Accelerating Effect of Poly(vinylpyrrolidone) Matrix on Thermal

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Cite This: Ind. Eng. Chem. Res. 2019, 58, 2891−2898

Accelerating Effect of Poly(vinylpyrrolidone) Matrix on Thermal Decomposition of Malonic Acid Dijana Jelic,́ †,‡ Tatsiana Liavitskaya,‡ Eugene Paulechka,§ and Sergey Vyazovkin*,‡ †

Ind. Eng. Chem. Res. 2019.58:2891-2898. Downloaded from pubs.acs.org by MACQUARIE UNIV on 02/27/19. For personal use only.

Department of Pharmacy, Faculty of Medicine, University of Banja Luka, Bulevar vojvode Bojovića 1a, Banja Luka, 78 000, Bosnia and Herzegovina ‡ Department of Chemistry, University of Alabama at Birmingham, 901 South 14th Street, Birmingham, Alabama 35294, United States § Protiro, Inc., 325 Broadway, Boulder, Colorado 80305-3337, United States ABSTRACT: Thermogravimetry in combination with isoconversional kinetic analysis is utilized to probe the effect of poly(vinylpyrrolidone) (PVP) on the decomposition of malonic acid (MA) in PVP matrices. The systems under study contain 4, 2, and 1 mol of PVP per 1 mol of MA. Although all systems demonstrate acceleration relative to neat MA, the strongest effect per mole of added PVP is observed in the 1:1 system. In the 4:1 system the acceleration effect weakens with the progress of decomposition and ultimately turns into deceleration. Kinetic analysis suggests that in the 1:1 and 2:1 systems, the decomposition rate at the advanced stages of the process is limited by vaporization of acetic acid. The unusual behavior of the 4:1 system at the advanced stages is proposed to be due to the decomposition rate being limited by a reversible step of dissolution of acetic acid in an excess of PVP.

1. INTRODUCTION Poly(vinylpyrrolidone) (PVP) is one of the most used polymers in medicine and the pharmaceutical, food, and textile industries.1−4 It has also shown promise for the preparation of nanocomposites5,6 and other hybrid materials.6,7 In addition to its nontoxicity, biocompatibility, good solubility in water and many organic solvents,8−11 PVP has a very high complexing and adhesion ability.12,13 PVP is a very common auxiliary component in the pharmaceutical field due to its chemical inactivity and high thermal stability.1,2,4 It is used as a binding or film-forming agent for pills, as a solubilizing agent, and as a component that can improve the bioavailability of drugs in their solid dispersions.1,4,8 In addition to being able to enhance the solubility of drugs, PVP also improves their physical stability during storage.14 PVP binds to other compounds primarily via hydrogen bonding and dipole interactions, which can be quite strong15−17 and are frequently identified in solid dispersions. Andrews et al. have reported hydrogen bonding between PVP and bicalutamide,18 while Marsac et al. have found dipole−dipole interaction between PVP and ketoconazole in their solid dispersion.19 It should be noted that the application of PVP is contingent on its chemical inertness by itself as well as toward drugs. However, it has been reported recently that PVP affects the thermal stability of such drugs as indomethacin, felodipine, and nifedipine.20 Also, PVP has been found to have a strong accelerating effect on the thermal decomposition of malonic acid (MA).21 While not a drug, MA is used to make cocrystals with drugs as a way of improving the solubility of the latter.22−28 Therefore, its interaction with PVP is still of pharmaceutical relevance. On the other hand, the thermal © 2019 American Chemical Society

decomposition of MA is of general interest because it represents a wide class of decarboxylation reactions. On heating, MA is well-known29−34 to decompose forming acetic acid and carbon dioxide: CH 2(COOH)2 → CH3COOH + CO2

(1)

Therefore, the results obtained on the effect of PVP on the thermal decomposition of MA should be of importance for understanding the thermal stability of various compounds containing the carboxylic group, including drugs. As was already mentioned, the previous study21 has discovered that the PVP matrix has a strong accelerating effect on the thermal decomposition of MA. No such effect has been found in poly(methyl methacrylate) and poly(vinyl acetate) matrices. This effect has been attributed21 to a catalytic action of the tertiary amino group of PVP. The present study aims to obtain further insights into the accelerating action of PVP on the thermal decomposition of MA. In the previous work,21 the system studied was a solid solution that contained a 2:1 molar ratio of PVP to MA. In terms of catalytic action, it means that there is one amino group of PVP available to catalyze decomposition of each carboxylic group of MA. However, from the entropic standpoint we can hypothesize that is it not very likely that inside the PVP matrix both carboxylic groups of each MA molecule are positioned favorably to interact with the Received: Revised: Accepted: Published: 2891

