artificial isothermal temperature will be out of the experimental temperature range. The artificial isothermal temperature values were all located within the experimental temperature range, which is evidence that the choice of the reaction model was correct. Then, the five sets of data were fitted as a whole and the total linear fitting relationship between them was lnA = −4.9783 + 0.17373E with R² = 0.9969. The variation in the pre-exponential factor with the conversion rate calculated from the kinetic compensation effect is given in Figure 8, which clearly shows the same pattern of activation energy variation, as shown in Figure 3.

3.4. Model Reconstruction

In the previous sections, the activation energy at different conversion rates was obtained by the isoconversional method, the model-free validation of the pyrolysis model was utilized, and then the pre-exponential factor was obtained by using the compensation effect. Now, it is necessary to use these kinetic parameters to calculate the Arrhenius equation, reconstruct the pyrolysis reaction rate, and verify the validity of the model. By modifying Equation (4), the following expression of f(α) can be achieved as follows:

f(α) = dα/dt × ꞵ/A × exp(E/RT)

(18)

By substituting the heating rate, activation energy, pre-exponential factor, temperature, and reaction rate dα/dT corresponding to the conversion rate into Equation (18), the values of f(α) corresponding to different conversion rates can be determined.

The highest matching Avrami–Eroféev model was used for the EPS pyrolysis model, and one should emphasize that this does not mean that it is the real model of the sample reaction. All models selected were available to reconstruct the reaction model from experimental data. Since the most commonly used models in pyrolysis kinetics do not apply to pyrolysis reactions in solids or porous structured solids, the reconstructed models do not necessarily match the experimental data [36]. In order to better reconstruct the reaction model, we then introduced the adjustment function Cα^m (C,m are both constants) to modify the model, and the modified function is expressed as the product of the reaction model and the modulation function, whose expression can be expressed as follows:

f(α) = Cα^m n(1 − α) {−ln(1 − α)}^(1−1/n)

(19)

Fitting the f(α) obtained by Equation (18) to the corresponding value of α yielded f(α) = 3.95335α^0.24174 (1 − α) [−ln(1 − α)]^1.64712. Figure 9 shows the comparisons of experimental profiles with modified models with the best-fitting coefficient. To verify whether the obtained f(α) is feasible, we substituted f(α) back into Equation (4) to gain the calculated value (dα/dt)_cal and compared it with the experimental value (dα/dt)_exp. The calculated mass loss rate values (dα/dt)cal were compared with experimental values (dα/dt)exp, as plotted in Figure 10. It is found that the mass loss rate calculations agree well with experimental values. Although the pyrolysis behavior of EPS is fundamentally investigated in the present study, further research is necessary to investigate its combustion characteristics as pyrolysis and combustion are considered the pilot step of fire spread. In future research, the obtained results like kinetic parameters will be provided as input parameters for sub-models during EPS fire spread numerical simulations.

3.5. Comparative Analysis of Kinetic Results

Table 4. Comparison of the kinetic parameters calculated in this study with those in previous studies.

Source of Samples (EPS)	$\mathit{E}$ (kJ/mol)	$\mathit{l}\mathit{n}\mathit{A}$	Atmosphere	Reference
Produced by a plastic chemical factory (40 mesh)	151.225	21.294	Nitrogen	This study
Obtained from a polymer chemical factory	136.26	21.896	Nitrogen	Jun et al. [11]
Collected locally	159.87	-	Nitrogen	Kannan et al. [12]
Cut into particles	245	-	Nitrogen	Jiao et al. [13]
Ground into powder	163.23	23.70	Nitrogen	Ni et al. [14]
Collected locally	123.8	20.72	Nitrogen	Ren et al. [17]
Produced by a polymer material factory	158.82	-	Nitrogen	Zhang et al. [18]

compares the kinetic parameters calculated in this study with the results of previous studies. Because the sample materials were obtained in different ways and handled differently after the acquisition, coupled with distinctions in how the materials were produced and processed, the resulting calculations may also exhibit slight deviations. First, all sample materials were experimented with and analyzed under a nitrogen atmosphere. The activation energy results were still relatively close, all around 150 kJ/mol. The lowest activation energy obtained was 123.8 kJ/mol in the study by Ren et al. and the highest was 245 kJ/mol in the study by Jiao et al., which is much higher than others. The results calculated in this study were very close to the mean values calculated by the previous authors, so the results have some reliability and accuracy.

3.6. Product Analysis by PY-GC-MS

Thermal cracking gas chromatography/mass spectrometry (PY-GC-MS), by high-temperature cracking, turns the sample into fragments, which are pyrolyzed in a high-temperature oven into small molecules of volatiles into the chromatograph/mass spectrometer to obtain chromatograms and mass spectra.

