Dextran

Ind. Eng. Chem. Res. 2005, 44, 3749-3760

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Solvent Property Characterization of Poly(ethylene glycol)/Dextran Aqueous Biphasic Systems Using the Free Energy of Transfer of a Methylene Group and a Linear Solvation Energy Relationship Melanie L. Moody, Heather D. Willauer,† Scott T. Griffin, Jonathan G. Huddleston,* and Robin D. Rogers Department of Chemistry and Center for Green Manufacturing, The University of Alabama, Tuscaloosa, Alabama 35487

Aqueous biphasic systems (ABSs) composed of poly(ethylene glycol) (PEG) and dextran have long been proposed as useful liquid/liquid extraction systems for biological macromolecules. More recently, they have been proposed as useful partitioning systems for molecular characterization in quantitative structure activity relationships. In this context, the distribution ratios of a wide range of organic solutes differing in structure and functionality were measured in a PEG/dextran ABS and the results compared to the corresponding 1-octanol/water partition coefficients. The relative hydrophobicity of the phases was quantified from the free energy of transfer of a methylene group measured for a homologous series of alcohols. A linear free energy relationship based on Abraham’s generalized solvation equation has been derived from the solute partitioning data, which allows a direct comparison to be made between the solvent properties of a PEG/ dextran ABS and those of traditional solvent/water systems used, for example, in the determination of log P. A comparison with similar parameters previously determined for ABSs composed of PEG and a salt is also enabled. Introduction Because separations procedures are commonplace in the chemical industry, interest in the development of environmentally friendly or “green” processes has increased in recent years.1-4 Consequently, aqueous biphasic systems (ABSs) have been proposed as an environmentally friendly alternative to volatile organic compounds in liquid/liquid biphasic extractions because they are safe, nontoxic, nonflammable, nonvolatile, and relatively benign extraction methods where both of the phases are over 80% water on a molal basis. Even though both phases are aqueous solutions of poly(ethylene glycol) (PEG) and either a salt [e.g., (NH4)2SO4 or K3PO4] or another polymer (e.g., dextran), the two phases are immiscible and have distinctly different solvent properties.5-8 Characterization of ABS solvent properties would allow the creation of a toolbox of different ABSs, which, in turn, would lead to efficient customization for desired analytical or separations processes. To date, the primary focus of our research in this area has involved the characterization of a PEG/salt ABS,9-18 that is, an ABS formed from the salting out of the water-soluble polymer in the presence of a kosmotropic salt.9-11 These ABSs have been characterized in terms of the PEG molecular weight, salt type, PEG and salt concentrations, solution pH, and temperature.9-18 Recently, partitioning in an ABS has been advocated as an analytical alternative to the 1-octanol/water partition coefficient, log P.19-21 log P may be used to measure the hydrophobicity in drug and toxicological studies and can be considered a descriptor of structural interactions.19,21 However, as outlined in previous publica†

Present address: Navy Technology Center for Safety and Survivability, Code 6180, 4555 Overlook Avenue SW, Washington, DC 20375.

tions22-31 and demonstrated in two previous studies,9,10 the use of log P from the 1-octanol/water and similar organic/aqueous solvent systems has limitations when log P is applied to hydrophilic solutes, including the effects on molecular conformation, difficulties in measuring concentrations of weakly soluble substances in the organic phase, and the health and safety aspects associated with the use of 1-octanol.24 The major limitation to the application of the 1-octanol/water system, for which the PEG/dextran system is proposed as the solution, is that the structural descriptor log P cannot be obtained for the aqueous conformation of conformationally flexible molecules.25 ABSs have none of these limitations and may represent a viable alternative to log P for the provision of hydrophobicity information on a wide range of organic molecules ranging from small molecules to the larger macromolecules associated with biological systems.26-30 In this paper, solute/solvent interactions previously studied in PEG/salt systems are applied to polymer/ polymer ABSs using a representative PEG/polymer system, PEG-6000/dextran-75000. In this way, the two principal types of aqueous partitioning systems can be compared in terms of the characteristic forms of their solute/solvent interactions and their potential application to industrial separations processes or analytical molecular property determination. Polymer/polymer systems have been considered to form as a result of the unfavorable interaction enthalpy arising from unlike polymer segment/segment contacts overcoming the loss of entropy inherent in the segregation of the polymers to different phases.32 Other thermodynamic models of the process have focused on differences in the hydrogen bond orientation in the two phases.33 Polymer/polymer aqueous phase separation may be observed above defined concentrations for a wide range of polymers and represent upper critical solution

10.1021/ie049491c CCC: $30.25 © 2005 American Chemical Society Published on Web 04/08/2005

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Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005

temperature phenomena because an increase in the temperature promotes miscibility.34 Polymer/polymer ABSs have been considered to be less economically viable and more difficult to handle than PEG/salt ABSs in industrial extractive operations.35 However, their recent application to the provision of molecular structural information is novel and exciting.36 Indeed, because of the very low interfacial tensions engendered in these systems, they are particularly suited to the partition of delicate biological particles and supramolecular assemblies37 as well as proteins,14 for which conventional partitioning systems (containing organic solvent) are wholly unsuited. Thus, they have recently been promoted as suitable for characterization of the solute properties of pharmacologically important compounds.38 It is therefore of some interest to compare the solvating properties of a representative example of a polymer/polymer ABS with those of a previously examined PEG/salt ABS. Of particular interest is whether the solution properties of the two ABSs are different enough to yield distinct molecular structural information or to recommend distinct advantages of one system over another in extractive applications. In the present study, we examine the partitioning of a series of aliphatic alcohols in an ABS composed of PEG-6000 (MW 6000) and dextran-75000 (MW 75 000). From these data, the free energy of transfer of a methylene group from the lower dextran-rich phase to the upper PEG-rich phase may be obtained. ∆GCH2 may be considered to represent the relative hydrophobicity of a partitioning system21 and can be considered to be a cohesive energy density related solvent descriptor. Additionally, using a data set consisting of the partition coefficients of 31 solutes, covering a wide range of functional groups, based on the Gibbs energy-related solute descriptors of Abraham, we have derived a linear solvation energy relationship for the PEG-6000/dextran75000 ABS. From these data, solute partitioning in PEG/dextran ABSs can be compared to partitioning in many different systems, but in particular the 1-octanol/ water system and PEG/salt ABS. The data gathered should aid in the further characterization and application of ABSs. Methods Boric acid was obtained from Aldrich (Milwaukee, WI). Acetic and phosphoric acids were obtained from Fisher (Pittsburgh, PA). A Barnstead (Dubuque, IA) commercial deionization system was used to purify water used in the experiments. Sodium chloride obtained from Aldrich (Milwaukee, WI) was added to keep the ionic strength at 0.01 M with respect to NaCl. PEG/dextran ABSs were prepared using a buffer consisting of boric, acetic, and phosphoric acids to give a final concentration of 0.04 M with respect to each acid. The pH of the buffer was adjusted by adding 0.2 M NaOH to the original 0.04 M stock buffer solution. For compounds with acidic pKa, the buffer (pH 1.8) was used without any adjustment. For substances having a neutral pKa, 57.5 mL of a 0.2 M NaOH solution was added to 100 mL of the buffer to make the final pH ca. 7.0. To adjust to pH 8.7, 65 mL of 0.2 M NaOH was added to 100 mL of buffer. For a pH 12.5 solution, 150 mL of NaOH was added to 100 mL of buffer. Ionizable solutes, other than phthalic acid, were partitioned under conditions of pH such that the solute could be expected to behave as a neutral (nondissociated) compound (2 pH units above or below pKa). This is shown in Table 1.39

Table 1. pKa Values of Ionizable Solutesa solute

pKa

system pH

benzoic acid acetic acid 4-hydroxybenzoic acid 1,2-phthalic acid salicylic acid 4-chloroaniline ethylamine n-propylamine n-hexylamine

4.19 4.75 4.48, 9.32 2.89, 5.51 2.97, 13.40 9.81 10.81 10.71 10.56

1.8 1.8 1.8 1.8 1.8 8.7 12.5 12.5 12.5

a

Adapted from ref 39.

