Pyrolysis Kinetic Study of Polylactic Acid

Polylactic acid (PLA) is a biodegradable polymer and is mainly used in the textile and food packaging fields. The aim of this work is to build knowledge on the kinetics of the pyrolysis of PLA with the help of thermogravimetric analysis (TGA) using four model-free methods, namely Friedman, Flynn–Wall–Qzawa (FWO), Kissinger–Akahira–Sunose (KAS), and Starink. Additionally, two model-fitting methods (the Coats–Redfern and Criado methods) were applied. TGA data at 5, 10, 20, and 30 K/min heating rates were collected. The obtained activation energies of the pyrolysis of PLA at different conversions by the model-free models were in good agreement and the average values were 97, 109, 104, and 104 kJ/mol for Friedman, FWO, KAS, and Starink, respectively. The Criado model was used together with the Coats–Redfern model to identify the most appropriate reaction mechanism. As per this work, the best controlling reaction mechanism of the PLA pyrolysis can be expressed by the geometrical contraction model (R2).


Introduction
The rapidly growing human population is faced with the problem of non-biodegradable polymers. Non-biodegradable materials are commonly incinerated or buried under the soil, but both methods pose environmental problems because they release toxic gases and contaminate the air, water and soil. By replacing non-biodegradable polymers with biodegradable polymers and composites, the use of harmful non-biodegradable polymers can be reduced (Halász and Csóka (2013) [1]).
Polymers, such as PLA, are an admirable alternative to non-biodegradable polymers. PLA, as an example, is a thermoplastic aliphatic polyester produced via fermentation processes from renewable resources such as corn and starch. Incineration of PLA biopolymer does not produce any harmful gases. It has high stiffness, good strength, and is easy to process mold, and shape. When PLA degrades, it releases H 2 O and CO 2 . A PLA product can be extruded, blown molded, or poured into a solvent. In comparison with other polymers such as polyethylene glycol (PEG), polycaprolactone, and polyhydroxybuterate, PLA has higher thermal stability. Due to its thermal properties, PLA finds applications in the textile and food packaging industries (Dhar et al. (2015) [3]).
As well as being biodegradable, PLA has respectable mechanical properties when compared to other biodegradable polymers. Many applications have been developed for PLA including but not limited to, drug delivery systems, textiles, films/membranes, tissue engineering scaffolds, biological scaffolds, and others. There are several limitations associated with PLA, including low impact resistance at room temperature, poor oxygen and water barrier properties, as well as high rigidity and brittleness. The poor barrier properties of PLA films make them unsuitable for food packaging. These problems must be overcome for PLA to have a wider range of commercial applications. To a certain extent, PLA limitations can be overcome by combining them with plasticizers, reinforcement fillers, and other polymers. Mortezaeikia et al. (2021) [4] reviewed and presented comprehensively the kinetic pyrolysis models and methods including model-free methods and modelfitting methods of TGA data for all polymers. Saad et al. (2021) [5] studied mainly the effect pyrolysis atmosphere (nitrogen or carbon dioxide) on the pyrolytic cracking of six different polymers: high-and low-density polyethylene (HDPE and LDPE), polypropylene (PP), polystyrene (PS), and polyethylene terephthalate (PET). They showed only one peak reaction for all polymers with shifting to higher temperature in a carbon dioxide atmosphere. They found the activation energy values decreasing in the following order: LDPE > HDPE > PS > PP > PET in the nitrogen atmosphere, and: HDPE > LDPE > PET > PP> PS in the carbon dioxide atmosphere. Pan et al. (2021) [6] investigated the kinetic pyrolysis of the waste polyethylene (WPE) and PE using genetic algorithm (GA) and isoconversional methods with thermogravimetric analysis (TGA). They found that the reaction-order model was the most convenient model describing the pyrolysis among the extended Prout-Tompkins and Sestak-Berggren models. Zhang et al. (2022) [7] studied the co-pyrolysis of lychee and plastic wastes (LPW) using TGA data at four different heating rates (10,20,30, and 40 K min −1 ). They found that the activation energy values ranged from 64 to 71 kJ mol −1 , using the FWO, KAS, and Starink methods. Soufizadeh et al. (2022) [8] used the kinetic approaches and the quality control techniques as new ways of estimating and optimizing the effect of plastic waste pyrolysis processes such as the conversion rate, heating rate, and pyrolysis temperature on the values of the activation energy. They concluded that the activation energy of the pyrolysis process would be minimized with the increase in the conversion rate, heating rate and with a reduction in temperature.
Generally, to examine the thermal degradation kinetics of polymeric blends, kinetic modeling using data gained from some thermal analysis techniques such as differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) can be extremely helpful. It is possible to estimate with precision the degradation reaction rate, as well as the mechanisms involved, by using the kinetic parameters obtained. Muravyev and Vyazovkin (2022) [9] reviewed the most proper options that should be chosen and as advised by the International Confederation for Thermal Analysis and Calorimetry (ICTAC). ICTAC mainly recommended using the model-free methods, where the data should be collected at more than three different heating rates. ICTAC emphasized that running TGA experiments should be according to its instructions in order to collect the proper data for kinetic parameters calculations. It recommended that the ratio between the highest and the lowest heating should be more than 10 (Osman et al. (2022) [10]). Since the TG curve shows only one peak reaction, single-step thermal decomposition can be considered to derive the proper kinetic parameters (Koga et al. (2023) [11]).
Using TGA analysis to obtain the pyrolysis kinetic parameters has grown in popularity over the years, and it has proven convincingly useful. Table 1 summarizes some of the research work studying the pyrolysis of PLA and its derived matrixes and different polymers.
This work aims to build knowledge on the kinetics of the pyrolysis of PLA non-porous films made through compression molding. TGA analysis at four different heating rates (5, 10, 20, and 30 K/min) was conducted. The kinetic triplets of the PLA pyrolysis were obtained using four isoconversional models (Friedman, FWO, KAS, and Starink) and two non-isoconversional models (Coats-Redfern, and Criado). This research project aimed to be extended further to study the effect of the incorporation of some biomass materials (agriculture wastes) in order to produce environmentally sustainable material(s) for the next generation. * microcrystalline cellulose. ** polypropylene. *** poly (butylene adipate-co-terephthalate).

