Kinetic model for thermal dehydrochlorination of poly(vinyl chloride)

*Graphical Abstract 1 Kinetic Model for Thermal Dehydrochlorination of Poly(vinyl chloride) Pedro E. Sánchez-Jiménez, Antonio Perejón, José M. Criado, María J. Diánez, and Luis A. Pérez-Maqueda* Instituto de Ciencia de Materiales de Sevilla (C.S.I.C. – Universidad de Sevilla) Americo Vespucio 49, Sevilla, Spain ABSTRACT In this paper, a novel method for calculating degradation kinetics is presented. The method has been applied to the thermal dehydrochlorination of two different samples of PVC. It has been observed that this dehydrochlorination is complex and involves two different processes. A model that accounts for the entire dehydrochlorination is proposed. This model involves nucleation and growth and diffusion controlled mechanisms. The kinetic parameters are obtained from linear heating rate, isothermal and sample controlled thermal analysis experiments. Kinetic results obtained from the macroscopic thermal analysis measurements demonstrate the correlation between the kinetics of the thermal dehydrochlorination of PVC and the structure of this macromolecule. KEYWORDS: PVC, dehydrochlorination, kinetics, kinetic model, nucleation and growth, diffusion *corresponding author: [email protected] *Manuscript Click here to view linked References 2 INTRODUCTION Poly(vinyl chloride) (PVC) is one of the most common polymers because its properties and low cost and, therefore, it has been extensively studied in literature. Due to the low thermal stability of this polymer, many studies deal with its thermal degradation. In general, it is established in literature that the thermal decomposition of PVC takes place in two processes [1-6]. The first one corresponds almost exclusively to a side group elimination or dehydrochlorination of the PVC leaving a conjugated polyene structure. Most of the Cl is released as HCl that represents up to 99% of the total volatiles; this HCl is accompanied with a small amount of hydrocarbons, mainly aromatics such as benzene [3-5, 7-16]. The relatively low thermal stability of PVC has been attributed by many researchers to the presence of thermally labile structural segments or defects that are responsible of this instability. Among those defects, the most important ones are structural defects such as branching, tertiary chlorine, unsaturations, oxygen containing groups, head-to-head structures and polymerization residues [14, 17- 32]. Due to the importance of defects from the point of view of the thermal degradation of PVC, several articles deal with the formation of these defects in PVC macromolecules [18, 31, 33]. Additionally, some authors have recognized the importance of the secondary molecular structure, namely the tacticity governed microstructure, on the thermal degradation of PVC. Thus, it has been claimed that the GTTG- conformer of the mm triads that occur in mmr segments of the polymer are responsible of the thermal instability [34-37]. The kinetics of the thermal dehydrochlorination of PVC has been extensively studied in literature using both isothermal and linear heating rate methods [12, 13, 38-57]. It is striking the very broad dispersion of results in terms of kinetic parameters reported in these papers. Most of the kinetic studies of thermal dehydrochlorination of PVC assume an n order kinetic model for the analysis [12, 13, 38-55, 58-62]. Additionally, some authors have used a more complex approach by proposing either two consecutive [8, 13, 50] or two competitive [49] n order kinetic models. The use of n order kinetic equations for describing solid state reactions is a very simple assumption commonly used in thermal 3 degradation of polymers. Thus, it is assumed that the reaction rate is proportional to the reacted fraction (or unreacted material) to the power of n, where n is the reaction order. From the formal point of view, the n order kinetic model has only physical meaning for n values equal to 1, ¾ and ½. For these values, the n order kinetic model corresponds to a phase boundary-controlled reaction contracting in one, two and three dimensions, respectively. Intermediate values could correspond to a mixed situation due to, for example, mixtures of particles with different morphologies [63]. In any case, for most of the polymer degradation studies, the n order kinetic models are used just as a fitting function without physical. In fact, the n parameter might have any value that fits the experimental curves, and no conclusions are drawn from the obtained values. It is worth noting that the assumption of a kinetic mechanism produces a significant effect on the kinetic parameters, i.e. activation energy and preexponential factor, resulting from the kinetic analysis. Thus, if an incorrect kinetic model is assumed, the resulting parameters will also be erroneous. Recently, it has been reanalyzed the kinetics of the thermal dehydrochlorination of PVC and it has been concluded that, despite the general believe, this process cannot be described by an n order kinetic model but by a mechanism of nucleation and growth of nuclei.