Solvent Properties of Aqueous Biphasic Systems Composed of

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Solvent Properties of Aqueous Biphasic Systems Composed of Polyethylene Glycol and Salt Characterized by the Free Energy of Transfer of a Methylene Group between the Phases and by a Linear Solvation Energy Relationship Heather D. Willauer, 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 salt have been examined as potential environmentally benign solvents for liquid/liquid extraction. These systems might also represent an alternative to traditional solvent/water systems used in quantitative structure-activity relationships (QSARs). For the application and design of these systems, it is important to have a thorough understanding of the nature of the solvent and its interactions with the solute, and thus, PEG/salt ABSs have been characterized to this end by a variety of methods. The relative hydrophobicities of several PEG/salt ABSs composed of different molecular weights of PEG (1000, 2000, and 3400) and a variety of inorganic salts [K3PO4, K2CO3, (NH4)2SO4, Li2SO4, MnSO4, ZnSO4, and NaOH] were measured by the free energy of transfer of a methylene group ∆GCH2. These results indicate that the relative hydrophobicity of a PEG/salt ABS is a function of only the degree of phase divergence of the biphasic system as expressed by the difference in polymer concentration between the phases [delta poly(ethylene glycol) (∆PEG), delta ethylene oxide monomer (∆EO)] or the tie line length (TLL). The distributions of a wide range of solutes differing in structure and functionality were also measured in PEG/salt ABSs, and the results were compared to the corresponding 1-octanol/water partition coefficients. These data were used to develop a linear free energy relationship (LFER) based on Abraham’s generalized solvation equation, enabling a direct comparison to be made between the solvent properties of PEG/salt ABSs and those of traditional solvent/water systems used, for example, in the determination of log P. Similar comparisons are also enabled with the properties of certain aqueous micellar systems. 1. Introduction Aqueous biphasic systems (ABSs) represent critical phenomena occurring in aqueous solutions when mixtures of polymers are combined with one another or with certain inorganic salts above critical concentrations or critical temperatures.1-4 These systems are unique because each of the phases is over 80% water on a molal basis and yet the phases are immiscible and differ in their solvent properties. Thus, they can be used for the differential distribution of added solutes. Because of their mild nature, which is consonant with the maintenance of macromolecular structure, such systems have been employed for the separation of biological macromolecules and particles for over 40 years.1-4 Recently, these systems have shown promise as unique, environmentally benign alternatives to traditional solventbased biphasic systems for the separation of metal ion species,5-9 small organic molecules,10-12 and lignins from cellulose in the paper pulping process.13-15 Separation processes are ubiquitous in the chemical industry, and as a result, increasing attention is being shown to these processes, particularly with regard to * Corresponding authors: Jonathan G. Huddleston and Robin D. Rogers, Department of Chemistry, Box 870336,The University of Alabama, Tuscaloosa, AL 35487. Phone: 205/ 348-4323. Fax: 205/348-0823. E-mail: [email protected], [email protected].

their environmental impact. Thus, more environmentally benign separation processes are being developed and utilized in industry such as solid-phase extraction (SPE),16 supercritical fluid extraction (SFE),17 and roomtemperature ionic liquids (RTILs).18,19 Aqueous biphasic systems represent safe, nontoxic, nonflammable, nonvolatile, and relatively environmentally benign extraction media that can be utilized in the separations of a wide range of molecular species ranging from metal ions through small organic molecules to macromolecules and even particles, both in industrial and analytical separations and in environmental applications.12,20-25 One interesting application of ABSs with considerable potential was proposed by Zaslavsky and co-workers. They suggested that these systems represent a viable alternative to the use of the 1-octanol/water partition coefficient (log P) for the determination of hydrophobicity used in the correlation of drug action or toxicological studies via QSARs (quantitative structure-activity relationships).26,27 Measurements of log P in 1-octanol/ water and similar aqueous/organic systems have a number of limitations when applied to the study of labile, highly hydrophilic biological solutes.26,28 These include their effect on molecular conformation, which might differ from the in vivo conformation, and the difficulty of measuring the partition coefficients of species that are substantially insoluble in the organic phase. In addition, 1-octanol is volatile and flammable and prolonged exposure can cause skin and respiratory

10.1021/ie0107800 CCC: $22.00 © 2002 American Chemical Society Published on Web 05/02/2002

