Transesterification of Lactic Acid Oligomers with Ethanol, a Way to Anhydrous Ethyl Lactate: A Kinetic Study

A new method for the preparation of anhydrous ethyl ester of lactic acid was studied. The selected method is based on catalytic transesterification of lactic acid oligomers, which were prepared for this purpose by autocatalytic oligomerization of lactic acid. In this work, a kinetic model for the case of catalytic alcoholysis of oligoesters was derived assuming a first-order reaction and equimolar content of reactants in the reaction mixture. The model makes it possible to obtain the values of the reaction rate and equilibrium constants and the equilibrium alcohol concentration by regression analysis at one time. The model was verified by measuring the rate of consumption of ethanol over the time at various reaction temperatures with anhydrous FeCl3 as the catalyst. The reaction was studied at overpressure under autogenous conditions in the temperature range of 100–180 °C. For the catalyst concentration of 1 mol %, the activation energy value was 64.35 kJ·mol−1. The dependence of equilibrium composition and rate constant on the temperature was obtained. The derived model is generally applicable to all first-order equilibrium reactions. The presumption is that the forward and reverse reactions are of the same order and have the same stoichiometry and equivalent amounts of reactants at the beginning of the reaction.


Introduction
Esters of lactic acid are an important group of derivates with increasing use as bio-solvents. The reason for this is that the use of these esters has a small environmental impact owing to their partial or complete renewability of feedstock, miscibility with water and organic phase, and their great dissolving power [1]. Ethyl lactate finds use as a solvent in organic synthesis, enzymatic reactions, and as an extraction agent in pharmacology [2][3][4]. Large-volume applications can be found in the consumer and industrial sectors. It may be used as a green solvent in painting systems, printing inks, and graffiti removers [1,5]. Ethyl lactate is a powerful nonvolatile degreasing agent [6]. It can be used as an ecological extraction agent for soil decontamination and in the electrotechnical industry to remove fluxes after soldering of printed circuit boards [7,8]. A potential new use may be found in polymer chemistry for low and high molecular weight lactic acid polymers via transesterification synthesis [9]. The most promising lactic acid ester in terms of no toxicity and a fully renewable raw material base is ethyl lactate. Its wider application as a bio-solvent is still hindered due to difficult production and the resulting higher price compared to classic solvents [10]. The preparation of ethyl lactate is complicated by the auto-oligomerization of lactic acid and the esters themselves.

Derivation of the Kinetic Model
Obtained concentration vs. time data points during the alcoholysis at different reaction temperatures serve to verify the correctness of the proposed kinetic model derived for the case of alcoholysis in a homogeneous reaction medium with homogeneous catalysis. The model is derived for an equimolar ratio of reactants. In this case, the course of the reaction already significantly influences the equilibrium character of alcoholysis (transesterification). The model was designed to find a simple method for the determination of rate constant, equilibrium constant, and equilibrium composition. As previously proven, the catalytic alcoholysis of polyesters follows first-order kinetics [28]. The model assumes the same reaction order for the reverse reaction. Because of a large number of alcoholysis oligomer products (the ester and its oligomers), the kinetic model was derived for the rate of ethanol consumption. From the viewpoint of ethanol consumption, the process is unambiguous and can be understood in more general terms as the reaction of alcohol with ester bonds. The influence of oligomer end groups on the reaction rate and equilibrium composition (water released by esterification

List of Symbols
= initial alcohol concentration, = alcohol concentration at equilibrium, = alcohol concentration at time t, = rate constant of forward reaction (alcohol consumption), = rate constant of reverse reaction (alcohol regeneration), = rate of forward reaction (alcohol consumption), = rate of reverse reaction (alcohol regeneration), = overall rate constant, = overall reaction rate, = equilibrium constant, T = thermodynamic temperature, R = universal gas constant The overall reaction rate is: At equilibrium, it is: The substitution in Equation (1) with (Equation (2)) for the equilibrium state: The expression of the rate constant of the reverse reaction of Equation (3) and the substitution in Equation (1) for the total rate: By the rearrangement of Equation (4): The differentiation of Equation (5): The separation of variables in Equation (6): The integration of Equation (7) for = 0 → = ; = ∞ → = Equation (8) for boundary conditions the following equation: The equilibrium constant equals:

List of Symbols
x 0 = initial alcohol concentration, x e = alcohol concentration at equilibrium, x = alcohol concentration at time t, → k = rate constant of forward reaction (alcohol consumption), ← k = rate constant of reverse reaction (alcohol regeneration), → r = rate of forward reaction (alcohol consumption), ← r = rate of reverse reaction (alcohol regeneration), ↔ k = overall rate constant, ↔ r = overall reaction rate, K = equilibrium constant, T = thermodynamic temperature, R = universal gas constant The overall reaction rate is: At equilibrium, it is: The substitution in Equation (1) with (Equation (2)) for the equilibrium state: The expression of the rate constant of the reverse reaction ← k of Equation (3) and the substitution in Equation (1) for the total rate: By the rearrangement of Equation (4): The differentiation of Equation (5): The separation of variables in Equation (6): The integration of Equation (7) for The equilibrium constant equals: Substituting Equation (10) into Equation (9): By the rearrangement of Equation (11) into the common linear equation y = a·t + b: Only the value of the total velocity constant of the equilibrium reaction is experimentally accessible. The value is the sum of the forward and reverse rate constants where the former represents the member of Equation (12): Substituting Equation (13), one obtains the equation for the total rate of the first-order equilibrium reaction. By expressing this equation in a linearized form, we obtain a linear equation where the slope is the total speed constant ↔ k and the member (lnK) is the intercept of this equation: By the exponentiation and rearrangement, we get the final relation for the concentration of reactant x at time t, including the equilibrium reaction constant K, the total velocity constant ↔ k , and the content of reactant in the equilibrium x e :

