Oligomer distribution in concentrated lactic acid solutions

Fluid Phase Equilibria 236 (2005) 125–135 Oligomer distribution in concentrated lactic acid solutions Dung T. Vu, Aspi K. Kolah, Navinchandra S. Asthana, Lars Peereboom, Carl T. Lira ∗ , Dennis J. Miller Chemical Engineering and Materials Science, Michigan State University 2527 Engineering Building, East Lansing (USA), 48824-1226 Received 21 April 2005; received in revised form 1 June 2005; accepted 3 June 2005 Available online 10 August 2005 Abstract Lactic acid (2-hydroxypropanoic acid) is a significant platform chemical for the biorenewable economy. Concentrated aqueous solutions of lactic acid (>30 wt.%) contain a distribution of oligomers that arise via intermolecular esterification. As a result, the titratable acidity changes non-linearly with acid concentration. In this work, the oligomer distribution of lactic acid is characterized using GC, GC/MS, and HPLC to extend existing literature data, and titratable acidity is measured via titration with NaOH. A thermodynamic model with a single parameter is proposed that accurately represents oligomer distribution and titratable acidity over the full range of lactic acid concentrations. © 2005 Elsevier B.V. All rights reserved. Keywords: Lactic acid; Oligomerization; Chemical theory; Esterification; Alpha-hydroxy acid; 2-Hydroxypropionic acid 1. Introduction In recent years, there is increasing emphasis on using biorenewable materials as substitutes for petroleum-based feedstocks. This paradigm shift is attributable to rising crude oil prices and the increasing desire to reduce dependence on petroleum. A major building block for the biorenewable economy is lactic acid (2-hydroxypropionic acid), an ␣hydroxy acid containing both a hydroxyl and carboxylic acid functional group. For an excellent review on lactic acid the reader is referred to Holten [1]. Lactic acid was first isolated by the Swedish scientist Scheele in 1780 [2], and first produced commercially in 1881 [3]. Applications for lactic acid are found in the food (additive and preservative), pharmaceutical, cosmetic, textile, and leather industries. Lactic acid can be formed either via fermentation of carbohydrate monomers or via a chemical route, but since about 1990 only the fermentation route is practiced commercially. The recent completion of the NatureWorks lactic acid facility for polylactic acid production, with an annual capacity of 140,000 metric tonnes of polylactic acid (PLA) [4], has greatly ∗ Corresponding author. Tel.: +1 517 355 9731; fax: +1 517 432 1105. E-mail address: lira@egr.msu.edu (C.T. Lira). 0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.06.021 enhanced the stature of lactic acid as a key biorenewable platform. Polylactic acid [5] is a versatile thermoplastic polymer that has useful mechanical properties including high strength and high modulus. Applications of PLA include household commodity products, polymers used in food contact, biomedical materials like surgical sutures, absorbable bone plates for internal bone fixation, artificial skin, tissue scaffolds, and controlled release drugs. PLA is one of the few polymers whose structure and properties can be modified by polymerizing a controlled composition of the l- and d-isomers to give high molecular weight amorphous or crystalline polymers. PLA has a degradation time of 6 months to 2 years in the environment. For more details on PLA the reader is referred to Garlotta [6]. Esters of lactic acid, formed via combination with alcohols like methanol and ethanol, are finding increased use as environmentally benign solvents. Lactic acid esters are biodegradable, non-toxic, and have excellent solvent properties, which make them attractive candidates to replace halogenated solvents for a wide spectrum of uses. Esterification of lactic acid with alcohol can also be used as a highly efficient method for purification of lactic acid from fermentation 126 D.T. Vu et al. / Fluid Phase Equilibria 236 (2005) 125–135 broths, especially when lactic acid is desired in concentrated solutions. It has been observed experimentally that dilute (<20 wt.%) lactic acid solutions contain only lactic acid monomer (LA1 ) [7], an observation that has been verified in this paper. However, many processes involving lactic acid, including polymerization and esterification, require concentrated lactic acid solutions, and lactic acid in these solutions undergoes intermolecular self-esterification to form higher oligomers. This oligomerization occurs to an increasing degree at high acid concentration, low water concentration, and high temperature. In oligomerization, two molecules of lactic acid first react to form a linear dimer, commonly called lactoyllactic acid (LA2 ), along with a mole of water. the quantities used to describe the concentration of lactic acid and its oligomers in solution. 1.1.1. Equivalent monomer lactic acid In the literature, it has been found convenient to express the concentration of lactic acid oligomers as a percent of equivalent monomer lactic acid on a waterfree basis. We abbreviate such a description with the acronym %EMLAj . To illustrate the concept, consider a solution consisting of 50 mol water, 9.20 mol LA1 , 0.343 mol LA2 , and 0.0128 mol LA3 . Upon hydrolysis of the oligomers, 9.20 + 2 × 0.343 + 3 × 0.0128 = 9.924 mol lactic acid monomer would be present. The amount of water present would be 50 − 0.343 − 2 × 0.0128 = 49.63 mol H2 O. The lactic acid in the original solution is reported as (1) Lactic acid also forms a cyclic dimer noted as lactide, but this compound is known to be unstable in water [1] and thus is not a concern in this work. Lactoyllactic acid (LA2 ) can further esterify with LA1 to form the trimer lactoyllactoyllactic