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irritations as well as headache and nausea. Extensive use mandates operation in a fume hood.29 The similar application of ABSs entails none of these limitations and represents a viable alternative that offers the possibility of establishing a scale of relative hydrophobicities for biological solutes and synthetic drugs extending from small molecules through macromolecules to supermolecular complexes and particles. As the potential utilization of ABSs continues to grow, it is clear that the mechanism of phase behavior and solute partitioning in these systems is of fundamental importance. Efforts to understand and predict macromolecular partitioning in ABSs have led to the development of models based on the partitioning of amino acids, small peptides, and normal alcohols.30-34 Recently, it has been shown that the partitioning of individual lowmolecular-weight neutral solutes in poly(ethylene glycol) (PEG)/salt ABSs is a function of only the degree of phase divergence of the biphasic system as expressed by the difference in polymer concentration between the phases.35 The nature of the solvent medium and its physiochemical interactions with the solute are also of critical importance in understanding solute partitioning in ABSs. Linear solvation energy relationships (LSERs) have been employed to describe the intermolecular forces in the form of solute-solvent interactions that govern solute partitioning in a wide range of solvent/ water systems. In the past, such approaches have proven invaluable in the development of QSARs.36,37 Recently, the application of LSERs has aided in determining the factors that contribute to micellar solubility of organic solutes, and as a result, quantitative structure-solubility relationships for these systems have been developed.38,39 An LSER was also used to determine the physiochemical interactions involved in solute distribution within aqueous micelles that are responsible for solute retention in micellar electrokinetic capillary chromatography (MEKC).40 The development of a fundamental understanding of the phase behavior and the nature of the solvent medium and its interactions with the solute will aid in an understanding of partitioning in ABSs and in the design of future applications of these systems. We have thus examined the partitioning of a series of aliphatic alcohols in ABSs formed with different molecular weights of PEG and a variety of different salts to determine the free energy of transfer of a methylene group from the salt-rich aqueous lower phase to the polymer-rich aqueous upper phase. The free energy of transfer of a methylene group is considered to be a measure of the relative hydrophobicity of the partitioning system.26,28,41-43 A linear solvation energy relationship based on the Gibb’s energy related solute descriptors of Abraham has been developed for a PEG-2000/(NH4)2SO4 ABS utilizing a data set consisting of 29 solutes covering a wide range of different functional groups. As a result of these studies, solute partitioning in ABSs can be directly compared to partitioning in the 1-octanol/water and other aqueous/organic systems, as well as similar aqueous micellar systems. A more precise picture of the molecular determinants of phase behavior and the nature of the solvent properties of ABSs is emerging that will be of significant use in the utilization and application of these systems.

) 1000, 2000, 3400), and H2SO4 utilized in these studies were of reagent grade and were purchased from Aldrich (Milwaukee, WI). A Barnstead (Dubuque, IA) commercial deionization system was used to purify all water used in experiments. The carbon-14 labeled solutes measured in the ABSs were obtained from Sigma (St. Louis, MO) (acetonitrile, ethanol, methanol, 1,3-dinitrobenzene, aniline, benzene, acetophenone, toluene, chlorobenzene, 1,4-dichlorobenzene, 1,2,4-trichlorobenzene, 4,4-dichlorobiphenyl, n-propanol, methyl iodide, 2-propanol, n-butanol, n-pentanol, 4-hydroxybenzoic acid, p-toluic acid, benzoic acid, acetic acid, and phenol) and American Radiolabeled Chemicals Inc. (St. Louis, MO) (ethyl acetate, benzamide, anisole, 1,2-dichloroethane, p-chloroaniline, nitrobenzene, octanol, and benzyl alcohol). The activity of the tracers used as the “spike” in the partitioning experiments was 0.06-0.08 µCi/µL. The liquid/liquid distribution ratios for each solute were measured in systems formed by mixing 1 mL of a 40% (w/w) PEG solution with 1 mL of a salt stock solution of known concentration. The pHs of the systems were adjusted by the addition of concentrated H2SO4 or concentrated NH4OH to achieve partitioning of the neutral form of the organic species where appropriate. Each system used in the partitioning experiments was characterized in terms of its system composition, ∆EO (difference in PEG composition between the phases measured in terms of molality of ethylene oxide monomers). A detailed discussion concerning how ∆EO is obtained for each PEG/salt ABS and how solute partitioning in each system is characterized by this parameter is provided elsewhere.35 Each system was equilibrated at 25 °C in a Neslab RTE-110 water bath (Neslab Instruments, Inc., Newington, NH). Tracer quantities (1-4 µCi) of each solute were added to a defined system, and the system was vortex-mixed and centrifuged (2000g) for 2 min. The systems were vortex-mixed a second time and allowed to phase-separate at experimental temperature before being centrifuged to ensure completely separated and equilibrated phases. Liquid scintillation analysis was performed on 100 µL of each phase using Ultima Gold Scintillation Cocktail (Packard Instruments, Downers Grove, IL) and a Packard Tri-Carb 1900 TR liquid scintillation analyzer (Packard Instruments). As equal amounts of the two phases were analyzed, the distribution ratios were defined as in eq 1

