Partitioning of water-soluble vitamins in biodegradable aqueous two-phase systems: Electrolyte perturbed-chain statistical associating fluid theory predictions and experimental validation

Funding information Acç~ao Integrada, Grant/Award Number: A08/17; Deutsche Forschungsgemeinschaft, Grant/Award Number: EXC 1069; Fundaç~ao para a Ciência e a Tecnologia, Grant/Award Number: PD/BD/114315/2016; German Academic Exchange Service, Grant/Award Number: 57340264; Open access funding enabled and organized by Projekt DEAL. Abstract Partition coefficients (K) of vitamins (riboflavin, nicotinic acid, nicotinamide, folic acid, cyanocobalamin) in aqueous two-phase systems (ATPS) composed by polyethylene glycol (PEG 4000, PEG 6000) and organic salt (sodium citrate and sodium tartrate) at T = 298.15 K and p = 1 bar have been studied. Data on liquid–liquid equilibria of the ATPS considered in this study have been taken from the literature (PEG-Na3Citrate) or measured in this work (PEG-Na2Tartrate) for PEG 4000 and PEG 6000 at T = 298.15 K and p = 1 bar. The experimental K values were validated by electrolyte perturbed-chainstatistical associating fluid theory predictions. The neutral cyanocobalamin has the highest K values among all studied vitamins at any ATPS studied in this work. This finding contrasted with expectations based on literature data which let assume that charged species have typically the highest K values in the considered ATPS. Thus, besides the typically strong charge–charge interactions especially specific forces (e.g., hydrogen bonding) explains the strong PEG-cyanocobalamin interaction resulting in the high K values.

ATPS is highly influenced by pH, and both the pH and interactions strongly depend on the kind and composition (the tie-line length, TLL) of ATPS, as well as on the properties of ATPS phase formers, for example, PEG's molecular weight, type of anion, and cation of salt. 16 The suitability of ATPS to separate different components can be evaluated experimentally based on partition coefficient (K) measurements. Prior to this, the binodal curves and phase compositions (tie-lines) of ATPS at equilibrium (TLL) must be determined. The binodal data allow a primary estimation of the potential cost of forming ATPS, as it gives information about the immiscibility region in phase diagrams. Although these data may be good enough to get some preliminary information on partitioning efficiency, K measurements over different TLL are decisive for choosing a system applicable to the separation of target components. By this, it becomes possible to evaluate the thermodynamic efficiency of an ATPS toward separation; the advantages of analyzing K values over TLL are (a) there is one parameter to describe the influence of ATPS composition on K, (b) it is possible to compare K of different solutes in the same ATPS and TLL, and (c) it is feasible to compare K of the same solute in different ATPSs but same TLL. Some previous studies show that K strongly depends on TLL of the ATPS and can either increase or decrease with increasing TLL. 11,[17][18][19] For systems that show increased K values with increasing TLL, ATPS compositions are favored with high concentrations of the phase formers. This is rather undesired from environmental perspective and calls to search for different ATPSs that are more suitable for the partitioning of a given compound. This requirement is met by choosing biodegradable ATPS and this way it can overcome one of the biggest bottlenecks of ATPS claimed in the literature. 5 Water-soluble vitamins have many applications and they were willingly applied among others as model drugs/ligands in controlledrelease and targeting drug-delivery studies. [20][21][22] Being low watersoluble and ionizable components, many vitamins face similar problems compared to active pharmaceutical ingredients, 23 for example, low solubility, partial dissociation in aqueous systems. Additionally, watersoluble vitamins are appropriate model compounds to prove the ability of separation by ATPS caused by the high diversity of the molecular structures and properties of these vitamins. Consequently, vitamins might be then used as model-compounds for further partitioning of alike components in these ATPS. To the best of our knowledge, there has not been any work yet in which experimental data on partitioning of water-soluble vitamins in PEG-salt ATPS was reported.
The experimental effort can be much reduced with thermodynamic models that are capable to predict the partitioning of different vitamins in ATPS. In previous works, authors tried to describe and correlate partitioning of different compounds in ATPS using models for example, extended Chen-NRTL, 24 Wilson 25 in PEG-inorganic salt ATPS and with Pitzer model, 26 extended NRTL 27 and modified UNIQUAC 27 in PEGorganic salt ATPS. Also, one model based on Statistical Associating Fluid Theory (SAFT) has been used for the modeling of protein partitioning in PEG-inorganic salt ATPS. 28 However, predictions of the partitioning of organic solutes in PEG-organic salt ATPS using any predictive model have not been yet reported in literature. Perturbed-Chain SAFT (PC-SAFT) has been already proposed for modeling of vitamin partitioning just in conventional systems containing organic solvents and water. 29 To predict the partitioning of ionizable molecules in PEG-organic salt ATPS, it is of importance to consider the interactions of different ionic species in an electrolyte solution. This was done in the present work using electrolyte PC-SAFT (ePC-SAFT) model with an implemented Debye-Hückel term. ePC-SAFT has already been applied to predict the activity coefficients in weak electrolyte systems. 30 It has been also applied for predicting the liquid-liquid equilibria (LLE) of PEG-organic salt systems. 31 The conventional modeling approach used in the present work considers a homosegmented PEG chain. The required pure-component ePC-SAFT parameters were taken from the literature (PEG, Na + , Citrate 3− , vitamins) or were estimated by fitting them to experimental densities and osmotic coefficients of binary water-Na 2 Tartrate systems (Tartrate 2− ). [32][33][34][35][36][37][38] The binary interaction parameters between phase formers (PEG, salt ions) were fitted to experimental tie-lines from the literature (PEG-Na 3 Citrate) or to data determined in this work (PEG-Na 2 Tartrate). 17 The partition coefficients of vitamins (VB2, VB3 acid , VB3 amide , VB9, VB12) were predicted using the activity coefficients obtained with ePC-SAFT in each phase and at different tie-line compositions.  [39][40][41][42][43][44][45][46][47] ( Table 1). The mean charge number q mean of all vitamin species present in aqueous solution over different pHs is shown in Figure 1.
The behavior of vitamins in ATPS cannot be described without considering the equilibria expressions for ionizable compounds. 48  description is included in Supplementary Information SI (Chapter S1, Table S1). To study the partitioning of vitamins considered in this work, it is necessary to look at the pH difference between the top and bottom phases of ATPS. Thus, the mole fractions of vitamin species were calculated for each phase of ATPS separately (SI Equations (S15) and (S16)). Wolbach-Sandler 54 (Equations (2)-(5)) were used. Typically, the binary interaction parameter (k ij ) is required to model mixtures according to:

| ePC-SAFT modeling
For modeling the partitioning of vitamins in ATPS the interactions were considered as schematically presented in Figure 2. At pH ≈ 8 (considered in this work) just neutral species (VIT) and negatively charged (VIT − ) vitamin species are expected while the positive (VIT + ) species will not be present.
The activity coefficient of a component i was calculated using ePC-SAFT according to Equation (6), in which the fugacity coefficient of the mixture (φ i ) is divided by the fugacity coefficient of the pure component (φ 0i ).
Activity coefficients are required for modeling the ATPS and the K values, see the following chapters.

| Phase equilibria of ATPS
Binary PEG/ion interaction parameters (k ij ) required in Equation (3) were fitted to LLE. Any LLE with n components is calculated through the isoactivity expression. In Equation (7), γ I i and γ II i represent the activity coefficients obtained with ePC-SAFT and x I i and x II i are the equilibrium mole fractions of component i in the phases I and II, respectively. To calculate the activity coefficients in ATPS, ePC-SAFT requires the parameters of all components present in solution.
F I G U R E 1 The mean charge number q mean of all species in aqueous solution (calculated from the ionic distribution using pKa values from Table 1) as a function of pH. Lines: dashed-VB3 (gray-VB3 amide , black-VB3 acid ), solid-VB2, dashed-dot-VB9, dotted-VB12. Vertical lines: PEG + Na 3 Citrate (gray), PEG + Na 2 Tartrate (black). The width of the vertical presents the pH range of the two phases of the aqueous two-phase systems (ATPSs) F I G U R E 2 Interactions between components present in vitamin partitioning in the aqueous two-phase system (ATPS) considered in this work. Fractions of vitamin and salt depend on pH. Solid lines: the interactions considered in this work for electrolyte perturbed-chain (ePC)-statistical associating fluid theory (SAFT) modeling; dashed lines: theoretically possible interactions between different vitamins species present in aqueous solution-for simplification not considered in ePC-SAFT modeling; dotted lines: interactions which could be considered by ePC-SAFT if positively charged species were present in solution