acid (LA3 ); this process can further continue to give higher chain intermolecular polyesters LA4 , LA5 and so on. 9.20/9.924 = 92.7% EMLA LA1 , 2 × 0.343/9.924 = 6.9% EMLA LA2 , and 3 × 0.0128/9.924 = 0.38% EMLA LA3 . Introducing the molecular weight of water and oligomers, the solution has a total mass of 50 × 18.02 + 9.20 × 90.08 + 0.343 × 162.14 + 0.0128 × 234.21 = 1788.3 g. (2) The inherent tendency of aqueous lactic acid to form intermolecular esters in solution poses a formidable obstacle in the modeling of its liquid-phase behavior and vapor-liquid phase equilibria. For design of reaction and separation processes involving concentrated lactic acid solutions, a model to predict thermodynamic properties of these complex chemically reactive mixtures is an indispensable tool. This paper presents such a model that requires only one parameter to adequately represent lactic acid solution behavior over the full range of concentration. 1.1. Definition of concentrations Experimental work on quantifying concentrations of lactic acid oligomers in aqueous solution has been previously reported by Montgomery [7], Ueda and Terashima [8], and Watson [9], but the methods used in reporting these concentrations and the definitions of concentrations are not always clearly presented. Therefore, we clearly define here 1.1.2. Superficial weight percent The superficial weight percent of lactic acid is expressed as the weight of total monomer with the corresponding water of hydrolysis divided by total solution weight. For the example above, the superficial wt.% is (9.924 mol LA × 90.08/1788.3 = 0.500) 50.0 wt.% lactic acid, and (49.63 × 18.02/1788.3 = 0.500) 50.0 wt.% water. When lactic acid is purchased, the concentrations expressed in wt.% should be interpreted as superficial wt.%. In this manuscript, we explicitly label such concentrations superficial wt.% to avoid confusion. When solutions are very concentrated, the superficial concentration of lactic acid can exceed 100 wt.%. The concept of 125 superficial wt.% lactic acid arises from the fact that 100 g of a polymer (C3 H4 O2 )n upon hydrolysis gives rise to 100 × 90.08/72.06 = 125 g of lactic acid, where 90.08 is the molecular weight of lactic acid monomer, and 72.06 is the molecular weight of the ester repeat unit in the polymer. D.T. Vu et al. / Fluid Phase Equilibria 236 (2005) 125–135 When an aqueous solution has a lactic acid content exceeding 100 superficial wt.%, the water of esterification (oligomerization) has been removed from the solution, and the solution is thus characterized by a negative superficial wt.% of water. 1.1.3. True weight percent True weight percent utilizes the mass of a particular sample and the total mass of the individual species within the solution. Using the same example again, the true wt.% values are 46.3 true wt.% LA1 (9.20 × 90.08/1788.3 = 0.463), 3.1 true wt.% LA2 (0.343 × 162.14/1788.3 = 0.031), 0.17 true wt.% LA3 (0.0128 × 234.21/1788.3 = 0.0017), and 50.4 true wt.% H2 O (50 × 18.02/1788.3 = 0.504). 2. Experimental 2.1. Chemicals Analytical grade aqueous lactic acid solutions were used in experiments: 85 superficial wt.% was purchased from J.T. Baker, Inc. and 50 superficial wt.% was purchased from Purac, Inc. HPLC grade water was purchased from J.T. Baker, Inc. HPLC grade acetonitrile was purchased from EMD Chemicals. An aqueous solution of 85 wt.% phosphoric acid was purchased from J. T. Baker, Inc. 127 For solutions containing more than 20 but less than 85 superficial wt.% lactic acid, the total free acidity of the solution was determined from titration with standard 0.1N NaOH In solutions above 85 superficial wt.%, titration with 0.1N NaOH occurred with too little base to accurate determine the endpoint. More reproducible results were found when using 0.01N NaOH. In addition, titrating the lactic solution in ice yielded more reproducible results due to decreased probability of hydrolysis. Ester bonds present in oligomers are susceptible to hydrolysis in the presence of aqueous NaOH at room temperature. This could lead to inconsistencies in determination of total acid content by titration, therefore the solution was titrated in ice to minimize hydrolysis. After titration of free acidity, excess NaOH was added and the solution was heated to about 80 ◦ C to hydrolyze the oligomers to monomeric sodium lactate. Hydrolysis was carried out for two hours for solutions below 100 superficial wt.% and for four hours for solutions above 100 superficial wt.%. The quantity of unreacted NaOH was determined by back titration of the resultant solution with standardized 0.1 N H2 SO4 solution (SigmaAldrich). For concentrations where only monomer and dimer exist, the quantity of LA1 in solution was calculated by the difference between NaOH consumed for neutralization of total acid and the quantity of NaOH consumed for the hydrolysis of ester linkage present in oligomers [11,12]. 2.2. Preparation of oligomer solutions Solutions of lactic acid below 50 superficial wt.% were prepared by adding water to 50 superficial wt.% lactic acid, whereas solutions between 50 superficial wt.% and 85 superficial wt.% were prepared by mixing the 50% and 85% solutions. After mixing, the solutions were heated at 80 ◦ C for 1 week to increase the rate of formation of various oligomers of lactic acid. To concentrate lactic acid above 85 wt.%, water was removed from 85 wt.% lactic acid at 45 mmHg using a vacuum distillation apparatus. At that pressure, the boiling point temperature started at 30 ◦ C for 90 superficial wt.% solution and rose to 135 ◦ C for solutions of 120 superficial wt.%. Following evaporation, the solutions were equilibrated by refluxing at 100 ◦ C for 30 h. 2.3. Analytical methods The composition of lactic acid and its oligomers in solution was characterized using a combination of three analytical techniques. 