Effectiveness of Esteriﬁcation Catalysts in the Synthesis of Poly(Ethylene Vanillate)

: Over the last few decades, bio-based polymers have attracted considerable attention from both academic and industrial ﬁelds regarding the minimization of the environmental impact arising from the excessive use of petrochemically-based polymeric materials. In this context, poly(ethylene vanillate) (PEV), an alipharomatic polyester prepared from 4-(2-hydroxyethoxy)-3-methoxybenzoic acid, a monomer originating from lignin-derived vanillic acid, has shown promising thermal and mechanical properties. Herein, the effects of three different catalysts, namely titanium butoxide (TBT), titanium isopropoxide (TIS), and antimony trioxide (Sb 2 O 3 ), on the synthesis of PEV via a two-stage melt polycondensation method are investigated. The progress of the reaction is assessed using various complementary techniques, such as intrinsic viscosity measurement (IV), end group analysis (AV), nuclear magnetic resonance spectroscopy (NMR), Fourier-transformed infrared spectroscopy (FTIR), and differential scanning calorimetry (DSC). The thermal stability of the produced polyesters is studied by evolved gas analysis mass spectrometry (EGA-MS). Moreover, as the discoloration in polymers affects their applications, color measurement is performed here. Finally, theoretical kinetic studies are carried out to rationalize the experimental observations.


Introduction
Contemporary industrial polymerization technologies make the production of versatile polymeric materials with highly tunable properties possible and subsequently a plethora of applications in areas including the packaging, automotive, and engineering sectors. In Europe, more than 61 million tons of polymers are produced annually [1,2], with the great majority of them being petrochemically-sourced; however, the interest in bio-based materials has flourished over the last few decades, both in academic and industrial fields due to increasing concerns about the depletion of fossil resources and the footprint of synthetic polymers on the environment, as it is estimated that roughly 80% of synthetic polymers are discarded in landfills or natural recipients [3][4][5]. In fact, the European Commission supports the synthesis of high added value products based on renewable sources by offering financial support for research, innovation, and industrial upscaling in this field [6].
The conversion of biomass to bio-based monomers, and subsequently polymers by means of biochemical and/or chemical transformations, constitutes the most important route toward the preparation of bio-based plastics like poly(lactic acid) (which, at

Effect of Catalysts on the Progress of the Esterification Reaction
Poly(ethylene vanillate) was produced using a two-step polycondensation method using three different metal-based catalysts, starting from 4-(2-hydroxyethoxy)-3-methoxybenzoic acid, which is a VA-based monomer (Scheme 1). The esterification step was performed for 3 h at 200 °C, while the polycondensation stage took place at gradually increasing temperatures up to 265 °C in a vacuum for the preparation of the final polymeric materials. The studied catalysts, i.e., TBT, TIS, and Sb2O3, were introduced/added in the beginning of the polymerization. Samples were taken from the reaction mixture every 30 min to observe the progress of the polymerization. The conversion of the carboxylic group (-COOH) of the monomer into the ester group (COOR) of PEV was evaluated using titration and nuclear magnetic resonance spectroscopy (NMR). NMR spectra were recorded in deuterated chloroform/trifluoroacetic acid (CDCl3)/(TFA-d1) (4/1 v/v). Indicative examples of 1 H NMR and 13 C NMR spectra of the crude reaction mixture are illustrated in Figure S1 and Figure 2, respectively. In 1 H NMR spectra, the methylene protons of the O-CH2b-CH2a-OH part were selected to monitor the reaction progress. In detail, as a result of the esterification of the hydroxyl group, a shift of the aforementioned protons from 4.42 (CH2a) and 3.91 ppm (CH2b) in the monomer to 4.48 and 3.99 ppm in PEV, respectively, is visible. As the reaction time increased, the monomer peaks gradually diminished, and the corresponding polymer peaks dominated the spectrum. Regarding the 13 C NMR spectra, a single peak, attributed to the carboxylic acid carbon of the monomer, appeared at 172.0 ppm (carbon a), while the corresponding peak of the ester carbon in PEV appeared at 168.4 ppm (carbon a'). As the reaction proceeded,

Effect of Catalysts on the Progress of the Esterification Reaction
Poly(ethylene vanillate) was produced using a two-step polycondensation method using three different metal-based catalysts, starting from 4-(2-hydroxyethoxy)-3-methoxybenzoic acid, which is a VA-based monomer (Scheme 1). The esterification step was performed for 3 h at 200 • C, while the polycondensation stage took place at gradually increasing temperatures up to 265 • C in a vacuum for the preparation of the final polymeric materials. The studied catalysts, i.e., TBT, TIS, and Sb 2 O 3 , were introduced/added in the beginning of the polymerization. Samples were taken from the reaction mixture every 30 min to observe the progress of the polymerization.
Catalysts 2021, 11, x FOR PEER REVIEW 3 of 17 thermal stability of the produced polyesters is investigated with the implementation of evolved gas analysis mass spectrometry (EGA-MS). As coloration in polymeric materials affects their field of application, crucial color parameters are defined. Finally, theoretical kinetic studies have been performed to support the experimental observations.