[56] More recently, Simoes et al have reached a similar conclusion in terms of the kinetics of this thermal degradation reaction when studying different PVC samples [57]. Nevertheless, the nucleation and growth of nuclei model does not describe the entire dehydrochlorination process, and deviations in the activation energy and the Arrhenius pre-exponential factor for large values of α, i.e. α>0.7, are observed. In addition, non-conventional thermal methods such as constant rate thermal analysis [64, 65], stepwise isothermal analysis [65] and high-resolution thermogravimetry [66], that provide a better resolution power than conventional procedures, have shown that the thermal dehydrochlorination of PVC is not a simple process but a complex one that involves two weight steps. These two weight steps have been attributed to different syndiotacticities in the PVC macromolecules, in agreement with results obtained from FTIR [66]. The objective of the present work is the study of the thermal dehydrochlorination of two different samples of PVC and the proposal of a kinetic mechanism that accounts for the entire complex process. 4 Kinetic parameters will be obtained from linear heating rate, isothermal and sample controlled thermal analysis experiments. THEORETICAL In a solid-state reaction, the general kinetic equation that describes the reaction rate is usually written as follows:       fRTEA dt d exp (1), where is the reacted fraction, t is the time, d /dt is the reaction rate, A is the Arrhenius pre-exponential factor, R is the gas constant, E the activation energy, T is the process temperature and f( ) accounts for the reaction rate dependence on . The kinetic model, f( ) is an algebraic expression which is usually associated with a physical model that describes the kinetics of the solid state reaction. Table 1 shows the functions corresponding to the most commonly used mechanisms found in literature. Recently, it has been reported that a modified Sestak-Berggren equation, i.e. f(α)=c αm (1-α)n, with values for n and m in the range from 0.4 to 0.8 and -1 and 0.7, respectively, not only fits every kinetic ideal model proposed for solid state reactions, but the deviations of the ideal kinetic models due to, for example, inhomogeneities in particle size and shape [63]. Thus, the use of this equation does not limit the kinetic analysis to the use of only ideal kinetic models that might yield erroneous results. Thus, it has been stated in literature that if the kinetic model is discriminated from a predefined set of kinetics models, one of them will be the “best model” even if the set does not contain the true model[67]. This is especially important for the analysis of real samples. The kinetic models reported in literature have been proposed by assuming ideal conditions in terms of reaction driving force and particle size and shape. Thus, it has been observed that deviations from these ideal situations will definitely produce a change in the form of the f(α) functions, and the experimental curves could not be properly fitted by the ideal models. Nevertheless, the use of the modified Sestak-Berggren equation instead of the equations corresponding to ideal models will fit the data, not only, when they are described by one of the proposed 5 ideal kinetic models, but when they follow a different mechanism not corresponding to any of the ideal ones. Thus, equation (1) can be written as nm RTEcA dt d)1()/exp(    (2) Equations (1) and (2) are general expressions that describe the relationship among the reaction rate, reacted fraction and temperature independently of the thermal pathway used for recording the experimental data. In the case that the experimental data were recorded at a constant heating rate β=dT/dt, equation (2) would be written as follows: nm RTE cA dT d)1()/exp(     (3) For experiments performed under isothermal conditions, the sample temperature is rapidly increased up to a certain temperature and maintained at this temperature while the reaction evolution is recorded as a function of the time. Under these experimental conditions, the term Aexp(-E/RT) remains constant at a value k, and therefore equation (2) becomes:   n m ck dt d)1(    (4) Sample Controlled Thermal Analysis (SCTA) is another alternative approach which is attracting a rising interest for decomposition reactions.