2. Experimental Section The salts [K3PO4, (NH4)2SO4, K2CO3, Li2SO4, MnSO4, NaOH, ZnSO4, and NH4OH], poly(ethylene glycol) (MW

3. Results

D) concentration in counts per minute of PEG-rich phase concentration in counts per minute of salt-rich phase (1) Each measurement was carried out at least in duplicate. A complete overview of the radiochemical methods used in these studies can be found elsewhere.44 The linear free energy relationship (LSER) model and the relative contribution of each regression coefficient to the LSER model was generated by multilinear regression using the program StatBox, release 2.5 (Grimmer Logiciels, 1995-1997), on a PC.

Hydrophobicity is one of the most important parameters in correlating drug effects in QSARs. The hydro-

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chain length of alcohol. Each of these relationships can be described by

ln K ) C + Enc

(2)

where K is the partition coefficient, C is a constant related to the hydration properties of the phases, nc refers to the number of carbons in the alkyl chain of the solutes partitioned, and E is a constant defined as the slope of ∆GCH2.41,46,47 Table 1 presents ∆GCH2 (calculated according to eq 3 in kcal/mol) for various ABSs, aqueous/organic systems, and micellar systems.

∆GCH2 ) -RTE

Figure 1. Natural logarithm (ln) of the distribution ratio of the series of aliphatic alcohols (1) methanol, (2) ethanol, (3) n-propanol, (4) n-butanol, and (5) n-pentanol in ABSs formed with 40% (w/w) PEG-3400 and equal quantities of K3PO4 [(b) 1 M K3PO4, (9) 1.5 M K3PO4, (2) 2.0 M K3PO4, (1) 2.5 M K3PO4] as a function of the number of carbons in the side chain of the alcohols partitioned.

phobicity parameter is often useful in describing the transport behavior of a drug from the point of delivery to its distribution throughout different compartments and across biomembranes in the body. It is also significant in describing a drug’s ability to bind to transport proteins and to hydrophobic receptor sites.26,45 Typically, the relative hydrophobicity of a drug is measured by its partition coefficient in the 1-octanol/water biphasic system.28,46 As a new field of biopharmaceuticals of increasing molecular complexity emerges, ABSs appear to represent a clear alternative to the 1-octanol/water biphasic system for the estimation of the relative hydrophobicities of solutes. This suggestion is supported by the feasibility of studying biological solutes in ABSs, because such solutes maintain their function and activity, as well as conformation, in these systems.26,28 Zaslavsky and co-workers proposed a scale of hydrophobicity based on the free energy of transfer of a methylene group between the phases (∆GCH2),26,28,46 and they successfully estimated the relative hydrophobicity of several ABSs by measuring ∆GCH2 values. The relative hydrophobicities (∆GCH2) of the systems were determined by measuring the partitioning of a homologous series of sodium salts of dinitrophenylated (DNP-) amino acids with aliphatic side chains in each system.41,46,47 We have employed similar methods to characterize phase behavior and solute partitioning in PEG/ salt ABSs for the evaluation and design of these systems. Utilizing a series of aliphatic alcohols (methanol, ethanol, n-propanol, n-butanol, n-pentanol), ∆GCH2 for transfer from the aqueous salt-rich phase to the aqueous polymer-rich phase of a given ABS was measured for a variety of PEG/salt ABSs formed with different molecular weights of poly(ethylene glycol) (MW ) 1000, 2000, 3400) and a wide range of different salt types [K3PO4, (NH4)2SO4, K2CO3, Li2SO4, MnSO4, NaOH, and ZnSO4]. Figure 1 shows the distribution ratios of the homologous series of aliphatic alcohols in a PEG-3400/(K3PO4) ABS. The partitioning of each alcohol is presented at increasing tie line length or phase divergence as a function of