Lactic Acid Oligomerization
The autocatalytic oligomerization of lactic acid was carried out according to Figure 2 under the conditions shown in Figure 3. The autocatalytic condensation of lactic acid allows virtually linear growth of the molecular weight to a degree of condensation of PD ≈ 11, (M n = 758 g·mol −1 ). The condensation rate is initially limited by the rate of condensate (water) removal and is thus mainly dependent on the temperature and pressure during the condensation. The conclusions on the oligomerization process cannot be generalized because they are mainly dependent on the experimental conditions. conditions shown in Figure 3. The autocatalytic condensation of lactic acid allows virtually linear growth of the molecular weight to a degree of condensation of PD ≈ 11, (M = 758 g·mol −1 ). The condensation rate is initially limited by the rate of condensate (water) removal and is thus mainly dependent on the temperature and pressure during the condensation. The conclusions on the oligomerization process cannot be generalized because they are mainly dependent on the experimental conditions.  The amount of water removed during the oligomerization is equal to the sum of the water contained in the crude lactic acid-water solution and the water produced by the condensation of lactate units. The total relative reduction of the water content (RW) in the reaction medium as compared to direct esterification of lactic acid water solution with ethanol is expressed in Equation (16).
where M = water molecular weight, M = lactic acid molecular weight, = lactic acid mass fraction in its water solution.
For the 80% lactic acid solution used and the polymerization degree of oligomer PD = 10.25, the water content of the system is reduced by RW = 95.67%. Compared to direct esterification carried out according to Figure 4, it is clear that water in the system, as one of the esterification products, directly affects the equilibrium composition of the mixture and, therefore, negatively affects the yield of ethyl lactate. Oligomeric ethyl esters and lactic acid oligomers are also produced in the real system. Oligomers together with water complicate the separation of pure ethyl lactate. Ethyl lactate forms an inseparable azeotrope with water resulting in product loss. In the case of direct esterification of 80% lactic acid with ethanol, this loss is theoretically equal to 14.7% of the product. The main purpose of LA condensation was to limit the amount of water in the system. The mass fraction of residual "free" water in the oligomer product was also monitored with respect to the degree of polymerization. This free water directly affects the rate and achievable degree of condensation. At the higher polycondensation degree, the residual free water can no longer be removed by distillation due to a quick increase in viscosity. Complete removal of free water The amount of water removed during the oligomerization is equal to the sum of the water contained in the crude lactic acid-water solution and the water produced by the condensation of lactate units. The total relative reduction of the water content (RW) in the reaction medium as compared to direct esterification of lactic acid water solution with ethanol is expressed in Equation (16).
where M H 2 O = water molecular weight, M LA = lactic acid molecular weight, x LA = lactic acid mass fraction in its water solution.
For the 80% lactic acid solution used and the polymerization degree of oligomer PD = 10.25, the water content of the system is reduced by RW = 95.67%. Compared to direct esterification carried out according to Figure 4, it is clear that water in the system, as one of the esterification products, directly affects the equilibrium composition of the mixture and, therefore, negatively affects the yield of ethyl lactate. Oligomeric ethyl esters and lactic acid oligomers are also produced in the real system. Oligomers together with water complicate the separation of pure ethyl lactate. Ethyl lactate forms an inseparable azeotrope with water resulting in product loss. In the case of direct esterification of 80% lactic acid with ethanol, this loss is theoretically equal to 14.7% of the product. The amount of water removed during the oligomerization is equal to the sum of the water contained in the crude lactic acid-water solution and the water produced by the condensation of lactate units. The total relative reduction of the water content (RW) in the reaction medium as compared to direct esterification of lactic acid water solution with ethanol is expressed in Equation (16).
where M = water molecular weight, M = lactic acid molecular weight, = lactic acid mass fraction in its water solution.
For the 80% lactic acid solution used and the polymerization degree of oligomer PD = 10.25, the water content of the system is reduced by RW = 95.67%. Compared to direct esterification carried out according to Figure 4, it is clear that water in the system, as one of the esterification products, directly affects the equilibrium composition of the mixture and, therefore, negatively affects the yield of ethyl lactate. Oligomeric ethyl esters and lactic acid oligomers are also produced in the real system. Oligomers together with water complicate the separation of pure ethyl lactate. Ethyl lactate forms an inseparable azeotrope with water resulting in product loss. In the case of direct esterification of 80% lactic acid with ethanol, this loss is theoretically equal to 14.7% of the product. The main purpose of LA condensation was to limit the amount of water in the system. The mass fraction of residual "free" water in the oligomer product was also monitored with respect to the degree of polymerization. This free water directly affects the rate and achievable degree of condensation. At the higher polycondensation degree, the residual free water can no longer be removed by distillation due to a quick increase in viscosity. Complete removal of free water represents a technical barrier for the realization of direct polycondensation of lactic acid to the high The main purpose of LA condensation was to limit the amount of water in the system. The mass fraction of residual "free" water in the oligomer product was also monitored with respect to the degree of polymerization. This free water directly affects the rate and achievable degree of condensation. At the higher polycondensation degree, the residual free water can no longer be removed by distillation due to a quick increase in viscosity. Complete removal of free water represents a technical barrier for the realization of direct polycondensation of lactic acid to the high molecular weight polymer. The free water content was monitored by titration of the taken samples by the Karl Fischer method. Figure 5 shows that even if reaching the average polymerization degree of 4 or more, the content of free water in the oligomer (relative to the original 20% in the lactic acid solution) is significantly reduced. The subsequent sharp drop at PD = 4 is due to the progressive reduction of pressure in the polycondensation reactor (Figure 3). At PD = 10.25, the free water content is 0.049%. The bound water releasable by oligomer end-group esterification (Figure 1 and Equation (16)) represents 4.33% as compared to direct esterification of 80% LA. The water content of the esterification system is reduced more than 20 times by polycondensation. The oligomer thus prepared was used for further experiments with transesterification of the oligomer with ethanol to ethyl lactate. Some properties of the prepared oligomer are shown in the Table 1.
Molecules 2018, 23, x FOR PEER REVIEW 6 of 12 Figure 5 shows that even if reaching the average polymerization degree of 4 or more, the content of free water in the oligomer (relative to the original 20% in the lactic acid solution) is significantly reduced. The subsequent sharp drop at PD = 4 is due to the progressive reduction of pressure in the polycondensation reactor (Figure 3). At PD = 10.25, the free water content is 0.049%. The bound water releasable by oligomer end-group esterification (Figure 1 and Equation (16)) represents 4.33% as compared to direct esterification of 80% LA. The water content of the esterification system is reduced more than 20 times by polycondensation. The oligomer thus prepared was used for further experiments with transesterification of the oligomer with ethanol to ethyl lactate. Some properties of the prepared oligomer are shown in the Table 1.