Effect of Catalysts on the Progress of the Esterification Reaction
Poly(ethylene vanillate) was produced using a two-step polycondensation method using three different metal-based catalysts, starting from 4-(2-hydroxyethoxy)-3-methoxybenzoic acid, which is a VA-based monomer (Scheme 1). The esterification step was performed for 3 h at 200 °C, while the polycondensation stage took place at gradually increasing temperatures up to 265 °C in a vacuum for the preparation of the final polymeric materials. The studied catalysts, i.e., TBT, TIS, and Sb2O3, were introduced/added in the beginning of the polymerization. Samples were taken from the reaction mixture every 30 min to observe the progress of the polymerization. The conversion of the carboxylic group (-COOH) of the monomer into the ester group (COOR) of PEV was evaluated using titration and nuclear magnetic resonance spectroscopy (NMR). NMR spectra were recorded in deuterated chloroform/trifluoroacetic acid (CDCl3)/(TFA-d1) (4/1 v/v). Indicative examples of 1 H NMR and 13 C NMR spectra of the crude reaction mixture are illustrated in Figure S1 and Figure 2, respectively. In 1 H NMR spectra, the methylene protons of the O-CH2b-CH2a-OH part were selected to monitor the reaction progress. In detail, as a result of the esterification of the hydroxyl group, a shift of the aforementioned protons from 4.42 (CH2a) and 3.91 ppm (CH2b) in the monomer to 4.48 and 3.99 ppm in PEV, respectively, is visible. As the reaction time increased, the monomer peaks gradually diminished, and the corresponding polymer peaks dominated the spectrum. Regarding the 13 C NMR spectra, a single peak, attributed to the carboxylic acid carbon of the monomer, appeared at 172.0 ppm (carbon a), while the corresponding peak of the ester carbon in PEV appeared at 168.4 ppm (carbon a'). As the reaction proceeded, Scheme 1. Synthesis of poly(ethylene vanillate) polyester with three different catalysts.
The conversion of the carboxylic group (-COOH) of the monomer into the ester group (COOR) of PEV was evaluated using titration and nuclear magnetic resonance spectroscopy (NMR). NMR spectra were recorded in deuterated chloroform/trifluoroacetic acid (CDCl 3 )/(TFA-d 1 ) (4/1 v/v). Indicative examples of 1 H NMR and 13 C NMR spectra of the crude reaction mixture are illustrated in Figure S1 and Figure 2, respectively. In 1 H NMR spectra, the methylene protons of the O-CH 2 b-CH 2 a-OH part were selected to monitor the reaction progress. In detail, as a result of the esterification of the hydroxyl group, a shift of the aforementioned protons from 4.42 (CH 2 a) and 3.91 ppm (CH 2 b) in the monomer to 4.48 and 3.99 ppm in PEV, respectively, is visible. As the reaction time increased, the monomer peaks gradually diminished, and the corresponding polymer peaks dominated the spectrum. Regarding the 13 C NMR spectra, a single peak, attributed to the carboxylic acid carbon of the monomer, appeared at 172.0 ppm (carbon a), while the corresponding peak of the ester carbon in PEV appeared at 168.4 ppm (carbon a'). As the reaction proceeded, the intensity of the peak at 172.0 ppm reduced, along with the increase of the peak a'. The conversion after every 30 min interval was calculated from the Catalysts 2021, 11, 822 4 of 17 13 C NMR spectra by integrating the peaks corresponding to the acid and the ester carbon following Equation (1): where a is the integral of the ester carbon and a is the integral of the acid carbon.
s 2021, 11, x FOR PEER REVIEW 4 of 17 the intensity of the peak at 172.0 ppm reduced, along with the increase of the peak a'. The conversion after every 30 min interval was calculated from the 13 C NMR spectra by integrating the peaks corresponding to the acid and the ester carbon following Equation (1): where is the integral of the ester carbon and ′ is the integral of the acid carbon. The assessment of the reaction progress during the esterification step, in the presence of each catalyst, is presented in Figure 3 and Table S1. As shown, the calculated conversion of -COOH groups using titanium-based catalysts ranged from 80% to 85%, while the use