Rapid and Efficient Optimization of Poly(1,2-Ethanediol Citrate) Synthesis Based on Magic Squares’ Various Methods

New biomaterials among aliphatic polyesters are in demand due to their potential applications in tissue engineering. There is a challenge not only to design scaffolds to regenerate defects in load-bearing tissues but also to ensure a proper blood supply to the reconstructed tissues. Poly-(1,2-ethanediol citrate) is one of the novel citrate-based polymers that could have the desired properties for cell scaffold fabrication and for enhancing cell adhesion. Both citric acid and 1,2-ethanediol are used in medicine and are fully resorbable by cells. This work aimed to synthesize poly(1,2-ethanediol citrate) in a catalyzed reaction with water removed by the Dean–Stark apparatus. The polyester structure was characterized by FTIR and NMR spectroscopy, and the HMBC experiment was performed to support the theory of successful polymer synthesis. The molecular weight was determined for the products obtained at 140 °C. The process was described via non-linear mathematical models. The influence of temperature and catalyst content on the degree of esterification and the conversion of acid groups in citric acid is described. The optimal process parameters are determined at 140 °C and 3.6% of p-toluenesulfonic acid content. The presented results are the starting point for scaffold design and scaling-up the process.


Introduction
In bioengineering, selecting suitable materials for a specific application is the key to success. Aliphatic polyesters possess desirable properties for biomedical applications, such as biocompatibility, biodegradability, and non-toxic degradation products [1]. Different polyesters have also received attention due to the reversibility of the esterification reaction in which they are obtained [2].
Nowadays, polylactide (PLA) is considered to be a valuable biodegradable polyester [3]. Its potential applications include bone grafting [4,5], ureteral stents [6] and controlled delivery carriers [7,8]. Nevertheless, PLA in biomedical applications may have limitations, such as poor hydrophilicity and slow degradation kinetics [9]. A relatively new and attractive polymer material is poly(glycerol sebacate) (PGS) which can interact with living cells [10]. The synthesis conditions determine its unique mechanical properties, opening up a wide range of possibilities for potential uses in soft tissues reconstruction [11,12]. PGS could be used to rebuild the myocardium and blood vessels [13,14] and eardrum [15] or act as a surgical sealer [16].
Despite numerous pieces of research showing the potential applications of PGS and PLA scaffolds for the regeneration of defects in load-bearing tissues, such as bones or cartilage, there is still concern about improving cell adhesion and growth. Modifying the process conditions, i.e., the ratio of glycerol and sebacic acid in PGS synthesis makes the material more hydrophilic; hence, the polymer shows better cell adhesion [17]. However, the change in substrates ratio also affects other properties such as the degradation time and mechanical strength, which is not desirable in scaffold fabrication [18,19]. further post-polymerization processes. We decided to maximize the degree of esterification to obtain polyesters with a high molecular mass. The influence of temperature and catalyst content on the properties of the obtained polymers was checked. The products were identified with spectral analysis and described with mathematical models.

Spectral Analysis of Synthesis Products
Fourier transform infrared spectroscopy (FTIR) and 13 C-NOE nuclear magnetic resonance ( 13 C-NOE NMR) directly characterized the structures of the synthesized polymers. This paper adopted the following terminology to simplify the record and avoid misunderstandings. For the structure of citric acid and its derivatives, the carbonyl group bound to the α-carbon is referred to as α-C(O)O-H/R, and the carbonyl group bound to the β-carbon is referred to as β-C(O)O-H/R (Scheme 1). Gels 2023, 9, x FOR PEER REVIEW 3 of 17 into using the obtained polyester to produce cell scaffolds will assess how the type of polyols used affects the cytotoxicity of the material. The increasing interest in citrate-based polymers was the reason for investigating the catalyzed polycondensation of citric acid and 1,2-ethanediol. The work aimed to determine the optimal conditions in the synthesis of poly(1,2-ethanediol citrate) pre-polymer for further post-polymerization processes. We decided to maximize the degree of esterification to obtain polyesters with a high molecular mass. The influence of temperature and catalyst content on the properties of the obtained polymers was checked. The products were identified with spectral analysis and described with mathematical models.