(3)

In eq 3, R is the universal gas constant, T is the absolute temperature in Kelvin, and E is the slope of ∆GCH2 for a given system obtained from eq 2.41,46,47 The data show that the relative hydrophobicity of the phases of a PEG/salt ABS, as measured by ∆GCH2, can be adjusted over a significantly wide range by simply altering the amount of polymer and salt added to the system (i.e., by adjusting the tie line length or the difference in PEG composition between the phases ∆EO).35 Thus, ∆GCH2 for transfer of a methyl group to the PEG-rich phase of a PEG/salt ABS can range from values close to that of 1-octanol/water biphasic systems28 to values of much less than those obtained for methyl ethyl ketone/water biphasic systems28 and, indeed, to approach zero at the critical point. The range of values for ∆GCH2 of PEG/salt ABSs is also found to be comparable to those for other aqueous systems such as aqueous micellar systems.40,48 These results are significant because PEG/salt ABSs can be designed to achieve a desired separation simply by adjusting the system composition, either by changing the phase-forming components or by adjusting the relative composition. Zaslavsky and co-workers measured the relative hydrophobicities of a series of PEG/salt ABSs composed of (NH4)2SO4 and different molecular weights of PEG (MW ) 300, 600, 6000, 20 000) by partitioning a homologous series of sodium salts of dinitrophenylated (DNP-) amino acids with aliphatic side chains in each system.47 The relative hydrophobicities (∆GCH2) of the PEG/(NH4)2SO4 ABSs ranged from 0.080 to 0.240 kcal/ mol depending on the polymer and salt concentration of the systems. These experiments also demonstrated that the parameter E, a constant related to the free energy of transfer of a methylene group from one phase to the other (eq 2), depended only on the difference in PEG composition between the phases, ∆PEG. Figure 2 is an example of similar results; however, we are now able to extend the same principles to include the wide range of PEG/salt ABSs listed above. Figure 2 shows ∆GCH2, measured for several PEG/salt ABSs differing in salt type and PEG molecular weight, as a function of the difference in PEG composition between the phases expressed in terms of ethylene oxide monomer concentrations, ∆EO. Regardless of the salt type, salt concentration, or polymer molecular weight used to form the biphase, the relative hydrophobicities of these systems appear to be the same, provided the system compositions are expressed in terms of the degree of phase divergence as measured by ∆EO, ∆PEG, or TLL. Both the salt type and the polymer molecular weight determine not only the concentrations of PEG and salt needed to bring about phase separation but also the approximate rate at which the phases diverge. The

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Table 1. Free Energy of Transfer of a Methylene Group from a Polar to an Apolar Phase of Various Aqueous/Organic Biphases, ABS Biphases, and Micellar Solutions system

-∆GCH2 (kcal/mol)

system

-∆GCH2 (kcal/mol)

hexanea chloroforma benzenea dodecanea octanea octanola octanolb methyl isobutyl ketone (MIBK)a diisopropyl ethera xylenea n-butanola methyl ethyl ketone (MEK)a

1.101 ( 0.043 0.846 ( 0.24 0.842 ( 0.066 0.774 ( 0.044 0.768 ( 0.053 0.727 ( 0.017 0.816 0.722 ( 0.015 0.676 ( 0.130 0.644 ( 0.092 0.542 ( 0.058 0.433 ( 0.006

PEG-3400 40% w/w 1.0 M K3PO4 (∆EO 9.14) PEG-3400 40% w/w 2.5 M K3PO4 (∆EO 27.26) PEG-2000 40% w/w 1.5 M K2CO3 (∆EO 10.88) PEG-2000 40% w/w 4.5 M K2CO3 (∆EO 41.78) PEG-2000 40% w/w 4 M NaOH (∆EO 15.82) PEG-2000 40% w/w 6 M NaOH (∆EO 27.15) PEG-2000 40% w/w 1.7 M Li2SO4 (∆EO 7.11) PEG-2000 40% w/w 2.12 M Li2SO4 (∆EO 14.50) PEG-2000 40% w/w 1.68 M (NH4)2SO4 (∆EO 11.07) PEG-2000 40% w/w 3.7 M (NH4)2SO4 (∆EO 25.61) Sodium dodecyl sulfate (SDS)c,d Sodium octyl sulfate (SOS)c

0.262 0.553 0.263 0.696 0.312 0.503 0.142 0.285 0.214 0.472 0.473-0.657 0.449-0.567

a

Values obtained from ref 28. b Values obtained from ref 11. c Values obtained from ref 40.

