Due to the massive increase in polymer manufacture, there has been a remarkable increase in plastic waste. With fewer landfills being used to dump plastic waste each year, it is becoming increasingly important to use effective recycling methods for plastic waste decomposition. In the present work, waste polystyrene was degraded in the presence of natural clay (K_{0.02}, Ca_{0.15} [Mg_{0.25}, Al_{0.69}, Fe_{0.06}], [Si_{2.0}, Al_{0.6}] O_{6.8} (O_{10}) nH_{2}O). The waste polymer was pyrolyzed at different heating rates i.e., 5, 10, 15 and 20°C min^{1} in an inert environment using nitrogen within the temperature range of 40 to 600°C. Thermogravimetric data were interpreted using various models, including fitting kinetic methods i.e., CoatsRedfern and modelfree methods i.e., OzawaFlynnWall, KissingerAkahiraSunose and Friedman method. The activation energy determined by CoatsRedfern, OzawaFlynnWall, KissingerAkahiraSunose and Friedman models were in the range of 83.22150.37, 74.52133.71, 73.16131.23, and 78.40140.67 kJmol^{1}, respectively. Among them, the lowest activation energy for polystyrene degradation was observed using KissingerAkahiraSunose method. The calculated kinetic parameters would be useful in determining the reaction mechanism of the solidstate reactions in a real system.
Polystyrene (PS) is a tough, lowcost plastic that is used in a wide range of applications in our daily life, such as kitchen appliances, toys, customer goods, food protective packaging, computers and hairdryer, etc. However, due to their nonbiodegradable nature, the disposal of these solid wastes causes serious environmental problems. Waste polystyrene (WPS) accounts for about 10 wt.% of total plastic waste [
For the decomposition of waste polymer into useful products through the pyrolysis process, it is important to understand the background knowledge of reaction pathways and pyrolysis mechanism. If the results of a complete mechanical model in relations of pyrolysis mechanism and overall rates can be thoroughly calculated as the kinetic rate parameters, then the reaction pathways to specific products can be examined [
Modelfitting techniques were commonly used for studying kinetics of solidstate reactions due to their capability to directly calculate activation energy (Ea) and frequency factor (A) from individual thermogravimetric analyzer data. However, these techniques are affected by several problems and one among them is their incapability to uniquely calculate the reaction model, particularly for nonisothermal data. Though these models can be found to be statistically equivalent, the fitted kinetic parameters can fluctuate by an order of magnitude and therefore, the choice of a proper model can be problematic. Application of modelfitting techniques to nonisothermal data can result in greater values for kinetic parameters. On other hand, the modelfree method is based on its straightforwardness and the anticipation of errors associated with the choice of a kinetic model [
Şenocak et al. [
Oh et al. [
According to the recommendations made by the Kinetics Committee of the International Confederation for Thermal Analysis and Calorimetry [
WPS was collected from a recycling site in a local shopping mall and shredded into small pieces with a size of 5070 mesh by a shredder. Clay was collected from a clay rock. WPS and catalyst were mixed in the ratio of 97:3 and stored in a desiccator for further studies.
Thermogravimetric analysis of WPS and clay mixture was carried out in a Simultaneous Thermogravimetric analyzer (PerkinElmer). Approximately 7 mg of each sample was taken in an alumina pan and heated at four different heating rates, i.e. 5, 10, 15 and 20°C/min, from 40°C to a final temperature of 600 °C. After complete weight loss, the data was collected and the kinetics parameters were calculated by CR, OFW, KAS and FM kinetic models.
Most of the solidstate degradation reaction follows Equation 1:
The rate can be investigated from the product in the form of three major variables: the pressure P, the temperature T, and the degree of conversion α [
where t is time and the pressure dependence, h(P) is neglected in most kinetic models used in thermal degradation. When the products or reactants are gases then the pressure may have a major effect on the kinetics of processes. The term h(P) is considered to be constant throughout the experiments. Therefore, most kinetic models used in the field of thermal analysis consider the rate as a function of only two variables, α and T, in such case the above equation becomes Equation 3:
In Equation 3, k(T) is the rate constant and f(α) is the fraction of conversion. Equation 3 explains the rate of singlestep reaction, however, the physical properties calculated by the pyrolysis methods are not reactants specific i.e. cannot be linked directly to particular reactions of molecules. Therefore, the value of α particularly reflects the development of the reactant to product conversion in all the cracking processes. The complete transformation commonly involves many reactions, in other words, each with its specific degree of conversion. The entire transformation process of the two parallel reactions can be explained by Equation 4 [
where α_{1} and α_{2} are the degree of conversion associated with two individual reactions, and their sum is the total conversion rate as shown in Equation 5:
However, if a process is found to follow a onestep equation, we should not determine that the mechanism of the reaction involves one single step. Generally, a mechanism involves many steps, one of which determines the overall rate of the reaction. This happens in the mechanism of two consecutive reactions when the first reaction is slower than the second. Then, the first reaction would determine the overall rate of reaction, which would obey a single step, although the mechanism involves two steps.
The dependence of the reaction rate of a process on temperature is elaborated by Arrhenius equation, as shown in Equation 6:
where R, Ea and A are universal gas constant, activation energy and preexponential factor, respectively. Normally, the actual kinetic parameters are functions of the intrinsic parameters of the separate steps. Hence, the kinetics of solidstate reaction can be explained by Equation 7:
where the temperature of the sample varies with time, so the rate of reaction is shown in Equation 8:
where β is the rate constant.
By combining and rearranging equations 7 and 8, the following Equation 9 is obtained:
By separating the variables and then integrating and rearranging Equation 9, Equation 10 was derived [
Equation 10 is the foundation for a variety of integral methods. Various approximate solutions have been proposed, leading to a variety of integral methods.
When x is equal to Ea/RT, the following Equation 11 is obtained:
Let the righthand side of Equation 11 be equal to p(x), Equation 12 is obtained:
By using integration by parts, Equation 12 leads to Equation 13:
The second term in Equation 13 can be neglected except that the values of p(x) becomes progressively smaller, so Equation 14 is obtained [
The molecular structure, nuclear structure and flow of heat evaluated by exponential integral are almost equal to the asymptotic equation 15:
As the p(x) is equal to Equation 16:
As the g(α) can be expressed as Equation 17:
Taking the natural log and rearranging Equation 17, we obtain Equation 18:
where Equation 18 is integrated with Doyle's approximation, i.e. when x≥20, the function p(x) can be expressed as Equation 19 [
The equation for p(x) is derived by numerical integration using the trapezoidal rule [
Equation 21 is OFW equation used to determine kinetic parameter of chemical reaction. A plot of ln(β) versus 1/T gives a straight line, where Ea can be determined from the slope (slope = 1.052Ea/R) whereas, A can be determined from the intercept [
Modelfree methods can be used to study the solidstate kinetics of isothermal and nonisothermal processes. Modelfree methods are used to calculate the Ea without assumptions and are commonly used to calculate Ea by grouping, such as A into intercept of linear equation and slope of the equation. Thus, modelfree methods only concentrate on activation energy [
By integrating the term e^{Ea/RT} and neglecting the higher order terms, we got Equation 23:
Taking the log of Equation 23, Equation 24 can be obtained:
The activation energy can be determined by plotting ln[1(1α)^{1n}/(1n)T^{2}] versus 1/T [
KAS used the integral isoconversional method for the determination of Ea. In the KAS method, Equation 25 was used to evaluate kinetics parameters [
Where g(α) is mathematical function, T is the absolute temperature, Ea is the activation energy, A is an exponential factor, R is the gas constant and β is the heating rate. Ea can be calculated from the slope of the curve by plotting lnβ/T^{2} versus 1/T keeping the x constant [
FM method is a differential isoconversional technique that is presented in Equation 26 [