A phase diagram for the system was determined using the cloud-point method.5,40 Tie lines were assigned using the method of Merchuk using the measured densities of the phases to find the mass ratio of selected systems.41 The systems used in this study were characterized according to system composition, in terms of the tieline length [TLL in % (w/w)] and ∆EO. ∆EO is defined as the difference in PEG composition between the phases of the system measured in terms of the molality of ethylene oxide (EO) monomers. Full details of this treatment can be found elsewhere.10 Stock solutions of PEG-6000 (Fluka, Milwaukee, WI) and dextran-75000 (average molecular weight 65 00085 000; catalog no. D-1390; Sigma, St. Louis, MO) were prepared on a % (w/w) basis in a solution of the appropriate buffer. For the linear solvent energy relationship (LSER) study specifically, the overall composition of the partitioning systems was 5% (w/w) PEG and 10% (w/w) dextran, giving a density of each phase of about 1 g/mL. The TLL of this system was 18.40% (∆EO ) 1.682 m). For the TLL studies, the overall composition of each system used was derived from the phase diagram. It was found that double dilution of a 1- or 2-mL aliquot of each stock solution [10% (w/w) PEG, 20% (w/ w) dextran] resulted in the formation of a system having equal volumes of each phase. Each system was prepared in duplicate for the partition of each solute to ensure reproducibility. Systems were equilibrated in a Neslab RTE-110 water bath at 25 °C for approximately 1 h. For the partitioning studies, 31 14C-labeled solutes were used. The following solutes were obtained from Sigma (St. Louis, MO): benzoic acid, 1,4-dichlorobenzene, acetic acid, benzene, 1-pentanol, 1-propanol, ethanol, methanol, phenol, 2-propanol, 1,2,4-trichlorobenzene, chlorobenzene, 1-propylamine, salicylic acid, 4-hydroxybenzoic acid, 1,2-phthalic acid, and caffeine. The following were obtained from American Radiolabeled Chemicals (St. Louis, MO): acetophenone, nitrobenzene, 1,2-dichloroethane, ethyl acetate, benzamide, benzyl alcohol, 4-chloroaniline, anisole, 1-octanol, 1-hexylamine, ethylamine, and sucrose. The following solutes were partitioned in pH 1.8 stock solutions: benzoic acid, acetic acid, 4-hydroxybenzoic acid, salicylic acid, and 1,2-phthalic acid. The following solutes were partitioned in pH 7.0 stock solutions: 1,4dichlorobenzene, benzene, 1-pentanol, 1-propanol, ethanol, methanol, phenol, 2-propanol, 1,2,4-trichlorobenzene, chlorobenzene, caffeine, acetophenone, nitrobenzene, 1,2-dichloroethane, ethyl acetate, benzamide, benzyl alcohol, anisole, 1-octanol, and sucrose. 4-Chloroaniline was partitioned in a pH 8.7 stock solution. The following solutes were partitioned in pH 12.5 stock solutions: ethylamine, n-propylamine, and n-hexylamine. The primary alcohols (methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol) were additionally partitioned at

Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005 3751

Figure 1. Phase diagram for the PEG-6000/dextran-75000 system using the Merchuk regression method. The letter a denotes phase compositions where the volume ratio (Vr) is 1, b denotes the phase composition at which the LSER study was conducted, c denotes the critical point of the phase diagram, and d denotes the phase compositions at which the different tie lines were generated. The closed circles denote the binodal curve. The open circles denote the tie lines.

the following tie lines to study the effect of TLL on partitioning in the PEG/dextran system: 9.94% (∆EO ) 0.836 m), 13.32% (∆EO ) 1.149 m), 18.40% (∆EO ) 1.682 m), 21.93% (∆EO ) 2.049 m), 24.39% (∆EO ) 2.253 m), 25.91% (∆EO ) 2.502 m). Each system was spiked with 5-7 µL (tracer activity ) 0.06-0.08 µCi/µL) of the solute prepared as detailed in a previous publication.42 After addition of the spike, each system was mixed and then centrifuged for 2 min. Mixing and centrifugation were repeated twice more. Upon completion of the third centrifugation, 100-µL aliquots were removed from each phase, placed into individual vials containing 5 mL of an Ultima Gold scintillation cocktail (Packard, Meridian, CT), and mixed for 2-3 min. Each vial was then counted on a Packard Tri-Carb 1900 TR liquid scintillation analyzer using the 14C protocol. Because equal amounts of the phases were used for the determination of the tracer activity in each phase, the partition coefficients (K) between the phases were calculated as in eq 1.14 A

K) counts per minute in the upper PEG-rich phase counts per minute in the lower dextran-rich phase (1) complete overview of the radiochemical methods used in this study can be found elsewhere.42 The linear free energy relationship (LFER) and the relative contribution of each regression coefficient were obtained by multilinear regression using the program StatBox, release 2.5 (Grimmer Logiciels, 1995-1997), on a PC. The mean deviations of the coefficients calculated in terms of 95% confidence levels based on the statistical analysis were determined using the Student’s t test in eq 2, where µ is the accepted value,

µ ) x + ts/N1/2

(2)

x is the average value, t is the percentile value for the Student’s t test, s is the standard deviation, and N is the number of measurements.43 Results Figure 1 shows the phase diagram for the PEG-6000/ dextran-75000 system, and the system composition at

Figure 2. Natural log of the partition coefficients of n primary alcohols as a function of the carbon chain length in the PEG-6000/ dextran-75000 ABS at the following TLLs: (O) 9.94% (∆EO ) 0.836 m); (]) 13.32% (∆EO ) 1.149 m); (2) 18.40% (∆EO ) 1.682 m); (3) 21.93% (∆EO ) 2.049 m); (9) 24.39% (∆EO ) 2.253 m); (b) 25.91% (∆EO ) 2.502 m).