| Partitioning of vitamins in ATPS
The experimentally accessible property is the partition coefficient K exp vit,total , which denotes the ratio of the total vitamin mole fraction in the first Phase I over the total vitamin mole fraction in the second Phase II. Access to modeling K values is realized by activity coefficients of the vitamin in the respective phases. As watersoluble vitamins are usually present at very small concentrations, the infinite dilution activity coefficient γ ∞ vit is very relevant, see Equation (8).
For neutral components, the procedure is rather simple. The case is different for charged vitamins. Depending on the pH of ATPS, several vitamins can be present as different species in solution. Thus, a connection between the experimentally observed K exp vit,total and the value obtained by thermodynamic modeling is required. The partition coefficient at infinite dilution K pred,∞ vit,j of a vitamin species j is defined as the concentrations ratio (in mole fraction and x I vit and x II vit ) of species j in the two Phases I (PEG phase) and II (salt phase), respectively (Equation (9)). 55 in which γ ∞,I vit and γ ∞,II vit are the activity coefficients at infinite dilution in the two phases. Partition coefficients higher than unity indicate that the vitamin species is partitioned mostly to the top (in this work: PEG) Phase I. If it is lower than one, the vitamin species are preferably present in the bottom (in this work: salt) Phase II.
The charge of vitamin species is explicitly considered in ePC-SAFT modeling. The ePC-SAFT pure-component parameters and binary interaction parameters for different species have been reported in the previous works. 29,35,38 The experimentally measured partition coefficient of a vitamin between the PEG phase and the salt phase is the total partition coefficient summed over all the vitamin species present in ATPS (K pred,∞ vit,total ). This value differs from the ePC-SAFT predicted K pred,∞ vit,j if pH I 6 ¼ pH II , where I and II are the Phases I and II. Conversion between the two values requires the species distributions (Equation (10)).
Due to a difference in pH between the ATPS phases, the distributions of each vitamin species were calculated separately for Phases I and II. To determine the species fractions α I j and α II j , the pKa values from the previous Section 2.1 were used (SI, Equations (S15) and (S16)).

| Materials
The water-soluble vitamins considered in this work are riboflavin (VB2), nicotinic acid (VB3 acid ), nicotinamide (VB3 amide ), folic acid (VB9), and cyanocobalamin (VB12). PEG of two different average molecular weights: 4,000 and 6,000 g/mol has been purchased from Sigma-Aldrich. All the dilutions and stock solutions were prepared in deionized Millipore water (Merck KGaA). The vitamins stock solutions of VB3 were prepared just with water, while the stock solutions of poorly water-soluble VB2, VB9, and VB12, required adding sodium hydroxide dropwise to increase the solubility through pH change of 1 unit at maximum (final pH ≈ 6 for all three vitamin solutions). The CAS numbers, purities, and suppliers are provided in Table 2. All products were used as supplied without any further purification. The chemicals were weighted on Mettler Toledo analytical balance (XS205 Dual Range) with an uncertainty of ±0.01 mg.