December 29, 2018 January 27, 2019 February 1, 2019 February 15, 2019 DOI: 10.1021/acs.iecr.8b06457 Ind. Eng. Chem. Res. 2019, 58, 2891−2898

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Industrial & Engineering Chemistry Research

rigid40,41 integration, i.e., the integration that assumes Eα to be constant within the whole integration range from 0 to α. The advanced isoconversional method uses flexible40,41 integration that assumes the constancy of Eα within a very narrow integration range, Δα. The size of Δα is typically selected to be 0.01 or 0.02, which is sufficient to practically eliminate the aforementioned systematic error. Within each Δα, Eα is determined by minimizing the function:

respective amino groups of PVP. If this hypothesis is true, we should be able to enhance the catalytic action of PVP by increasing its amount in the PVP/MA system. On the other hand, as a catalyst, the same tertiary amino group of PVP can possibly participate in decarboxylation of more than one group of MA. In this situation, decreasing the amount of PVP should not result in significant diminishing of the catalytic action. To test these hypotheses, the present study explores the effect of the PVP to MA ratio on the acceleration of the thermal decomposition of MA. The thermal decomposition is measured thermogravimetrically, and the effect is quantified by isoconversional kinetic analysis of the resulting data.

n

Ψ(Eα) =

n

∑∑ i=1 j≠i

J[Eα , Ti(tα)] J[Eα , Tj(tα)]

(2)

ÄÅ É ÅÅ −Eα ÑÑÑ Å ÑÑ dt J[Eα , Ti(tα)] ≡ expÅÅÅ Ñ ÅÅÇ RTi(t ) ÑÑÑÖ tα −Δα

where

2. EXPERIMENTAL SECTION Commercial (Sigma-Aldrich) malonic acid (white crystalline powder, 99% purity) was used as purchased. Poly(vinylpyrrolidone) (PVP), white powder, ≥ 97% pure, average molecular weight 58 000 was purchased from Acros Organics. PVP/MA systems were prepared in the form of thin films containing different PVP to MA ratios as follows: ∼48 wt % of MA (system with 1:1 mol ratio), ∼30 wt % of MA (2:1 system),21 and ∼18 wt % of MA (4:1 system). The respective amounts of PVP were dissolved in methanol. After dissolution of PVP, malonic acid was added in a beaker and dissolved as well. The obtained solution was transferred into a glass Petri dish and kept in an oven at 60 °C for 48 h. In addition, a sample of neat PVP film was obtained from a methanolic solution in a similar manner. Thermal decomposition of the PVP/MA systems was measured by using a thermogravimetric analyzer, under flow of N2, at a flow rate 80 mL·min−1. The purity of N2 was 99.995 vol %. The device used for thermogravimetric measurements was a Mettler Toledo TGA/DSC 3+ instrument. Indium and zinc standards were used to perform temperature and tau-lag calibrations.35 Samples of all PVP/MA mixtures were placed in open Al pans (100 μL) and heated in a non-isothermal regime with the following heating rates, β = (1.25, 2.5, 5, 7.5, and 10) °C·min−1. The sample masses of PVP/MA systems were (6.6 ± 0.1, 9.7 ± 0.3, and 16.3 ± 0.2) mg corresponding to 1:1, 2:1, and 4:1 PVP/MA systems, respectively. The masses of PVP/ MA samples were selected so that they all contained ∼3 mg of MA. Since the MA content was different for the three systems, keeping approximately the same mass of MA required use of respectively different masses for different systems. Selected runs were performed in duplicate and found to be repeatable. As already stated, the 2:1 system has been studied earlier, so that the respective data were taken from the previous work21 and used here for the sake of comparison. The same applies for the data obtained for neat MA that were taken from another publication.36