of Sb2O3 resulted in a 73% conversion. These results indicate that TBT and TIS demonstrate greater catalytic activity during the esterification stage of PEV, in accordance with its terephthalate and furan-2,5-dicarboxylate homologues [22,23,27,35]. The assessment of the reaction progress during the esterification step, in the presence of each catalyst, is presented in Figure 3 and Table S1. As shown, the calculated conversion of -COOH groups using titanium-based catalysts ranged from 80% to 85%, while the use of Sb 2 O 3 resulted in a 73% conversion. These results indicate that TBT and TIS demonstrate greater catalytic activity during the esterification stage of PEV, in accordance with its terephthalate and furan-2,5-dicarboxylate homologues [22,23,27,35].
Catalysts 2021, 11, x FOR PEER REVIEW 4 of 17 the intensity of the peak at 172.0 ppm reduced, along with the increase of the peak a'. The conversion after every 30 min interval was calculated from the 13 C NMR spectra by integrating the peaks corresponding to the acid and the ester carbon following Equation (1): where is the integral of the ester carbon and ′ is the integral of the acid carbon. The assessment of the reaction progress during the esterification step, in the presence of each catalyst, is presented in Figure 3 and Table S1. As shown, the calculated conversion of -COOH groups using titanium-based catalysts ranged from 80% to 85%, while the use of Sb2O3 resulted in a 73% conversion. These results indicate that TBT and TIS demonstrate greater catalytic activity during the esterification stage of PEV, in accordance with its terephthalate and furan-2,5-dicarboxylate homologues [22,23,27,35].  The FTIR spectrum of the monomer is displayed in Figure 4, as well as the spectra of the crude reacting mixture at different time intervals during the first stage of the reaction. Briefly, the monomer exhibited a broad absorption band at 3350-3500 cm −1 , which can be attributed to the stretching vibrations of the hydroxyl group of the O-CH 2 -CH 2 -OH segment, two separate bands at 2600-3000 cm −1 , linked to the stretching vibrations of the bound, through hydrogen bonds, carboxylic O-H groups, and a sharp, characteristic band at 1677 cm −1 , owing to the C=O stretching vibration of the carboxylic acid [36]. Concerning the first 2 h of the esterification step, two absorption peaks were apparent in the carbonyl area of the spectrum, representing the acid and the ester bond (at 1684 and 1708 cm −1 ) stretching vibrations, respectively. As the reaction proceeded, the first peak diminished, and the formation of a unique peak at 1720 cm −1 was visible. Furthermore, the decrease of the absorption bands at 3350-3500 cm −1 and 2600-3000 cm −1 proved the successful esterification of the hydroxyl group and carboxylic acid. These observations are in agreement with the reaction progress determined by NMR and titrimetry.  The FTIR spectrum of the monomer is displayed in Figure 4, as well as the spectra of the crude reacting mixture at different time intervals during the first stage of the reaction. Briefly, the monomer exhibited a broad absorption band at 3350-3500 cm −1 , which can be attributed to the stretching vibrations of the hydroxyl group of the O-CH2-CH2-OH segment, two separate bands at 2600-3000 cm −1 , linked to the stretching vibrations of the bound, through hydrogen bonds, carboxylic O-H groups, and a sharp, characteristic band at 1677 cm −1 , owing to the C=O stretching vibration of the carboxylic acid [36]. Concerning the first 2 h of the esterification step, two absorption peaks were apparent in the carbonyl area of the spectrum, representing the acid and the ester bond (at 1684 and 1708 cm −1 ) stretching vibrations, respectively. As the reaction proceeded, the first peak diminished, and the formation of a unique peak at 1720 cm −1 was visible. Furthermore, the decrease of the absorption bands at 3350-3500 cm −1 and 2600-3000 cm −1 proved the successful esterification of the hydroxyl group and carboxylic acid. These observations are in agreement with the reaction progress determined by NMR and titrimetry.