Figure 2. ∆GCH2 as a function of ∆EO for a series of ABSs formed with 40% (w/w) PEG-2000 and increasing concentrations of salt [(b) K3PO4, (9) K2CO3, (2) (NH4)2SO4, (1) NaOH, ([) Li2SO4, (0) MnSO4, (3) ZnSO4] or with K3PO4 and (O) 40% (w/w) PEG-1000 or (]) 40% (w/w) PEG-3400.

relative hydrophobicity of a PEG/salt ABS in the context of the partitioning of small neutral organic solutes seems to depend only on the degree of phase divergence ∆EO. Correlations between small organic solute partitioning in PEG/salt ABSs and the 1-octanol/water solvent system have been widely studied and commented upon.10,11,30,34,35,41,46,47 Figure 3 shows the distribution ratios for a series of 30 small organic solutes partitioned in their neutral forms in a PEG-2000/(NH4)2SO4 ABS at a defined difference in PEG concentration (∆EO ) 16.0 m) between the phases as a function of the 1-octanol/water partition coefficient.49 Figure 3 illustrates the complexity of utilizing the Collander equation50 to compare the partitioning of a wide range of solutes, differing in structure and functionality, in ABSs with their partitioning in 1-octanol/water or other aqueous/organic systems. The Collander equation is usually expressed as

log P(2) ) a log P(1) + b

(4)

where subscripts 2 and 1 represent the systems compared (ABS and 1-octanol/water, respectively) and a and b are constants. Figure 3 illustrates that a simple straight-line relationship of this type is illusory, however convenient it might seem to estimate the partition coefficient in different systems in this way. The obvious

d

Values obtained from ref 48.

Figure 3. Logarithm of the distribution ratio (D) for a series of small organic molecules [1 (1) methanol, (2) ethanol, (3) 2-propanol, (4) n-propanol, (5) n-butanol, (6) n-pentanol, (7) benzyl alcohol, (8) phenol, (9) n-octanol; 0 (10) acetic acid, (11) 4-hydroxybenzoic acid, (12) benzoic acid, (13) p-toluic acid; 9 (14) acetonitrile, (15) ethyl acetate, (16) methyl iodide, (17) 1,2-dichloroethane; 4 (18) aniline, (19) p-chloroaniline; O (20) benzamide, (21) 1,2dinitrobenzene, (22) acetophenone, (23) nitrobenzene, (24) benzene, (25) anisole, (26) toluene, (27) chlorobenzene, (28) 1,4-dichlorobenzene, (29) 1,2,4-trichlorobenzene, (30) 4,4-dichlorobyphenyl] in a PEG-2000/(NH4)2SO4 ABS at a defined difference in PEG concentration (∆EO ) 16.0 m) between the phases vs logarithm of the 1-octanol/water partition coefficient (P).

complexity of the relationship between the two systems can be attributed to the differing solute-solvent molecular interactions existing in the different systems compared.51 ∆GCH2 is only a measure of hydrophobicity, or the relative free energy of cavity formation, as a result of the limited molecular interactions possible, but solutes in general differ in hydrophobicity because of differences in the solute-solvent interactions in the phases. It is generally assumed that all of these interactions are encapsulated in a generalized solvation equation of the form

some property ) cavity terms + polarity terms + hydrogen bonding terms + constant (5) The assumption is made that solute-solvent interactions can be described by various additive molecular properties of molecules that can be isolated as formal descriptors of the solvation process. Thus, when the solutes shown in Figure 3 are grouped into distinct

Ind. Eng. Chem. Res., Vol. 41, No. 11, 2002 2595 Table 2. Solute Distribution Ratios for PEG/Salt ABSs and Abraham Solute Descriptors solute

log P oct/water

log D PEG/salt

π2H

ΣR2H

Σβ2H

Vx

R2

ref LSER

acetophenone ethanol n-propanol methyl iodide benzene toluene chlorobenzene 1,4-dichlorobenzene 1,2,4-trichlorobenzene 4,4-dichlorobiphenyl acetonitrile methanol n-butanol n-pentanol 2-propanol aniline p-toluic acid phenol benzoic acid 4-hydroxybenzoic acid acetic acid ethyl acetate benzamide anisole 1,2-dichloroethane nitrobenzene benzyl alcohol 4-chloroaniline 1-octanol