Transesterification of Oligomer with Ethanol
The data obtained of ethanol concentration change over the time for different alcoholysis temperatures were plotted in the linearized form according to Equation (14) and are shown in Figure  6. The iterative calculation was used to obtain the model parameters. The free ethanol concentration at equilibrium (Figure 1) xe was set so that the deviation from the linear trend was minimal. The Pearson correlation coefficient (r 2 ) was used as the iteration parameter and xe was adjusted to get r 2 as close to 1 as possible. When the equilibrium concentration was adjusted, the equilibrium constant K was calculated from the intercept of the linearized trend according to Equation (14) and the overall rate constant . Linearized data according to the model equation show a very close correlation with the linear trend, as indicated by the correlation coefficient values given in Table 2. The comparative experiment carried out under the same conditions with an equimolar amount of lactic acid in the form of 80% aqueous solution instead of oligomer shows a much faster rate of esterification compared

Transesterification of Oligomer with Ethanol
The data obtained of ethanol concentration change over the time for different alcoholysis temperatures were plotted in the linearized form according to Equation (14) and are shown in Figure 6. The iterative calculation was used to obtain the model parameters. The free ethanol concentration at equilibrium (Figure 1) x e was set so that the deviation from the linear trend was minimal. The Pearson correlation coefficient (r 2 ) was used as the iteration parameter and x e was adjusted to get r 2 as close to 1 as possible. When the equilibrium concentration was adjusted, the equilibrium constant K was calculated from the intercept of the linearized trend according to Equation (14) and the overall rate constant ↔ k. Linearized data according to the model equation show a very close correlation with the linear trend, as indicated by the correlation coefficient values given in Table 2. The comparative experiment carried out under the same conditions with an equimolar amount of lactic acid in the form of 80% aqueous solution instead of oligomer shows a much faster rate of esterification compared to the transesterification. The reaction rate was roughly 11 times greater under the same reaction conditions (100 • C). It is also apparent that the equilibrium composition of the mixture is affected by the presence of water, as shown by the equilibrium constant K and the conversion. The transesterification is an endothermic equilibrium process, as evidenced by the dependence of the equilibrium constant on the temperature. Its value increases with temperature roughly linearly, as shown in Figure 7. Dependence of the equilibrium composition (constants) on the temperature is based on the different temperature coefficients of the forward and reverse rate constants.
Molecules 2018, 23, x FOR PEER REVIEW 7 of 12 equilibrium constant on the temperature. Its value increases with temperature roughly linearly, as shown in Figure 7. Dependence of the equilibrium composition (constants) on the temperature is based on the different temperature coefficients of the forward and reverse rate constants.    equilibrium constant on the temperature. Its value increases with temperature roughly linearly, as shown in Figure 7. Dependence of the equilibrium composition (constants) on the temperature is based on the different temperature coefficients of the forward and reverse rate constants.     The measurements carried out at 180 • C were not further processed because of the presence of a significant experimental error due to short sampling intervals (1 min). Heating and cooling of the pressure reactor represented a substantial part of the reaction time. Figure 8 shows the tight match of the model dependencies resulting from the finding of derived constants from Table 2 to Equation (17). It should be noted that the combination of purely kinetic variables, such as the rate constant of the reaction, with the equilibrium constant of thermodynamic nature needs to be used with great caution. This special case can be used only when both directions of the reaction show the same reaction mechanism, order of reaction, and the same stoichiometry. The esterification and transesterification of carboxylic acids with alcohol fulfill these conditions. The order of the reaction may change during the reaction course; therefore, reliable data can be obtained by measuring the reaction rate from the beginning to high conversion. The speed constants obtained using the initial velocity method do not provide reliable results. The measurements carried out at 180 °C were not further processed because of the presence of a significant experimental error due to short sampling intervals (1 min). Heating and cooling of the pressure reactor represented a substantial part of the reaction time. Figure 8 shows the tight match of the model dependencies resulting from the finding of derived constants from Table 2 to Equation (17). It should be noted that the combination of purely kinetic variables, such as the rate constant of the reaction, with the equilibrium constant of thermodynamic nature needs to be used with great caution. This special case can be used only when both directions of the reaction show the same reaction mechanism, order of reaction, and the same stoichiometry. The esterification and transesterification of carboxylic acids with alcohol fulfill these conditions. The order of the reaction may change during the reaction course; therefore, reliable data can be obtained by measuring the reaction rate from the beginning to high conversion. The speed constants obtained using the initial velocity method do not provide reliable results. Good consistency of the data obtained allowed the calculation of the activation energy of transesterification. The activation energy and the pre-exponential factor were obtained from the Arrhenius equation in a linearized form: The values of the activation energy and pre-exponential factor of the transesterification obtained by the linear regression of data shown in Figure 9 are equal to Ea = 64.35 kJ·mol −1 ; A = 1.445·10 7 ·s −1 . Good consistency of the data obtained allowed the calculation of the activation energy of transesterification. The activation energy and the pre-exponential factor were obtained from the Arrhenius equation in a linearized form: The values of the activation energy and pre-exponential factor of the transesterification obtained by the linear regression of data shown in Figure 9 are equal to E a = 64.35 kJ·mol −1 ; A = 1.445·10 7 ·s −1 . Arrhenius equation in a linearized form: The values of the activation energy and pre-exponential factor of the transesterification obtained by the linear regression of data shown in Figure 9 are equal to Ea = 64.35 kJ·mol −1 ; A = 1.445·10 7 ·s −1 .