Spectral Analysis of Synthesis Products
Fourier transform infrared spectroscopy (FTIR) and 13 C-NOE nuclear magnetic resonance ( 13 C-NOE NMR) directly characterized the structures of the synthesized polymers. This paper adopted the following terminology to simplify the record and avoid misunderstandings. For the structure of citric acid and its derivatives, the carbonyl group bound to the α-carbon is referred to as α-C(O)O-H/R, and the carbonyl group bound to the β-c Scheme 1. Synthesis of poly(1,2-ethanediol citrate).
Analysis of the characteristic bands on the FTIR spectrum shows that polyesters were obtained in the process. The formation of compounds with the polyesters' structure was confirmed by comparison of the characteristic bands for poly(1,2-ethanediol citrate) with spectra of the substrates. (Figure 1). The obtained spectrum shows: Analysis of the characteristic bands on the FTIR spectrum shows that polyesters were obtained in the process. The formation of compounds with the polyesters' structure was confirmed by comparison of the characteristic bands for poly(1,2-ethanediol citrate) with spectra of the substrates. (Figure 1). The obtained spectrum shows: (K) is observed; • A broad band corresponding to the deformation vibrations of the hydroxyl g related to hydrogen bonding in 1,2-ethanediol in the range 800-550 cm −1 (G); • A band around 1080 cm −1 (L) derived from C-O stretching vibrations in the O group.
The absence or distortion of many of the bands on the poly(1,2-ethanediol c spectrum present in the case of citric acid and 1,2-ethanediol indicates that the subs have reacted and a polyester-structured compound has been formed. In particular, supported by the changes within the bands in the range 3500-3000 cm −1 of hyd groups. This change is due to the formation of ester bonds. Additionally, the charact bands for carbonyl groups in the esters appear to be about 1700 cm −1, and the band the C-O stretching vibrations in the C-C(O)-O group is shifted towards lower range discussed relationships confirm the positive synthesis of a compound with a pol structure.  The absence or distortion of many of the bands on the poly(1,2-ethanediol citrate) spectrum present in the case of citric acid and 1,2-ethanediol indicates that the substrates have reacted and a polyester-structured compound has been formed. In particular, this is supported by the changes within the bands in the range 3500-3000 cm −1 of hydroxyl groups. This change is due to the formation of ester bonds. Additionally, the characteristic bands for carbonyl groups in the esters appear to be about 1700 cm −1, and the band from the C-O stretching vibrations in the C-C(O)-O group is shifted towards lower ranges. The discussed relationships confirm the positive synthesis of a compound with a polyester structure.
The polyester formation may be affirmed in detail based on the characteristic range of carbonyl carbons in the 13 C-NOE NMR. As shown in Figure 2  acid [31]. The carbonyl carbons of carboxylic acid derivatives, e.g., esters, are strongly deshielded (165-180 ppm) due to the close presence of highly electronegative oxygen. Based on the differences in the values of the chemical shifts of the signals of the α-C(O)O-H and β-C(O)O-H carbon atoms for pure citric acid and synthesized product, complete conversion of citric acid molecules was confirmed. The signals from the carboxylic groups were derived from incompletely converted acid groups in the polymer chain. Additionally, the characteristic peaks in the range δ125-δ130 ppm were noticed for some polyester samples synthesized with a catalyst content exceeding 1% of the citric acid mass content (Figure 3). The discussed relationship was also apparent in the slightly yellow color of these samples. In conclusion, the increase in the catalyst content apparently promotes dehydration. Additionally, the characteristic peaks in the range δ125-δ130 ppm were noticed for some polyester samples synthesized with a catalyst content exceeding 1% of the citric acid mass content ( Figure 3). The discussed relationship was also apparent in the slightly yellow color of these samples. In conclusion, the increase in the catalyst content apparently promotes dehydration. The heteronuclear multiple bond coherence (HMBC) experiment (Figure 4), which gives correlations between 1 H and 13 C nuclei separated by several bonds, shows the interconnection of the protons of the methylene groups in acid-derived ester fragments (signal