2.3.1. Titration The composition of dilute solutions containing less than 20 superficial wt.% lactic acid contains >98%EMLA LA1 and water [1]. Lactic acid solution containing less than 10 superificial wt.% of lactic acid contains 99.6% EMLA LA1 [1,10], and direct titration with standardized 0.1N NaOH (SigmaAldrich) gave an accurate analysis of LA1 in solution. 2.3.2. GC analysis and GC/MS analysis Water concentrations in lactic acid standard solutions were verified using a Varian 3600 gas chromatograph (GC) equipped with a thermal conductivity detector (TCD). The GC column was 3.25 mm OD × 4 m long and was packed with 80/100 mesh Porapak-Q. The oven temperature was held constant at 413 K for 2 min, ramped at 20 ◦ C/min to 493 K, and held at 493 K for 6 min. The injector temperature was maintained at 493 K and the TCD block temperature was held at 523 K. Helium was used as the carrier gas. HPLC grade acetonitrile was used as an internal standard. Qualitative analysis of LA1 and its higher oligomers LA2 , LA3 LA4 , etc. by GC–MS was carried out on a JEOL AX-505H double-focusing mass spectrometer coupled to a Hewlett-Packard 5890J gas chromatograph via a heated interface. GC separation employed a J&W DB-23 fused-silica capillary column (30 m length × 0.25 m ID. with a 0.25 ␮m film coating). Splitless injection was used. Helium gas flow was maintained at 1 mL/min. The GC temperature program was initiated at 323 K and was ramped at 10 ◦ C/min to 533 K. MS conditions were as follows: interface temperature 523 K, ion source temperature 523 K, electron energy 70 eV, and scan frequency was l Hz over the m/z range of 45–750. Prior to its injection for analysis by GC–MS, LA1 , LA2 , LA3 , and LA4 were derivatized with TMS {Propanoic acid, 2[(trimethylsilyl)oxy]-trimethyl silyl ester} to enhance their volatility. 128 D.T. Vu et al. / Fluid Phase Equilibria 236 (2005) 125–135 2.3.3. HPLC analysis The concentration of LA1 and oligomers in concentrated lactic acid solutions were quantified using a Hewlett Packard 1090 Liquid Chromatograph equipped with an auto sampler, gradient flow pump, oven and a Hitachi-L400H UV detector set at 210 nm. Lactic acid samples below 85 superficial wt.% were analyzed using a mobile phase of water + acetonitrile in gradient concentration at a flow rate 1 mL/min on a Novapak C18 column (3.9 mm × 150 mm). Both water and acetonitrile were acidified using 2 ml of 85% (w/v) phosphoric acid in 1 L of solvent. The water was analyzed to be pH 1.3. The column oven temperature was maintained at 40 ◦ C. Beginning with a mobile phase of 100% acidified water, the acetonitrile concentration was ramped linearly to 60 vol.% from zero to 20 min and then ramped linearly up to 90% from 20 min to 25 min. The mobile phase composition was maintained constant at 90% to 28 min and then returned to 100% water. For analysis of solution concentrations above 85 superficial wt.% lactic acid, the total flow rate and column temperature were maintained as above, but the gradient was modified. The mobile phase was ramped linearly from 10% to 100% acetonitrile from 0 to 25 min. Acetonitrile concentration of mobile phase was brought back to 10% at 35 min. 2.3.3.1. Response factor for LA1 . Dilute solutions of lactic acid (<20 superficial wt.%) contain >98% EMLA LA1 ; their concentrations can be accurately determined by titration as described in Section 2.3.1. To prepare a standard containing only LA1 , a dilute solution containing 7–8 superficial wt.% total lactic acid in water was prepared and heated for 6 h in presence of Amberlyst-15 cation exchange resin to facilitate hydrolysis of any LA2 or higher oligomers present. Titration of this solution with 0.1N NaOH showed a value of 7.3 true wt.% LA1 . This solution was used to create HPLC calibration standards for LA1 that spanned the range of LA1 concentrations (0.1–1 true wt.%) used in HPLC analysis. A linear UV response was observed from the calibration curve obtained by sample dilution. The response factor for LA1 obtained from this calibration was used for quantitative determination of LA1 in concentrated lactic acid solutions. 2.3.3.2. Response factor for LA2 . A 50 superficial wt.% lactic acid solution, containing LA1 and LA2 , was titrated/hydrolyzed/back-titrated with standardized 0.1 N NaOH solution as described in Section 2.3.1. By this method the composition of LA1 and LA2 were quantified as 46 and 3 true wt.%, respectively. HPLC analysis was performed on the sample and LA1 was quantified using the response factor from calibration described in Section 2.3.3.1. GC analysis of the sample showed the presence of 51 true wt.% water, and closed the material balance. This standardized solution was diluted in water to provide a series of calibration standards that spanned the pertinent range of true wt.% of LA1 (0.1 to 1 wt.% by appropriate dilution with water) and LA2 . A linear UV response with concentration was observed for LA2 following prompt analysis. The response factor from this calibration curve for LA2 was used for quantitative determination of the superficial LA2 concentration in lactic acid solutions. The ratio of response factors for superficial wt.% was found to be LA2 /LA1 = 1.43 in all HPLC analyses. 2.3.3.3. Response factors for LA3 and LA4 . In a solution with approximately 93 superficial wt.% aqueous lactic acid solution, the linear oligomers LA3 and LA4 are observed in significant quantities in addition to LA2 . HPLC analyses of the solution showed compositions of 58 and 22 true wt.% for LA1 and LA2 , respectively, with the remaining lactic acid in the form of higher oligomers. GC analysis of the solution showed the presence of 12 true wt.