[64, 68-70] In SCTA experiments, the evolution of the reaction rate with the time is predefined by the user and, most usually, it is maintained at a constant value, C= d/dt, along the entire process. In this case, the technique is named Constant Rate Thermal Analysis (CRTA). This way, by selecting a decomposition rate that is slow enough, the mass and heat transfer phenomena occurring during the reaction are minimized, what is an useful asset when dealing 6 with reactions as complex as polymer pyrolysis. Thus, the results obtained by CRTA are more representative of the forward reaction than those resulting from more conventional methods [68, 69, 71- 73]. Under constant rate thermal analysis (CRTA) conditions, equation (2) becomes: mm RTEcAC)1())(/exp(   (5). Model-free methods Model-free methods are used for determining the activation energy as a function of the reacted fraction without any previous assumption on the kinetic model fitted by the reaction. The Friedman isoconversional method [74] is a widely used differential method that, unlike conventional integral model-free methods, provides accurate values of activation energies even if the activation energy were a function of the reacted fraction [75]. Equation (1) can be written in logarithmic form:   RT E Af dt d      )(lnln   (6) Moreover, at a constant value of , f() would be also constant and equation (6) would be written in the form:     RT E Const dt d       ln (7) The activation energy at a constant  value, Eα , can be determined from the slope of the plot of the left hand side of equation (7), that is the logarithm of the reaction rate at a constant value of α, against the inverse of the temperature at the same value of α. 7 EXPERIMENTAL Two samples of PVC with different molecular weight purchased from Aldrich have been used in this study: Sample 1 (Aldrich 389323): average Mn ~47,000; average Mw ~80,000; fine powder. Sample 2 (Aldrich 346764): average Mn ~99,000; average Mw ~233,000; fine powder. The samples were used as received without any further modification. A homemade thermogravimetric instrument that allows working, not only under conventional linear heating and isothermal conditions, but also under sample controlled thermal analysis conditions has been used for the present study. A detailed description of the instrument can be found in references [64, 65]. In order to avoid heat and mass transfer phenomena, very small amounts of sample were used. Thus, about 10 mg and 25 mg of sample were used for the experiments under conventional conditions (linear heating rate and isothermal) and sample controlled thermal analysis conditions, respectively. Additionally, the reproducibility of the measurements was checked by repeating experiments with different amounts of material. In the case of the sample controlled conditions, a slightly larger amount of sample was used to obtain a better control of the reaction rate. Nevertheless, it has to be taken into consideration that under these experimental conditions, the heat and mass transfer phenomena are minimized because the reaction rate is controlled all over the process. All experiments were performed in nitrogen atmosphere (flow: 100 cc min-1). The evolved gas analysis was performed under high vacuum using another homemade instrument with a reactor and a quadrupole mass spectrometer (Prism, Pfeiffer) [76]. In this case, 3.5 mg of sample was used for the experiment. 8 RESULTS Fig. 1 shows the thermogravimetric curves, in its integral and differential forms, corresponding to the thermal dehydrochlorination of PVC sample 1 under different linear heating rates. Weight losses have been normalized, as it is commonly done for kinetic analysis of solid state reaction, and the process is described in terms of reaction fraction or α. Nevertheless, the weight loss for all curves in Fig. 1 was about 59% that is the stoichiometric value corresponding to the release of HCl due to total thermal dehydrochlorination of PVC, in agreement with previous literature data [3-5, 7-16]. It is quite clear from Fig. 1 that curves show a shoulder for all heating rates. This behaviour suggests a complex dehydrochlorination mechanism. In addition the evolution of the HCl mass signal recorded by mass spectrometry as a function of the temperature shows that HCl is evolved in two overlapping stages (Fig. 2), corresponding to both weight losses in the TG traces (Fig. 1). It is noteworthy to point out that, although thermogravimetric results show that both processes are not totally resolved (Fig. 1), the shoulder is observed at a reacted fraction, , roughly closed to 0.6 independently of the heating rate selected, what suggests that thermal dehydrochlorination of PVC takes place through two independent reactions. This behaviour is not consistent with the proposal of Wu et al [49] that consider that the thermal dehydrochlorination of PVC is described by two competitive processes. In the case that a solidstate reaction is described by two competitive processes with different kinetic parameters, the