which the partitioning experiments were conducted is denoted on the graph by the letter b. The phase diagram generated for this study is similar to those for similar polymer pairs given in the literature.5,8 The system chosen for the LSER study is relatively close to the critical point (c), having a TLL of 18.40% (w/w) (∆EO ) 1.682 m). In addition to the system chosen for the LSER study, partitioning studies were performed at the following additional tie lines: 9.94% (∆EO ) 0.836 m), 13.32% (∆EO ) 1.149 m), 21.93% (∆EO ) 2.049 m), 24.39% (∆EO ) 2.253 m), and 25.91% (∆EO ) 2.502 m). Figure 2 presents the results of the distribution ratios of several radiolabeled short-chain alcohols (methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol) in the PEG-6000/dextran-75000 ABS over a series of TLLs. This relationship can be defined by eq 3,10 where ln K

ln K ) A + Enc

(3)

is the natural logarithm of the partitioning coefficient, K. The carbon chain length is defined by nc, and A and E are constants. Because the free energy of transfer of a solute between the phases is given by eq 4, where R

∆G ) -RT ln K

(4)

is the universal gas constant and T is the absolute temperature in Kelvin, it follows that

∆GCH2 ) -RTE

(5)

where E is the slope of the regression line of the relationship between the alkyl chain length and partition coefficient (∆ ln K/∆n) shown in Figure 2. The leastsquares method was used for the determination of the regression line.44-47 Table 2 gives the free energy of transfer of a methylene group, ∆GCH2, calculated using eq 5 for different PEG/salt ABSs, aqueous/organic systems, and polymer/polymer ABSs. As a general trend, Figure 2 shows an increase in the line slope and thus an increase in the free energy of transfer of a methylene group with an increase in TLL, which is consistent with the literature.9,21 We have previously shown that ∆GCH2 increases linearly with TLL9 because TLL is a sensitive measure of the chemical potential difference between the phases of the system. At a TLL of zero, i.e., the critical point,

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Table 2. ∆GCH2 from Polar to Less Polar Phases of Various Biphasic Systems system

-∆GCH2 (kcal/mol)

hexane/watera chloroform/watera octanol/watera butanol/watera methyl ethyl ketone/watera toluene/watera benzene/watera methyl isobutyl ketone/watera diethyl ether/watera PEG-2000/(NH4)2SO4b PEG-3400/K3PO4b PEG-2000/K2CO3b PEG-2000/NaOHb PEG-2000/Li2SO4b PEG-6000/dextran-75000 (this study)c PEG-6000/dextran-70000 (Zaslavsky)d

1.010 0.846 0.730 0.540 0.430 0.959 0.849 0.722 0.732 0.210 to 0.412 0.262 to 0.553 0.263 to 0.696 0.312 to 0.503 0.142 to 0.285 -0.00347 to 0.0235 0.0214

a Values obtained from ref 49. b Value obtained from ref 9. Partitioned at the following TLLs: ∆EO ) 0.836 m; ∆EO ) 1.149 m; ∆EO ) 2.049 m; ∆EO ) 2.253 m; ∆EO ) 2.502 m. d Value obtained and adapted from ref 21. Partitioned in ∆EO ) 1.744 m for the PEG/dextran system. c

the distribution coefficient is assumed to be 1 because the phases are assumed to be of identical composition and the chemical potential difference is zero, which would make the ∆GCH2 values equal to or close to zero, a fact that is borne out in our findings. Figure 3 plots ∆GCH2 values as a function of increasing TLL (∆EO) found in a previous study using a PEG-2000/ (NH4)2SO4 ABS9 and those found in the current study using the PEG/dextran ABS. Because the degree of phase divergence of the systems is represented as a function of ∆EO, the TLL is given a consistent quantitative expression for the two systems. The ∆GCH2 values determined for the PEG/salt system are almost 1 order of magnitude larger than those determined for the PEG/ dextran ABS. Even though the studies in the PEG/ dextran ABS were not performed at the same TLL as those in the PEG/salt ABS, comparisons between the systems can still be made using the relationship between ∆GCH2 and this consistent quantitation of phase divergence. For the PEG/dextran system, Figure 3 shows that the increase in ∆GCH2 with an increase in TLL is not as large as that found for the PEG/salt systems. This is consistent with the findings of Zaslavsky, who reported that, for polymer/polymer ABSs, the values for ∆GCH2 did not exceed -0.100 kcal/mol,19 because while theoretically possible, the higher values could not be achieved, in practice, because of the

Figure 3. Plot of ∆GCH2 as a function of ∆EO for (O) PEG-2000/ (NH4)2SO4 (adapted from ref 9) and (b) PEG-6000/dextran-75000 ABSs.

experimental difficulties associated with handling highly concentrated polymer solutions.11 A comparison of the PEG/salt ABSs and the current PEG/dextran systems shows that the linear relationship between TLL and the free energy of transfer for each system may be approximated by a single continuous function between the two systems. This result is only possible because we have used an expression for the TLL that gives a consistent expression to the chemical potential between the phases in each system. This relationship does not hold, for example, if the % (w/w) composition is used to describe the TLL. This is consistent with the use of amino acids to characterize the relative hydrophobicity of phase systems developed by Kuboi and co-workers48 because the free energy of transfer of a methylene group represents a quantitative determination of the relative hydrophobicity of the phases of the ABS and is approximately equivalent to the relative free energy difference in cavity formation between the phases. For this particular system, the PEG-rich phase is less structured than either the dextran-rich phase or the salt-rich phase, which leads to a relatively large free energy of cavity formation in both the dextran- and salt-rich phases tending to increase the driving force toward partition to the less structured PEG-rich phase. This driving force increases with solute molecular size. Table 2 provides the magnitude of ∆GCH2 for a number of aqueous/organic systems as well as for PEG/salt and other polymer/polymer ABSs.11,49 It can be seen that the free energy of transfer found in the current PEG/dextran system is very small in comparison to that of some of the other systems shown, and this is consistent with other values reported in the literature11 for similar polymer/polymer systems. This rather low value of the free energy of transfer has a number of practical consequences. On the one hand, these ABSs, based on the phase separation of aqueous polymers, will tend to be rather undiscriminating because small changes in the molecular structure will produce negligible changes in the distribution coefficient. On the other hand, this also means that molecules differing widely in size and chemical type should produce measurable distribution coefficients in PEG/dextran ABSs. In aqueous organic systems, partitioning of very hydrophilic or very hydrophobic compounds can result in the inconvenience and inaccuracy of measuring log K values greater than +4 or less than -4. Polymer/ polymer ABSs, while perhaps inappropriate for highly hydrophobic species because of solubility issues in aqueous systems, may offer enhanced discrimination for hydrophilic solutes compared to aqueous/organic systems. Polymer/salt systems, meanwhile, apparently offer a degree of discrimination that can be manipulated over a wide range but that can be almost as great as that offered by aqueous/organic systems. The likely effect for this molecular characterization and for the development of scales of hydrophobicity currently contemplated36 seems not to have been fully appreciated. The optimal choice of ABSs for molecular property determination seems never to have been specifically outlined, nor does the possibility that different ABSs offering differing degrees of discrimination may be used to cover multiple ranges of solute hydrophobicity while still allowing an expression on a common hydrophobic or solute property scale. The current results (e.g., Figure 3), when only the free energy of transfer of a hydropho-