% water. The presence of lactic acid oligomers up to LA4 was also verified by GC–MS analysis. The assignment of response factors for higher oligomers was based on the following premises: (1) the difference in successively higher oligomers of lactic acid is the presence of an additional ester group; (2) the UV detector response is related to the presence of carbonyl groups in the ester functionality; and (3) the ratio of LA2 /LA1 response factors was 1.43. Therefore, the same ratio of response factors was assigned to each of the successively higher oligomers of lactic acid for superficial wt.% (LAj /LA1 = 1.43). Using these response factor ratios for LA3 and LA4 , the concentrations of LA3 and LA4 were determined from HPLC to be 6 and 2 true wt.% respectively. Using these values, the material balance closed (58 + 22 + 6 + 2 + 12 = 100). To further test the calibration, a series of dilutions where prepared from a solution that was determined by titration to be 73.8 superficial wt.% lactic acid. The dilutions spanned the range of various wt.% of LA1 , LA2 , LA3 , and LA4 acids (0.1–1 wt.% by appropriate dilution with water), and the HPLC analysis showed a linear concentration response. Using the response factors determined above, the total superficial concentration was determined to be 74%, in excellent agreement with titration and thus verifying the reliability of the oligomer HPLC response factors. 2.3.3.4. Analysis of higher (>LA4 ) lactic acid oligomers. High oligomers of lactic acid are insoluble in water, but they are miscible in acetonitrile. Mixtures of acetonitrile + water have intermediate solvent strength. To dilute a sample of 115 superficial wt.% lactic acid to an overall concentration of 2 wt.% in a homogeneous phase, a solution of at least 50 wt.% acetonitrile was needed. However, this composition was not suitable for injection because HPLC could not provide reliable resolution between LA1 and LA2 if more than 20 wt.% acetonitrile was present in an injected sample containing large quantities of LA1 and LA2 . The difficulties did not arise when the quantities of LA1 and LA2 were small. To provide reliable results, lactic acid solutions greater than 105 superficial wt.% were analyzed in two fractions. Approximately 0.1 g lactic acid solution was transferred to a microcentrifuge tube and weighed. Approximately 1 mL of water was added, the D.T. Vu et al. / Fluid Phase Equilibria 236 (2005) 125–135 129 Table 1 Summary of HPLC results and comparison with total superficial acid by titration Overall superficial wt.% LA% HPLC analysis (%EMLA) Titration HPLC LA1 LA2 LA3 LA4 LA5 LA6 LA7 LA8 LA9 LA10 LA4+ 12.24 24.36 44.47 53.43a 59.59 70.60 81.46 87.13b 88.06 96.75 100.18 103.27 106.41 113.61 115.47 119.57 10.81 26.88 47.62 51.25a 62.02 71.93 81.90 89.62b 89.63 96.42 102.05 104.43 105.65 108.07 116.25 120.02 99.63 96.31 94.74 94.53a 89.95 84.61 75.66 65.92b 66.85 54.42 45.19 33.36 33.10 29.29 7.62 2.18 0.37 3.59 5.06 5.28a 9.33 13.58 19.49 25.05b 24.09 28.56 29.03 30.11 25.33 24.20 10.47 4.49 0.00 0.10 0.20 0.19a 0.72 1.65 3.88 6.90b 6.87 11.48 14.69 18.97 17.46 17.83 11.44 5.02 0.00 0.00 0.00 0.00 0.00 0.16 0.69 1.63b 1.72 3.84 6.49 9.68 10.76 11.74 12.06 5.83 0.00 0.00 0.00 0.00 0.00 0.00 0.28 0.49b 0.48 1.38 2.98 4.73 6.30 7.28 12.50 8.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.32 1.25 1.87 3.47 4.32 11.86 10.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.37 0.81 1.91 2.54 10.84 13.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.33 0.96 1.45 9.01 13.81 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.14 0.43 0.77 6.72 12.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.19 0.42 3.96 10.54 0.00 0.00 0.00 0.00 0.00 0.16 0.97 2 12 2.20 5.55 11.10 17.56 24.11 28.69 70.47 88.31 Percentages by HPLC analysis are calculated as explained in the introduction and are also plotted on Fig. 4. a Commercial LA 50%. b Commercial LA 85%. solution was shaken, and then centrifuged at 4000 rpm in a desktop microcentrifuge for 4 min. The water phase was carefully removed using a pipette. The water extraction was repeated four to five times. This water-soluble fraction was weighed and held for analysis. Next, the water-insoluble high oligomers were recovered in 100% acetonitrile and this acetonitrile phase was weighed. All steps were done at room temperature. The oligomer contents in both water and acetonitrile were combined in calculation of superficial wt.% oligomer distribution in the two fractions, and then combined to calculate the superficial wt.% of the original sample and %EMLAj . The response factors for the higher oligomers where assumed to be the same as the values for LA3 and LA4 . The HPLC results for total lactic acid content determined by adding the superficial wt.% of the individual oligomers is in good agreement with the results from titration as shown in Table 1. 3. Mathematical model We present here a model of infinite oligomer formation using chemical theory. There are a few examples in the literature of compounds whose phase equilibria properties have been described with the help of chemical theory or chemical theory along with physical intermolecular forces. The most strikingly related example is that of formaldehyde in aqueous and/or methanolic solutions, which reveals extreme deviations from ideality caused mainly by chemical reactions. Formaldehyde in the presence of water gives methylene glycol and polyoxomethylenes; in the presence of methanol it gives hemiformal and higher hemiformals [13]. VLE for formaldehyde-containing systems has been described using chemical theory by Kogan [14], Kogan and Ogorodnikov [15,16], Brandani et al. [17] and Masamoto and Matsuzaki [18]. Maurer [13] presented for the first time a model in which chemical reactions together with physical intermolecular forces were used successfully to describe the VLE and enthalpy for formaldehyde-containing systems containing both reactive and inert components such as trioxane. Maurer’s model was subsequently extended and tested using new data; for an update on the model up to 1992 the reader is referred to Hahnenstein et al. [19]. This approach has also been used by Brandani et al. [20–22]. For the system formaldehyde-water, the mole fraction of compounds in the liquid phase is calculated by modeling the oligomerization as two equilibrium constants—one for methylene glycol formation from formaldehyde and water and the second for subsequent higher methylene glycol oligomer formation. 