∫

tα

(3)

and R is the gas constant. The minimization is carried out for the set of data obtained at n temperature programs. The integral was estimated numerically by the trapezoid method. A minimum of eq 2 was found by using the COBYLA nongradient method42 from the NLOPT library.43 The Monte Carlo bootstrap method44 was applied to evaluate the uncertainties (standard deviations) in the Eα values. The preexponential factors were estimated by substituting the values of Eα into the equation of the compensation effect:37 ln Aα = a + bEα

(4)

The parameters a and b were determined by fitting the pairs of ln Ai and Ei into eq 4. The respective pairs were determined by substituting several reaction models, f i(α), into the linear form of the basic rate equation:37 E i dα y lnjjj zzz − ln[fi (α)] = ln Ai − i RT k dt {

(5)

Alternatively, the ln Ai and Ei values suitable for evaluating the parameters of the compensation effect can be obtained by using an accurate integral method45 that allows one to avoid differentiation of the thermogravimetric analysis (TGA) data. For each given reaction model, ln Ai and Ei values were found respectively from the slope and intercept of the linear plot of left-hand side of eq 5 versus the reciprocal temperature. On the basis of previous analysis,46 four f(α) functions that represent the power law (P2, P3, P4) and Avrami-Erofeev (A2) models are sufficient for accurate estimation of the preexponential factor. The isoconversional activation energy and preexponential factor were used to evaluate the rate constant and reaction model. The rate constant was evaluated in the form of the Arrhenius plot:20,21

3. COMPUTATIONS The activation energy, preexponential factor, and the reaction model were determined according the recommendations of the ICTAC Kinetic Committee.37 The extent of conversion, α, was determined as the partial mass loss. The effective activation energy, Eα, as a function of conversion, was evaluated by an advanced isoconversional method38 that is applicable to data obtained at an arbitrary temperature program, T(t). Another important advantage of this method is that it eliminates a systematic error in Eα when it varies with α. This error can be significant,38,39 and it is found in the methods that use the

ln k(Tα) = ln Aα −

Eα RTα

(6)

The reaction model was estimated in the integral form as follows: g (α ) =

∑ AαJ[Eα , Ti(tα)] α

(7)

Molecular dynamics simulations were carried out with the GROMACS v. 2018 package47 using the OPLS-AA/L force field.48 This force field was selected because of its good performance toward prediction of the enthalpies of vapor2892

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Industrial & Engineering Chemistry Research ization at T = 298 K.49 Molecular topologies were generated with the TPPMKTOP topology generator.50 The atomic charges of hydrogens in N-isopropylpyrrolidone, which was used as a structural analogue of the PVP monomeric unit, were decreased by 9% to keep the molecule neutral. Parameters of the torsions in all molecules were specified explicitly to provide consistency with the force field specifications. A cubic box contained 512 molecules for pure liquid and 512 molecules of N-isopropylpyrrolidone + 128 molecules of acetic acid for the mixture. The boxes were filled with the molecules using the Packmol package.51 Three-dimensional periodic boundary conditions were applied. The long-range electrostatic interactions were treated with the smooth particle-mesh Ewald method52,53 using the initial Coulomb cutoff distance of 1.5 nm. Van-der-Waals interactions were cut off at the same distance. The energy minimization was followed by the NPT simulation for 20 ns, in which the Berendsen thermostat and barostat54 were used. The last snapshot of the trajectory served as a starting point for the subsequent NVT simulation. The velocity rescaling scheme with the time constant of 0.1 ps was applied for thermostatting. 55 The simulation box was equilibrated for 30 ns, and the production run was 70 ns long. A time step was 1 fs in all simulations. The molar enthalpies of mixing ΔmixH were calculated per mole of an acid using the total energies E from the simulations:

Figure 1. Kinetic curves for the thermal decomposition of neat PVP (squares), neat MA (circles), and MA in PVP/MA systems: 1:1 (diamonds), 2:1 (stars), and 4:1 first (pentagons) and second (solid line) samples. Heating rate is 2.5 °C·min−1. Neat PVP was in the form of a film cast from a methanolic solution. For PVP the α axis is on the right-hand side.

