Kinetics and Thermodynamics of the Pyrolysis of Waste Polystyrene over Natural Clay
National Centre of Excellence in Physical Chemistry, University of Peshawar, 25120, Peshawar, Pakistan
Academic Editor: Amanda Laca
Received: July 22, 2022 | Accepted: October 23, 2022 | Published: November 01, 2022
Adv Environ Eng Res 2022, Volume 3, Issue 4, doi:10.21926/aeer.2204044
Recommended citation: Ali G, Nisar J. Kinetics and Thermodynamics of the Pyrolysis of Waste Polystyrene over Natural Clay. Adv Environ Eng Res 2022; 3(4): 044; doi:10.21926/aeer.2204044.
© 2022 by the authors. This is an open access article distributed under the conditions of the Creative Commons by Attribution License, which permits unrestricted use, distribution, and reproduction in any medium or format, provided the original work is correctly cited.
Abstract
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., Coats-Redfern and model-free methods i.e., Ozawa-Flynn-Wall, Kissinger-Akahira-Sunose and Friedman method. The activation energy determined by Coats-Redfern, Ozawa-Flynn-Wall, Kissinger-Akahira-Sunose and Friedman models were in the range of 83.22-150.37, 74.52-133.71, 73.16-131.23, and 78.40-140.67 kJmol^{-1}, respectively. Among them, the lowest activation energy for polystyrene degradation was observed using Kissinger-Akahira-Sunose method. The calculated kinetic parameters would be useful in determining the reaction mechanism of the solid-state reactions in a real system.
Graphical abstract
Keywords
Waste polystyrene; pyrolysis; thermogravimetry; kinetic models; activation energy
1. Introduction
Polystyrene (PS) is a tough, low-cost 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 non-biodegradable nature, the disposal of these solid wastes causes serious environmental problems. Waste polystyrene (WPS) accounts for about 10 wt.% of total plastic waste [1,2,3]. Numerous techniques have been used to recycle WPS, the most commonly used are physical recycling by blending and mixing and chemical recycling [4,5]. Another common technique used to dispose of plastic waste is thermal decomposition. Recycling of WPS by thermal incineration collects many useful products and therefore plays an important role in solving waste disposal problems [6].
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 [7,8]. Therefore, the focus of the present work was to study the thermal degradation of waste PS at low temperatures and to determine the kinetic parameters using model fitting i.e., Coats-Redfern (CR), and model-free methods i.e., Ozawa-Flynn-Wall (OFW), Kissinger-Akahira-Sunose (KAS), and Friedman (FM). The most appropriate kinetic model along with their thermodynamic parameters was determined by the pyrolysis process.
Model-fitting techniques were commonly used for studying kinetics of solid-state 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 non-isothermal 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 model-fitting techniques to non-isothermal data can result in greater values for kinetic parameters. On other hand, the model-free method is based on its straightforwardness and the anticipation of errors associated with the choice of a kinetic model [9,10,11]. Current studies have widely focused on the degradation of WPS for the production of fuel-like substances, however, there is still a lack of exploration of the kinetics of degradation [12,13].
Şenocak et al. [14] investigated the thermal decomposition of WPS using a TGA, and the thermogravimetric data collected from TGA was further applied to the OFW equation to determine the kinetic parameters. The calculated activation energy for different fractions was in the range of 179.74 to 200.36 kJmol^{-1} with first-order kinetics. Aboulkas and Nadifiyine [15] determined the activation energy of PS using the OFW method at a wide range of temperatures i.e., 600 to 900°C, and found an activation energy of 169 kJmol^{-1}. Singh and Singh [16] carried out the kinetics analysis of the decomposition of PS. Several catalysts were utilized to study the kinetic parameters of PS at 400°C and the values of activation energy at different heating rates were 359, 360, 361 and 361 kJmol^{-1}.