γMG xMG K1 = (3) (xw xFA ) (γw γFA )
 
xn xw γn γw Kn = 2≤n (4) (xn−1 xMG ) (γn−1 γMG ) These assumptions are reasonable since methylene glycol is a chemically different structure than formaldehyde, while the higher oligomers of methylene glycol are chemically similar to each other. The formaldehyde–methanol system is treated in a similar way. 3.1. Literature models for lactic acid based on chemical theory Prior modeling work to determine the distribution of lactic acid oligomers in solutions above 20 wt.% concentration has been performed by Bezzi et al. [23] and reported by 130 D.T. Vu et al. / Fluid Phase Equilibria 236 (2005) 125–135 Holten [1]. In the first modeling approach, only the dimers of lactic acid (LA2 ) were considered. This approach, however, becomes inaccurate at higher concentrations of lactic acid (>50 wt.%), where significant oligomerization occurs. In a second modeling approach, polylactic acids were taken into account, giving a more realistic representation at high concentrations. However, this model was limited in that solutions were characterized only by concentration of free lactic acid (LA) and total oligomer species; no distributions of oligomers was generated. This polylactic model works poorly at low concentrations, and is interpretative rather than predictive in its application. We are unaware of published mathematical models, apart from the ones described above, that attempt to represent the liquid phase distribution of lactic acid and its oligomers in solution. Therefore, we propose here a model that is based on chemical theory and incorporates an infinite series of oligomer components. The model accurately predicts liquid phase compositions of lactic acid in a method similar to Maurer’s for formaldehyde systems, and represents a clear advancement of the characterization of concentrated lactic acid solutions. In order to compare the present model to those in the literature, this work utilizes the terminology used by Montgomery [7] and Ueda and Terashima [8] as clarified in Section 1.1. This reasoning is analogous to the treatment of the formaldehyde model, where all polyoxomethylenes have the same equilibrium constant since they are chemically very similar but the formaldehyde to methylene glycol reaction involves different chemical structures and therefore has a different equilibrium constant [13]. Eq. (9) can be rearranged to the following form nLAj = nLA(j−1) r where r= nLA1 K nW nLAj = nLA1 r(j−1) (5) LA2 + LA1 ⇋ LA3 + W (6) LA3 + LA1 ⇋ LA4 + W (7) Generally, oligomer formation can be written as LA(j−1) + LA1 ⇋ LAj + W (8) The chemical reaction equilibrium constants for the above reactions in a generalized form by nLAj nW j>2 (9) Kj = (nLA(j−1) nLA1 ) Note that since the number of moles of products and reactants is equivalent regardless of the degree of oligomerization, the equilibrium constant written in Eq. (9) is equivalent to an equilibrium constant written in mole fractions. Since lactic acid oligomers (LA2 , LA3 , etc.) are all formed via identical reaction pathways and are themselves chemically similar, it is reasonable to assume that the esterification reactions (Eqs. (5)–(8) above) have the same value of equilibrium constant. K = K1 = K2 = K3 = K4 = . . . = Kj (10) (13) A total lactic acid superficial mole balance is given by  jnLAj = nLA1 (1 + 2r + 3r 2 + 4r 3 + · · ·) niLA = 3.2. Infinite series polymer model 2LA1 ⇋ LA2 + W (12) and it is recognized that nLA1 and nW are properties of the solution, identical for all oligomers at a specific superficial concentration. Because of the recursion, it is possible to write = From a thermodynamic standpoint, the formation of oligomeric intermolecular esters of lactic acid can be described as the set of successive reactions shown below, where W denotes water (11) nLA1 (1 − r)2 (14) where the left hand side is the superficial number of moles of lactate in solution, the second and third expressions represent the infinite converging series obtained by inserting Eq. (13), and the final term represents the closed form solution. The water superficial mole balance is given by taking the difference between the true moles present, and those consumed by hydrolysis of oligomers  niW = nW − (j − 1)nLAj = nW − nLA1 r(1 + 2r + 3r 2 + 4r 3 + · · ·) nLA1 r = nW − (1 − r)2 (15) where Eq. (13) is substituted into the summation between the second expression and the third, and the right hand side is the closed form solution. The left-most variable in Eq. (15) is the superficial number of moles of water. Eq. (14) can be inserted into (15) to give nW = niW + niLA · r (16) Inserting Eqs. (14) and (16) into Eq. (12) provides a relation between K and r in terms of the superficial concentrations of lactic acid and water K=r (niW + niLA r) niLA (1 − r)2 (17) D.T. Vu et al. / Fluid Phase Equilibria 236 (2005) 125–135 Free acid and all oligomers contribute to titratable acidity that can be calculated by  nLA1 nLAj = nLA1 (1 + r + r 2 + r 3 + · · ·) = (18) (1 − r) 3.3. Application To apply the model, an overall superficial number of moles niW , niLA and K are specified. Eq. (17) is rearranged as a quadratic in r and solved explicitly for the value of r. The value of r is then used to calculate nLA1 from Eq. (14), and subsequently the distribution of oligomers from Eq. (13) as well as the remaining balances. The equations can be manipulated to express the various oligomer concentrations in terms of the overall superficial wt.