decomposition of the 4:1 system at very high (α > 0.8) conversions. The occurrence of decomposition at lower temperature means that PVP has an accelerating effect on decomposition of MA. When comparing the initial stages of decomposition, e.g., the region of α < 0.1, we can see that on addition of PVP the accelerating effect reaches saturation. For example, α = 0.05 is reached respectively at 96, 101, and 110 °C in the 4:1, 2:1, and 1:1 systems, and at 137 °C in MA. That is, addition of one mole of PVP (1:1 system) lowers the decomposition temperature of MA by more than 25 °C. Then, the addition of two moles of PVP (2:1 system) lowers the decomposition temperature by less than 10 °C relative to the 1:1 system, whereas upon addition of four moles of PVP (4:1 system) the temperature decreases by ∼5 °C relative to the 2:1 system. In other words, addition of first two moles of PVP (2:1 system) depresses the decomposition temperature of MA by ∼35 °C, whereas addition of another two moles (4:1 system) increases this depression by only 5 °C. Therefore, the temperature depression per mole of added PVP becomes progressively smaller. Apparently, the accelerating action persists but its efficiency decreases; i.e., the acceleration is close to its saturation. Note that the aforementioned temperature depressions are comparable to those reported58 for the thermal decomposition of MA catalyzed by molybdophosphoric acid and its bismuth salts. For the 4:1 system we have obtained unexpected results at higher extents of conversion (Figure 1). If we compare the α vs T curves for the 2:1 and 1:1 systems, their shapes are nearly identical. They also have practically the same width of approximately 100 °C. In other words, they look like one can be obtained from another by a parallel shift. Thus, for the 4:1 system, we expected to see a α vs T curve of the same shape and width as for the 2:1 and 1:1 systems just shifted to a lower temperature. The expected behavior is observed only at low conversions (α < 0.2). However, the α vs T curve for the 4:1 system is quite different in shape and width. First of all, it spans a much broader temperature range of ∼160 °C. Second, it has a very asymmetric shape; i.e., the temperature range corresponding to the α range of (0.5 to 1.0) is markedly broader than that for the α range (0 to 0.5). As a result, we can

Δmix H = E(mixture)/128 − E(N ‐isopropylpyrrolidone) /128 − E(acid)/512

(8)

The denominators for the mixture and pure acid terms were equal to the number of the acid molecules in the corresponding boxes. The N-isopropylpyrrolidone and mixture boxes contained the same number of the N-isopropylpyrrolidone molecules. Therefore, the same denominator was used in both cases. The uncertainties were defined as the standard deviations of the obtained values.

4. RESULTS AND DISCUSSION Thermogravimetric Data. Conversion curves α vs T for the PVP/MA systems with different ratios of PVP to MA for the same heating rate 2.5 °C min−1 are presented in Figure 1. Note that in the range of the heating rates used in this study MA decomposes below 200 °C,36 whereas neat PVP decomposes above 350 °C.56 PVP samples reproducibly show56 a small (∼2 wt %) mass loss around 200 °C that is apparently associated with outgassing of the residual monomer, vinylpyrrolidone, whose boiling temperature is reported57 to be 193 °C at 400 mmHg (53 kPa). This minute event overlaps only with the final stages (α > 0.9) of the 4:1 system decomposition and cannot be of any relevance to the effect discussed later because this effect already becomes detectable at significantly lower conversions (α ≈ 0.3) and temperatures. Decomposition of the 1:1 system starts at ∼100 °C and ends at ∼190 °C with the mass loss of 48.1 wt %. This is consistent with the actual content (48 wt %) of MA in this system. Decomposition of the 4:1 system covers the temperature region from ∼80 °C to ∼240 °C with the mass loss of 18.7 wt %, which also agrees well with the MA content (18 wt %). These results indicate that the decomposition observed in the PVP/MA systems is associated with decomposition of MA. If we compare the α vs T curves (Figure 1), we can see that decomposition of all PVP/MA systems occurs at lower temperature than that of neat MA. The only exception is 2893