| Measuring ATPS-phase diagrams
The binodal curves of the ATPS were determined with the cloud-point method according to the procedure previously reported in literature. 17,56 Different amounts of aqueous stock solutions, containing PEG and Na 2 Tartrate, were added to assay tubes, thoroughly mixed in a vortex (VWR, model VV3) and placed in a thermostatic bath (Techne, Tempette TE-8D) at T = 298.15 ± 0.2 K. Then, water was added dropwise to the tubes using a syringe. The tubes were again mixed and located in a thermostatic bath. The procedure was repeated until one homogeneous phase was present. To determine the tie-lines, ATPS with different water + PEG + Na 2 Tartrate feed compositions, within the biphasic region, were prepared in 15 ml tubes. The tubes were then vigorously shaken for 2 min in a vortex mixer and left for phase separation for at least 48 hr at T = 298.15 ± 0.2 K in a thermostatic bath. Preliminary studies pointed out these times as required for thorough mixing and total phase separation. Concentrations of PEG and salt were determined in both phases as described in literature. 17,56,57 Prior to this, the samples were withdrawn in triplicate with a syringe and appropriately diluted with water. The salt concentrations in each phase were measured in triplicate with a precision of ±0.5% at T = 298.15 K by electrical conductivity (Crison GLP31 Meter). The calibration curve was prepared using standard solutions of known salt concentration of 0.5-20 mM. In this range, no polymer interference was observed. Polymer concentrations in both phases were determined gravimetrically, after lyophilization according to published elsewhere procedure. 17,56,57 Samples of the top/bottom phase were diluted with water and frozen (T = 255 ± 1 K) for at least 24 hr. Then, they were placed in freeze-dryer for at least 72 hr. Following the procedure from the literature, the polymer concentrations were calculated by subtracting salt concentrations from masses of dried phase formers in each phase. 17,56,57 The TLL were determined as shown in Equation (11), where w I P , w II P , and w I S , w II S are the mass fractions of PEG or sodium salt in the top (I) and bottom (II) phases at equilibrium.
It is very common in literature to provide phase equilibrium compositions of ATPS in mass fractions and to calculate TLL based on this unit of concentration. Thus, for better data comparison between different sources, phase compositions are given in this work based on mass fraction. The mass fractions w i can be converted to mole fractions x i with Equations (12) and (13) (P-PEG, S [cation: Na + , anion: anion − ]-salt, W-water). In these equations, v i denotes the number of moles into which a salt dissociates in aqueous solution. In the ATPS studied in this work, citrates and tartrates fully dissociate leading to the presence of Na + and Citrate 3− or Tartrate 2− in a solution (α citrate 3 − = α tartrate 2− = 0:99Þ. For this reason, only these three ion species were considered for ePC-SAFT modeling.
water ð12Þ Experimental results can be found in Figure S2, Table S2, and

| Measuring partition coefficients
Measuring partitioning of vitamins in ATPS was carried out using the procedure previously published in literature. 11  The experimental partition coefficient K exp,x vit,total at high vitamin dilution was determined using Equation (14).
Each vitamin considered in this work, except VB9, is fully present as just one species in both ATPS Phases I and II, and the total experimental partition coefficient K vit, total is then the same as for the respective species partition coefficient K vit, j . In case of VB9, two species (VB9 2− , VB9 3− ) will be present at the conditions under investigation (pH ≈ 8). Thus, both species will contribute to the total measured partition coefficient. The two species of VB9 (VB9 2− , VB9 3− ) will be differently partitioned in ATPS due to a pH difference between the phases. This can be considered with Equation (15) which includes the species fractions α I j and α II j in Phases I (top) and II (bottom). These fractions are based on the pH-dependent species distribution in ATPS phases (results for species distribution can be found in SI in Table S1). were fitted to experimental densities and osmotic coefficients of binary water-Na 2 Tartrate solutions, 36,37 and Tartrate 2− was treated equally as

T A B L E 4 ePC-SAFT binary interaction parameters for all components considered in this work
To accurately describe the interactions between the ATPS phase formers the binary PEG-salt ions interaction parameters (k ij ) were fitted to the equilibrium compositions from the literature or measured in this study. 17 The AAD values from the modeling of all ATPS considered in this work are listed in Table 5. One example for modeling results of the ATPS PEG-Na 3 Citrate for two different PEG molecular weights (4,000 and 6,000 g/mol) is presented in Figure 4, which illustrates the reasonable modeling results compared to experimental data. It is worth to note that these results only aimed at determining the interaction parameters between phase formers in ATPS as listed in Table 4. The ePC-SAFT modeled equilibrium compositions were not used as input for the prediction of the partition coefficients, rather the experimental equilibrium compositions were used for this purpose.
The pure-component parameters of vitamins were already published elsewhere. 29,35,38 The k ij between water and negatively charged vitamins VB2 − , VB9 2− , and VB9 3− were fitted to pH-dependent solubility data in previous work. 38 The k ij water-VB3 acid− was estimated in this study using pH-dependent solubilities reported in previous work and according to the approach from the literature (SI, Figure S1). 35 The k ij values between vitamins and ATPS phase formers are considered with ePC-SAFT for the following pairs: vitamin-PEG, vitamin-Na + , and vitamin-salt anion (Tartrate 2− , Citrate 3− ). This modeling is described in more detail in the next sections.  Tables 3 and 4. Overall, using these parameters enabled to predict the partition coefficients with reasonable accuracy. The ARD% between ePC-SAFT predictions and the experimental mole fraction-based K x values are listed in Table 6.

