Thermal Stability and Non-Isothermal Kinetic Analysis of Ethylene–Propylene–Diene Rubber Composite

The purpose of this study was to investigate the thermal stability and the decomposition kinetics of ethylene–propylene–diene monomer (EPDM) composite samples loaded with and without lead powder (50, 100, and 200 phr lead) using thermogravimetric analysis (TGA). TGA was carried out at different heating rates (5, 10, 20, and 30 °C/min) under inert conditions in the temperature range of 50–650 °C. Lead addition did not significantly change the onset temperature or peak position corresponding to the maximum decomposition rate of the first derivative of the TGA curve (DTGA) (onset at about 455 °C and Tm at about 475 °C). Peak separation for the DTGA curves indicated that the main decomposition region for EPDM, the host rubber, overlapped the main decomposition region for volatile components. The decomposition activation energy (Ea) and pre-exponent factor (A) were estimated using the Friedman (FM), Kissinger–Akahira–Sunose (KAS), and Flynn–Wall–Ozawa (FWO) iso-conversional methods. Average activation energy values of around 231, 230, and 223 kJ/mol were obtained for the EPDM host composite using the FM, FWO, and KAS methods, respectively. For a sample loaded with 100 phr lead, the average activation energy values obtained via the same three methods were 150, 159, and 155 kJ/mole, respectively. The results obtained from the three methods were compared with results obtained using the Kissinger and Augis–Bennett/Boswell methods, and strong convergence was found among the results of the five methods. A significant change in the entropy of the sample was detected with the addition of lead powder. For the KAS method, the change in entropy, ΔS, was −3.7 for EPDM host rubber and −90 for a sample loaded with 100 phr lead, α = 0.5.


Introduction
EPDM is one of the most popular rubbers due to its many advantages and properties. This type of rubber is utilized in the preparation of composite materials with additives and ingredients. It is also used for the preparation of blended rubber composites with another type of rubber or polymer such as NBR, PVC, etc., to acquire new characteristics and open wide horizons for technological applications. This type of rubber is famous for its radiation shielding properties, especially against gamma rays and neutrons [1][2][3][4]. This is due to its hydrogen abundance. EPDM composites are also used in thermal insulation, leakage prevention, and other relevant applications. Additionally, composites based on EPDM can be made for electromagnetic shielding using additives with magnetic and electrical properties [5,6].
The thermal stability and decomposition mechanisms for polymeric and rubber composites are among the key properties of materials exposed to high temperatures. In view of the exposure of many products based on EPDM rubber to a heating environment, such as reactors, the automobile industry, etc., it is important to study the effect of any additives on The sample ingredients and components are outlined in Table 1. The values are expressed in phr (parts per hundred).

Thermogravimetric Analysis
Thermogravimetric analysis (TGA) was performed using a TA Instruments Q50 thermogravimetric analyzer, under a nitrogen (N 2 ) flow of 20 mL/min. The measurements were carried out at different heating rates (5,10,20, and 30 • C/min) with constant mass of about 10 mg.

Models for Thermal Kinetic Analysis
The decomposition or conversion rate (alpha) is used in analyzing thermal decomposition mechanisms and can be expressed as follows [27]: where w 0 , w t , and w f are the initial, residual (at time t), and final weights of the material, respectively. The rate of conversion (dα/dt) is directly proportional to the conversion function f (α): where dα dt is the rate of conversion in s −1 , k is the rate constant, α is the degree of conversion, and n is the order of reaction.
In the Arrhenius equation, the activation energy is quantitatively related to the reaction rate. The equation thus provides a quantitative basis for understanding how the reaction rates depend on the activation energy. The rate constant as a function of temperature is given by where E is the activation energy (J.mo1 −1 ), A is the pre-exponential factor, R is the gas constant (8.31 J.mo1 −1 .K −1 ), and T is the absolute temperature (K). Using these equations, one can obtain Let Polymers 2023, 15, 1890 4 of 22 The above integral cannot be solved exactly, but it can be expressed in numerical form or by some approximations. For estimating the kinetic parameters, model-free isoconversional methods such as Friedman's (FM), Kissinger-Akahira-Sunose (KAS) [28], and Flynn-Wall-Ozawa (FWO) [29,30] were chosen.
Using the KAS method and according to (6), the relationship between ln[β/T 2 ] and 1/T was plotted for each value of conversion α. From the slope and the intersection, E a and A can be calculated.
Based on Doyle's approximation (Doyle 1962), the integral in (5) yields the following Equation (7) via simplification, which forms the basis of further iso-conversional methods developed by Flynn and Wall (Chan and Balke 1997) and Ozawa [29,30].
Thus, the activation energy and pre-exponential factor can be determined from the slope and intercept of the linear relation ln β vs. 1/T for constant values of α.
According to Friedman (1964) [31], the Friedman method (a differential iso-conversional method) provides correct values of the kinetic parameters: where ln(β da/dT) is plotted against 1/T at constant values of α, and from the slope and intercept, both E a and A can be determined.