DOI: 10.1021/acs.iecr.8b06457 Ind. Eng. Chem. Res. 2019, 58, 2891−2898

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Industrial & Engineering Chemistry Research see that it crosses consecutively the α vs T curves for the 2:1 system at α ≈ 0.3, for the 1:1 system at α ≈ 0.6, and for neat MA at α ≈ 0.8. It means that the accelerating action of PVP in the 4:1 system gradually weakens with reaction progress and ultimately turns into deceleration. To confirm that the unexpected behavior of the 4:1 system is not due to a chance, another sample of this system was prepared and analyzed by TGA. The result is shown in Figure 1. It is seen that the α vs T curve obtained for this sample is virtually identical to the one obtained for the first sample. Therefore, the unexpected behavior of the 4:1 system is definitely not accidental. Some clues about this unexpected behavior are provided by the asymmetric shape of the α vs T curve. The appearance of a longer tail at higher extents of conversion is generally indicative of the presence of a process that slows down the reaction rate. Typically this process is diffusion, and the appearance of the tail may serve as a sign of the kinetics switching to the diffusion control mode. Diffusion control is quite commonly found at final stages of various processes such as polymerization40,59−61 and thermal decomposition.62,63 In the latter case, diffusion retardation is associated with a reaction medium that impedes outgassing of volatile reaction products. This is what is likely to happen in the PVP/MA systems. The carbonyl group of PVP is a strong acceptor of hydrogen bonds and as such can bind effectively to various species capable of hydrogen bond donation. This certainly applies to acetic acid, which is a decomposition product of MA. Due to hydrogen bonding, acetic acid should have strong affinity to the PVP matrix, which would delay its outgassing. Naturally, this effect should increase with increasing concentration of PVP, as PVP would be able to dissolve more of the acetic acid. This can explain the unusual appearance of the α vs T curve for decomposition of the 4:1 system, in which each molecule of acetic acid formed faces on an average two carbonyl groups of PVP. Further insights into this effect are provided by kinetic analysis of the thermogravimetric data. Kinetic Analysis. The use of any isoconversional method requires obtaining data at multiple temperature programs (cf., eq 2). All our data on decomposition of MA and PVP/MA systems have been obtained by using multiple heating rates. Figures 2 and 3 display the α vs T curves for the 1:1 and 4:1 systems, whose decomposition has been measured in the

Figure 3. Kinetic curves for the thermal decomposition of MA in the 4:1 PVP/MA system at multiple heating rates. The numbers by the curve type are the heating rate values in °C·min−1.

present work. As seen from these figures, for each of these two systems, the shape of the α vs T curves is virtually independent of the heating rate. This indicates that the respective mechanisms of decomposition remain the same within the corresponding ranges of the heating rates and temperatures. On the other hand, the shapes of the curves for the 1:1 and 4:1 systems are distinctly different, which hints at the difference of the decomposition mechanisms in these two systems. As normally is the case, increasing the heating rate causes the α vs T curves to shift to a higher temperature. This is a kinetic phenomenon that arises from the fact that with increasing the heating rate the reaction spends less time within the same temperature interval and, thus, attains smaller conversion of the reactants to products. As a result, reaching the same conversion at a faster heating rate requires a higher temperature. Figures 4 and 5 present the isoconversional Arrhenius parameters, Eα and ln Aα, for all three PVP/MA systems in comparison to neat MA. There are three elements of note in these figures. First, at lower extents of conversion (α < 0.4) for all PVP/MA systems, the Arrhenius parameters are very similar to those found for neat MA. The previous extensive study36 of

Figure 4. Dependence of the activation energy on the extent of conversion for the thermal decomposition of neat MA (dash line) and MA in PVP/MA systems: 1:1 (diamonds), 2:1 (stars), and 4:1 (pentagons).

Figure 2. Kinetic curves for the thermal decomposition of MA in the 1:1 PVP/MA system at multiple heating rates. The numbers by the curve type are the heating rate values in °C·min−1. 2894

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explored by using simulations to estimate the enthalpy of mixing of one molecule of acetic acid with four molecules of Nisopropylpyrrolidone. The simulations have been conducted for temperature of 500 K and pressure 0.5 MPa (to prevent vaporization of N-isopropylpyrrolidone). The resulting enthalpy of mixing has been found to be −(8 ± 5) kJ·mol−1. This value indicates that the enthalpy of vaporization of acetic acid from its mixture with N-isopropylpyrrolidone will be about 8 kJ·mol−1 larger than that for vaporization of neat acetic acid. Therefore, the observed large values of Eα at α → 1 cannot be explained by an increase in the vaporization enthalpy of acetic acid due to its specific interactions with PVP. Another unexpected result obtained for the 4:1 system is encountered when the Arrhenius plots for all PVP/MA systems are calculated (Figure 6). First of all, one can see Figure 5. Dependence of the preexponential factor on the extent of conversion for the thermal decomposition of neat MA (dash line) and MA in the PVP/MA systems: 1:1 (diamonds), 2:1 (stars), and 4:1 (pentagons).