contribution of each of them will depend on temperature and due to the fact that a change in the heating rate produces a shift in the average temperature at which the process takes place, the contribution of each individual process to the overall reaction will be different for the different heating rates [75]. Moreover, the activation energy values plotted in Fig. 3 as a function of the reaction progress as calculated by means of the model free method previously described in the theoretical section seems to support this conclusion. Thus, it is clear from Fig. 3 that the activation energy remains near constant at a value close to 125 kJ/mol until the reacted fraction at the shoulder is reached, while for higher values of  the activation energy sharply increases up to values larger than 190 kJ mol-1. It would be expected that 15 suggest that certain degree of cross-linking is developed impeding the escape of the HCl in the final stage of dehydrochlorination. As a matter of fact, in PVC the cross-linking, whereby there is a creation of bonds between two adjacent polymer chains, generates a more compact, less easily volatilized structure [85]. Interestingly, a similar behaviour has been reported for the pyrolysis of rice husk, where a high thermal stability Si-O carcass is formed and gives rise to a diffusion controlled process, in such a way that the resulting material presents a typical globular structure [86]. From the practical point of view, the presence of this diffusion controlled process determines the globular like or foam microstructure of the residue. As a matter of fact, some authors have proposed the pyrolysis of PVC as a procedure to prepare porous carbon materials without further activation [87]. In conclusion, the thermal dehydrochlorination of PVC is complex and involves two different processes: a first process with an activation energy of about 114 kJ mol-1 that follows a nucleation and growth type kinetic model and a second process with an activation energy of about 202 kJ mol-1 that follows a diffusion controlled kinetic model. The first process that follows a nucleation and growth mechanism could be related with the presence of the well described labile sites in PVC where the reaction starts and follows from these nuclei into the rest of the material. 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Mechanism Symbol f() Equivalent reduced Sestak- Berggren equation Phase boundary controlled reaction (contracting area, i. e. bidimensional shape) R2 21 )1(   21 )1(   Phase boundary controlled reaction (contracting volume, i. e. tridimensional shape) R3 32 )1(   3/2 )1(   Unimolecular decay law (instantaneous nucleation and unidimensional growth) F1 )1(   )1(   Random instant nucleation and twodimensional growth of nuclei (Avrami- Erofeev equation) A2   2/1 )1ln()1(2   515.0806.0 )1(079.2   Random instant nucleation and threedimensional growth of nuclei (Avrami- Erofeev equation) A3   3/2 )1ln()1(3   693.0748.0 )1(192.3   Two-dimensional diffusion (bidimensional particle shape) D2 1 1 ln( )  008.1425.0 )1(973.0    Three-dimensional diffusion (tridimensional particle shape) Jander equation D3          3/1 3/2 112 )1(3   004.1951.0 )1(431.4    20 FIGURE CAPTIONS Figure 1. Thermogravimetric curves in its integral (top) and differential (bottom) forms corresponding to the thermal dehydrochlorination of PVC sample 1 obtained under different linear heating ratesThe dots are the experimental curves while solid lines are the theoretical ones simulated using the kinetic parameters obtained from the analysis. The contribution of the two processes to the overall reactions are represented by the dashed lines. Figure 2. Ion current corresponding to HCl mass signals recorded by mass spectrometry as a function of the temperature for sample 1 at a heating rate of 10 K min-1 Figure 3. Activation energy values as a function of the reaction progress obtained by means of the model free method for the PVC sample 1. Figure 4. Comparison of the modified Sestak-Berggren f(α) functions resulting from the kinetic analysis (points) with some of the conversion functions often used in the literature and listed in Table 1 (lines). a) first process and b) second process. Figure 5. Thermogravimetric curves obtained under linear heating rate conditions at (a) 20 and (b) 40 K min-1 for the PVC sample 1. Experimental curves are represented by points while the theoretical reconstructed ones are represented by lines. Figure 6. Isothermal experiment at 543 K for the PVC sample 1. Experimental curve is represented by points while the theoretical reconstructed one is represented by a line. The inset figure shows a detail of the initial part of the degradation curve. Figure 7. Sample controlled thermal analysis curve resulting from the thermal dehydrochlorination of PVC sample 1 