Optimization of the Synthesis Conditions
This paper used an optimization technique based on the magic square plan to investigate the effect of optimized parameters on pre-polymer molecular weight. The synthesis of poly(1,2-ethanediol citrate) was optimized with the design of experimental (DOE) methods. Conducting a limited number of experiments enabled a reliable synthesis model to be obtained. The mathematical models describing the change in the ester degree (ED) and conversion of α-C(O)O-H (Xα NMR ) and β-C(O)O-H (Xβ NMR ) acid groups were used to find the optimal conditions for the synthesis process. The input variables were the reaction temperature and the catalyst content, depending on the mass of the citric acid used in the polycondensation. The discussed process is presented as a "black box" in Figure 5. On the basis of preliminary research, the process variables and their values were determined. The most favorable is polymerization while maintaining an equimolar ratio of the moieties. However, the negligible availability of the hydroxyl group (spatial hindrances) in citric acid was not considered when determining the molar ratio. Due to the process' limitations, upper and lower limits were established for the other synthesis pa-

Optimization of the Synthesis Conditions
This paper used an optimization technique based on the magic square plan to investigate the effect of optimized parameters on pre-polymer molecular weight. The synthesis of poly(1,2-ethanediol citrate) was optimized with the design of experimental (DOE) methods. Conducting a limited number of experiments enabled a reliable synthesis model to be obtained. The mathematical models describing the change in the ester degree (ED) and conversion of α-C(O)O-H (X α NMR ) and β-C(O)O-H (X β NMR ) acid groups were used to find the optimal conditions for the synthesis process. The input variables were the reaction temperature and the catalyst content, depending on the mass of the citric acid used in the polycondensation. The discussed process is presented as a "black box" in Figure 5.