neat MA has demonstrated that both Eα and ln(Aα/s−1) are practically independent of conversion, and for the liquid state decomposition are respectively equal to (107 ± 4) kJ·mol−1 and (24 ± 1). This independence indicates that the process rate is controlled by the decomposition kinetics of MA rather than diffusion of the reaction products. Second, as the extent of conversion rises (α > 0.4), all PVP/MA systems show a growing systematic deviation from the Arrhenius parameters of the neat MA. Third, the trend in variation of the Arrhenius parameters with conversion that is observed for the 1:1 and 2:1 systems is opposite to that observed for the 4:1 system. Let us consider the 1:1 and 2:1 systems first. In both systems, the values of Eα decrease systematically with conversion down to the value around (50−60) kJ·mol−1 (Figure 4). A change in the activation energy suggests that there is a change in the rate limiting step. As mentioned earlier, PVP should be capable of dissolving acetic acid formed as a decomposition product. Therefore, it is likely that, as the production rate of acetic acid increases, a significant fraction of it does not immediately leave the PVP matrix but rather becomes dissolved in it. As a result, the overall rate of decomposition becomes limited by the rate of vaporization of acetic acid from the PVP matrix. It should be noted that for the process of vaporization, the activation energy is typically found to be equal within experimental uncertainty to the enthalpy of vaporization.40 The latter value for acetic acid is (51.6 ± 0.8) kJ·mol−1 at T = 298.15 K,64 which is similar to the Eα values obtained at α → 1 for the 1:1 and 2:1 systems. This obviously supports our idea about the effect of dissolution of acetic acid on the decomposition kinetics of MA in the PVP matrix. Of course, an argument can be raised that the enthalpy of vaporization of acetic acid may be larger when the process occurs from the PVP matrix. As we show later, this is not the case. Unlike the 1:1 and 2:1 systems, the 4:1 system demonstrates the Arrhenius parameters that increase dramatically with conversion. At α → 1, the Eα value reaches around 240 kJ· mol−1. Clearly, there is a change in the rate limiting step. Note that this step is not likely to be associated with diffusion or vaporization of the gaseous products. The activation energy for diffusion of gases in solids is usually tens of kJ·mol−1. The enthalpy of vaporization of acetic acid may become larger due to the interaction with the PVP matrix. This issue has been

Figure 6. Arrhenius plots for the thermal decomposition of neat MA (circles) and the PVP/MA systems: 1:1 (diamonds), 2:1 (stars), and 4:1 (pentagons).

that for decomposition of all PVP/MA systems, the rate constants are larger than that for decomposition of neat MA. For the 1:1 and 2:1 systems, an increase in ln k is consistent with the depression of the decomposition temperature discussed above. However, for the 4:1 system, the situation is not that straightforward. As follows from analysis of the thermogravimetric data (Figure 1), this system shows acceleration relative to the 2:1 system only at α < 0.3. Relative to neat MA, the acceleration is detected at α < 0.8. That is, the rate constant alone does not characterize adequately the kinetic effect of PVP in the 4:1 system. Indeed, the reaction rate is proportional not only to the rate constant but also to the conversion function that represents the reaction model.37 Therefore, we estimated the reaction models for all our PVP/MA systems. They are presented in Figure 7. Note that the reaction models have been evaluated in the integral form, g(α). Unlike the differential form, f(α), which is directly proportional to the rate (eq 5), g(α) is inversely proportional to it. It means that larger values of g(α) correspond to a slower reaction rate. As seen in Figure 7, the 4:1 system demonstrates the g(α) values that are significantly larger than the respective values for other PVP/ MA systems, except within the small range of α < 0.1. Considering that the reaction model is linked to the reaction mechanism, we can conclude that the unusual behavior of the 4:1 system should result from the fact that decomposition of 2895

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toward equilibrium, both Eα and ln Aα should be expected to increase with conversion, which is exactly what we see in Figures 4 and 5.