| Predicting the vitamin partitioning in ATPS
While the pure-component parameters of vitamins and binary interaction parameters vitamin-water were taken from the literature, F I G U R E 3 Densities ρ and osmotic coefficients ϕ of binary water-Na 2 Tartrate system versus molality of Na 2 Tartrate m Na2Tartarte at T = 298.15 K, p = 1 bar. Experimental data (symbols) from literature. 36,37 Lines: electrolyte perturbed-chain (ePC)-statistical associating fluid theory (SAFT) modeling using parameters from Tables 3 and 4 T A B L E 5 Modeling accuracies for all ATPS considered in this work (T = 298.15 K, p = 1 bar) the binary interaction parameters vitamin-salt ions and vitamin-PEG were estimated in this work. The following procedure has been applied for the estimation of k ij .
• Negatively charged vitamins: One rather very positive k ij was required between each pair vitamin-anion (independent of M PEG ), and a slightly positive k ij was applied to a pair vitamin-PEG (independent of M PEG ). Obviously, strong repulsion occurs between charged vitamin and the salt ions (especially the organic anions).
• Neutral vitamins: One k ij was required between each pair vitaminion, and no parameter was required for vitamin-PEG. For VB3 amide just one binary interaction parameter was introduced (vitamin-Tartrate 2− ). This means that solely with parameters available in literature it was possible to predict K of VB3 amide in ATPS composed by PEG (PEG 4000 or PEG 6000) and Na 3 Citrate with deviations ARD% ≤ 5.92. This is a very good result in a sense that ePC-SAFT could quantitatively predict K of VB3 amide without introducing any additional binary parameters.
The number of ePC-SAFT binary interaction parameters (≤4) between species and ATPS phase formers used for the prediction of K is lower than the number of parameters used only for data correlation, for example, with extended Chen-NRTL (6 interaction parameters). 24 Also, the high deviations of extended Chen-NRTL of ≈30% between the experimental and correlated data have been much reduced with ePC-SAFT (Table 6). This is a great result; it means that using these parameters ePC-SAFT allows a priori predicting K values in similar systems with reasonable accuracy ( Table 6).
The K values of water-soluble vitamins in ATPS composed by PEG and either one of two salts: Na 3 Citrate and Na 2 Tartrate is illustrated in Figure 5a

| Influence of vitamin properties on vitamin partition coefficients in ATPS
The pH of ATPS can change the charge of vitamin. 59 60 It is then expected that VB9 3− will have higher K than VB9 2− in ATPS considered in the present study. Equation (15) allows calculating the theoretical K exp,x vit,j of each VB9 species j in ATPS by accounting on species distribution of VB9 at a given pH. The K exp,x vit,j of species j = VB9 2− , VB9 3− , and the experimental value K exp,x vit,total of VB9 in ATPS composed by PEG 6000 and Na 3 Citrate are presented in Figure 6. The pure-component parameters needed to predict the partitioning of VB9 species in all ATPS from this study are given in Tables 3 and 4. The k ij values for water-VB9 species were fitted in the previous study 35 to pH-dependent solubilities of VB9. The binary interaction parameters between one VB9 species and phase-forming components were fitted to one data point K exp,x vit,j for each species. One data point means one tie-line in the ATPS composed by PEG 6000 and salt (Na 3 Citrate or Na 2 Tartrate). This procedure was accurate enough to predict partition coefficients very well over a wide range of TLL. K pred,∞ vit,total were obtained using Equation (10). Besides that, the expected behavior as reported in the literature is observed: the most negative VB9 3− possesses the highest K values, 60 which is reflected by to the very weak attractive interactions (very big k ij values) between the multivalent negative VB9 species and the organic anions (see Table 4). The ARD% values presented in Table 6 prove that ePC-SAFT can very accurately predict the partition coefficients of VB9 species in PEG 6000-Na 3 Citrate  Figure 6 is caused by the presence of different VB9 species.
However, the pH and thus electrostatic interactions are not dominating vitamin partitioning for those vitamins that are exclusively present at one species in the ATPS. 61 This can be seen in Figure 5, as the monovalent VB3 acid− has just slightly higher K values than the neutral VB3 amide .
The partition coefficient can be influenced by steric entropic effects of the vitamins. VB3 is the smallest vitamin of lowest molecular weight over all studied in this work (m VB3 acid − ð Þ = m VB3 amide = 122.11 g/mol). The highest K determined in this work was found for VB12.
This behavior can be explained by different effects related to the F I G U R E 5 Partition coefficients at T = 298.15 K and p = 1 bar in aqueous two-phase system (ATPS): (a) PEG 6000-Na 3 Citrate, (b) PEG 6000-Na 2 Tartrate at different TL compositions. Experimental data K exp,x vit,total measured in this work: closed symbols (  25 Besides the fact that the very big VB12 just might have more interactions with PEG due to its size, it might additionally have also stronger interactions due to the presence of many diverse functional groups (hydrophobic interactions to PEG, or even hydrogenbonding effects between PEG and VB12). All these enthalpic and entropic effects are considered explicitly in ePC-SAFT modeling.