Taking the natural log for both sides of Equation 26 the following Equation 27 is obtained:
It is supposed that the conversional factor f(x) remains constant, suggesting that the degradation depends only on the rate of mass loss, independent of temperature. Hence activation energy can be calculated from the slope of the line given by the plot of ln(dx/dt) versus 1/T [
The thermodynamic parameters such Gibbs free energy, entropy and enthalpy of catalytic pyrolysis of WPS can be calculated using Equations 28 and 29, respectively:
Where ∆G is the Gibbs free energy, ∆S is the entropy and ∆H is the enthalpy or heat change in a chemical reaction [
To determine the degradation temperature of each component, thermogravimetric analysis of the catalyst, WPS and WPS catalyst mixture (97:3) was carried out at a heating rate of 10°C min^{1}.
TG/DTG of (a) pure and catalytic degradation of WPS and (b) TG/DTG of natural clay.
For kinetic analysis, thermogravimetric analysis of WPS with clay as catalyst was performed at 5, 10, 15 and 20°C/min and the obtained data was interpreted using OFW, CR, KAS and FM models to determine the kinetic parameters.
CR equation was used for the determination of kinetic parameters, where the lefthand side of the equation was plotted against 1000/T and fraction conversion as shown in
CR plots of various conversions for WPS degradation in the presence of natural clay.
83.22  1.0 × 10^{6}  0.996  
93.28  4.7 × 10^{6}  0.997  
99.10  1.1 × 10^{7}  0.991  
10^{4}.75  2.7 × 10^{7}  0.992  
111.57  7.9 × 10^{7}  0.992  
123.37  6.4 × 10^{8}  0.985  
129.19  1.6 × 10^{9}  0.988  
144.24  2.1 × 10^{10}  0.999  
150.31  5.1 × 10^{10}  0.998  
115.45  8.3 × 10^{9} 
According to the literature, the thermal degradation of PS was carried out in an inert atmosphere using nitrogen as an inert gas. Using the Arrhenius equation, Ea was calculated to be 255 kJmol^{1} in the absence of a catalyst, while in the presence of a catalyst Ea was calculated in the range of 196 to 224 kJmol^{1}, which is about 40 kJmol^{1} less compared to the catalytic decomposition [
OFW, a nonisothermal was used for the determination of the kinetic parameters of WPS. Lnβ was plotted against 1000/T and fraction conversion using OFW model and the resultant plots were shown in
OFW plots at different fraction conversions for WPS decomposition.
74.52  6.7 × 10^{5}  0.995  
83.06  4.7 × 10^{6}  0.998  
88.27  1.4 × 10^{7}  0.993  
93.25  3.6 × 10^{7}  0.991  
99.42  1.1 × 10^{8}  0.992  
10^{9}.77  8.0 × 10^{8}  0.983  
115.22  2.1 × 10^{9}  0.993  
128.42  2.1 × 10^{10}  0.999  
133.71  4.9 × 10^{10}  0.994  
102.85  8.2 × 10^{9} 
Previous studies have investigated the single decomposition of PS by thermogravimetry within the temperature range of 250 to 400°C. The results showed that at the initial stage, a lower Ea was observed, which then increased with fraction conversion. The average activation energy calculated was 200 kJmol^{1} [
Kinetic parameters were investigated using KAS equation, where ln(βT^{2}) was plotted against 1000/T and fraction conversion, the resultant plots were shown in
Kinetic plots of WPS using KAS model at various fraction conversions.
73.16  4.9 × 10^{4}  0.994  
81.56  4.2 × 10^{5}  0.997  
86.715  1.4 × 10^{6}  0.993  
91.53  4.2 × 10^{6}  0.990  
97.60  1.5 × 10^{7}  0.992  
10^{7}.74  1.2 × 10^{8}  0.983  
113.15  3.9 × x10^{8}  0.993  
126.12  4.9 × 10^{9}  0.999  
131.27  1.5 × 10^{10}  0.993  
100.98  2.2 × 10^{9} 
Westerhout et al. [
In the FM model, Ln(dx/dt) was plotted against fraction conversion and 1000/T, and the observed straight lines were shown in
FM plots of WPS decomposition at different fraction conversions for determining kinetic parameters.
78.40  1.3 × 10^{6}  0.995  
87.38  5.9 × 10^{6}  0.998  
92.86  1.4 × 10^{7}  0.993  
98.10  3.4 × 10^{7}  0.991  
10^{4}.59  1.1 × 10^{8}  0.992  
115.48  8.9 × 10^{8}  0.983  
121.21  2.8 × 10^{9}  0.993  
135.10  4.1 × 10^{10}  0.999  
140.67  1.7 × 10^{11}  0.994  
10^{8}.20  2.4 × 10^{10} 
Marcilla and Beltran [
Variation of Ea obtained from different models with fraction conversion for WPS decomposition.
Chrissafis [
The order of reaction was determined using the CR model. Various orders (n = 0, 1, 2, 3) were applied to the CR model and the result are shown in
Plots for determination of reaction order for WPS degradation using CR method.
As shown in
Vacuum  165176  6.1 × 10^{12}3.6 × 10^{13}  Risby and Yergey  [ 