5. CONCLUSIONS The study has explored the effect of the amount of PVP on the acceleration of MA decomposition in PVP matrices. The systems compared contained 4, 2, 1 mol of PVP per 1 mol of MA. It has been found that relative to neat MA, the largest acceleration is observed in the 1:1 system. Further addition of PVP results only in minor acceleration relative to the 1:1 system. This result is consistent with the idea that one tertiary amino group of PVP can catalyze more than one carboxylic group of MA. Unlike for the 1:1 and 2:1 systems, TGA data for the 4:1 system have demonstrated the accelerating effect that decreases with the reaction progress and turns into deceleration at large extents of conversion. Isoconversional kinetic analysis has also revealed a drastic difference in decomposition of the 4:1 system as compared with the 1:1 and 2:1 systems. Both 1:1 and 2:1 systems have demonstrated activation energy that decreases significantly with conversion, reaching values characteristic of the enthalpy of vaporization of acetic acid. This suggests that decomposition of MA becomes controlled by the rate of vaporization of acetic acid from the PVP matrix. On the contrary, the 4:1 system has exhibited a significant increase of the Arrhenius parameters at advanced conversions. This effect has been proposed to be associated with a reversible step of dissolution of acetic acid in PVP. Overall, this study indicates that PVP may have a complex effect on the thermal stability of the compounds dissolved in the PVP matrix. This result is of high practical relevance considering the broad usage of PVP as a polymer matrix for a variety of compounds, especially in the area of pharmaceuticals.

Figure 7. Dependencies of g(α) on the extent of conversion for the PVP/MA systems with a different ratio of PVP: 1:1 (diamonds), 2:1 (stars), and 4:1 (pentagons).

MA in this system occurs in a different way than in the two other systems. Unfortunately, the obtained values of g(α) cannot provide any further insights into the behavior of the 4:1 system. More clues can be obtained from the Eα and ln Aα values and dependencies shown in Figures 4 and 5. First, the large values of Eα and, especially, of ln Aα seem quite similar to those observed65−67 earlier for reversible decomposition of crystal hydrates. These compounds start to decompose when the temperature rises above the equilibrium temperature, i.e., the temperature at which the equilibrium pressure of the gaseous decomposition product becomes equal to its partial pressure. As discussed in detail,67 the Eα values for such decomposition processes are inversely proportional to the difference between the equilibrium and partial pressure, so that Eα values can be very large close to equilibrium but much smaller further from it. Decomposition of crystal hydrates starts at equilibrium and progresses via increasing departure from it. As a result, both Eα and ln Aα start at large values but decrease with increasing α, i.e., with the reaction progress.65−67 Having the idea of the reversible kinetics in mind, we propose that the unusually large values of the Arrhenius parameters and their specific dependencies on α (Figures 4 and 5) may be associated with a reversible step of dissolution of acetic acid in PVP: CH3COOH + PVP ⇔ CH3COOH· PVP

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Eugene Paulechka: 0000-0002-6441-8364 Sergey Vyazovkin: 0000-0002-6335-4215 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.J. gratefully acknowledges the Fulbright Visiting Scholar Program 2018/19 (ID: PS00266728).

The significance of this step would depend on the amount of PVP available for dissolution of the acetic acid forming during decomposition. When it is small (1:1 and 2:1 systems), the acetic acid that forms during decomposition quickly saturates PVP so that an excess of the acid vaporizes without any significant accumulation and delay. However, when the amount of PVP is large (4:1 system), the CH3COOH·PVP solution is undersaturated so that the acetic acid formed continues to dissolve in PVP, moving the process of dissolution toward a saturated solution, i.e., toward equilibrium. As a result, vaporization of acetic acid becomes delayed by dissolution, and the kinetics of the process becomes limited by the aforementioned reversible step. As already noted, the Arrhenius parameters of a reversible process are very large in vicinity of equilibrium but significantly smaller away from it. Since in the 4:1 system the limiting reversible step progresses

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REFERENCES

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DOI: 10.1021/acs.iecr.8b06457 Ind. Eng. Chem. Res. 2019, 58, 2891−2898