% lactic acid. The %EMLA for LAj is %EMLAj = jr(j−1) (1 − r 2 ) (19) The superficial wt.% of LAj is (Superficial wt.% of LAj ) = (%EMLAj )(overall superficial wt.% LA) (20) The true wt.% of water is (True wt.% water) = 100 + (overall superficial wt.% LA)(0.2r − 1) (21) The true wt.% of a LA is (True wt.% LAj ) = (0.8j + 0.2)(overall superficial wt.% LA)r (j−1) (1 − r)2 (22) 131 4. Results and discussion 4.1. Analytical results and modeling Aqueous solutions of lactic acid were prepared and analyzed for oligomer concentrations up to 120 superficial wt.% lactic acid. Table 1 gives a summary of the HPLC results and a comparison with total acidity of the solution determined by titration. The HPLC results for overall superficial wt.% were calculated by summing the peak areas for the individual oligomers. As a check of the HPLC method, the total acid content by the HPLC and titration agreed within ±3 wt.% for solutions up to 105 wt.% lactic acid. The value of the equilibrium constant K = 0.2023 was obtained by least squares regression of %EMLA for species LA1 through LA4 simultaneously. Using this value, the distribution is modeled with an average deviation of ±0.12% of the reported %EMLA. For each composition from Table 1, calculated %EMLA of the oligomers is presented in Table 2. From the HPLC results, the material balance provided the superficial number of moles of lactic acid and water. Using the value of K and the superficial moles, the value of r was determined for each overall composition, and then Eq. (19) was applied. Fig. 1 shows a GC/MS result for an 85 superficial wt.% lactic acid solution, demonstrating by molecular weights that only linear oligomers of lactic acid are present. All four components, namely LA1 , LA2 , LA3 and LA4 , were identified and verified by their respective mass fragmentation data obtained from GC/MS. Fig. 2 shows an example HPLC chromatograph of a 115 superficial wt.% solution of lactic acid. Fig. 3 shows total titratable acidity as a function of lactic acid concentration as summarized by Holten [1] from various sources and from this work. The titratable acidity reflects a balance between increasing total acid content and increasing Table 2 Summary of calculated %ELMA for oligomers at each of the experimental compositions from Table 1 Sample (g) 0.081 0.293 0.213 0.116 0.111 0.115 0.107 0.093 0.086 0.081 0.093 0.079 0.054 0.111 0.198 Acid superficial (wt.%) niW (mmol) niLA (mmol) r 10.8 26.9 47.6 51.25 62.0 71.9 81.9 89.6 96.4 102.0 104.4 105.7 108.1 116.2 120.0 3.99 11.9 6.21 3.14 2.34 1.80 1.08 0.533 0.171 −0.093 −0.228 −0.249 −0.240 −1.01 −2.20 0.097 0.876 1.13 0.660 0.763 0.922 0.977 0.921 0.920 0.923 1.07 0.931 0.642 1.44 2.64 0.005 0.014 0.034 0.039 0.058 0.084 0.126 0.180 0.255 0.348 0.397 0.425 0.484 0.721 0.840 Calculated (%EMLAj ) LA1 LA2 LA3 LA4 LA5 LA6 LA7 LA8 LA9 LA10 LA4 + 99.0 97.1 93.3 92.4 88.8 84.0 76.4 67.3 55.5 42.5 36.3 33.1 26.6 7.80 2.57 0.96 2.80 6.36 7.20 10.2 14.0 19.2 24.2 28.3 29.6 28.9 28.1 25.8 11.2 4.32 0.007 0.061 0.326 0.421 0.884 1.76 3.62 6.51 10.8 15.4 17.2 17.9 18.7 12.2 5.440 0.000 0.001 0.015 0.022 0.068 0.196 0.607 1.56 3.68 7.16 9.11 10.1 12.1 11.7 6.095 0.000 0.000 0.001 0.001 0.005 0.020 0.095 0.350 1.17 3.11 4.52 5.39 7.32 10.5 6.402 0.000 0.000 0.000 0.000 0.000 0.002 0.014 0.075 0.358 1.30 2.16 2.75 4.25 9.10 6.456 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.016 0.107 0.527 1.00 1.36 2.40 7.65 6.329 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.031 0.209 0.454 0.662 1.33 6.30 6.078 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.009 0.082 0.203 0.316 0.725 5.11 5.746 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.032 0.090 0.149 0.390 4.09 5.365 0.000 0.001 0.015 0.023 0.073 0.218 0.719 2.00 5.36 12.4 17.6 20.9 28.9 68.8 87.7 The first four columns are from experimental results, and the remaining columns are calculated based on the model using K = 0.2023. 132 D.T. Vu et al. / Fluid Phase Equilibria 236 (2005) 125–135 Fig. 1. GC/MS of 85 wt.% LA. The mass fragments (not shown) were used to verify that linear oligomers of LA are present. No lactide was observed. Fig. 2. HPLC chromatograph of the water soluble fraction from 115 superficial wt.% lactic acid demonstrating the separation of oligomers. degree of oligomerization that eliminates free acid groups. The titratable acidity goes through a maximum at about 90 wt.% lactic acid. The model represents the experimental data with an average deviation of ±2% of titratable acidity. Fig. 4 shows the experimental distribution of LA1 , LA2 , LA3 and higher oligomers collected in this work and Fig. 3. Total titratable acidity tabulated from various workers by Holten [1] and measured in this work compared with the model proposed in this work. () data compiled by Holten; () this work. compared to data from Ueda and Terashima [8] and Montgomery [7]. Higher oligomers are denoted by LA4+ , i.e. sum of tetramers and higher oligomers. The abscissa of Fig. 4 denotes the superficial lactic acid concentration; note that it runs through 125% as explained in the introduction. The ordinate of Fig. 4 denotes the %EMLA distribution of lactic acid between monomer and its oligomers on a water-free basis. The percentages are calculated as described in the introduction. The lines shown in Fig. 4 are the calculated values of LA1 , LA2 , LA3 . LA4 and LA4+ from the model. Excellent agreement is seen between the experimental values of this work and the values calculated from the model. It can be seen from the experimental data of this work and also from Montgomery [7], that there is a maximum value of approximately 15% EMLA LA3 occurring at 114 superficial wt.