Catalyst Effect on PEV Molecular Weight Increase
Except for the effect of the catalyst type on the esterification step, emphasis was also given to the evaluation of their activity on the polycondensation stage. The IV of the samples was measured in a phenol/1,1,2,2-tetrachloroethane mixture at 25 °C. As shown in Figures 5 and S2, the samples exhibited different intrinsic viscosity values and subsequently various number average molecular weights, owing to the different reactivity of each catalyst. More specifically, PEV/TBT with [η] = 0.27 dL/g, PEV/TIS with [η] = 0.29 dL/g, and PEV/Sb2O3 with [η] = 0.25 dL/g were prepared. Similarly, the presence of a TIS catalyst resulted in a final polymer where Mn = 5014 g/mol, while TBT and Sb2O3 led to polyesters where Mn = 4375 g/mol and Mn = 3886 g/mol, respectively. It is evident that the use of titanium-based based catalysts provided higher IV values, and consequently final products with a higher molecular weight. Furthermore, as the reaction progressed, regardless of the catalyst type used, there was an obvious increase of both the IV and

Catalyst Effect on PEV Molecular Weight Increase
Except for the effect of the catalyst type on the esterification step, emphasis was also given to the evaluation of their activity on the polycondensation stage. The IV of the samples was measured in a phenol/1,1,2,2-tetrachloroethane mixture at 25 • C. As shown in Figure 5 and Figure  It is evident that the use of titanium-based based catalysts provided higher IV values, and consequently final products with a higher molecular weight. Furthermore, as the reaction progressed, regardless of the catalyst type used, there was an obvious increase of both the IV and Mn values. Overall, the two-step melt polycondensation reaction was interrupted at preselected times to retrieve samples from the reacting mixture. Despite the brevity of each sampling, the interruptions may affect the final IV and Mn values of the produced polyesters.  IV measurements were further supported by FTIR analysis. As depicted in Figure S3, in all samples, as the polycondensation proceeded, the band at 3500-3600 cm −1 gradually decreased. This phenomenon can be linked to the reaction between the hydroxyl and carboxyl end groups of i-mers (i = 2,3,4,…,n) towards the formation of polymers; however, the C=O stretching band at 1720 cm −1 appeared to not be strongly influenced during the 4-h duration of this step, supporting that the conversion of the -COOH groups was completed at a high degree during the esterification step.
As thermal transitions and phase changes dominate the processing of polymeric materials and determine the temperature window of this procedure, melting (Tm), cold crystallization (Tcc), and glass transition (Tg) temperatures of the synthesized polyesters during the polycondensation step were measured by DSC. The curves, shown in Figure 6, clearly depict that Tg, Tcc, and Tm gradually shift to higher values, following the increase of the molecular weight with increasing polycondensation time and temperature, as analyzed above. In detail, the sample that was prepared in the presence of TIS catalyst after the esterification step exhibits a Tg value of 73.2 °C, and due to its highly amorphous nature, it exhibits cold crystallization (Tcc) at 106.7 °C, while the formed crystals melt at 253.1 °C. Not surprisingly, by increasing the reaction time and temperature (4 h, 265 °C), Tg, Tcc, and Tm values were observed at higher temperatures. A similar pattern was noticed when the reaction was catalyzed by the other two catalysts (TBT and Sb2O3). Thermal transitions occur at higher temperatures for the polymer prepared in the presence of TIS, where it can thus be concluded that TIS exhibited a higher catalytic activity. The characteristic temperatures of each polymer and at each time interval during the second heating scan are presented in detail in Table 1. IV measurements were further supported by FTIR analysis. As depicted in Figure S3, in all samples, as the polycondensation proceeded, the band at 3500-3600 cm −1 gradually decreased. This phenomenon can be linked to the reaction between the hydroxyl and carboxyl end groups of i-mers (i = 2,3,4, . . . ,n) towards the formation of polymers; however, the C=O stretching band at 1720 cm −1 appeared to not be strongly influenced during the 4-h duration of this step, supporting that the conversion of the -COOH groups was completed at a high degree during the esterification step.
As thermal transitions and phase changes dominate the processing of polymeric materials and determine the temperature window of this procedure, melting (T m ), cold crystallization (T cc ), and glass transition (T g ) temperatures of the synthesized polyesters during the polycondensation step were measured by DSC. The curves, shown in Figure 6, clearly depict that T g, T cc , and T m gradually shift to higher values, following the increase of the molecular weight with increasing polycondensation time and temperature, as analyzed above. In detail, the sample that was prepared in the presence of TIS catalyst after the esterification step exhibits a T g value of 73.2 • C, and due to its highly amorphous nature, it exhibits cold crystallization (T cc ) at 106.7 • C, while the formed crystals melt at 253.1 • C. Not surprisingly, by increasing the reaction time and temperature (4 h, 265 • C), T g , T cc , and T m values were observed at higher temperatures. A similar pattern was noticed when the reaction was catalyzed by the other two catalysts (TBT and Sb 2 O 3 ). Thermal transitions occur at higher temperatures for the polymer prepared in the presence of TIS, where it can thus be concluded that TIS exhibited a higher catalytic activity. The characteristic temperatures of each polymer and at each time interval during the second heating scan are presented in detail in Table 1.

Effect of Catalysts on the Thermal Stability of PEV
The thermal stability of the produced polyesters was evaluated using EGA/MS. As can be observed in Figure 7, the catalyst used appeared to have a small impact on the decomposition temperature peak of the final sample; however, not surprisingly, PEV synthesized with a titanium-based catalyst showed higher thermal stability [29], with a peak (corresponding to the temperature where the largest quantity of degradation products are produced) at 407 • C and 412 • C in the presence of TBT and TIS, respectively, while the Sb 2 O 3 -catalyzed material degraded at 405 • C. These observations support the hypothesis of the superior performance of these catalysts in the synthesis of PEV polyesters.

Effect of Used Catalysts on PEV Coloration
Besides their effect on the molecular weight of the final polyesters, the three catalysts also resulted in differences in the coloration of the materials. As shown in Figure 8, the titanium-based catalysts led to reddish-yellowish products, while the use of Sb 2 O 3 gave a greyish color to the synthesized polymer.
Concerning CIEL*a*b* color system values, in all three polymers, there was a relatively large decrease in lightness (∆L* = 10) after the first hour of the polycondensation reaction, followed by a gradual one as time increased. Furthermore, the a* and b* values (linked to the green-red and blue-yellow axes, respectively) of each sample were also calculated (Figure 9b,c), demonstrating that TBT and TIS offered stronger red-yellow hues to the corresponding materials in comparison with Sb 2 O 3 . Finally, the K/S fraction, which is connected to the concentration of the color on the polyester, was determined ( Figure 9d). As can be seen, samples that were synthesized with the presence of Sb 2 O 3 catalyst possessed higher concentrations of color on their surface.

Effect of Catalysts on the Thermal Stability of PEV
The thermal stability of the produced polyesters was evaluated using EGA/MS. As can be observed in Figure 7, the catalyst used appeared to have a small impact on the decomposition temperature peak of the final sample; however, not surprisingly, PEV synthesized with a titanium-based catalyst showed higher thermal stability [29], with a peak (corresponding to the temperature where the largest quantity of degradation products are produced) at 407 °C and 412 °C in the presence of TBT and TIS, respectively, while the Sb2O3-catalyzed material degraded at 405 °C. These observations support the hypothesis of the superior performance of these catalysts in the synthesis of PEV polyesters.

Effect of Used Catalysts on PEV Coloration
Besides their effect on the molecular weight of the final polyesters, the three catalysts also resulted in differences in the coloration of the materials. As shown in Figure 8, the titanium-based catalysts led to reddish-yellowish products, while the use of Sb2O3 gave a greyish color to the synthesized polymer.