Thermodynamic Analysis
By applying the following equations with the obtained activation energy, the thermodynamic parameters, including the pre-exponential factor (A), changes in enthalpy (∆H), Gibbs free energy (∆G), and entropy (∆S), can be determined [32,33]: where k B is the Boltzmann constant, h is the Plank constant, T m is the temperature of the maximum decomposition rate, and T α is the temperature corresponding to α.

Thermogravimetric Analysis
The TGA and DTGA curves of the EPDM host sample and samples loaded with 50, 100, and 200 phr lead are presented in Figure 1. The composite samples underwent two main decomposition stages.

Thermogravimetric Analysis
The TGA and DTGA curves of the EPDM host sample and samples loaded with 50, 100, and 200 phr lead are presented in Figure 1. The composite samples underwent two main decomposition stages. As illustrated in Figure 2, by using the Origin−Lab program (version 8.6), the main interaction stage (in DTGA) can be resolved to two main decomposition process. The first decomposition process (Region I) starts at about 50 °C and theoretically (according to the peak profile) ends at about 600 °C, while the second process (Region II) starts at about 350 As illustrated in Figure 2, by using the Origin−Lab program (version 8.6), the main interaction stage (in DTGA) can be resolved to two main decomposition process. The first decomposition process (Region I) starts at about 50 • C and theoretically (according to the peak profile) ends at about 600 • C, while the second process (Region II) starts at about 350 • C and ends at about 580 • C. There are no references indicating that EPDM rubber decomposes at temperatures below 350 • C [34][35][36]. Decomposition in region I can thus be attributed to the volatile components used during the preparation of the host rubber composite, such as paraffin oil. Comparing the peak position of the maximum decomposition rate for region II with the literature confirms that the decomposition in this region is caused by the decomposition of the host rubber, EPDM. °C and ends at about 580 °C. There are no references indicating that EPDM rubber composes at temperatures below 350 °C [35][36][37]. Decomposition in region I can thus attributed to the volatile components used during the preparation of the host rub composite, such as paraffin oil. Comparing the peak position of the maximum deco position rate for region II with the literature confirms that the decomposition in this gion is caused by the decomposition of the host rubber, EPDM. The curves clearly indicate that as the concentration of lead powder in the samp increases, the sample becomes more thermally stable, and the residual mass increa [27]. As a result of the addition of lead, the position of maximum decomposition 277.5 to 275 °C) did not change significantly, indicating that the influence of lead thermal behavior is physical rather than chemical. Table 2 lists some of the parameters that could be extracted from the thermal composition curves for the EPDM composite samples. The curves clearly indicate that as the concentration of lead powder in the samples increases, the sample becomes more thermally stable, and the residual mass increases [26]. As a result of the addition of lead, the position of maximum decomposition (≈ 277.5 to 275 • C) did not change significantly, indicating that the influence of lead on thermal behavior is physical rather than chemical. Table 2 lists some of the parameters that could be extracted from the thermal decomposition curves for the EPDM composite samples. It can be seen from the above analysis that the introduction of lead powder to the EPDM host composite had an important influence on the thermal stability of the host composite. The results can be summarized as follows: • The effect of lead powder on the main decomposition peak (maximum decomposition rate) indicates that there was no chemical interaction between lead and EPDM. The variations in these peak positions are within the experimental error. Through previous research, we note that some additives may not affect position the maximum decomposition rate of EPDM rubber [37,38]. • Lead powder's effect is evident between 200 and 400 • C, especially at higher concentrations.