% and a maximum value of 29% EMLA LA2 occurring at 105 superficial wt.%. Experimental data from Ueda and Terashima [8] are also presented; this set of experimental data runs up to 87% total acidity. Watson’s [9] experimental data are not plotted because he reports the presence of lactide, which is known to be unstable in aqueous solutions. Fig. 5 compares the experimental analysis and model concentrations of LA5 through LA10 for solutions with Fig. 4. Experimental oligomer distribution compared with the model expressed as %EMLA. Solid lines represent the model, solid symbols are measured in this work and open symbols are from literature as reported by [7] and [16]. The curve labeled LA4 + indicates the sum of all oligomers LAj ; where j ≥ 4. D.T. Vu et al. / Fluid Phase Equilibria 236 (2005) 125–135 Fig. 5. Experimental oligomer distribution compared with the model expressed as %EMLA. Experimental difficulties in analyzing the two highest concentrations are discussed in the text. superficial lactic acid content of 80 to 125 wt.%. The agreement is excellent for analyzed solutions up to 108 superficial wt.% of acid. The agreement is not as good for the solutions with superficial concentrations of 116 wt.% and 120 wt.%. These samples were analyzed in two fractions as discussed above. Since the total acid content is in good agreement by HPLC and titration (Table 1), we believe that the disagreement between the model and HPLC results is due to the incomplete separation of oligomers in the HPLC, even though distinct peaks appear on the HPLC chromatogram. Attempts to refine the HPLC method further for these very high molecular weight solutions have not been successful. 133 Concentrated solutions of lactic acid (>105 superficial wt.%) are fluid at 120 ◦ C, but are very viscous at room temperature. The solutions had a very slight amber tint, but none of the dark coloration indicated by Montgomery [7]. Our results are in good agreement with those of Montgomery [7] except at the highest concentration. Montgomery reported incomplete separation of LA3 and higher oligomers—a problem that we experienced only for higher oligomers (>LA5 ). To test for hydrolysis under analysis conditions in this work, ethyl lactate was analyzed using the same HPLC method as for the lactic acid oligomers and was found to be stable. Also, our results are also consistent with those of Montgomery, who tested extensively for hydrolysis. In discussion of the distribution of weight percentages in lactic acid solutions, it is appropriate to express the concentrations in terms of superficial wt.%. The superficial wt.% for oligomers can be quickly calculated from the values in Table 1 by multiplying the total acid superficial wt.% by the % EMLA. A summary of true weight percentages calculated by the oligomer model is shown in Table 3. 4.2. Implementation of lactic acid model into ASPEN plus Implementation of the model is extended to ASPEN Plus, which is the most widely used simulation software in the chemical process industry. Use of this model will be shown in future publications for the esterification of lactic acid with ethanol from the authors’ laboratories [24]. Table 3 Model calculations of true wt.% of water and lactic acid oligomers for various superficial compositions Superficial wt.% LA Superficial wt.% water 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 123 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 −5 −10 −15 −20 −23 True weight percent compositions Water LA1 LA2 LA3 LA4 LA5 LA6 LA7 LA8 LA9 LA10 LA11+ 95.0 90.0 85.0 80.0 75.1 70.1 65.1 60.2 55.3 50.4 45.5 40.6 35.8 31.1 26.4 21.9 17.5 13.3 9.49 6.20 3.61 1.79 0.689 0.149 0.0219 4.98 9.91 14.8 19.6 24.3 29.0 33.6 38.0 42.3 46.3 50.2 53.8 56.9 59.6 61.5 62.5 62.2 60.1 55.4 47.6 36.6 23.7 11.6 3.09 0.506 0.019 0.079 0.187 0.350 0.575 0.874 1.26 1.75 2.35 3.11 4.03 5.18 6.58 8.31 10.4 13.0 16.2 19.8 23.6 26.6 27.0 22.9 14.3 4.67 0.853 0.000 0.001 0.002 0.005 0.011 0.021 0.038 0.064 0.105 0.167 0.260 0.400 0.611 0.931 1.42 2.18 3.37 5.23 8.04 11.9 16.0 17.7 14.1 5.66 1.15 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.004 0.008 0.015 0.028 0.051 0.094 0.175 0.330 0.636 1.25 2.48 4.83 8.56 12.4 12.5 6.22 1.41 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.004 0.009 0.020 0.047 0.113 0.282 0.725 1.85 4.34 8.21 10.6 6.45 1.63 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.007 0.019 0.061 0.204 0.684 2.12 5.24 8.58 6.44 1.82 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.013 0.056 0.246 1.01 3.25 6.79 6.27 1.97 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.015 0.087 0.469 1.98 5.27 5.99 2.10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.004 0.030 0.216 1.19 4.03 5.64 2.20 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.010 0.098 0.708 3.05 5.25 2.29 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.005 0.079 0.989 8.55 44.2 84.1 134 D.T. Vu et al. / Fluid Phase Equilibria 236 (2005) 125–135 Fig. 6. Process flow diagram and results for the truncated ASPEN simulation compared to the complete oligomer model. The comparisons of composition are for a superficial composition of 92.72 wt.% lactic acid. The proposed model could be incorporated into the process simulator via a user-written subroutine. As an alternative, we assume that oligomerization is adequately approximated by a truncated series. Fig. 4 implies that solutions up to 90 wt.