1.58 -0.31 0.25 1.51 2.13 2.73 2.84 3.44 4.02 5.23 -0.34 -0.77 0.88 1.51 0.05 0.90 2.27 1.46 1.87 1.58 -0.17 0.73 0.64 2.11 1.48 1.85 1.10 1.83 3.00

1.38 0.25 0.49 0.75 1.48 1.55 1.81 2.12 2.14 3.14 0.23 0.10 0.68 0.92 0.40 1.08 1.69 1.32 1.45 1.63 0.23 0.57 1.24 1.53 0.90 1.36 1.16 1.44 1.54

1.01 0.42 0.42 0.43 0.52 0.52 0.65 0.75 0.81 1.31 0.90 0.44 0.42 0.42 0.36 0.96 0.90 0.89 0.90 0.90 0.65 0.62 1.50 0.74 0.64 1.11 0.87 1.13 0.42

0 0.37 0.37 0 0 0 0 0 0 0 0.04 0.43 0.37 0.37 0.33 0.26 0.60 0.60 0.59 0.81 0.61 0 0.49 0 0.10 0 0.33 0.30 0.37

0.49 0.48 0.48 0.13 0.14 0.14 0.07 0.02 0 0.20 0.33 0.47 0.48 0.48 0.56 0.50 0.38 0.31 0.40 0.56 0.45 0.45 0.67 0.29 0.11 0.28 0.56 0.35 0.48

1.0139 0.4491 0.5900 0.5077 0.7164 0.8573 0.8388 0.9612 1.0836 1.5690 0.4042 0.3082 0.7309 0.8718 0.5900 0.8160 1.0730 0.7751 0.9320 0.9904 0.4648 0.7466 0.9728 0.9160 0.6352 0.8906 0.9160 0.9386 1.2950

0.818 0.246 0.236 0.676 0.610 0.601 0.718 0.825 0.980 1.640 0.237 0.278 0.224 0.219 0.212 0.955 0.730 0.805 0.730 0.930 0.265 0.106 0.990 0.708 0.416 0.871 0.803 1.060 0.199

52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 53, 55 53 52 53 63 52 52 52 52 52 52 52 52, 55 52

series having similar chemical natures such as (methanol, ethanol, n-propanol, n-butanol, n-pentanol, octanol), or (aniline, chloroaniline), or (benzyl alcohol, phenol), and (benzene, chlorobenzene, 1,4-dichlorobenzene, 1,2,4trichlorobenzene), a strong correlation between log D for the ABS and log P for octanol/water exists. This behavior can be attributed to similar hydrogen-bonding interactions between solutes of similar natures and the solvent in the two phases of each of the systems. As far as the free energy of transfer of a methylene group is concerned, it can be assumed that each increment in CH2 involves only an incremental change in the free energy of cavity formation and is complicated only by dispersion forces. Consideration of the generalized solvation equation (eq 5) suggests that ∆GCH2 is a direct measurement of the relative solvophobicity (hydrophobicity) of the phases of the system as all other forces are essentially solvophilic (hydrophilic) in nature. Linear free energy relationships (LFERs) based on the generalized solvation equation shown in eq 5 have been widely used to model many processes such as partitioning in aqueous/organic systems, solubility, and transport across biological membranes.37,51,52 Abraham, in particular, has expended considerable effort on the determination of Gibb’s energy based molecular descriptors for use in the development of LFERs.51-56 Linear solvent energy relationships (LSERs), a subset of LFERs,57 have been used to characterize solvation in a wide variety of solvent systems including the description of partition in various aqueous/organic systems36,53,58 and aqueous micellar systems.38-40 We have previously published an LSER describing partitioning in a PEG/salt ABS determined by the partitioning of a very limited set of radiochemically labeled solutes.59 The present study extends and supersedes the previously developed LSER by the inclusion of additional compounds to the solute set. The distribution ratios of 29 solutes partitioned in their neutral forms in a PEG-2000/(NH4)2SO4 ABS (∆EO ) 16.0 m)