•
The decomposed mass at T > 250 • C decreased with increasing lead concentration. This can be attributed to the following: Lead particles absorb a large amount of thermal energy and, in turn, delay the decomposition of the host composite. During the preparation and vulcanization process, the lead increases the thermal homogeneity of the sample, leading to the formation of a homogenous network of cross-linked chains. There has been some evidence that conductive fillers impact EPDM's thermal behavior, especially its thermal conductivity [39][40][41].

•
As the lead powder concentration increased, the residual mass increased [42].

Kinetic Analysis
The decomposition of both the host composite and the composites loaded with lead takes place in two stages: a main one for EPDM rubber [43] and a weak one for the volatile matter and other ingredients. There is an overlap between both decompositions in a range of temperatures (as previously shown in Figure 2). This behavior was not affected by change in the heating rate for both sample types, as shown in Figures 3 and 4. In Figures 3b and 4b, the peak corresponding to the maximum decomposition rate shifted to a higher temperature with the heating rate. Based on these data, the kinetic parameters (E a and A) were estimated for both the host composite and the composites loaded with lead. Figure 5 shows the relationship between ln(β/T p 2 ) and 1000/T, as well as that between ln(β/T p ) and 1000/T, according to the Kissinger [28] and Augis-Bennett/Boswell methods [44,45], respectively, for determination of the activation energy. Both methods gave approximately equal results within the permissible error. The activation energy value calculated using the Kissinger method was about 227 kJ/mol, while the Augis-Bennett/Boswell method gave a value of about 229 kJ/mol. The error was less than 1% between the two methods. These results are largely consistent with the references [46,47].
By applying the same two methods (Kissinger and Augis-Bennett), the activation energy was calculated for the sample loaded with 100 phr lead powder ( Figure 6). The activation energies calculated by the Kissinger and Augis-Bennett methods were 141 and 144 kJ/mol, respectively. The addition of lead produced a significant decrease in the activation energy of decomposition, and the two methods gave values that are very close to each other. The decrease of the activation energy with the addition of lead can be attributed to the increase in the thermal conductivity of the composite sample and the decrease of entanglements in the composite matrix.    Figure 5 shows the relationship between ln(β/Tp 2 ) and 1000/T, as well as that between ln(β/Tp) and 1000/T, according to the Kissinger [29] and Augis-Bennett/Boswell methods [45,46], respectively, for determination of the activation energy. Both methods gave approximately equal results within the permissible error. The activation energy value calculated using the Kissinger method was about 227 kJ/mol, while the Augis-Bennett/Boswell method gave a value of about 229 kJ/mol. The error was less than 1% between the two methods. These results are largely consistent with the references [47,48].   Figure 5 shows the relationship between ln(β/Tp 2 ) and 1000/T, as well as that between ln(β/Tp) and 1000/T, according to the Kissinger [29] and Augis-Bennett/Boswell methods [45,46], respectively, for determination of the activation energy. Both methods gave approximately equal results within the permissible error. The activation energy value calculated using the Kissinger method was about 227 kJ/mol, while the Augis-Bennett/Boswell method gave a value of about 229 kJ/mol. The error was less than 1% between the two methods. These results are largely consistent with the references [47,48]. The Kissinger and Augis-Bennett methods ignore the changes in conversion rates (dα/dt) and conversion (α). They assume that Ea is independent of α. Three methods that are derived from (5) and account for the conversion function f (α) will be illustrated. These methods are Kissinger-Akahira-Sunose, Flynn-Wall-Ozawa, and Friedman ((6), (7), and (8), respectively). Figure 7 illustrates the dependence of the conversion α ( Figure 7a) and its first derivative ( Figure 7b) on the temperature. Using these results, the main decomposition stage of the host EPDM with and without lead was analyzed, and a comparison among the three methods was carried out. By applying the same two methods (Kissinger and Augis-Bennett), th energy was calculated for the sample loaded with 100 phr lead powder (Fi activation energies calculated by the Kissinger and Augis-Bennett methods w 144 kJ/mol, respectively. The addition of lead produced a significant decrea The Kissinger and Augis-Bennett methods ignore the changes in conversion rates (dα/dt) and conversion (α). They assume that Ea is independent of α. Three methods that are derived from (5) and account for the conversion function f(α) will be illustrated. These methods are Kissinger-Akahira-Sunose, Flynn-Wall-Ozawa, and Friedman ((6), (7), and (8), respectively). Figure 7 illustrates the dependence of the conversion α ( Figure 7a) and its first derivative (Figure 7b) on the temperature. Using these results, the main decomposition stage of the host EPDM with and without lead was analyzed, and a comparison among the three methods was carried out.  The Kissinger and Augis-Bennett methods ignore the changes in conversion rates (dα/dt) and conversion (α). They assume that Ea is independent of α. Three methods that are derived from (5) and account for the conversion function f(α) will be illustrated. These methods are Kissinger-Akahira-Sunose, Flynn-Wall-Ozawa, and Friedman ( (6), (7), and (8), respectively). Figure 7 illustrates the dependence of the conversion α ( Figure 7a) and its first derivative ( Figure 7b) on the temperature. Using these results, the main decomposition stage of the host EPDM with and without lead was analyzed, and a comparison among the three methods was carried out.   