Optimization of the Synthesis Conditions
This paper used an optimization technique based on the magic square plan to investigate the effect of optimized parameters on pre-polymer molecular weight. The synthesis of poly(1,2-ethanediol citrate) was optimized with the design of experimental (DOE) methods. Conducting a limited number of experiments enabled a reliable synthesis model to be obtained. The mathematical models describing the change in the ester degree (ED) and conversion of α-C(O)O-H (Xα NMR ) and β-C(O)O-H (Xβ NMR ) acid groups were used to find the optimal conditions for the synthesis process. The input variables were the reaction temperature and the catalyst content, depending on the mass of the citric acid used in the polycondensation. The discussed process is presented as a "black box" in Figure 5. On the basis of preliminary research, the process variables and their values were determined. The most favorable is polymerization while maintaining an equimolar ratio of the moieties. However, the negligible availability of the hydroxyl group (spatial hindrances) in citric acid was not considered when determining the molar ratio. Due to the process' limitations, upper and lower limits were established for the other synthesis parameters. The thermal decomposition of citric acid determines the upper limit at 175 °C. As for the temperature, the reaction should not have proceeded under 100 °C because water is removed from the process. In the most extreme case, the polycondensation could be solvent-free, complying with the principles of green chemistry. On the basis of preliminary research, the process variables and their values were determined. The most favorable is polymerization while maintaining an equimolar ratio of the moieties. However, the negligible availability of the hydroxyl group (spatial hindrances) Gels 2023, 9, 30 7 of 15 in citric acid was not considered when determining the molar ratio. Due to the process' limitations, upper and lower limits were established for the other synthesis parameters. The thermal decomposition of citric acid determines the upper limit at 175 • C. As for the temperature, the reaction should not have proceeded under 100 • C because water is removed from the process. In the most extreme case, the polycondensation could be solvent-free, complying with the principles of green chemistry.
On the other hand, the more catalyst, the greater risk of side reactions, including dehydration. In this paper, the following input variables were adopted for optimization: citric acid/ethylene glycol 2:3 (molar ratio of COOH/OH 1:1), temperature: 120-140 • C, and the catalyst content 0-5%. The reaction time was established as 60 min, including 10 min of reaching the set temperature.
The performance properties of the obtained products varied depending on the reaction parameters. There were visible differences in the viscosity and the color of the samples, from colorless semi-liquids to light yellow resins. Brief descriptive characteristics of the materials are outlined in Table 1. The GPC analysis was initially performed for products obtained at 140 • C. According to the authors' knowledge, it was assumed that in the experiment area, the polymer molecular weight would be the highest for the maximum temperature. The results of the polyester molecular weight are presented in Table 2. Surprisingly low molecular weight results may arise from obtaining poly(1,2-ethanediol citrate) as oligomers. The synthesis ought to result in a polymer characterized by a high molecular weight. Despite that assumption, the synthesis of oligomers is not considered a significant drawback due to the further cross-linking step.
Another explanation of this phenomenon is the imprecision of the GPC method and linear PEG standards, which are unsuitable for testing branched structures such as poly(1,2ethanediol citrate).
The discussed problem was also presented in the studies on synthesizing glycerol and citric acid [31]. Taking into consideration the questionable outcome of the polymer molecular weight and the irrelevance of these results for further work, it was decided for Gels 2023, 9, 30 8 of 15 them not to be included in the optimization. The mathematical model for molecular weight is not presented in this paper.
The mathematical models describing temperature dependence and the catalyst content, built on the experimental data, were determined using StatSoft Statistica. In all instances, the quadratic equations with the factor of synergism of variables were obtained. The experiments were planned on a square plan to simplify the statistical analysis and eliminate the row and column variation of the experimental results ( Figure 6). The design of experiments included nine coded experiments on the sides of the square and one following corresponding to a non-catalyzed reaction. To dispel doubts about the fitting of the model in the original square plan, two additional experiments were performed in the central part of the plan (Table 3-N o 8-9). The input variables were presented in a codded manner to correctly determine their impact on the process (Table 4).  (Table 3-N o 8-9). The input variables were presented in a codded manner to correctly determine their impact on the process (Table 4).     The following equations were obtained: The variability of the process depending on the temperature and catalyst content is visualized as response surfaces (Figures 7-9).  The variability of the process depending on the temperature and catalyst content is visualized as response surfaces (Figures 7-9).      The residual coefficients of variation and determination determine the quality of the model fit to the experimental values ( Table 5). As the residual variation tends to zero, the best fit is in the conversion model of the β-C(O)O-H acid group (X β NMR ). The high value of the coefficient of determination also confirms it. The compliance of all of the presented mathematical models is sufficient to recognize their usefulness in scaling-up the process. Both the presented equations and the response surfaces are designated for standardized (coded) input variables and require translation into the values of normed variables in the experimental area. Operating normalized dimensionless variables allows us to directly evaluate the effect of given parameters based on appropriate coefficients. For all equations, the most influential is the constant term, which suggests the occurrence of other important variables influencing the process, not included in this optimization.
The presented response surfaces allow several conclusions to be drawn about the course of the process. The temperature has a much more significant effect on the conversion of α-C(O)O-H groups than β-C(O)O-H. This may indicate that as the process temperature increases, the selectivity of the attack of the hydroxyl group of the diol on the carboxyl group decreases. The steric hindrance then becomes less significant. It is also associated with a greater risk of gelling of the reaction mixture, for which esterification of the α- Increasing the temperature for a given reaction time increases the conversion ratio.
Nevertheless, introducing the catalyst into the process may obtain the same product using a lower temperature. The product obtained in a non-catalyzed reaction at 140 • C should have the same performance properties as that obtained at 120 • C with a 0.5% catalyst. On the other hand, it should be pointed out that the increase in catalyst content affects the color of the polymer.
An increase in the catalyst content above around 3.5% results in a progressive decrease in ED. The most probable cause of this phenomenon is a catalyst promoting acidic dehydration. Due to the process's complexity, the conversion ratio increase is observed only in the specified range of variability of input variables.
Moreover, by analyzing Table 2  This work aimed to find the optimal parameters of the process. The main optimization criterion was the ED's maximization, not the total conversion of X NMR . Although both parameters refer to the same phenomenon, the error in NMR analysis is more significant.
The following optimal process parameters were designated: 140 • C and 3.6% catalyst content. The synthesis performed under the optimal conditions confirmed the model's good fit-the values predicted with the mathematical model do not differ significantly from real ones ( Table 2-N o 14). It is worth noting that the obtained polymer was slightly yellow.
In scaling-up the process, it should be taken into account that reducing the temperature and catalyst content compared to the optimal determined values might be favorable for obtaining the linear structure of the polymer. An increase in the degree of branching of the polymer above the critical value may result in the gelling effect, which is particularly undesirable in the technological process. More detailed research in this area should be completed. Nevertheless, the presented mathematical models can be considered helpful in scaling-up the synthesis of poly(1,2-ethanediol citrate) and will be further investigated for biomedical applications.