| Influence of kind of ATPS phase formers on vitamin partition coefficients in ATPS
Changing PEG and salt concentrations influences the partitioning of vitamins in ATPS in a way that higher K are expected with increasing TLL (Figures 5-8). Increasing the salt concentration impacts the ionic strength, and the higher repulsion between salt anion and vitamin − might cause higher K values. 63 Tables 3 and 4), closed symbols: experimental data. Lines represent the best fit to ePC-SAFT predictions applied only to guide the eye F I G U R E 8 Anion effect on partition coefficients of VB3 acid and VB12 in aqueous two-phase system (ATPS) at T = 298.15 K and p = 1 bar. ATPS formed by PEG 6000-Na 3 Citrate (solid lines and circles) and PEG 6000-Na 2 Tartrate (dashed lines and triangles). Lines and open symbols: ePC-SAFT (electrolyte Perturbed-Chain Statistical Associating Fluid Theory) predictions (using parameters from Tables 3 and 4), closed symbols: experimental data. Lines represent the best fit to ePC-SAFT predictions applied only to guide the eye molecular weight (4,000 or 6,000 g/mol) influences K values.
K observed for ATPS formed by PEG 4000 are higher (Figure 7) than their pendants in ATPS formed by PEG 6000. Similar behavior has been already reported in the literature for other organic molecules, namely DNP-amino acids, partitioned in PEG 4000 or PEG 6000-Na 3 Citrate ATPS. 17 The lower PEG molecular weight usually allows higher K values. 63 In general, it can be concluded that the highest K values are expected in a system formed by PEG with rather low molecular weight (preferably M PEG < 4,000) and Na 3 Citrate salt.
The influence of all system-dependent properties is also illustrated by the activity coefficients of the vitamin at infinite dilution in both phases, PEG phase and salt phase. The details are shown in the SI ( Figures S3-S6). These diagrams show that the activity coefficients in the PEG phase are much lower than those in the salt phase. It might help other researchers to be able to relate the results on K values discussed in this manuscript to the activity coefficients that determine the modeled K values.

| CONCLUSIONS
Partitioning of organic compounds such as vitamins in PEG-organic salt ATPS strongly depends on the pH, as the vitamin might be present as different species depending on pH, and these species might have different partition coefficients. This is the reason why understanding the phenomena which rule the partitioning of vitamins in ATPS usually requires high experimental effort. In this work, the partition coefficients of five water-soluble vitamins over different tie-line compositions were determined experimentally. A modeling framework was developed within the thermodynamic model ePC-SAFT, which required pure-component and binary interaction parameters. Some of these parameters were already established and reported in the literature and were used in this work, while the binary interaction parameters between vitamin species and phase-forming components of the ATPS were estimated in the present study using only a very few experimental data points. In the modeling approach, the charge of the vitamins and the according species distribution depending on pH difference between the phases of ATPS were considered explicitly. The highest partition coefficient was observed for VB12, which might be related to large molecular size of VB12 and the strength of PEG-VB12 cross interactions. Further, the anion effect and PEG molecular weight influence on the vitamin partitioning were evaluated. The study shows that partitioning of vitamins in ATPS formed by citrate salt and PEG of lower molecular weight (PEG 4000) leads to the highest partition coefficients for all vitamins under consideration.

ACKNOWLEDGMENTS
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