Vacuum  177  3.5 × 10^{11}  Arrhenius  [ 

Nitrogen  219  1.3 × 10^{14}  1st Order K. Model  [ 

Nitrogen  200    Modified Arrhenius  [ 

Nitrogen  312  1.31 × 10^{9}  Parallel reac; model  [ 

Nitrogen  251.9  5.2 × 10^{14}  CR  [ 

Nitrogen  261.4  1.5 × 10^{15}  FreemanCarol  [ 

Nitrogen  260.1  1.2 × 10^{15}  ReichLevi  [ 

Nitrogen  138194    K  [ 

Nitrogen  199  7.1 × 10^{15}  CR, Achar  [ 

Nitrogen  94.7211.4  2.6 × 10^{4}3.1 × 10^{14}  Arrhenius  [ 

Nitrogen  151161  24.629.2  MacCllum Model  [ 

Nitrogen  161  31  Wilkinson Model  [ 

Nitrogen  152  29  Arrhenius  [ 

Nitrogen  149  24.6  K  [ 

Vacuum  360    OFW  [ 

Nitrogen  179200  7.2 × 10^{10}3.9 × 10^{12}  OFW  [ 

Nitrogen  122242  1.8 × 10^{14}2.65 × 10^{18}  FM  [ 

Nitrogen  126239  1.8 × 10^{14}2.65 × 10^{18}  KAS  [ 

Nitrogen  188206  1.8 × 10^{14}2.65 × 10^{18}  CR  [ 

Nitrogen  179200  7.2 × 10^{10}3.9 × 10^{12}  OFW  [ 

Nitrogen  83150  1.0 × 10^{6}5.1 × 10^{10}  CR  Present work  
Nitrogen  74133  6.7 × 10^{5}4.9 × 10^{10}  OFW  Present work  
Nitrogen  73131  4.9 × 10^{4}1.5 × 10^{10}  KAS  Present work  
Nitrogen  78140  1.3 × 10^{6}1.7 × 10^{11}  FM  Present work 
Thermodynamic parameters were used to investigate whether the reaction was spontaneous or nonspontaneous. Thermodynamic study of WPS was carried out at various temperatures and the resultant plots are shown in
Plots of WPS decomposition for determination of thermodynamic parameters.
0.1  73.16  134.97  195.71  
0.2  81.47  126.88  197.95  
0.3  86.46  122.34  199.74  
0.4  92.53  117.05  202.20  
0.5  10^{9}.07  100.58  204.22  
0.6  113.15  97.22  205.79  
0.7  126.95  83.48  206.91  
0.8  132.94  78.14  208.26  
0.9  134.68  77.55  210.05 
In the present work, catalytic degradation of WPS was carried out under nonisothermal conditions. Thermogravimetric analysis was performed at different heating rates (5, 10, 15 and 20°C min^{1}) within the temperature range of 40 to 600°C. Kinetic parameters were determined at different fraction conversions using CR, OFW, KAS and FM models and were found to range from 83150, 74133, 73131 and 78140 kJmol^{1} respectively. Similarly, the Afactor range was determined as 1.0 × 10^{6}5.1 × 10^{10}, 6.7 × 10^{5}4.9 × 10^{10}, 4.9 × 10^{4}1.5 × 10^{10} and 1.3 × 10^{6}1.7 × 10^{11} min^{1} respectively. The values of Ea and Afactor calculated by KAS were consistent and lowest. However, the kinetic parameters investigated by all four models are in good agreement with each other and the reported literature. Hence, it has been concluded that natural clay catalyst shows great efficiency by decreasing the Ea. The kinetic parameters are very helpful in determining the reaction mechanism of solidstate reactions in industrial systems.
Higher Education Commission of Pakistan is highly acknowledged.
Dr. Ghulam Ali: Investigation, Visualization, Conceptualization, Methodology, Writing original draft, Writing  review & editing, Results and analysis. Dr. Jan Nisar: Conceptualization, Funding acquisition, Supervision, Project administration.
It is declared that the authors have no conflicts of interest that could have appeared to influence the work reported in this paper.