Oh et al. [17] evaluated the thermal decomposition of PS at different heating rates in supercritical acetone and inert conditions. The thermogravimetric data was interpreted using Arrhenius equation and kinetic parameters determined in supercritical acetone were compared with nitrogen atmosphere. The results showed that the average activation energy calculated in supercritical acetone medium ranged from 167.0 to 195.8 kJmol^{-1}, while in the nitrogen atmosphere it ranged from 245.4 to 251.5 kJmol^{-1}. Kyaw et al. [18] studied the pyrolysis of PS in the temperature range of 370 to 420°C and observed that the selectivity for styrene trimers, dimers and monomers decreased as the reaction proceeded, due to the difficulty in the decomposition of benzene rings phenyl radicals. The degradation was formulated to be first-order kinetics with activation energy equal to 157 kJmol^{-1}. Peterson [19] carried out the thermal and thermo-oxidative decomposition of WPS through thermogravimetry. The thermogravimetric data was interpreted for the determination of kinetic parameters. Under inert conditions, the activation energy was 200 kJmol^{-1}.
According to the recommendations made by the Kinetics Committee of the International Confederation for Thermal Analysis and Calorimetry [20,21], consistent kinetics parameters could be gained if the sample is exposed to the pyrolysis process at not less than three different heating rates in an appropriately standardized instrument. Therefore, considering this recommendation, the present study was performed at four different heating rates of 5, 10, 15 and 20°C/min on an appropriately calibrated instrument and the kinetics parameters were determined using CR, OFW, KAS and FM models. Thermodynamic parameters of WPS decomposition reaction would be very helpful for the optimization of reaction engineering in industrial processes. Moreover, the kinetics and thermodynamic parameters would be very useful in determining the solid-state reaction mechanisms in a real system.
2. Experimental
2.1 Material
WPS was collected from a recycling site in a local shopping mall and shredded into small pieces with a size of 50-70 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.
2.2 Thermogravimetric Analysis
Thermogravimetric analysis of WPS and clay mixture was carried out in a Simultaneous Thermogravimetric analyzer (Perkin-Elmer). 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.
2.3 Kinetics Analysis
Most of the solid-state degradation reaction follows Equation 1:
\[ A_{ {solid }} \leftrightarrow B_{ {solid }}+C_{ {gas }} \tag{1} \]
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 [20,22], as shown in Equation 2.
\[ \frac{d \alpha}{d t}=k(T) f(\alpha) h(P) \tag{2} \]
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:
\[ \frac{d \alpha}{d t}=k(T) f(\alpha) \tag{3} \]
In Equation 3, k(T) is the rate constant and $f(\alpha)$ is the fraction of conversion. Equation 3 explains the rate of single-step 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 [20,23].
\[ \frac{d \alpha}{d t}=k_{1}(T) f\left(\alpha_{1}\right)+\frac{d \alpha}{d t}=k_{2}(T) f\left(\alpha_{2}\right) \tag{4} \]
where $\alpha_{1}$ and $\alpha_{2}$ are the degree of conversion associated with two individual reactions, and their sum is the total conversion rate as shown in Equation 5:
\[ \alpha=\alpha_{1}+\alpha_{2} \tag{5} \]
However, if a process is found to follow a one-step 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:
\[ k(T)=A e^{^{-E \ a} / _ {R T}} \tag{6} \]
where R, Ea and A are universal gas constant, activation energy and pre-exponential factor, respectively. Normally, the actual kinetic parameters are functions of the intrinsic parameters of the separate steps. Hence, the kinetics of solid-state reaction can be explained by Equation 7:
\[ \frac{d \alpha}{d t}=A e^{^{-E \ a} / _ {R T}} f(\alpha) \tag{7} \]
where the temperature of the sample varies with time, so the rate of reaction is shown in Equation 8:
\[ \beta=\frac{d T}{d t} \tag{8} \]
where β is the rate constant.