Effect of Used Catalysts on PEV Coloration
Besides their effect on the molecular weight of the final polyesters, the three catalysts also resulted in differences in the coloration of the materials. As shown in Figure 8, the titanium-based catalysts led to reddish-yellowish products, while the use of Sb2O3 gave a greyish color to the synthesized polymer. Concerning CIEL*a*b* color system values, in all three polymers, there was a relatively large decrease in lightness (ΔL* = 10) after the first hour of the polycondensation reaction, followed by a gradual one as time increased. Furthermore, the a* and b* values (linked to the green-red and blue-yellow axes, respectively) of each sample were also  (Figure 9b,c), demonstrating that TBT and TIS offered stronger red-yellow hues to the corresponding materials in comparison with Sb2O3. Finally, the K/S fraction, which is connected to the concentration of the color on the polyester, was determined ( Figure  9d). As can be seen, samples that were synthesized with the presence of Sb2O3 catalyst possessed higher concentrations of color on their surface. Overall, the formation of the colored polycondensation products can be attributed to prolonged heating at a temperature above 240 °C. At these temperatures, a high degree of yellowing can be caused either due to the possible decarboxylation of the starting monomer [34] or due to the potential formation of organic contaminants during the polymerization. Moreover, the grey discoloration of PEV in the case of Sb2O3 catalysts may be attributed to the reduction of Sb +3 to elementary Sb 0 in the presence of carbon oxides. These observations are in agreement with the effect of the aforementioned catalysts on the discoloration of PET and poly(ethylene furan-2,5-dicarboxylate) (PEF). [37][38][39].

Reaction Kinetic Analysis
In general, there are three approaches to model the kinetics of esterification/polycondensation reactions. In order of increasing complexity, they are (i) the simple empirical laws for the rate of decrease of reactant concentration (e.g., in [40]); (ii) the functional Overall, the formation of the colored polycondensation products can be attributed to prolonged heating at a temperature above 240 • C. At these temperatures, a high degree of yellowing can be caused either due to the possible decarboxylation of the starting monomer [34] or due to the potential formation of organic contaminants during the polymerization. Moreover, the grey discoloration of PEV in the case of Sb 2 O 3 catalysts may be attributed to the reduction of Sb +3 to elementary Sb 0 in the presence of carbon oxides. These observations are in agreement with the effect of the aforementioned catalysts on the discoloration of PET and poly(ethylene furan-2,5-dicarboxylate) (PEF). [37][38][39].