This may be attributed to the dependence of Friedman's method (8) on the first derivative with respect to time of the degree of conversion (dα/dt). Despite this apparent difference in behavior, there are some common points that could be concluded. The total average values of activation energy for the three methods are distinctly close (229, 229.6, and 231 kJ/mole for the KAS, FWO, and Friedman methods, respectively). Additionally, the pre-exponential factors for the three methods are of the same order of magnitude (10 +15 ) (see Figures 8,9 and 10d).   (Figure 10c,d). This may be attributed to the dependence of Friedman's method (8) on the first derivative with respect to time of the degree of conversion (dα/dt). Despite this apparent difference in behavior, there are some common points that could be concluded. The total average values of activation energy for the three methods are distinctly close (229, 229.6, and 231 kJ/mole for the KAS, FWO, and Friedman methods, respectively). Additionally, the pre-exponential factors for the three methods are of the same order of magnitude (10 +15 ) (see Figures 8-10d). In accordance with the E(α) relation for the three methods mentioned above, there is a region where the activation energy dependence on the degree of conversion (α) is weak or not significant and can be considered constant after looking at the value of its standard deviation (0.64, 0.53, and 3.31, respectively). The average activation energy for each method is close to those of the Kissinger and Augis-Bennett methods, with a slight difference not exceeding 5%, as shown in Table 3.    Figures 11-13 show the application of the KAS, FWO, and Friedman methods, respectively, for EPDM host loaded with 100 phr lead powder. It was observed that the activation energy values are close to each other at alpha greater than 0.4, but the activation energy changes when alpha is less than 0.4. There is no specific behavior for the three samples within this range (α < 0.4). In accordance with the E(α) relation for the three methods mentioned above, there is a region where the activation energy dependence on the degree of conversion (α) is weak or not significant and can be considered constant after looking at the value of its standard deviation (0.64, 0.53, and 3.31, respectively). The average activation energy for each method is close to those of the Kissinger and Augis-Bennett methods, with a slight difference not exceeding 5%, as shown in Table 3.         Table 3 summarizes the average values of activation energy over the entire range of degree of conversion, as well as the mean value of activation energy in the less dependent region (from 0.4 to 0.9) and the standard deviation for each data set. Tables 4-6 illustrate the values of the activation energy and the pre-exponent factor, respectively (for the host composite and that loaded with 100 phr lead). The deviation in the activation energy values between the KAS and FWO methods does not exceed 4%; when compared with the Friedman method, however, the difference may reach more than 10% at some values of α. This difference may be due to the dependence of the Friedman method on the time derivative of α. The pre-exponential factor, A, varies between 10 15 and 10 16 for the three methods. The behavior of A is similar for the KAS and FWO methods, while it differs in the Friedman method. The fluctuation in the predicted values is larger in the case of Friedman method, as shown in Table 5.  For the three methods (KAS, FWO, and FM), (9)-(12) were used to evaluate the preexponential factor and thermodynamic parameters, namely, the enthalpy change (∆H), Gibbs free energy change (∆G), and entropy change (∆S), based on the values of activation energy determined via the iso-conversion free-model methods [48]. Their values are listed in Tables 7-9. It is evident from these three tables that the activation energy and preexponential factors do not depend significantly on the conversion [49], except for small values; this indicates that the material decomposed simply and not in a complex manner. It is noted that the entropy of the rubber composite sample is much higher than the entropy of the host rubber sample (for the KAS method, ∆S was −3.7 for EPDM host rubber and −90 for a sample loaded with 100 phr lead, with α = 0.5). This result is logical, as the randomness of the system is increased by the introduction of lead particles into the host rubber system [50]. The Gibbs free energy for the EPDM composite sample is still close to the activation energy (for each alpha). This can be attributed to the fact that the nature of the rubber is still the same, and it decomposes in a simple and uncomplicated process.
The values of the pre-exponential factor (A) in Table 6 differ from those values calculated in Tables 7-9. This can be attributed to the fact that the former values depend on the value of the activation energy (calculated from the slope of the straight line) and the intercept for each value of α (according to the model or methods (6)-(8)), while the latter values (in Tables 7-9) were calculated using the general model (9) that depends on the heating rate and temperature at the maximum decomposition (T m ) of the DTGA curve, besides other constants.   Table 10 summarizes the maximum, minimum, and average values of the basic thermodynamic parameters (enthalpy change, Gibb's free energy change, and entropy change), activation energies (E), and pre-exponent factors (A).  Figure 14 shows great convergence and agreement among the three methods (KAS, FWO, and FM), as well with the two other methods (the Kissinger and Augis-Bennett/Boswell methods ( Figure 5)). Based on the KAS method, for example, Figure 14d shows the scope of convergence between the activation energy and Gibbs free energy change in the host sample. There is a high degree of harmony in this reaction, suggesting that it is an uncomplicated process.