The material generates a large number of volatile gases during the pyrolysis process, and the gases released at different stages are recovered and stored, reflecting the environmental concept of effective utilization. EPS pyrolysis only has a single peak, mainly ranging from 620 K to 780 K, so we selected 683 K as the study temperature. The total gas ion counts (TICs) from EPS pyrolysis in a helium environment are plotted in Figure 11. Seventeen compounds with high relative abundance were identified for analysis, and their TICs were characterized and analyzed, as shown in

Table 5. Compounds identified by PY-GC-MS.

NO.	Apex R.T.	Compound Name	Formula	Height%	Area%
1	1.30	Carbon dioxide	CO2	1.91	1.54
2	1.44	Butane,2-methyl-	C5H12	7.42	7.68
3	2.92	Toluene	C7H8	4.74	4.71
4	4.49	Styrene	C8H8	7.04	9.4
5	4.81	Styrene	C8H8	6.62	8.5
6	5.88	α-Methylstyrene	C9H10	1.56	1.47
7	13.58	Bibenzyl	C14H14	6.15	4.48
8	13.91	Benzene,1,1′-(1-methyl-1,2-ethanediyl)bis-	C15H16	3.13	2.01
9	15.90	Naphthalene,1,2,3,4-tetrahydro-2-phenyl-	C16H16	7.55	15.47
10	16.02	Naphthalene,1,2,3,4-tetrahydro-2-phenyl-	C16H16	6.61	2.06
11	16.12	1,2-Diphenylcyclopropane	C15H14	1.43	0.77
12	17.04	Benzene,1,1′-(1-butene-1,4-diyl)bis-,(Z)-	C16H16	5.06	3.91
13	17.72	2,5-Diphenyl-1,5-hexadiene	C18H18	7.28	4.95
14	18.92	1,5-Diphenyl-1,5-hexadiene	C18H18	1.42	0.98
15	21.55	Benzene,1,1′,1″,1‴-(1,2,3,4-butanetetrayl)tetrakis-	C28H26	1.44	0.71
16	22.70	Heptane,1,1-diphenyl-	C19H24	7.2	17.04
17	22.83	Heptane,1,1-diphenyl-	C19H24	5.95	1.34

. Of these, the compounds were identified as the substances that occupied the highest probability in comparison with the NIST database.

From Table 5, it can be seen that peak 3 is Compound 3, peaks 4 and 5 are Compounds 4 and 5, peak 6 is Compound 6, and peak 7 is Compound 7. Peaks 9 and 10 (Compounds 9 and 10), peak 12 (Compound 12), peak 13 (Compound 13), peak 14 (Compound 14), and peaks 16 and 17 (Compounds 16 and 17) all belong to the styrene dimer group. Finally, the detailed names of these compounds are listed in Table 5. The results of PY-GC-MS show that EPS pyrolysis produces all carbon and hydrogen compounds, which are unsaturated compounds. The volatiles mainly belong to compounds of benzene, naphthalene, and biphenyl, all with the chemical formula of the form C_nH_n. With the rapid development of urbanization, green building technologies and new building materials have been increasingly applied on a broader scale [37,38,39]. The findings of this study contribute to ensuring the safe and large-scale engineering application of insulation materials.

4. Conclusions

To effectively recycle and convert waste typical thermal insulation materials into fuels by using thermal reactors, the pyrolysis characteristics of EPS were studied in detail. Model-free kinetic analysis showed that the average Eα values are estimated to be 154.40, 150.85, 151.22, and 151.23 kJ/mol via the advanced FWO, KAS, Senum–Yang and Advanced Vyazovkin methods, respectively. Then, the model-fitting method suggested that the A2 model was the most probable reaction mechanism for EPS degradation. Finally, the kinetic triplets for the whole process of EPS pyrolysis were obtained as E = 151.225 kJ/mol and lnA = 21.294. Based on model reconstruction, the reconstructed reaction model was found to be f(α) = 3.95335α^0.24174(1-α)[-ln(1-α)]^1.64712. Further, the PY-GC-MS experiment was performed to identify the composition of EPS pyrolysis volatiles, and the results showed that the products were mainly compounds of benzene, naphthalene, and biphenyl. In future research, the obtained results like kinetic parameters will provided as the input parameters for sub-models during EPS fire spread numerical simulations. In addition, the parameter results obtained can guide the reactor design and optimization in the industry to better convert polymer wastes into fuels and manage wastes.