Oligomeric LA Preparation
Total of 1.8 kg of 80% aqueous solution of lactic acid was auto-catalytically polycondensed in a 2.5 dm 3 double-jacketed glass reactor. The jacket temperature was kept constant at 165 • C throughout the condensation. The reactor was equipped with an anchor stirrer and stirred at a rate of 600 rpm. The reactor lid was equipped with a thermometer, sampling port, and a 20 cm long, glass packed column. A spiral cooler was connected to the column. The condensate was collected in a round two-neck flask attached to a vacuum gauge and vacuum pump. In the first two hours the condensation was carried out at atmospheric pressure and then the pressure in the reactor was gradually reduced to 2 kPa. The maximum temperature was limited by the jacket and was not regulated during the process. The reaction samples were taken in hourly intervals. The samples were titrated to determine the number average molecular weight and free water content. The pressure, temperature, and number average molecular weight progress during the condensation are documented in Figure 3. Upon the completion of condensation, the oligomer was drained into a silicone bowl at about 100 • C and cooled to laboratory temperature. The glassy oligomer was disintegrated to coarse particles and stored in a desiccator.

Oligomer Alcoholysis
The prepared lactic acid oligomer was subjected to alcoholysis with ethanol under autogenous pressure. The reaction mixture for the experimental alcoholysis was prepared in one run for all samples representing one series (reaction temperature). Then, 20 g of oligomeric lactic acid (0.270 mol of lactate units) was melted at 120 • C in a 50 mL round-bottom flask equipped with a reflux condenser and magnetic stirrer. Anhydrous ethanol was added to the melt through the condenser in an equimolar amount with respect to lactate units of oligomer (i.e., 0.207 mol, 12.54 g). Anhydrous ferric chloride in the amount of 1 mol% (0.43 g) was dissolved in ethanol as an alcoholysis catalyst before the addition. The oligomer was homogenized for 30 s with ethanol and the catalyst using a magnetic stirrer. The resulting homogeneous solution was rapidly cooled with ice water. The reaction mixture was transferred into glass test tubes (2.5 g) immediately after the preparation. The test tubes were tightly sealed in brass pressure containers, allowing the work at elevated pressure. A total of eight samples was simultaneously immersed in a glycerol circulating thermostat bath. At given time intervals, the individual pressure containers were removed and cooled in ice water. The samples were diluted with 1,4-dioxane in a weight ratio of 1:1 after the alcoholysis. Dioxane acts both as a solvent for the crystalline part of the oligomer and as an internal standard to determine the concentration of free ethanol and ethyl lactate by GC. The measurement was performed for reaction temperatures of 100-180 • C with 20 • C steps and sampling intervals of 15; 7.5; 5; 2.5, and 1 min.