Conclusions
The thermal stability of ethylene-propylene-diene monomer (EPDM) composite samples loaded with and without lead powder (50, 100, and 200 phr lead) was examined via thermogravimetric analysis (TGA) at a 10 C/min heating rate. Lead addition did not significantly change the onset temperature or peak position corresponding to the maxi-

Conclusions
The thermal stability of ethylene-propylene-diene monomer (EPDM) composite samples loaded with and without lead powder (50, 100, and 200 phr lead) was examined via thermogravimetric analysis (TGA) at a 10 C/min heating rate. Lead addition did not significantly change the onset temperature or peak position corresponding to the maximum decomposition rate of DTGA (onset at about 455 • C and Tm at about 475 • C). Through peak separation of the DTGA curves, it was confirmed that some degradation processes overlapped with the EPDM decomposition peak. Kinetic thermal analysis was conducted for the host sample and a sample loaded with 100 phr lead. The TGA measurements were carried out at different heating rates (5, 10, 20, and 30 • C/min). Average activation energy values of around 231, 230, and 223 kJ/mol were obtained for the EPDM host composite using the Friedman (FM), Flynn-Wall-Ozawa (FWO), and Kissinger-Akahira-Sunose (KAS) methods, respectively. Using 100 phr lead as a sample, the average activation energy values obtained via the three methods were 150, 159, and 155 kJ/mole, respectively. There was strong convergence between the results obtained via these three methods and the results obtained via the Kissinger and Augis-Bennett/Boswell methods. A significant change in the entropy of the sample was detected with the addition of lead powder.  Data Availability Statement: Detailed data supporting the findings of this study are included in the article, as the authors confirm. In any case, the original collected data are available on request from the corresponding author.