By combining and rearranging equations 7 and 8, the following Equation 9 is obtained:
\[ \frac{d \alpha}{d T}=\frac{A}{\beta} e^{^{-E \ a} / _ {R T}} f(\alpha) \tag{9} \]
By separating the variables and then integrating and rearranging Equation 9, Equation 10 was derived [24]:
\[ g(\alpha)=\int_{\alpha_{_0}}^{\alpha} \frac{d \alpha}{\int(\alpha)}=\frac{A}{\beta} \int_{T_{_0}}^{T} e^{^{-E \ a} / _ {R T}} \tag{10} \]
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:
\[ \int_{T_{_0}}^{T} e^{^{-E \ a} / _ {R T}} d T=-\frac{E a}{R} \int_{x_{_0}}^{x} \frac{e^{-x}}{x^{2}} d x \tag{11} \]
Let the right-hand side of Equation 11 be equal to p(x), Equation 12 is obtained:
\[ p(x)=-\frac{E a}{R} \int_{x_{_0}}^{x} \frac{e^{-x}}{x^{2}} d x \tag{12} \]
By using integration by parts, Equation 12 leads to Equation 13:
\[ p(x)=\frac{E a}{R} \frac{e^{-x}}{x} l^{x}{ }_{_0}+\frac{E a}{R} \int_{x_{_0}}^{x} \frac{e^{-x}}{x} d x=\frac{E a}{R}\left[\frac{e^{-x}}{x}-\int_{x}^{\infty} \frac{e^{-x}}{x} d x\right]-\frac{E a}{R}\left[\frac{e^{-x_{_0}}}{x_{_0}}-\int_{x}^{\infty} \frac{e^{-x}}{x} d x\right] \tag{13} \]
The second term in Equation 13 can be neglected except that the values of p(x) becomes progressively smaller, so Equation 14 is obtained [25,26].
\[ p(x)=\frac{E a}{R}\left[\frac{e^{-x}}{x}-\int_{x}^{\infty} \frac{e^{-x}}{x} d x\right] \tag{14} \]
The molecular structure, nuclear structure and flow of heat evaluated by exponential integral are almost equal to the asymptotic equation 15:
\[ \int_{x}^{\infty} \frac{e^{-x}}{x} d x \cong e^{-x} (\frac{1}{x}-\frac{1 !}{x^{2}}+\cdots+\bigg(-1)^{n-1} \frac{(n-1) !}{x^{n}}+\cdots \bigg) \tag{15} \]
As the p(x) is equal to Equation 16:
\[ p(x)=(-1)^{n} \frac{(n-1) !}{x^{n}} e^{x} \tag{16} \]
As the g(α) can be expressed as Equation 17:
\[ g(\alpha)=\frac{A E a}{\beta R} p(x) \tag{17} \]
Taking the natural log and rearranging Equation 17, we obtain Equation 18:
\[ ln \beta=ln \frac{A E a}{\beta R}+\ln p(x) \tag{18} \]
where Equation 18 is integrated with Doyle’s approximation, i.e. when x≥20, the function p(x) can be expressed as Equation 19 [27,28]:
\[ p(x)=0.0048 e^{-1.0516} \tag{19} \]
\[ \ln p(x)=-2.315+0.4567 x \tag{20} \]
The equation for p(x) is derived by numerical integration using the trapezoidal rule [29]. Substituting Equation 20 into Equation 18 obtained Equation 21:
\[ \ln (\beta)=\ln \left[\frac{A E a}{R_{g}(x)}\right]-5.331-1.052 \frac{E a}{R T} \tag{21} \]
Equation 21 is OFW equation used to determine kinetic parameter of chemical reaction. A plot of $\ln (\beta)$ 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 [28,30].
Model-free methods can be used to study the solid-state kinetics of isothermal and non-isothermal processes. Model-free 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, model-free methods only concentrate on activation energy [9]. The Coats-Redfern equation is commonly used to study the kinetics analysis and various kinetics parameters, such as A and Ea [31]. By integrating and rearranging Equation 9, Equation 22 can be obtained:
\[ \frac{1-(1-x)^{1-n}}{1-n}=\frac{A}{\beta} \int\limits_{_0}^{T} e^{^{-E \ a} / _ {R T}} d T \tag{22} \]
By integrating the term e^{-Ea/RT} and neglecting the higher order terms, we got Equation 23:
\[ \frac{1-(1-x)^{1-n}}{1-n}=\frac{A R T^{2}}{\beta E a}\left[1-\frac{2 R T}{E a} e^{^{-E \ a} / _ {R T}}\right] \tag{23} \]
Taking the log of Equation 23, Equation 24 can be obtained:
\[ \ln \left[\frac{1-(1-x)^{1-n}}{T^{2}(1-n)}\right]=\ln \left[\frac{A R}{\beta E a}\left[1-\frac{2 R T}{E a}\right]\right]-\frac{E a}{R T} \tag{24} \]
The activation energy can be determined by plotting ln[(1-(1-α)^{1-n}/(1-n)T^{2}] versus 1/T [31,32].