Reaction Kinetic Analysis
In general, there are three approaches to model the kinetics of esterification/polycondensation reactions. In order of increasing complexity, they are (i) the simple empirical laws for the rate of decrease of reactant concentration (e.g., in [40]); (ii) the functional group models (e.g., in [41]) which are restricted to the description of the evolution of the active molecular groups (e.g., hydroxyl and carboxyl in the present case); and (iii) detailed molecular species models, which describe in detail all the reaction occurring in the process. The number of unknown kinetic parameters increases from (i) to (iii). The physical meanings of parameters also increase as we move from empirical (i.e., in (i)) to detailed (i.e., in (iii)) models. Here, a combination of approaches (ii) and (iii) will be followed.
The particular problem at hand is linear chain polymerization with a single monomer. Actually, the same reaction occurs in both esterification and transesterification steps. The detailed kinetic model for the evolution of the concentration of the i-mers (molecules consisted of i-primary units) is (i = 1, 2, . . . , N max ) where N max corresponds to the larger i-mer in the system and K i,j is the reaction constant for the reaction between an i-mer and a j-mer. The above equation is used in an approximate way to model the esterification step. The conversion of a functional group is experimentally measured in this step. This conversion corresponds to the loss of monomers from the system (i.e., evolution of variable C 1 ). It can be assumed that during esterification the main mechanism for monomer loss is the reaction between monomers. In reality, some larger molecules are formed, but the concentrations are too low and the reaction rates of monomers with them are negligible. In such a situation, Equation (2) is transformed to the following form: This is a simple second-order reaction (with k = K 1,1 ). This equation is integrated and transformed to give the percentage conversion R as R = 100(1 − 1 1+kC o t ), where C o is the initial concentration of the reactant. To exploit the experimental conversions measured by both techniques employed in the present work their average values are considered. Then, the above expression for R is fitted to the average conversion data. The results of the fittings are presented in Figure 10.
Catalysts 2021, 11, x FOR PEER REVIEW 10 of 17 molecular species models, which describe in detail all the reaction occurring in the process. The number of unknown kinetic parameters increases from (i) to (iii). The physical meanings of parameters also increase as we move from empirical (i.e., in (i)) to detailed (i.e., in (iii)) models. Here, a combination of approaches (ii) and (iii) will be followed.
The particular problem at hand is linear chain polymerization with a single monomer. Actually, the same reaction occurs in both esterification and transesterification steps. The detailed kinetic model for the evolution of the concentration of the i-mers (molecules consisted of i-primary units) is (i = 1,2,…Nmax) where Nmax corresponds to the larger i-mer in the system and Ki,j is the reaction constant for the reaction between an i-mer and a j-mer. The above equation is used in an approximate way to model the esterification step. The conversion of a functional group is experimentally measured in this step. This conversion corresponds to the loss of monomers from the system (i.e., evolution of variable C1). It can be assumed that during esterification the main mechanism for monomer loss is the reaction between monomers. In reality, some larger molecules are formed, but the concentrations are too low and the reaction rates of monomers with them are negligible. In such a situation, Equation (2) is transformed to the following form: This is a simple second-order reaction (with k = K1,1). This equation is integrated and transformed to give the percentage conversion R as = 100(1 − ), where Co is the initial concentration of the reactant. To exploit the experimental conversions measured by both techniques employed in the present work their average values are considered. Then, the above expression for R is fitted to the average conversion data. The results of the fittings are presented in Figure 10. The values found for the single fitting parameter kCo are 0.018, 0.02, 0.0137 min −1 for the catalysts TBT, TIS, and Sb2O3, respectively. Considering that Co is the same for all catalysts, the esterification reaction constant appears to be largest for TIS, followed by TBT, leaving Sb2O3 as the least effective catalyst. The validity of the approximation of the sys- The values found for the single fitting parameter kC o are 0.018, 0.02, 0.0137 min −1 for the catalysts TBT, TIS, and Sb 2 O 3, respectively. Considering that C o is the same for all catalysts, the esterification reaction constant appears to be largest for TIS, followed by TBT, leaving Sb 2 O 3 as the least effective catalyst. The validity of the approximation of the system by Equation (3) is confirmed by assuming the reaction order exponent as a second fitting parameter. The fitting with two parameters led to values of the exponent very close to two. The next step was the examination of the polycondensation reaction. The reactions in the presence of the three catalysts started from different initial conditions (i.e., average molecular weight) as a consequence of the different extents of preceding esterification reactions. To eliminate the effect of initial conditions, the normalized molecular weight M/M o evolution is presented in Figure 11, where M is the average molecular weight in the reaction mixture and M o denotes its value at the beginning of polycondensation step. fitting parameter. The fitting with two parameters led to values of the exponent very close to two. The next step was the examination of the polycondensation reaction. The reactions in the presence of the three catalysts started from different initial conditions (i.e., average molecular weight) as a consequence of the different extents of preceding esterification reactions. To eliminate the effect of initial conditions, the normalized molecular weight M/Mo evolution is presented in Figure 11, where M is the average molecular weight in the reaction mixture and Mo denotes its value at the beginning of polycondensation step. It is very interesting that the evolution curves of M/Mo practically coincided for the three catalysts, implying that the performances of the three catalysts for polycondensation were similar to each other. To model the (unique for all catalysts) polycondensation kinetics, the system (2) of Nmax ordinary differential equations must be numerically integrated. A choice of the kinetic function Ki,j is needed. It is expected that the motion of the polymer chains is inhibited as their molecular weight increases so the choice Ki,j ∝ (i −λ + j −λ ) (where λ is a positive parameter) is a reasonable one. There are no experimental data for the complete molecular weight distribution, but only for its average value so the system is solved approximately using the monodisperse method of moments to give the following simple equation for the evolution of the ratio M/Mo (details of the derivation can be found in [22]): Data fitting (shown in Figure 11) was achieved using the values λ = 2.5 and Ko = 0.037 min −1 (for all the catalysts). The value λ = 2.5 implies a large reduction of reaction rate as the chain length of the reactant increases. This is due to a combination of reduced molecule mobility (i.e., diffusivity) and increased mixture viscosity, as the size of the molecules increases.

Materials
Vanillic acid (VA, purum 99%) was supplied by J & K Scientific (GmbH, Pforzheim, Germany). Sodium iodide (>99%), used in the synthesis of the monomer, was purchased by Acros Organics N.V. (Geel, Belgium). Furthermore, the 2-chloroethanol (>99%), titanium butoxide (Ti(OBu)4), titanium isopropoxide (Ti(iΟPr)4), and antimony trioxide (Sb2O3) (analytic grade) catalysts were provided by Sigma-Aldrich Co (Chemie GmbH, It is very interesting that the evolution curves of M/M o practically coincided for the three catalysts, implying that the performances of the three catalysts for polycondensation were similar to each other. To model the (unique for all catalysts) polycondensation kinetics, the system (2) of N max ordinary differential equations must be numerically integrated. A choice of the kinetic function K i,j is needed. It is expected that the motion of the polymer chains is inhibited as their molecular weight increases so the choice K i,j ∝ (i −λ + j −λ ) (where λ is a positive parameter) is a reasonable one. There are no experimental data for the complete molecular weight distribution, but only for its average value so the system is solved approximately using the monodisperse method of moments to give the following simple equation for the evolution of the ratio M/M o (details of the derivation can be found in [22]): Data fitting (shown in Figure 11) was achieved using the values λ = 2.5 and K o = 0.037 min −1 (for all the catalysts). The value λ = 2.5 implies a large reduction of reaction rate as the chain length of the reactant increases. This is due to a combination of reduced molecule mobility (i.e., diffusivity) and increased mixture viscosity, as the size of the molecules increases.