% can be represented by monomer lactic acid and the first four oligomers (LA2 –LA5 ). We have used this assumption to simulate a distillation column for the purpose of evaluating its suitability for process simulation. Fig. 6 shows the ASPEN Plus simulation to remove water from a 22 superficial wt.% lactic acid solution (nonequilibrated) and form an equilibrated 92.72 superficial wt.% solution. The reactive distillation column is assumed to operate with equilibrium stages, so the bottoms product contains an equilibrium mixture of lactic acid oligomers at an overall concentration of 92.72 superficial wt.%. The oligomer concentrations obtained from the ASPEN Plus simulation with the truncated model compare well with those from the nontruncated oligomer model as summarized in the inset table within Fig. 6. The simulation verifies that the model can be used to model a distillation column where a dilute solution of lactic acid is converted to concentrated solution consistent with oligomer distribution represented by the full model. Other options for comparison of the truncated and full model could have been used, such as an equilibrium reactor with a non-equilibrium feed; the selection of a distillation column was arbitrary. 4.3. Effect of temperature and its effect on equilibrium constant (K) There are no experimental reports available on heats of formation of oligomers of lactic acid. Other esterification reactions involving carboxylic acids and alcohols are either thermoneutral or have very low heats of formation in the range of 2–6 kJ/mol [25–27], resulting in negligible to modest changes (10–15%) in equilibrium constants with temperature changes of 80 K. In this work, the series of esterification reactions leading to formation of oligomers are assumed to be thermoneutral, resulting in a temperature-independent K = 0.2023. Also, the oligomerization reactions are extremely slow at room temperature, which makes it very difficult to assess the reaction kinetics and time required to reach any redistribution at room temperature [1]. Experiments over a period of eight weeks showed no measurable redistribution of oligomers from the solutions that were prepared at the elevated temperatures reported above. 5. Conclusions In this work, we provide new data to complement and extend literature data for oligomerization of lactic acid in aqueous solutions. We present a model based on chemical theory that consists of an infinite sequence of equilibrium D.T. Vu et al. / Fluid Phase Equilibria 236 (2005) 125–135 homo-esterification reactions between successive oligomers of lactic acid. We show that a single value of the equilibrium constant (K = 0.2023) applied to all oligomerization reactions accurately predicts titratable acidity and oligomer concentrations for solution concentrations ranging from very dilute to greater than 100 superficial wt.% lactic acid. We demonstrate that inclusion of oligomers only up to LA5 is suitable for process modeling of lactic acid solutions up to 90 wt.%. List of Symbols Kj chemical reaction equilibrium constant for j order oligomer LA1 monomeric lactic acid LA2 dimer lactic acid, lactoyllactic acid LA3 trimer lactic acid, lactoyl-lactoyllactic acid LAj polymeric lactic acid consisting on j units of lactic acid nj molar concentration of component j r defined by Eq. (12) xj Mole fraction of component j ␥j activity coefficient of component j Superscripts i initial (used for superficial number of moles) Subscripts FA formaldehyde j component LAj polymeric lactic acid consisting of j units of lactic acid MG methylene glycol MGn higher polyoxomethylene glycols n order of oligomer W water Acknowledgement The authors extend appreciation to the National Corn Growers Association and the Department of Energy for financial support. 135 References [1] C.H. Holten, Lactic acid: Properties and Chemistry of Lactic Acid and Derivatives, Verlag Chemie, 1971. [2] C.H. Scheele, Om Mjolk: Kgl. Vetenskaps-Academiens nya Handlingar, 1 Stockholm (1780) 116–124. [3] M.H. Hartmann, in: D.L. Kaplan (Ed.), Biopolymers from Renewal Resources, Springer-Verlag, Berlin, 1998, pp. 367– 411. [4] S.K. Ritter, Chem. Eng. News 82 (22) (2004) 31–34. [5] W. Robert, Chem. Week. April 10 (2002) 31. [6] D. Garlotta, J. Polym. Environ. 9 (2002) 63–84. [7] R. Montgomery, J. Am. Chem. Soc. 74 (1952) 1466–1468. [8] R. Ueda, T. Terashima, Hakko Kogaku Zaashi. 36 (1958) 371– 374. [9] P.D. Watson, Ind. Eng. Chem. 32 (1940) 399–401. [10] K. Tanaka, R. Yoshikawa, C. Ying, H. Kita, K. Okamoto, Chem. Eng. Sci. 57 (2002) 1577–1584. [11] Holten, ibid, pp. 200. [12] A. Engin, H. Haluk, K. Gurkan, Green Chem. 5 (2003) 460–466. [13] G. Maurer, AIChE J. 32 (1986) 932–948. [14] L.V. Kogan, Zhur. Prikl. Khim. 52 (1979) 2149. [15] L.V. Kogan, S.K. Ogorodnikov, J. Appl. Chem. USSR 53 (1980) 98–101. [16] L.V. Kogan, S.K. Ogorodnikov, J. Appl. Chem. USSR 53 (1980) 102. [17] V. Brandani, G.D. Giacomo, P.U. Foscolo, Ind. Eng. Chem. Process. Res. Dev. 19 (1980) 179–185. [18] J. Masamto, K. Matsuzaki, Chem. Eng. Jpn. 27 (1994) 6– 11. [19] I. Hahnenstein, M. Hasse, Y.-Q. Liu, G. Maurer, AIChE Symp. Ser. 298 (1994) 141–157. [20] S. Brandani, V. Brandani, G.D. Giacomo, Ind. Eng. Chem. Res. 30 (1991) 414–420. [21] S. Brandani, V. Brandani, G.D. Giacomo, Fluid Phase Equil. 63 (1991) 27–41. [22] S. Brandani, V. Brandani, G.D. Giacomo, Ind. Eng. Chem. Res. 31 (1992) 1792–1798. [23] S. Bezzi, L. Riccoboni, C. Sullam, Mem. cl. sci. fis. mat. nat. 8 (1937) 181–200. [24] N.S. Asthana, A.K. Kolah, C.T. Lira, D.J. Miller, US. Patent Appl. 2004. Improved Process for Production of Organic Acid Esters. [25] J. Gangadwala, S. Mankar, S. Mahajani, Ind. Eng. Chem. Res. 42 (2003) 2146–2155. [26] W. Song, G. Venimadhavan, J.M. Manning, M.F. Malone, M.F. Doherty, Ind. Eng. Chem. Res. 37 (1998) 1917–1928. [27] W. Jiu, C. Tan, Ind. Eng. Chem. Res. 40 (2001) 3281–3286.