Material
PLA2003D semi-crystalline biopolymer (M W ≈ 200 KDa) was supplied by Ingeo™ Biopolymer, Minnetonka, USA. Some of its physical properties are presented in Table 2.

Proximate Analysis
Proximate analysis was made to determine the moisture, volatile matter, fixed carbon, and ash contents using the Simultaneous Q50 Thermal Analyzer manufactured by TA Instruments, USA. Results are presented in Table 3 and details of this analysis are fully described elsewhere (Dubdub and Al-Yaari (2020) [16]). PLA pellets were melted at 190 • C for 15 min using a conventional oven. Subsequently, molten PLA cooled down at room temperature for 10 min. Synthesized PLA sheets were used for the TGA analysis.

Thermogravimetry
PLA non-porous matrixes were carried out directly to the thermogravimetric analyzer. Forty mg of PLA samples were used throughout the study. TGA experiments were performed in an inert atmosphere of pure N 2 (flowrate 60 mL/min) at four different heating rates (5, 10, 20, and 30 K/min).

Determination of the Kinetic Triplets
Generally, the reaction rate (r) depends on conversion (α), temperature (T), and pressure (P). However, for the solid-state reactions, the pressure effect is negligible. Therefore, using the Arrhenius relationship, we found that the reaction rate equation of the PLA pyrolysis can be expressed as (Aboulkas et al. (2010) [17]): where: t is time, A is the frequency factor, E is the activation energy, R is the universal gas constant, and f (α) is the conversion-dependent term which depends on the reaction mechanism as presented in Table S1. From the TGA experimental data, the reaction conversion can be obtained as a fraction of the PLA weight loss.
For the non-isothermal pyrolysis of PLA, the heating rate (β = dT/dt) can be included in the reaction rate equation to become (Khodaparasti et al. (2022) [18]): and thus: where: , and T o is the initial PLA pyrolysis temperature.
The temperature integral Researchers utilized different numerical methods and series expansions to approximate the polynomial term P − E RT and thus different models were proposed. Those models are used to obtain the kinetic triplets (A, E, and mechanism) (Aboulkas et al.  [20], Al-Yaari and Dubdub (2020) [21]). Tables 4 and 5 list four of the most used isoconversional models and two of the non-isoconversional models, respectively.  [20]).

Model Equation Comment
Coats-Redfern ln g(α) Applies an asymptotic series expansion.
* The subscript of 0.5 refers to the condition at which α = 0.5.
In this work, the isoconversional models (Friedman, FWO, KAS, and Starink) were used to obtain initially the activation energy of the PLA pyrolysis. Subsequently, the non-isoconversional models (Coats-Redfern and Criado) were used to determine the most appropriate reaction mechanism. Finally, the pre-exponential factor (A) was obtained by the isoconversional models.

TG-DTG Analysis
TG and DTG at four different heating rates (5, 10, 20, and 30 K/min) of pyrolytic cracking of PLA are shown in Figure 1. Thermograms were similar for all different heating rates. As in the pyrolysis of other polymers [21][22][23], the pyrolytic temperature characteristics (T onset , T peak , and T endset ) were shifted to higher temperatures as the heating rate raised. Additionally, it has been shown that PLA polymers degrade by only one reaction. Table 6 shows the onset, peak, and final temperatures of the pyrolytic degradation of PLA at different heating rates. Table 7 shows the reported peak temperatures for PLA pyrolysis at a 10 K/min heating rate [10][11][12][13]. In this work, the peak temperature was observed to be 647 K, which lies between the lowest (622 K) and the highest (657 K) reported temperatures. DTG curves show that the peak value decreased from 2.75 1/min at 5 K/min to 2 1/min at 30 K/min.