KAS used the integral iso-conversional method for the determination of Ea. In the KAS method, Equation 25 was used to evaluate kinetics parameters [33].
\[ \ln \left(\frac{\beta}{T^{2}}\right)=\ln \left[\frac{A R}{E a g \alpha}\right]-\frac{E a}{R T} \tag{25} \]
Where $g(\alpha)$ is mathematical function, T is the absolute temperature, Ea is the activation energy, A is an exponential factor, R is the gas constant and $\beta$ 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 [34,35].
FM method is a differential iso-conversional technique that is presented in Equation 26 [36]:
\[ \frac{d x}{d t}=\beta\left[\frac{d x}{d t}\right]=A e^{^{-E \ a} / _ {R T}} f(x) \tag{26} \]
Taking the natural log for both sides of Equation 26 the following Equation 27 is obtained:
\[ \ln \left[\frac{d x}{d t}\right]=\ln \left[\beta\left(\frac{d x}{d t}\right)\right]=\ln [A f(x)]-\frac{E a}{R T} \tag{27} \]
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 [37,38].
The thermodynamic parameters such Gibbs free energy, entropy and enthalpy of catalytic pyrolysis of WPS can be calculated using Equations 28 and 29, respectively:
\[ \Delta G=E+R T\left[\ln \left(\frac{K T}{h A}\right)\right] \tag{28} \]
\[ \Delta S=\frac{\Delta H-\Delta G}{T} \tag{29} \]
Where $\Delta G$ is the Gibbs free energy, $\Delta S$ is the entropy and $\Delta H$ is the enthalpy or heat change in a chemical reaction [39,40].
3. Results and Discussion
3.1 Thermogravimetric Analysis
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}. Figure 1a showed the TG/DTG results of WPS in the absence and presence of catalyst at 10°C min^{-1}. The results showed that WPS degraded in the temperature range of 350 to 420°C. The nature, composition and structure of the catalyst were not affected during the experiments as all the decomposition of WPS took place at temperatures below 420°C. The results also indicated that clay catalyst decreased the degradation temperature of WPS. The degradation of pure catalyst is shown in Figure 1b, and the results indicated that natural clay had two-step degradation, with the first step occurring at about 68°C, indicating the loss of water molecules from the clay. The second degradation step took place at 817°C, which was the decomposition of alumina and silica from the clay.
Figure 1 TG/DTG of (a) pure and catalytic degradation of WPS and (b) TG/DTG of natural clay.
3.2 Kinetic Study
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.
3.2.1 Coats Redfern Model
CR equation was used for the determination of kinetic parameters, where the left-hand side of the equation was plotted against 1000/T and fraction conversion as shown in Figure 2. Ea and A were calculated from the slope and intercept of the plots, respectively, as shown in Table 1. The results showed that the correlation coefficient for each straight line was above 0.985. Ea was calculated at various fraction conversions and was found to range from 83.22 to 150.31 kJmol^{-1}. The results in Table 1 indicated that Ea increased with increasing fraction conversion. Where the largest increment of Ea was observed for fraction conversion from 0.7 to 0.8, i.e., 15 kJmol^{-1}. Similarly, A-factor calculated from the intercept ranged from 1.0 × 10^{6} to 5.1 × 10^{10} min^{-1}. The A-factor value also increased with the increase in fraction conversion, and the average A-factor value was 8.3 × 10^{9} min^{-1}. By comparing our results with the literature, a good agreement was observed. The increase in Ea and A-factor with fraction conversion may be attributed to the complex mechanism of the solid-state reaction.
Figure 2 CR plots of various conversions for WPS degradation in the presence of natural clay.
Table 1 Kinetics parameters of WPS calculated using CR method at different degrees of conversion.
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 [41].