Figure 4. Log of the partition coefficients [b: (1) methanol; (2) ethanol; (3) 1-propanol; (4) 1-butanol; (5) 1-pentanol; (6) 1-octanol; (7) 2-propanol. 0: (8) benzyl alcohol; (9) benzene; (10) anisole; (11) benzamide; (12) nitrobenzene; (13) 1,4-dichlorobenzene; (14) toluene; (15) chlorobenzene; (16) 1,2,4-trichlorobenzene; (17) acetophenone; (18) phenol. 4: (19) acetic acid; (20) 4-chloroaniline; (21) benzoic acid; (22) 1,2-phthalic acid; (23) salicylic acid; (24) ethylamine; (25) 1-propylamine; (26) 4-hydroxybenzoic acid; (27) 1-hexylamine. 1: (28) ethyl acetate; (29) sucrose; (30) 1,2dichloroethane; (31) caffeine] in ABS formed with 5% (w/w) PEG6000 and 10% dextran-75000 (TLL ) 18.40%; ∆EO ) 1.682 m) vs log 1-octanol/water partition coefficient (P). The regression line is drawn through the linear alcohols only.

bic group is considered, suggest that polymer/polymer and polymer/salt systems could be arranged so as to represent a continuum of partitioning systems having different degrees of resolution driven by differences in chemical potential. However, this conclusion presupposes that differences in hydrophilic solute/solvent interactions in different ABSs are insignificant, and this has not been shown. In a previous publication, solute distribution ratios in a PEG-2000/(NH4)2SO4 ABS were compared to distribution ratios in the 1-octanol/water solvent system.9 Figure 4 shows a similar comparison based on the distribution ratios of 31 small organic solutes partitioned in their neutral forms in the current PEG/dextran ABS and shown as a function of their 1-octanol/water partition coefficient (log P).50 As is well-known, an approximately linear relationship exists between any two partitioning systems, and this is generally expressed in the form of the Collander equation51 (eq 6),

log P2 ) a log P1 + b

(6)

where subscripts 2 and 1 represent the systems being compared, in this case PEG/dextran ABS and 1-octanol/ water, respectively. Figure 4 illustrates the difficulties found in using the Collander equation, in practice, to predict the partition of a wide range of solutes differing in structure and function and emphasizes the importance of molecular interactions beyond simple hydrophobicity in determining the solute distribution. A regression line through the linear alcohols emphasizes that when molecules differ only in hydrophobicity, having identical functional groups, then the Collander relationship may accurately describe the data. However, when, for example, those alcohols are compared with compounds with similar carbon chain length but differing functional groups, a simple linear relationship between the partition coefficients in the different systems is lacking. Using the examples of ethanol, acetic acid, and ethylamine (solutes 2, 19, and 24, respectively, as shown in Figure 4), the log P values are relatively similar, but the log K values

show distinct differences with a change in the functional group. The complexity of the relationship between these two systems is defined by the existence of differing molecular interactions between the solute and solvent in the different systems being compared. While it is often thought that log P is a measure of hydrophobicity, in fact, as shown in Figure 4, log P is determined by the totality of the molecular interactions with the phase. In practice, ∆GCH2 seems to be a better measure of hydrophobicity because it is defined only by the interactions of methylene groups with the phases. It is thus strongly related to the relative free energy of cavity formation in each of the phases. However, as illustrated by Figure 4, the distribution of solutes in different solvent systems is not solely based on differences in hydrophobicity but is also based on differences in solute/solvent-phase interactions (hydrophilicity and solvophilicity). The complexity of these molecular interactions may be formalized at least conceptually in the form of a general solvation equation such as eq 7.

some property ) cavity terms + polarity terms + hydrogen bonding terms + constant (7) It is generally recognized that solute/solvent interactions are described by several additive molecular properties of molecules and that such properties can be isolated as formal descriptors of the solvation process. For example, by grouping the solutes of Figure 4 into categories based on chemical nature, e.g., alkyl alcohols or the aryl derivatives, a stronger correlation between log D for the ABS and log P for the 1-octanol/water system is evident. Thus, similarities in solute partitioning behavior are, in part, attributable to the existence of similar hydrogen-bonding interactions between solutes of a similar nature and the solvents comprising the phases of the system. Considering ∆GCH2, incremental changes to n(CH2) are related to incremental changes in the free energy of cavity formation, complicated only by dispersion forces. The use of eq 5 to obtain the free energy of transfer of a methylene group seems to be a direct measure of the relative hydrophobicity of the phases in the system because the other intermolecular forces in determining solute distribution in the system are essentially hydrophilic in nature. The use of LFER, often based on quantitative versions of eq 7, to model molecular processes such as partitioning in ABS, inter alia, is well established.23,46,47,52 Abraham has developed a generalized solvation equation using Gibbs free-energy-based molecular property descriptors. A subset of LFERs, LSERs, have been used to characterize a wide variety of solvent systems including partitioning in various aqueous/organic systems and aqueous micellar systems.9,47,52 Abraham’s generalized solvation equation is usually given as in eq 8, where H H log SP ) c + rR2 + sπH 2 + aΣR2 + bΣβ2 + vVx

(8)

log SP refers to some solubility-related property of a series of solutes, R2 refers to the excess molar refraction of each solute, πH 2 is the solute dipolarity/polarizability, H ΣRH 2 is the effective hydrogen bond acidity, Σβ2 is the effective hydrogen bond basicity, and Vx is the McGowan volume. It should be noted that, in the case of solutes such as haloanilines, for example, 4-chloroaniline, Σβ has two values, βH 2 for partitioning in water/alkane

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Table 3. Abraham Solute Descriptors and Solute Distribution Ratios for a PEG-6000/Dextran-75000 ABS solute

R2

π2

ΣRH 2

ΣβH 2

Vx

log K, expt

log Pa

log K, calc

squared error (×10-3)

descriptor ref

methanol ethanol 1-propanol 1-butanol 1-pentanol 2-propanol benzyl alcohol benzene anisole benzamide 1-octanol ethyl acetateb acetic acidb 4-chloroanilinec nitrobenzene 1,4-dichlorobenzene toluene chlorobenzene 1,2,4-trichlorobenzene sucrose benzoic acid 1,2-phthalic acid salicylic acid acetophenone 1,2-dichloroethaneb phenol ethylamine 1-propylamine 4-hydroxybenzoic acidb 1-hexylamine caffeine

0.278 0.246 0.236 0.224 0.219 0.212 0.803 0.610 0.708 0.990 0.199 0.106 0.265 1.060 0.871 0.825 0.601 0.718 0.980 1.970 0.730 0.850 0.890 0.818 0.416 0.805 0.236 0.225 0.930 0.197 1.500

0.440 0.420 0.420 0.420 0.420 0.360 0.870 0.520 0.750 1.500 0.420 0.620 0.650 1.130 1.110 0.750 0.520 0.650 0.810 2.500 0.900 1.600 0.840 1.010 0.640 0.890 0.350 0.350 0.900 0.350 1.630

0.430 0.370 0.370 0.370 0.370 0.330 0.330 0 0 0.490 0.370 0 0.610 0.300 0 0 0 0 0 2.100 0.590 0.820 0.710 0 0.100 0.600 0.160 0.160 0.810 0.160 0

0.470 0.480 0.480 0.480 0.480 0.560 0.560 0.140 0.290 0.670 0.480 0.450 0.450 0.310 0.280 0.020 0.140 0.070 0 3.200 0.400 0.750 0.380 0.490 0.110 0.310 0.610 0.610 0.560 0.610 1.240