Determination of Molecular Weight and Polymerization Degree of Oligomer
The number average molecular weight M n of lactic acid oligomers was determined by the acid-base titration of terminal carboxyl groups. The titration was performed in an acetone solution with bromothymol blue as an indicator. The sample amount was about 0.5 g. The standard solution was 0.1 mol·dm −3 KOH in methanol standardized with potassium hydrogen phthalate. The number average molecular weight corresponds to the relation: where m s is the mass of the sample in grams, V t is the titration solution consumption in liters, and c s is the concentration of titration solution in mol·dm −3 . The number average degree of polymerization PD of oligomeric lactic acid corresponds to the relation: where M LAU = 72.08 g·mol −1 is the molecular weight of lactic acid repeating unit, M H 2 O = 18 g·mol −1 is the molecular weight of water (correction of end groups).

Ethanol and Ethyl Lactate Concentration Determination by Gas Chromatography
The ethanol and ethyl lactate concentrations were determined by gas chromatography using fast GC system of our construction (90 s per sample analysis). The manual sample injection of 0.2 µL with 1,4-dioxane as an internal standard (1:1 by mass mixture with sample) was performed. The column was 2.2 m long with an inner diameter of 2.1 mm. The stationary phase was 10% Carbowax 20 M on a Chromosorb W-AW, 80-100 mesh. The carrier gas was hydrogen at a flow rate of 15 cm 3 ·min −1 . TCD detection was used and the isothermal column thermostat was set at 135 • C. The calibration was with ethanol and ethyl lactate standards with the addition of the internal standard 1,4-dioxane. The concentrations of ethanol and ethyl lactate in the reaction mixture were determined simultaneously on the basis of linear calibration dependencies (six standards for each of the components). For each sample series corresponding to one reaction temperature, it was necessary to replace the injector liner due to accumulation of non-volatile oligomeric residue and the catalyst contained in the samples. Samples were injected without further treatment or derivatization.

Melting Point of the Oligomer
The melting point of the oligomer was determined using DSC (TA Instruments 2920, New Castle, DE, USA). The sample (10 mg) was measured in an aluminum pan. The first scan was used to determine the melting temperature. Before the measurement, the sample was crystallized for 30 min at 80 • C. The heating rate was 10 • C/min −1 in the range of 30-190 • C.

Determination of Water Content
The water content of the oligomer samples and ethyl lactate was determined by the Karl Fischer method. The volumetric titration unit of our construction with the biamperometric endpoint detection was used. The titrating solution was standardized with sodium tartrate dihydrate. The titration was carried out in a 1:1 mixture of methanol and chloroform. Used sample weight was in the range of 0.1-1 g with respect to the water content.

Conclusions
The kinetic model for the transesterification of polyester with alcohol with respect to alcohol sufficiently reflects the real behavior of the system, even in the case of transesterification of the oligomer of a relatively small chain length. The verification of the model with the example of oligomeric lactic acid alcoholysis with ethanol demonstrated the advantage of this previously unused route of preparation of anhydrous ethyl lactate. By the pre-oligomerization of lactic acid, the reaction medium is substantially free of water. The subsequent alcoholysis to ester takes place already in an anhydrous environment. The anhydrous environment allows the use of a variety of catalysts that otherwise hydrolyze. By removing water, the chemical equilibrium is also greatly shifted to the formation of ethyl lactate. Achieving a good yield of ethyl ester is thus already possible with molar equivalence of reactants. Anhydrous ferric chloride was experimentally confirmed as an appropriate and environmentally friendly transesterification catalyst. This strong Lewis acid cannot be used for direct esterification of lactic acid because of rapid hydrolysis in water. The pre-oligomerization step, therefore, expands the possible selection of catalysts. The pre-oligomerization step, in fact, does not affect the energy balance of the ethyl lactate preparation since it does not matter whether the water is removed from the mixture before or after ester formation. The energy required to evaporate the water during the distillation step is constant.