at a constant reaction rate of 6 10-3 min-1. Experimental curve is represented by points while the theoretical reconstructed one is represented by a line. 21 Figure 8. Thermogravimetric curves in its integral (top) and differential (bottom) forms corresponding to the thermal dehydrochlorination of PVC sample 2 obtained under different linear heating rates. The dots are the experimental curves while solid lines are the theoretical ones simulated using the kinetic parameters obtained from the analysis. The contribution of the two processes to the overall reactions are represented by the dashed lines. Figure 9. Activation energy values as a function of the reaction progress obtained by means of the model free method for the PVC sample 2. Figure 10. Comparison of the modified Sestak-Berggren f(α) functions resulting from the kinetic analysis (points) with some of the conversion functions often used in the literature and listed in Table 1 (lines). a) first process and b) second process. Figure 11. Thermogravimetric curves obtained under linear heating rate conditions at (a) 20 and (b) 40 K min-1 for the PVC sample 2. Experimental curves are represented by points while the theoretical reconstructed ones are represented by lines. Figure 12. Isothermal experiment at 543 K for the PVC sample 2. Experimental curve is represented by points while the theoretical reconstructed one is represented by a line. Figure 13. Sample controlled thermal analysis curve resulting from the thermal dehydrochlorination of PVC sample 2 at a constant reaction rate of 6 10-3 min-1. Experimental curve is represented by points while the theoretical reconstructed one is represented by a line. Figure 14. Optical micrograph of the PVC sample 1 dehydrochlorinated (a) up to an extend of 70% and (b) totally dehydrochlorinated 22 Figure 1. Thermogravimetric curves in its integral (top) and differential (bottom) forms corresponding to the thermal dehydrochlorination of PVC sample 1 obtained under different linear heating rates. The dots are the experimental curves while solid lines are the theoretical ones simulated using the kinetic parameters obtained from the analysis. The contribution of the two processes to the overall reactions is represented by the dashed lines. 480 500 520 540 560 580 600 620 640 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 480 500 520 540 560 580 600 620 640 660 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 480 500 520 540 560 580 600 620 640 660 0.000 0.005 0.010 0.015 0.020 0.025 0.030 450 500 550 600 650 0.0 0.2 0.4 0.6 0.8 1.0 460 480 500 520 540 560 580 600 620 640 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 d/dT T (K) 5 K/min 10 K/min d/dT T (K) d/dT T (K) 15 K/min 2.5 K/min 5 K/min 10 K/min 15 K/min  T (K) d/dT T (K) 2.5 K/min 23 425 450 475 500 525 550 575 600 625 650 675 0.00E+000 2.00E-011 4.00E-011 6.00E-011 8.00E-011 1.00E-010 Ion Current T (K) m/Z=36 m/Z=38 Figure 2. Ion current corresponding to HCl mass signals recorded by mass spectrometry as a function of the temperature for sample 1 at a heating rate of 10 K min-1. 24 0.0 0.2 0.4 0.6 0.8 1.0 120 130 140 150 160 170 180 190 200 Ea  Figure 3. Activation energy values as a function of the reaction progress obtained by means of the model free method for the PVC sample 1. 31 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.00.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 f()/f(0.5)  D3 F1 R3 L2 A2 (b) f()/f(0.5) D3 F1 R3 L2 A2 (a) Figure 10. Comparison of the modified Sestak-Berggren f(α) functions resulting from the kinetic analysis (points) with some of the conversion functions often used in the literature and listed in Table 1 (lines). a) first process and b) second process. 32 500 550 600 650 700 0.0 0.2 0.4 0.6 0.8 1.0 500 550 600 650 0.0 0.2 0.4 0.6 0.8 1.0  T (K) (b)  (a) Figure 11. Thermogravimetric curves obtained under linear heating rate conditions at (a) 20 and (b) 40 K min-1 for the PVC sample 2. Experimental curves are represented by points while the theoretical reconstructed ones are represented by lines. 33 0500 1000 1500 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 30 35 40 0.0 0.2 0.4 0.6 0.8 1.0  t (min)  t (min) Figure 12. Isothermal experiment at 543 K for the PVC sample 2. Experimental curve is represented by points while the theoretical reconstructed one is represented by a line. 34 480 500 520 540 560 580 600 620 640 0.0 0.2 0.4 0.6 0.8 1.0  T (K) Figure 13. Sample controlled thermal analysis curve resulting from the thermal dehydrochlorination of PVC sample 2 at a constant reaction rate of 6 10-3 min-1. Experimental curve is represented by points while the theoretical reconstructed one is represented by a line. 35 Figure 14. Optical micrograph of the PVC sample 1 dehydrochlorinated (a) up to an extend of 70% and (b) totally dehydrochlorinated