0.308 0.449 0.590 0.731 0.872 0.590 0.916 0.717 0.916 0.973 1.295 0.747 0.465 0.939 0.891 0.961 0.857 0.839 1.084 2.228 0.932 1.147 0.990 1.014 0.635 0.775 0.490 0.631 0.990 1.054 1.363

0.058 0.069 0.087 0.116 0.130 0.093 0.147 0.161 0.172 0.166 0.188 0.167 0.062 0.165 0.171 0.188 0.187 0.173 0.193 0.023 0.173 0.203 0.170 0.164 0.117 0.184 0.040 0.074 0.228 0.132 0.077

-0.770 -0.310 0.250 0.880 1.510 0.050 1.100 2.130 2.110 0.640 3.000 0.730 -0.170 1.830 1.850 3.440 2.730 2.840 4.020 -3.700 1.870 0.730 2.260 1.580 1.480 1.460 -0.130 0.480 1.580 2.060 -0.070

0.059 0.075 0.096 0.116 0.138 0.080 0.134 0.145 0.160 0.159 0.201 0.123 0.104 0.174 0.171 0.204 0.166 0.177 0.224 0.033 0.177 0.196 0.185 0.152 0.155 0.166 0.049 0.070 0.163 0.132 0.087

0.001 0.047 0.081 0.001 0.072 0.185 0.169 0.235 0.143 0.054 0.175 1.896 1.747 0.084 0.000 0.291 0.413 0.018 0.947 0.091 0.017 0.045 0.247 0.125 1.495 0.336 0.086 0.016 4.203 0.000 0.101

47 47 47 47 47 47 47 47 47 47 47 47 47 47, 52, 53 47 47 47 47 47 55 52 54 55 47 47 47 47 47 54 47 54

a

Obtained from ref 50. b Not included in the final subset. c Used the Σβ02 parameter for this solute.

systems and β02 for partitioning between water and those partly miscible solvents such as 1-octanol.52 For this study, the latter value is used because of the aqueous nature of ABSs. These are related to the solubility property through the coefficients describing the interaction with the solvent and, thus, c is a constant for the linear regression, r reflects the ability of the solvent to interact through π- and n-electron pairs, s is the solvent dipolarity/polarizability, a is the solvent hydrogen bond basicity, b is the solvent hydrogen bond acidity, and v is the phase lipophilicity. It should be noted that hydrogen bond interactions occur through opposite pairs in solute and solvent interactions. Gibbs energy-related solute descriptors determined in a variety of partitioning processes have been tabulated and published by Abraham.47,52-55 The magnitudes and signs of the regression coefficients characterizing eq 8, as applied to partitioning, are determined by multiple linear regression of the solute descriptors on the logarithm of the partition coefficient, and thus they reflect the relative solvent properties of the phases corresponding to the appropriate solute descriptors. Consequently, r represents the relative strengths in each of the phases of the solute/solvent interactions in the equilibrium phases determined by interactions of nonbonding and π electrons of the solute, and a represents the relative contribution of solvent hydrogen bond basicity, in each phase, because it corresponds to those interactions involving solute hydrogen bond acidity, and so on. A positive sign indicates a positive influence and a negative sign demonstrates a negative influence on the magnitude of the predicted property (partition coefficient). As mentioned above, we have previously applied this approach to the study of solute distribution in PEG/salt

ABSs.9 Here, we adopt the same approach to the study of partitioning in PEG/dextran ABSs. Presently, the results should be considered preliminary because the distribution of rather few compounds has been examined and thus the results may not be statistically robust. In addition, for reasons that are not fully understood, there seems to be more statistical uncertainty associated with these results than were previously seen for the PEG/salt ABSs. It is possible that this is due to the aforementioned lack of discrimination in these systems. However, in principle, one would expect the greatest uncertainty in the measurement of partition coefficients to be attached to very large or very small values of the partition coefficients rather than the modest finite values (i.e., distribution coefficients close to 1) found here. However, it should also be noted that, although the Abraham parameters are generally considered to work well over large ranges of log K, it is possible that they may not perform so well over small ranges of log K. The greater uncertainties seen in this study may arise from a failure of the Abraham descriptors to fully capture the subtleties of partitioning in the current system. Numerous potential sources of experimental error should also be mentioned. Solutes were partitioned at various pH values, as described in the Methods section. Clearly, this may give rise to random experimental errors, but it could also give rise to systematic errors because the buffer composition and ionic strength are significantly altered for each molecular group based on pKa. The magnitude and nature of such effects have not been specifically investigated. Table 3 presents the complete set of 31 radiolabeled solutes whose distribution coefficients were used to examine the solvent properties of the PEG/dextran ABSs by multiple linear regression using Abraham’s molecular property descriptors for each solute. For the


Figure 5. Log of the partition coefficients [b: (1) methanol; (2) ethanol; (3) 1-propanol; (4) 1-butanol; (5) 1-pentanol; (6) 1-octanol; (7) 2-propanol. 0: (8) benzyl alcohol; (9) benzene; (10) anisole; (11) benzamide; (12) nitrobenzene; (13) 1,4-dichlorobenzene; (14) toluene; (15) chlorobenzene; (16) 1,2,4-trichlorobenzene; (17) acetophenone; (18) phenol. 4: (19) acetic acid; (20) 4-chloroaniline; (21) benzoic acid; (22) 1,2-phthalic acid; (23) salicylic acid; (24) ethylamine; (25) 1-propylamine; (26) 4-hydroxybenzoic acid; (27) 1-hexylamine. 1: (28) ethyl acetate; (29) sucrose; (30) 1,2dichloroethane; (31) caffeine] in ABS formed with 5% (w/w) PEG6000 and 10% (w/w) dextran-75000 (TLL ) 18.40%; ∆EO ) 1.682 m) as a function of values determined by the calculated regression coefficients (Tables 4-6) and the solute descriptors (Table 3) utilizing eq 8. Table 4. Comparison of Equation Coefficients through the Elimination of Solutes data set

no. of solutes

r(R2)

complete w/out (1)a w/out (2)b w/out (3)c w/out (4)d

31 30 29 28 27

-0.03 -0.06 -0.03 -0.04 -0.05

H H s(πH 2 ) a(ΣR2 ) b(Σβ2 ) v(Vx)

0.05 0.07 0.05 0.06 0.07

0.04 0.02 0.03 0.04 0.04

-0.16 -0.15 -0.15 -0.15 -0.16

0.15 0.15 0.14 0.13 0.13

c

R2

0.06 0.05 0.05 0.06 0.06

0.82 0.88 0.90 0.91 0.94

a 4-Hydroxybenzoic acid was not included. b 4-Hydroxybenzoic acid and ethyl acetate were not included. c 4-Hydroxybenzoic acid, ethyl acetate, and acetic acid were not included. d 4-Hydroxybenzoic acid, ethyl acetate, acetic acid, and 1,2-dichloroethane were not included.