Synthesis of 4(2-Hydroxyethoxy)-3-Methoxybenzoic Acid
In short, 33.6 g of vanillic acid (0.20 mol) and 12 g of sodium iodide (0.08 mol) were dissolved in an aqueous potassium hydroxide solution (33.75 g (0.6 mol) in 260 mL of water). Then, 17.7 g (0.22 mol) of 2-chloroethanol, dissolved in 520 mL of ethanol, was added dropwise over 4 h at 100 • C, after having been degassed by N 2 bubbling. The reacting mixture was refluxed and 6.0 g of 2-chloroethanol was added approximately every 12 h. After 4 days, the obtained mixture was concentrated using a rotary evaporator, and the residue was diluted in water. The aqueous solution was washed with ether and acidified with aqueous hydrochloric acid solution. The precipitated solid was separated by filtration and purified by two subsequent recrystallizations in ethanol to obtain the product in 64% yield [34].

Synthesis of Poly(Ethylene Vanillate) Polyesters
The synthesis of PEV polyesters was carried out via a two-stage melt polycondensation procedure in a glass batch reactor according to previous studies by our research group [42]. First, 8 g of 4-(2-hydroxyethoxy)-3-methoxybenzoic acid was charged into the reaction tube of the polycondensation apparatus. Then, 500 ppm (0.5 mL) of TBT, TIS, or Sb 2 O 3 was subsequently added in the polycondensation reactor and the apparatus was subsequently evacuated and filled with N 2 three times to remove oxygen. The reacting mixture was heated at 200 • C under N 2 flow (50 mL/min) for 3 h. At 30 min time periods, samples were collected from the reaction mixture for analysis. During the second stage, a vacuum (5.0 Pa) was progressively applied over 20 min and the temperature was gradually increased to 240 • C while the stirring speed was increased from 360 to 750 rpm over an hour. The reacting mixture was heated for 2 h at 240 • C and the temperature was further increased to 255 • C and 265 • C for 1 h each time. Finally, the resulting materials were milled and washed with methanol. Samples after 1, 2, 3, and 4 h of the second step were gathered and characterized using various techniques.

Acid Value Measurements
The carboxyl end group content was defined by titration with a potassium hydroxide methanolic solution (0.1 M) and phenol red as an indicator. For each sample, the titration was repeated in triplicate and the mean value was estimated. The acid value (AV) represents the unreacted acid groups, and it is defined as the milliliters of potassium hydroxide solution required to neutralize one gram of sample. The AV of the resulted polyesters was determined based on Equation (5): where V is the volume of KOH solution consumed (in mL); C is the concentration of the KOH solution (in M); m stands for the mass of the sample (in grams); and 56.11 is potassium hydroxide molar mass (in g/mol).
Furthermore, the conversion of the monomer to polyester was subsequently calculated with the implementation of Equation (6): where AV 0 is the initial AV and AV t is the AV value at each sampling interval.

Intrinsic Viscosity Measurements (IV)
The intrinsic viscosity was measured with an Ubbelohde viscometer (Schott Gerate GMBH, Hofheim, Germany) at 25 • C in a phenol and 1,1,2,2-tetrachloroethane (60/40, w/w) solution. To reach complete dissolution, the sample was heated in the solvent mixture at 70 • C for 20 min. After cooling, the solution was filtered through a disposable Teflon filter, to eliminate possible solid residues. The calculation of the intrinsic viscosity values of the produced polyesters performed applying the Solomon-Cuita equation (Equation (7)) for a single point measurement: where c is the solution concentration, t is the flow time of the solution and t 0 is the flow time of the solvent. The experiment was performed three times and the average value was estimated.

Molecular Weight
Intrinsic viscosity values [η] were used to calculate the number average molecular weight (Mn) of the PEV samples, using the Berkowitz equation (Equation (8)), as it was modified in our previous work [43]:

Fourier-Transformed Infrared Spectroscopy (FTIR)
FTIR spectra of the produced polyesters were obtained by FTIR-2000 (Perkin Elmer, Waltham, MA, USA). A small amount of each sample was triturated with a proper amount of potassium bromide (KBr) and the disks were formed under pressure. All spectra were collected in the range from 4000 to 500 cm−1 using a resolution of 4 cm−1 and 32 co-added scans. The presented spectra were further baseline corrected, normalized, and converted into an absorbance mode.

Differential Scanning Calorimetry (DSC)
Differential scanning calorimetry measurements were performed using a PerkinElmer Pyris Diamond DSC (PerkinElmer Corporation, Waltham MA, USA), updated to the DSC 8500 level, combined with an Intracooler 2P cooling accessory, calibrated with pure indium and zinc standards. Samples of 5 ± 0.1 mg sealed in aluminum pans were applied for assessing the thermal behavior of the produced polymers. All samples were initially heated at 20 • C/min up to 300 • C and held at this temperature for three minutes to erase any previous thermal history. The glass transition (T g ) and cold crystallization (T cc ) temperatures were measured by performing a heating scan of the melt-quenched samples at 20 • C/min.