Fourier Transform Infrared Spectroscopy (FTIR)
A Bruker FTIR ALPHA II spectrometer was used to obtain Fourier transform infrared (FTIR) spectra at room temperature. The method performed thirty-two scans in the range of 400-4000 cm −1 each time.

Nuclear Magnetic Resonance (NMR)
An Agilent 400 MHz NMR spectrometer was used to record the spectra. The samples were prepared by dissolving about 150 mg of poly(1,2-ethanediol citrate) in 1 mL of acetone for 24 h. MestReNova NMR software was used for data processing. The following formulas were applied for calculations of the degree of conversion of the carboxyl groups of citric acid: where:

Gel Permeation Chromatography (GPC)
The molecular weight of poly(1,2-ethanediol citrate) was determined with the HPLC easy mate 3000 apparatus (pre-column and two Tosoh Bioscience columns cat. 17368 and 17355) equipped with a Shodex RI-101 refractive index detector with a flow ratio of 0.8 mL/min at 30 • C. About 60 mg of each sample was weighed into a 10 mL heart flask, and 5 mL of THF was added. The samples were dissolved for 24 h at 30 • C. The solutions were filtered using 45 µm syringe filters. Curve calibration was performed using PEG standards (Easy Vials, Agilent).

Acid Number
About 1-1,5 g of the sample was weighed and dissolved in 25 mL of methanol. Four drops of indicator-thymol blue-for each trial were added. The samples were titrated with 1 M NaOH (aq) until the change in color from yellow to blue was observed. The result is a mean of two/three determinations for each sample of poly(1,2-ethanediol citrate). A blank test was performed under the same conditions. The acid number (AN) was calculated by using the following equation: where: V-the volume of 1 M NaOH aqueous solution consumed in the actual test; V o -the volume of 1 M NaOH aqueous solution consumed in the blank test; M NaOH -the titer of solution used for titration (1 M); m-the sample weight.

Ester Number
About 1-1,5 g of the sample was weighed and dissolved in a solution of 15 mL of methanol and 20 mL of 1 M aqueous NaOH. Then, the solutions were refluxed for 1 h at a temperature of around 150 • C. The solutions were left to cool, and then four drops of phenolphthalein indicator were added for each trial. The samples were titrated with 1 M HCl (aq) until discoloration of the pink solution. A blank test was performed under the same conditions. The result is a mean of two/three determinations for each sample of The ester degree (ED) was calculated by using the following equation: where: EN-ester number: AN-acid number.

Synthesis Procedure
Poly(1,2-ethanediol citrate) was synthesized in the MultiMax Mettler Toledo reactor systems, in Hastelloy reactors (50 mL) equipped with a mechanical stirrer, a temperature sensor, and Dean-Stark apparatus. The anhydrous citric acid (28.83 g; 0.15 mol), ethanediol (13.97 g; 0.225 mol), and p-toluenesulfonic acid monohydrate (0-1.4415 g; 0-0.0076 mol) were weighed into the reactor. Initially, the reaction mixture was heated to the set point temperature (120-140 • C) for 10 min. Once the set temperature had been reached, the set point temperature was held constant for 50 min, and a Dean-Stark apparatus was used for water removal.
StatSoft Statistica software was used for graphics and calculations preparation.

Conclusions
The polycondensation of citric acid with 1,2-ethanediol was investigated and described with mathematical models, which allow the prediction of product properties depending on the temperature and catalyst content. Polyester formation was confirmed with detailed spectral analysis, including FTIR and NMR correlations.
The matrix equations determined the optimal process parameters at 140 • C and 3.6% of p-toluenesulfonic acid content. The high temperature favored the maximization of the esterification degree. Nevertheless, introducing a catalyst into the process lowers the temperature needed for obtaining the product with comparable performance properties. Although non-catalyzed reactions are safer for biomedical applications, adding the catalyst reduces energy consumption, and hence, the economy of the process is more favorable.
Regenerative medicine requires using multifunctional materials covering a wide range of mechanical properties. Poly(1,2-ethanediol citrate) meets these requirements. What is more, considering its potential for functionalization, scientist should consider poly(1,2ethanediol citrate) as a potential drug delivery carrier of interest. Finally, considering the growing interest in aliphatic polyesters for scaffold design, polyesters of citric acid will undoubtedly attract attention.