most part, ionizable solutes were partitioned under conditions of pH (2 pH units above or below pKa) such that the solute could be expected to behave as a neutral (nondissociated) compound. The only exception to this was 1,2-phthalic acid, where this was not experimentally possible, as noted in Table 1. The results of the multiple regression of Abraham’s generalized solvation equation for the complete set of 31 solutes are shown in Figure 5. A number of solutes proved to have rather large squared-error values in this regression, and these were omitted in a stepwise fashion to give a final solute set of 27 different solutes, with the regression being redetermined at each stage. Table 4 provides the coefficients of Abraham’s generalized solvation equation for the various subsets from Table 3 for which it was computed. The substances that were eliminated in the final regression are denoted in Table 4. It can be seen that removal of various solutes significantly improves the regression coefficient but has very little effect on the absolute and relative magnitudes of any of the coefficients of the generalized solvation equation. This is indicated by the fact that the determined coefficients show little or no change with each regression. The improvement of the regression without a significant change in its coefficients may indicate that the regression gives a reasonable description of the

solvent properties of the system despite rather large errors associated with the determination of some of the data. Tables 5 and 6 provide a statistical analysis of the multiple linear regression of the distribution ratios as well as a comparison with the results obtained in the earlier study.9 Table 5 shows the magnitudes and signs of the coefficients obtained through the regression. The substances that were eliminated in the final regression (4-hydroxybenzoic acid, ethyl acetate, acetic acid, and 1,2-dichloroethane) are denoted in Table 3. As mentioned above, removal of these solutes improves the regression coefficient but has little effect on the coefficients of the generalized solvation equation. Further speculative reasons for the deviation of these particular solutes from the overall regression can be attributed to internal hydrogen bonding (4-hydroxybenzoic acid), volatility (1,2-dichlorethane), and similarities in structure between buffer components and solutes (ethyl acetate and acetic acid). Table 6 shows the stepwise significance of the solvent descriptors in describing the distribution of the solutes in the PEG/dextran system for two of these data sets, the full 31 solutes and the reduced set of 27 solutes, as well as that of the PEG/salt system.9 For the PEG/ dextran systems, the most statistically significant parameter is b, which corresponds to the solvent hydrogen bond acidity (the corresponding solute parameter for this term is ΣβH 2 ). Another significant finding is that the significance of this term shows a marked increase with the elimination of the solutes associated with large errors in the regression. The b parameter accounts for approximately 25% of the variability in the partitioning for the full solute set and 32% for the reduced solute set, indicating a higher degree of scatter for some strong hydrogen-bonding bases. The high degree of significance of this parameter differs from previous findings for the PEG/salt ABS in that the v term was the most significant term in that system. This could be attributed to the nature of the two systems, i.e., the fact that the biphase is formed between two polymer-rich aqueous phases. Thus, the relative difference in the cohesive energy density between the phases is very low. This is clearly reflected in the very low interfacial tensions found for polymer/polymer systems, allowing, for instance, for equilibrium distribution of particles between the phases of such systems.14,15 Regression of the individual parameters b and v on log K (data not shown) shows that the likely cause of the higher significance of b over v is the influence of the highly basic solutes caffeine and sucrose on the regression. In the PEG/dextran system, the v term is the secondmost statistically significant parameter. This is related to the relative free energy of cavity formation in these coexisting phases, as well as the relative phase lipophilicity. The corresponding molecular descriptor is the McGowan volume, a simplified molecular volume parameter, related to the van der Waals volume of the solute. This coefficient is considered to be a measure of the relative hydrophobicity of the system and is similar to ∆GCH2 in that it reflects the difference in free energy needed for cavity formation between the two phases, each enriched in a different polymer. A large and positive v value is typical for aqueous/organic systems because the most significant intermolecular interaction is an extensive amount of hydrogen bonding in the

3756


Table 5. Comparison of Equation Coefficients for PEG/Dextran and PEG/Salt Systems PEG-6000/dextran-75000 (31 solutes)

PEG-6000/dextran-75000 (27 solutes)a

PEG-2000/(NH4)2SO4 (29 solutes)b

parameter

coefficient

probability

coefficient

probability

coefficient

probability

r(R2) s(πH 2) a(ΣRH 2) b(ΣβH 2) v(Vx) c R2 F

-0.03 0.05 0.04 -0.16 0.15 0.06 0.82 27.74

0.210 0.0513 0.0159 1.69 × 10-10 8.45 × 10-7

-0.05 0.07 0.04 -0.15 0.13 0.06 0.94 84.19

0.0113 0.00027 0.001963 3.12 × 10-14 1.47 × 10-9

0.65 -0.21 0.21 -1.31 1.71 -0.05 0.97 187.58

9.97 × 10-5 0.154 0.0887 4.3 × 10-7 1.32 × 10-13

a

Solute exclusions noted in Table 3. b Adapted from ref 9.

Table 6. Stepwise Relative Contributions of the Descriptors for the PEG-6000/Dextran-75000 and PEG-2000/(NH4)2SO4a ABSs system (no. of solutes) PEG-6000/dextran-75000 (31 solutes) full LSER (eq 8)

PEG-6000/dextran-75000 (31 solutes) reduced LSER (eq 10) PEG-6000/dextran-75000 (27 solutes)a



a

coefficients

adjusted R2 for LSER

b

0.24

b+v b+v+a b+v+a+s b+v+a+s+r b

0.75 0.80 0.81 0.82 0.24

b+v b+v+a b

0.75 0.80 0.32

b+v b+v+a b+v+a+s b+v+a+s+r v

0.83 0.89 0.92 0.94 0.78

b+v b+v+r a+b+v+r s+a+b+v+r v

0.93 0.97 0.97 0.97 0.78

b+v b+v+r

0.93 0.97

Solute exclusions noted in Table 3. b Adapted from ref 9.

aqueous phase, which provides an energetic penalty to cavity formation. The v parameter for the PEG/dextran system is significantly reduced compared to the aqueous/organic and PEG/salt partitioning systems, as shown in Table 7. The confidence levels for the PEG-6000/dextran-75000 are reported as well. A comparison of the v values for the PEG/salt (v ) 1.71; ∆EO ) 16 m) and PEG/dextran (v ) 0.15; ∆EO ) 1.682 m) systems with ∆GCH2 values for each system (0.285 and 0.019 kcal/mol, respectively) shows a similar proportionality between ∆GCH2 and v in both systems, based on the assumption that ∆GCH2 increases linearly with TLL. The order of significance of the coefficients for the PEG/dextran system was b > v > a. However, the coefficient a is on the margins of significance particularly for the full solute set. The parameters for the complete 31-solute data set are shown in Table 5. All of the other coefficients have a little influence on the regression. Thus, the molecular properties of the solute that have the most influence on its distribution in the PEG/ dextran system are the solute molecular weight (corresponding to the Vx term) and solute hydrogen bond acceptor basicity (corresponding to the ΣβH 2 term). These parameters work in opposition to one another, with an

increase in the molecular size leading to a preference for distribution to the PEG-rich phase and an increase in the solute basicity leading to an increased preference for distribution to the dextran-rich phase. An examination of the dextran and PEG structures (Figures 6 and 7, respectively) further illustrates this. For PEG solutions, there is a relative decline in the hydrogen bond acidity but little decline in the hydrogen bond basicity, which suggests that PEG/hydrogen bond acceptors reduce the donor ability of water. Because dextran has more balanced acceptor and donor sites, this leaves the structure of water relatively unchanged. This is remarkably similar to the solute molecular properties that have the greatest influence on the solute distribution in the PEG/salt system reported in a previous publication.9 In terms of the major influencing parameters, it is also quite similar to the 1-octanol/water system, which is indicated in Table 7, where the volume and solute basicity also dominate the distribution. However, the relative magnitudes of the b and v coefficients are quite different in the 1-octanol/water systems and the coefficients r and s are also much higher than those in the PEG/dextran system. The ability of the PEG/dextran system to partition macromolecules and particles without denaturation or coagulation is reflected in the small size of the b and v coefficients. A second point in this discussion should be noted by a discrepancy between ∆GCH2 calculated experimentally and ∆GCH2 determined from the general LSER. Substituting vVx in eq 5 for E gives the following equation:

∆G ) -RTvVx

(9)

Using 0.141 for ∆Vx and v ) 0.15 and multiplying by 2.303 to convert the number to a natural log scale give ∆GCH2 as -0.029 kcal/mol. This is indicated by the regression line for the alcohols in Figure 5. This could be attributed to the solvent nature of these systems, for instance, the possibility of the interactions of the solutes with the polymers. It is also possible that, in an aqueous solution containing cosolutes, different domains or chemical environments may exist that differ in their interactions with different solutes. For example, it is conceivable that EO groups may show the potential for interaction with aromatic molecules or that the end OH groups may show a preference for interaction with hydrogen bond donor solutes. Consequently, if the solute partitioning is governed by different interactions in different regions of the solvent, analysis using the LSER approach may be confounded. On the other hand, there is a strong correlation between the increase in the free energy of transfer of the alcohols with an increase in the chain length and a


Figure 6. Structure of the dextran polymer. For dextran-75000, n is approximately 77. Table 7. Abraham’s Solvent Descriptors for Various Partitioning Systems solvent

c

PEG-6000/dextran-75000 (31 solutes) PEG-2000/(NH4)2SO4 (29 solutes) SDS (Merck) sodium decyl sulfate (SDecS; Merck) sodium octyl sulfate SDS CTAB dodecyltrimethylammonium bromide nonionic Brij-35 1-octanol chloroform hexane di-n-butyl ether propylene glycol dipelargolate

r(R2)

0.06 ( 0.03 -0.03 ( 0.05

0.05 ( 0.05

1 RH 2 βH 2

v(Vx)

ref

0.04 ( 0.03 -0.16 ( 0.03 0.15 ( 0.05 this study

0.65

-0.21

0.21

-1.31

1.71

9

-2.16 -2.43

0.42 0.32

-0.34 -0.24

-0.11

-1.72 -1.60

2.90 2.69

56 56

-1.97 -0.62 -0.57 -0.87

0.45 0.32 0.57 0.57

-0.31 -0.57 -0.15 -0.40

-0.12 -0.08 0.85 0.28

-1.87 -1.84 -3.61 -1.82

2.85 3.25 3.36 2.98

56 57 57 58

-0.31 0.09 0.13 0.36 0.18 0.13

0.88 0.56 0.12 0.58 0.82 0.37

-0.15 -1.05 -0.37 -1.72 -1.50 0.62

1.06 0.03 -3.39 -3.60 -0.83 -1.02

-3.58 -3.46 -3.47 -4.76 -5.09 -4.91

2.83 3.81 4.52 4.34 4.69 4.18

57 23, 46, 52, 59, 60 61 60 22, 61 22, 61

Table 8. Correlation Tables for LSER Data

R2 π2 Σ Σ Vx

b(ΣβH 2)

-0.05

Figure 7. Structure of PEG. For PEG-6000, n is approximately 134.

R2

a(ΣRH 2)

s(π2)

π2

ΣRH 2

Σ

βH 2 Vx

0.904 1

0.448 0.600 1

0.555 0.708 0.781 1

0.773 0.785 0.540 0.708 1

combination of Abraham’s molecular volume (Vx) and polarizability (R2) parameters.53 A closer examination of the relationship between the increase in the distribution of the alcohols (∆ ln K, obtained by the difference from methanol) and the parameters Vx and R2 gives evidence of this (data not shown). The overall correlation of the parameters is shown in Table 8. It may be seen from Table 8 that there is a cross correlation between the parameters R2, Vx, and ΣβH 2 and also between some other pairs of parameters. This may be considered a deficiency in the current study, rising in part from the

constraints on our solute set. Thus, the discrepancy between the volume coefficient of the full LSER and the free energy of transfer of a methylene group may arise from the inability of the LSER to strictly separate the contributions arising from the molecular size and polarizability. Obviously, these are rather closely related chemical properties. Consequently, the intriguing question of whether the analysis by LSER reveals details of the structuredness of these polymeric solvent systems and the existence of different solvent domains, as might be assumed from the behavior of the volume parameter and the free energy of transfer term, cannot really be addressed with the present limited data. Abraham’s generalized solvation equation for the 31solute data set is shown in eq 10: H log K ) 0.06 - 0.03R2 + 0.05πH 2 + 0.04ΣR2 -

0.16ΣβH 2 + 0.15Vx (10) For the previously examined PEG-2000/(NH4)2SO4 system, Abraham’s generalized solvation equation was found to be as shown in eq 11.9 In both cases, the

3758


H log K ) -0.05 + 0.65R2 - 0.21πH 2 + 0.21R2 -

1.31ΣβH 2 + 1.71Vx (11) equations can be simplified by recalculation following elimination of the least significant parameters. For the PEG/dextran system, the simplified equation is expressed as in eq 12. For the PEG-2000/(NH4)2SO4 H log K ) 0.06 + 0.05ΣRH 2 - 0.15Σβ2 + 0.16Vx (12)

system, the simplified equation is expressed as in eq 13.9 These two regressions are strikingly similar; how-

log K ) -0.05 + 0.50R2 - 1.22ΣβH 2 + 1.70Vx (13) ever, the magnitude of the parameters is much smaller for the PEG/dextran system than for the PEG/salt ABS, reflecting the much smaller free energy of transfer between the PEG- and dextran-rich phases, as already shown by the magnitude of ∆GCH2. It is noteworthy that the cavity parameter (v) in the PEG/salt ABS (1.71) is about 10 times the magnitude of its value in the PEG/ dextran system (0.15), closely matching the difference in magnitude of the free energy of transfer of a methyl group described earlier. Similarly, the solvent acidity parameter (b) shows a similar difference (-1.31 for PEG/salt and -0.16 for PEG/dextran) in magnitude between these two systems. It is possible to compare the distributions in the PEG/ dextran and PEG/salt systems directly, and this has been done in Figure 8, where log K in the present PEG/ dextran system is compared to log K in the PEG/(NH4)2SO4 ABS. It should be noted that Figure 8 only contains 24 solutes, which is the number of solutes common to the two studies. The results are unusually well correlated for a comparison between two partitioning systems, with a few exceptions, most notably the haloaromatics and 4-hydroxybenzoic acid (solutes 13, 15, 16, and 26 in Figure 8). The distribution of 4-hydroxybenzoic acid appears to be higher than expected in the PEG/ dextran system, as discussed previously (see Figure 4); however, the distribution of the haloaromatics may be attributable to the change of sign and magnitude of the r term between the two systems. The haloaromatics are rich in nonbonding electrons and thus have a significant R2 solute descriptor term. This appears to result in an increase in the partition coefficient relative to the other solutes in the PEG/salt system, compared to the PEG/ dextran system. This difference is also reflected in the LSERs for each system and may be a significant difference between them. However, it must be remembered that the TLLs of these two systems are quite different. The PEG/dextran system lies reasonably close to the critical point (TLL ) 18.40%; ∆EO ) 1.682 m), whereas the PEG/salt system is relatively removed from the critical point (TLL ) 44.92%; ∆EO ) 16 m). This may result in some departure from linearity of the relationship between partitioning and TLL, as was noted in previous work.9 The similarity between the LSERs and the correlation apparent in Figure 8 could be interpreted to imply that there is little to be gained in the use of PEG/dextran systems compared to PEG/salt systems except reduced salting-out strength (decreased precipitation of biosolutes) and increased biocompatibility (isotonicity). It also seems implicit that the use of these systems to give access to molecular properties such as hydrophobicity