3.2.2 Ozawa-Flynn-Wall Model
OFW, a non-isothermal 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 Figure 3. Where Ea was calculated from the slope and A-factor was determined from the intercept of the plots, and the resultant kinetic parameters determined were listed in Table 2. As the fraction conversion increased from 0.1 to 0.9, the Ea value increased from 74.52 to 133.71 kJmol^{-1}. From the gradual increase in Ea and A-factor, it has been concluded that there is a linear relationship between the conversion degree and kinetic parameters which indicates the existence of progressive bond breakage, i.e., the weaker bonds break first, followed by the stronger ones.
Figure 3 OFW plots at different fraction conversions for WPS decomposition.
Table 2 Ea and A-factor for WPS decomposition obtained from OFW method.
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} [19]. In another study, Kwak et al. [42] performed thermal degradation of PS within the temperature range of 370 to 420°C . First-order kinetics and Arrhenius equation were applied for the determination of the rate constant and Ea respectively. The calculated activation energy was 157 kJmol^{-1} in supercritical water and 132 kJmol^{-1} in supercritical n-hexane. These results in the literature are in good agreement with our results in terms of kinetic parameters.
3.2.3 Kissinger-Akahira-Sunose Model
Kinetic parameters were investigated using KAS equation, where $\ln \left(\frac{\beta}{T^{2}}\right)$ was plotted against 1000/T and fraction conversion, the resultant plots were shown in Figure 4, and the resultant data was presented in Table 3. The results in Table 3 showed correlation coefficients at each fraction conversion ranging from 0.990 to 0.999. Ea determined using KAS equation showed a good linear relationship with fraction conversion, starting from 73.16 kJmol^{-1} and ending with 131.27 kJmol^{-1}. And the Ea investigated using KAS method was the lowest among all models. By comparing kinetic factors, it can be concluded that the variation of both Ea and A-factor with fraction conversions is in good agreement with the relevant literature.
Figure 4 Kinetic plots of WPS using KAS model at various fraction conversions.
Table 3 Ea and A-factor calculated using KAS method for WPS decomposition.
Westerhout et al. [43] performed the pyrolysis of PS below 450°C by thermogravimetry .First-order kinetics was applied for the determination of kinetic parameters, and Ea and A-factor were evaluated using the random chain dissociation method with 204 kJmol^{-1} and 3.3 × 10^{13} sec^{-1} respectively. Kim et al. [44] investigated the thermal degradation of PS in the presence and absence of the catalyst. The isothermal Ea was calculated using Arrhenius equation and the non-isothermal Ea was calculated using Kissinger equation. It was observed that Ea decreased from 194 to 138 kJmol^{-1} with the use of arcillite as catalyst.
3.2.4 Friedman Model
In the FM model, Ln(dx/dt) was plotted against fraction conversion and 1000/T, and the observed straight lines were shown in Figure 5. Ea and A-factor determined by the FM method are given in Table 4. Ea calculated using the FM model ranged from 78.40 to 140.67 kJmol^{-1}, which was higher than that calculated by other models. However, the FM method showed a linear correlation of Ea with fraction conversion. The average Ea for WPS using natural clay catalyst was 108.90 kJmol^{-1}, this activation is still lower than reported in the literature. Similarly, A-factor investigated by the FM model was also in linear relation with conversion. The average A-factor calculated from the FM method was 2.4 × 10^{10} min^{-1}. When compared to fraction conversion, all the kinetic parameters showed a linear increment, indicating that the breakage of linkage is gradual, with weaker bonds broken first followed by complex ones. Those stronger bonds need more energy for breakage, hence higher Ea was observed.
Figure 5 FM plots of WPS decomposition at different fraction conversions for determining kinetic parameters.
Table 4 Kinetics parameters determined at different degrees of conversion for WPS using the FM method.
Marcilla and Beltran [45] carried out thermal degradation of PS at different heating rates and first-order kinetics were applied for the determination of kinetic parameters. All the experiments were carried out in an inert atmosphere using nitrogen gas. The results indicated that Ea and A-factor ranged from 186 to 276 kJmol^{-1} and 8.5 × 10^{13} to 3.6 × 10^{19} min^{-1} respectively.
3.3 Comparison of Activation Energies
Figure 6 showed that the Ea increased linearly with the fraction conversion. The initial low Ea showed the cleavage of weak bonds and the elimination of volatile compounds. However, the cleavage of strong bonds required high temperatures, so the cleavage of stable compounds required greater Ea. It can be also seen in Figure 6 that the Ea calculated by the CR model is greater than that calculated by other models, while the Ea calculated by the KAS method is the lowest of all models. However, the apparent Ea determined by these models are in good agreement with each other and the literature.