Isoconversional Kinetics Models
Equation (1) is considered the startup equation from which all the models' equations can be derived. Four isoconversional models have been used to calculate the main kinetic parameter (activation energy in kJ/mol) at conversions ranging from 0.1 to 0.9. Figure 2 shows the regression lines of the experimental data of the PLA pyrolysis by Friedman, FWO, KAS, and Starink models. Muravyev et al. (2019) [24] pointed to the importance of considering the recommendation of the kinetic committee of ICTAC. They mentioned that the activation energy values calculated by any of the isoconversional methods for a single-step reaction (integral method: FWO, or differential method: Friedman) should be ideally constant with the range values of the conversion. However, this is not the case in the real results, and this can be attributed to the changes in the reaction condition, reaction geometry, and rate limiting as the reaction moves from low to high conversion. Good linear relationships, with high values of R 2 , were obtained and the E values obtained by the isoconversional models are presented in Figure 3 and Table 8. The highest and lowest values of E were obtained by FWO, and Friedman, respectively. However, KAS and Starink gave the same value of E. The obtained values for all four isoconversional models are consistent with the reported values as presented in Table 9. There is somehow a trend in decreasing the E values by increasing the conversion from 0.1 to 0.9 for FOW, KAS, and Starink. However, for the Friedman method, the obtained values of E started high (115 kJ/mol at α = 0.1), then decreased as the conversion increased (89 kJ/mol at α = 0.5), and after that, they increased steadily (91 kJ/mol at α = 0.9). Mróz et al. (2013) [12] reported that the E values dependency on the conversion (between 0.1 and 0.9) has two regions, and thus the reaction mechanism changes as well. In addition, Aoyagi et al. (2002) [25] confirmed that the reaction of PLA pyrolysis occurred with more than a single mechanism. In addition, this finding is in respectable agreement with the results reported by Li et al. (2009) [26].

Model-Fitting Kinetics Methods
The first non-isoconversional method "Coats-Redfern" was used by plotting ln g(α) T 2 versus 1/T for different reaction mechanisms (See Table S1) and straight-line correlations were obtained. The most appropriate reaction mechanism can be determined by comparing the obtained E value (with high R 2 ) by the Coats-Redfern method with those obtained by the isoconversional models. Table 10 presents the values of the activation energy attained by the Coats-Redfern models for 15 different reaction mechanisms and different values (with different values of R 2 ). As per the results reported in Table 11, the obtained E value for the second Avrami-Erofeev (A2) and the geometrical contraction model (R2) were 97 kJ/mol (with a regression coefficient of 0.9991), and 119 kJ/mol (with a regression coefficient of 0.9999), respectively, which are the closest values to the ones obtained by the isoconversional models. Thus, the A2 and R2 reactions can be the most suitable mechanisms for PLA pyrolysis.  Furthermore, reaction mechanisms can also be evaluated by the Criado model as shown in Figure 4. Graphs of D4, R1, P2, P3, and P4 were excluded from Figure 4 because their curves are far from the experimental curves in all tests. As shown in Figure 4, as per the Criado model, although the A2 model did not fit the experimental data, the threedimensional diffusion (D3), and the geometrical contraction cylinder (R2) models have the closest curves to the experimental ones. However, since the E value obtained by the Coats-Redfern for the D3 models (354 kJ/mol) is far from the obtained value by the isoconversional model, the D3 model is not suitable to represent the PLA pyrolysis. Table 11 shows the values of E, ln(A), and R 2 for each heating rate for the most suitable reaction mechanism (R2). Bhiogade et al. (2020) [13] used the Coats-Redfern model together with the Mampel (first-order reaction) model to determine the kinetic parameters. An E value of 79.21 kJ/mol was reported.

Conclusions
In this work, the PLA pyrolysis was investigated and non-isothermal TGA data were analyzed. Kinetic studies at 5, 10, 20, and 30 K/min using both isoconversional (Friedman, FWO, KAS, and Starink) and non-isoconversional (Coats-Redfern and Criado) models were performed. The obtained values of activation energy by both methods were comparable. The average E values found by the four isoconversional models at different conversions were in good agreement (Friedman: 97 kJ/mol, FWO: 109 kJ/mol, KAS: 104 kJ/mol, and Starink: 104 kJ/mol). In addition, the Coats-Redfern and Criado nonisoconversional models were used to identify the most appropriate reaction mechanism of PLA pyrolysis. Accordingly, the best controlling reaction mechanism of the PLA pyrolysis was the geometrical contraction model (R2).
The obtained kinetic parameters (E, A, and the reaction mechanism) are of great importance for the reactor design. However, it is highly recommended that the type of pyrolysis products together with their caloric values be determined as soon as possible.