Figure 8. Log of the partition coefficients [b: (1) methanol; (2) ethanol; (3) 1-propanol; (4) 1-butanol; (5) 1-pentanol; (6) 1-octanol; (7) 2-propanol. 0: (8) benzyl alcohol; (9) benzene; (10) anisole; (12) nitrobenzene; (13) 1,4-dichlorobenzene; (14) toluene; (15) chlorobenzene; (16) 1,2,4-trichlorobenzene; (17) acetophenone; (18) phenol. 4: (19) acetic acid; (20) 4-chloroaniline; (21) benzoic acid; (26) 4-hydroxybenzoic acid. 1: (28) ethyl acetate; (30) 1,2-dichloroethane] in a PEG-2000/(NH4)2SO4 ABS (TLL ) 44.92%; ∆EO ) 16 m) vs the distribution values obtained in a PEG-6000/dextran75000 ABS (TLL ) 18.40%; ∆EO ) 1.682 m). The data used for PEG-2000/(NH4)2SO4 were adapted from ref 9.

would yield identical results, but on scales having different ranges. However, such conclusions are probably premature given the small size of the solute sets studied so far. In addition, the apparent influence of aromaticity and nonbonding electrons on partitioning in PEG/salt ABSs may represent an important consideration. Such conclusions also stand in contradiction to the conclusions of Zaslavsky, who has suggested that PEG/salt systems are relatively unsuited to the determination of molecular properties compared to PEG/ dextran systems because of large differences in electrostatic properties between the two phases.20,45 Conclusions Free energy relationships have been applied to the study of the molecular properties that govern solute partitioning in a PEG/dextran ABS, an approach that allows comparisons to other solvent/water systems such as 1-octanol/water and PEG/salt ABSs. A significant feature of the PEG/dextran ABS LSER is the statistical significance of the b coefficient, which accounts for at least 24% of the partitioning variability. The secondmost statistically significant term is v, which corresponds to the relative free energy of cavity formation in these coexisting phases. The corresponding molecular descriptor is the McGowan volume (Vx), related to the van der Waals volume of the solute. The v term is significantly smaller than is typical for aqueous/organic systems or even PEG/salt systems at moderate TLL. In aqueous/organic systems, extensive hydrogen bonding in the aqueous phase is the most significant intermolecular interaction, which provides an energetic penalty to cavity formation and results in a large v coefficient. Here, the meaning of the v coefficient is the same and reflects the fact that the aqueous PEG-rich phase is less structured than the aqueous dextran-rich phase. Because the coefficients have a relatively small magnitude in comparison to other solvent/water systems, this allows for the partition, fractionation, and study of labile, highly hydrophilic biological solutes such as proteins in PEG/dextran ABSs. Another advantage is that the proteins and other labile macromolecules


studied maintain their structure, activity, and molecular conformation as close to the native state as is currently possible to achieve. In biochemical applications, this provides distinct advantages because many biological proteins and molecules are labile and the PEG/dextran system is “soft” enough to support them and clearly not as “harsh” as solvent/water systems or PEG/salt ABSs.17,25-31,36,37 Because of the similarities between the phases, the application of PEG/dextran for industrialscale extraction of small organics is unlikely to be economically feasible because partition coefficients tend to unity. However, the work presented here may be useful in promoting the use of partitioning in polymer/ polymer and polymer/salt systems as an analytical tool for the determination of solute molecular properties. This may be of some importance in proteomic studies in providing, in quantitative hydrophobicity, a further molecular parameter by which proteins may be characterized in addition to the charge and size to the benefit of structure/property relationships and the design of separations strategies. These results provide some explanation and further confirmation of the utility of using PEG-based ABSs as an alternative to solvent/water biphasic systems for quantitative structure activity relationships and for the characterization and separation of biomolecules, macromolecules, and supramolecular assemblages, nanoparticulates, organelles, and particulates. These preliminary studies indicate that the PEG/salt and PEG/ dextran systems examined thus far seem to have rather similar solvent properties in that the volume and basicity are the principle determinants involved in solute distribution between the phases. The signs of the coefficients for these property descriptors in the LFER are the same, but their magnitudes are smaller in the PEG/dextran ABS as compared to the PEG/salt ABS. This has implications for the use of these systems for the determination of molecular properties because partition coefficients determined in these systems may, with care, be used to derive common scales of hydrophobicity and basicity over considerably different ranges. Acknowledgment Funding for this research was made possible by the Division of Chemical Sciences, Geosciences, and Bioscience, Office of Basic Energy Research, U.S. Department of Energy (Grant DE-FG02-96ER14673). The authors also thank the reviewers for their beneficial comments prior to publication of this paper. Literature Cited (1) Bennett, B.; Larter, S. R. Quantitative Separation of Aliphatic and Aromatic Hydrocarbons Using Silver Ion-Silica Solid-Phase Extraction. Anal. Chem. 2000, 72, 1039-1044. (2) Sen˜ora´ns, F.; Ruiz-Rodrı´gues, A.; Iban˜ez, E.; Tabera, T.; Regiero, G. Countercurrent Supercritical Fluid Extraction and Fractionation of Alcoholic Beverages. J. Agric. Food Chem. 2001, 49, 1895-1899. (3) Visser, A. E.; Swatloski, R. P.; Rogers, R. D. pH-Dependent Partitioning in Room-Temperature Ionic Liquids. Green Chem. 2000, 2, 1-4. (4) Visser, A. E.; Swatloski, R. P.; Reichert, W. M.; Griffin, S. T.; Rogers, R. D. Traditional Extractants in Nontraditional Solvents: Groups 1 and 2 Extraction by Crown Ethers in RoomTemperature Ionic Liquids. Ind. Eng. Chem. Res. 2000, 39, 35963604. (5) Partitioning in Aqueous Two-Phase Systems: Theory, Methods, Uses and Applications to Biotechnology; Walter, H., Brooks, D. E., Fisher, D., Eds.; Academic Press: Orlando, FL, 1985.

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Received for review June 11, 2004 Revised manuscript received February 4, 2005 Accepted February 17, 2005 IE049491C

Dextran

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