Figure 6 Variation of Ea obtained from different models with fraction conversion for WPS decomposition.
Chrissafis [46] established a relationship between Ea and fraction conversion, obtaining a constant average value. A small difference in Ea was observed, which was due to systematic error. A constant Ea was calculated by the OFW method. In another study, a relationship between Ea and fraction conversion was investigated using different models. It was found that there was a close agreement between Ea from OFW and KAS models. Al-Bayaty and Farhan [47] determined Ea for the decomposition of PS at different heating rates and observed a slight variation in Ea with fraction conversion.
3.4 Order of Reaction
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 Figure 7. The results indicated that the highest correlation coefficient value was observed for n = 1, suggesting that thermal degradation of WPS follows first-order kinetics. Thermocatalytic degradation of WPS and polyethylene were carried out by Miskolczi et al. [41]. The effect of catalyst on WPS degradation was investigated through non-isothermal studies and kinetic study was carried out by applying the Arrhenius equation. It was found that the order of reaction of WPS thermocatalytic decomposition was first order. Similarly, several researchers used different kinetic models to investigate the order of reaction for thermal and catalytic pyrolysis of waste polymers and concluded that degradation of WPS follows first-order reaction, which is in good agreement with our results [48,49,50].
Figure 7 Plots for determination of reaction order for WPS degradation using CR method.
3.5 Comparison with the Literature
As shown in Table 5, Ea and A-factor determined by CR, OFW, KAS and FM models in previous literature were compared with those determined in this study. The table showed that the Ea determined by all four methods were quite reasonable. It can be seen that the Ea and A-factor determined in our research work are in good agreement with the values previously reported in the literature. In our work, the consistency and low values of Ea are due to the use of a suitable natural catalyst.
Table 5 Comparison of kinetics parameters of WPS with those described in the literature.
3.6 Thermodynamic Study
Thermodynamic parameters were used to investigate whether the reaction was spontaneous or non-spontaneous. Thermodynamic study of WPS was carried out at various temperatures and the resultant plots are shown in Figure 8. The results indicated a linear relation of fraction conversion with the inverse of temperature and ln(K/T). Slope and intercept were used to investigate thermodynamic parameters i.e., entropy, enthalpy and Gibbs free energy are shown in Table 6. The enthalpy at the beginning of the conversion was 73.16 kJmol^{-1}and grew to 134.68 kJmol^{-1} at the end of the conversion, indicating a linear increase in enthalpy with fraction conversion. Similarly, the entropy of the decomposition reaction ranged from -134.97 to -77.55 Jmol^{-1}K^{-1 }and Gibbs free energy ranged from 195.71 to 210.05 kJmol^{-1}. Gibbs free energy showed linear relation with fraction conversion, indicating larger molecules have greater free energy compared to low molecular weight molecules. Chen et al., [59] investigated the decomposition of waste material under non-isothermal conditions. Thermogravimetric analysis was carried out at different heating rates the resultant data was interpreted for kinetics and thermodynamics. Thermodynamic parameters such as Gibbs free energy, enthalpy and entropy ranged from 151.18 to 189.6, 90.94 to 95.31 kJmol^{-1} and -131.4 to -147.5 Jmol^{-1}K^{-1 }respectively. Similarly, several other studies have reported thermodynamic parameters of various waste materials that are in good agreement with our results [60,61,62].
Figure 8 Plots of WPS decomposition for determination of thermodynamic parameters.
Table 6 Thermodynamic parameters of thermocatalytic degradation of WPS at various fractions of conversion.
4. Conclusion
In the present work, catalytic degradation of WPS was carried out under non-isothermal 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 83-150, 74-133, 73-131 and 78-140 kJmol^{-1} respectively. Similarly, the A-factor 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 A-factor 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 solid-state reactions in industrial systems.
Acknowledgments
Higher Education Commission of Pakistan is highly acknowledged.
Author Contributions
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.
Competing Interests
It is declared that the authors have no conflicts of interest that could have appeared to influence the work reported in this paper.
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