Color Measurements
Color measurements were performed using a Datacolor Spectraflash SF600 plus CT UV reflectance colorimeter (Datacolor, Marl, Germany) with the implementation of the D65 illuminant, a 10 • standard observer with the UV component excluded and the specular component included. In each case, five measurements were performed using a special holder (Datacolor) and the mean values were calculated. The color values were calculated via the CIE L*a*b* color space system and the modified CIELCH system [44]. In this system, L* represents the lightness (L* = 0, black, L* = 100, white). As depicted in Figure 12, the a* value corresponds to the green-red axis, where negative a* values indicate green and positive a*values indicate red hues. The b* value represents the blue-yellow axis, where negative b* values indicate blue and positive b* values indicate yellow hues. holder (Datacolor) and the mean values were calculated. The color values were calculated via the CIE L*a*b* color space system and the modified CIELCH system [44]. In this system, L* represents the lightness (L* = 0, black, L* = 100, white). As depicted in Figure 12, the a* value corresponds to the green-red axis, where negative a* values indicate green and positive a*values indicate red hues. The b* value represents the blue-yellow axis, where negative b* values indicate blue and positive b* values indicate yellow hues. Furthermore, the fraction R/S, linked to the concentration of the color on the polyester, was determined following Equation (5): where K is the absorbance coefficient, S stands for the scattering coefficient, and R is the percent reflectance of each sample.

Evolved Gas Analysis Mass Spectroscopy (EGA/MS)
For the performance of the Py-GC/MS analysis of the resulting polyesters, a very small quantity of the material has been set primarily into the "Double-Shot" EGA/PY-3030D Pyrolyzer (Frontier Laboratories Ltd., Fukushima Japan) with a CGS-1050Ex (Kyoto, Japan) carrier gas selector. For evolved gas analysis (EGA), the furnace temperature was programmed from 100 °C to 600 °C with a heating rate of 20 °C/min, using He as the purge gas and air as the cooling gas. The GC oven temperature was set at 300 °C for 25 min. The pyrolyzates were separated using the temperature programmed capillary column of a Shimadzu QP-2010 Ultra Plus (Shimadzu, Kioto, Japan) gas chromatograph and were analyzed by the mass spectrometer MS-QP2010SE of Shimadzu (Shimadzu, Kioto, Japan) at 70 eV. For the mass spectrometer, the following conditions were used: ion source heater at 200 °C, interface temperature at 320 °C, vacuum of 10−4-100 Pa, m/z range of 45-500 amu, and scan speed of 10,000 u/s.

Conclusions
Within this study, the efficiency of three different metal-based catalysts (TBT, TIS, and Sb2O3) during two-step melt polycondensation of PEV was examined for the first time. The evolution of the esterification step was investigated using various techniques, such as NMR, end group analysis, and FTIR. Based on the acquired results, titaniumbased catalysts seem to exhibit higher catalytic activity. In the second stage of the reaction, Furthermore, the fraction R/S, linked to the concentration of the color on the polyester, was determined following Equation (5): where K is the absorbance coefficient, S stands for the scattering coefficient, and R is the percent reflectance of each sample.

Evolved Gas Analysis Mass Spectroscopy (EGA/MS)
For the performance of the Py-GC/MS analysis of the resulting polyesters, a very small quantity of the material has been set primarily into the "Double-Shot" EGA/PY-3030D Pyrolyzer (Frontier Laboratories Ltd., Fukushima Japan) with a CGS-1050Ex (Kyoto, Japan) carrier gas selector. For evolved gas analysis (EGA), the furnace temperature was programmed from 100 • C to 600 • C with a heating rate of 20 • C/min, using He as the purge gas and air as the cooling gas. The GC oven temperature was set at 300 • C for 25 min. The pyrolyzates were separated using the temperature programmed capillary column of a Shimadzu QP-2010 Ultra Plus (Shimadzu, Kioto, Japan) gas chromatograph and were analyzed by the mass spectrometer MS-QP2010SE of Shimadzu (Shimadzu, Kioto, Japan) at 70 eV. For the mass spectrometer, the following conditions were used: ion source heater at 200 • C, interface temperature at 320 • C, vacuum of 10−4-100 Pa, m/z range of 45-500 amu, and scan speed of 10,000 u/s.

Conclusions
Within this study, the efficiency of three different metal-based catalysts (TBT, TIS, and Sb 2 O 3 ) during two-step melt polycondensation of PEV was examined for the first time. The evolution of the esterification step was investigated using various techniques, such as NMR, end group analysis, and FTIR. Based on the acquired results, titanium-based catalysts seem to exhibit higher catalytic activity. In the second stage of the reaction, the efficiency of the used catalysts followed the same pattern, resulting in polyesters with higher molecular weights and subsequently superior thermal transitions (higher T g , T cc , and T m values), as well as elevated thermal stability. Since coloration in materials plays an important role toward their future applications, color measurements were also performed, proving that the reaction time and temperature strongly affect the discoloration of the final materials, resulting in reddish-yellowish products in the case of titanium-based catalysts and a greyish polymer when in the presence of Sb 2 O 3 . Finally, theoretical kinetic studies were carried out and rate constants for the reactions that took place in each step were calculated, indicating that TIS possesses superior catalytic activity during the esterification stage, while all three catalysts exhibited similar behavior during the polycondensation process.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/catal11070822/s1. Figure S1: 1H NMR spectra of the crude reaction mixture of the esterification performed at 200 • C, in the presence of TIS. Table S1: Conversions obtained/observed in the presence of TBT, TIS and Sb2O3 catalysts. Figure S2: Evaluation of number average molecular weight at different time intervals during the polycondensation step. Figure