have been determined. This is the same solute set used above to illustrate the relationship between partitioning in ABSs and in 1-octanol/water with the exception of 1,3-dinitrobenzene. The solute distribution ratios and their corresponding Gibbs’s energy related solute descriptors obtained from published values determined by Abraham and coworkers are shown in Table 2.52,53,55 The solute descriptors include the McGowan volume (Vx) in units of cm3 mol-1/100, which is related to the solute’s van der Waals volume and can be considered to be related to the relative free energy of cavity formation in the phases. This descriptor is closely related to molar refraction and therefore includes solute London dispersion force effects. The excess molar refraction (R2) is determined from the refractive index of the solutes, and the dipolarity/ polarizability (π2H) is obtained from gas liquid chromatographic measurements on polar stationary phases or from the partitioning of the solutes in water/solvent systems. The solutes’ overall hydrogen-bond-acceptor basicity and hydrogen-bond-donor acidity are denoted by the terms Σβ2H and ΣR2H, respectively. However, because of the aqueous nature of ABSs, the descriptor Σβ2H has been replaced by Σβ2O for solutes such as aniline and 4-chloroaniline shown in Table 2.55 These terms encapsulate the interactions between the hydrogenbond donors and hydrogen-bond acceptors of the solute and solvent. Comparison of the solute descriptors in Table 2 revealed no significant cross-correlation between them. The logarithm of some property (SP) of a series of solutes in a given system (in this study, the partition coefficient of a series of neutral organic solutes in a PEG/ salt ABS) is related to the descriptors through Abraham’s generalized solvation equation36,37,51,53-56,58

log SP ) c + rR2 + sπ2H + aΣR2H + bΣβ2H + vVx (6) The signs and magnitudes of the regression coefficients

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Table 3. Relative Contributions of the Descriptors for PEG-2000/(NH4)2SO4 ABSs coefficients

adjusted R2 for full LSER (eq 6)

v b+v b+v+r a+b+v+r s+a+b+v+r F statistic

0.78 0.93 0.97 0.97 0.97 187.58

adjusted R2 for reduced LSER (eq 10) 0.78 0.93 0.97 265.31

obtained from eq 6 (r, s, a, b, and v), established by multiple linear regression of the solute descriptors on the logarithm of the partition coefficient, reflect the relative solvent properties of the phases corresponding to the appropriate solute descriptor. Thus, r corresponds to the relative strengths of the solute-solvent interactions determined by the molar reactivity of the solute (see below), and for instance, a corresponds to the relative solvent hydrogen-bond basicity since it corresponds to the solute hydrogen-bond acidity. In eq 6, c is a constant of proportionality. The relative contributions of the regression coefficients to the partitioning of the solutes in the PEG2000/(NH4)2SO4 ABS are shown in Table 3. The regression coefficients for v and b account for approximately 93% of the variability in the partitioning data. The v parameter can be considered to be a measure of the relative hydrophobicity of the system and is similar to ∆GCH2 in that it reflects the difference in the free energy required for cavity formation between the salt- and polymer-rich phases. Typically, this parameter is large in solvent/water systems (Table 4), reflecting the fact that, for most solvents, there are few intermolecular forces hindering cavity formation other than dispersion forces whereas the free energy of cavity formation in aqueous phases is dominated by its extensively hydrogenbonded nature. This parameter is often seen to be reduced for solvents containing water at equilibrium such as 1-octanol,58 which might be seen as confirmatory evidence that the equilibrium water-containing octanol phase has some hydrogen-bonded structure.60 Of all the terms in the LSER describing partitioning in the PEG/salt ABSs, the volume parameter is the most significant (Table 3), yet it is relatively small in magnitude (Table 4). The relatively small value for v might reflect the aqueous nature of both phases of the PEG/ salt ABSs, or it might be the result of a highly structured PEG-rich phase. However, the parameter is positive, reflecting a tendency to partition to the PEGrich phase as a consequence of an increase in molecular size; therefore it can be assumed that the polymer-rich phase is less structured than the salt-rich phase. It has long been assumed that molecular size is important in determining the distribution in ABSs.61 Whereas volume accounts for 78% of the regression, an additional 15% is contributed by the b coefficient, which encapsulates the relative hydrogen-bond acidities of the phases of the PEG/salt ABSs. As has been found for many solvent systems, this term is highly negative (Table 4). The PEG/salt ABSs do not favor the partitioning of solutes that are strong hydrogen-bond acceptors. For PEG/salt ABSs, this might be the result of a deficiency in hydrogen-bond-donating ability in the PEG-rich phase resulting from the extensive hydrogenbonded water network surrounding the polymer.62 The relative hydrogen-bond basicity between the phases of solvent/water systems is reflected in the a

coefficient. For the 1-octanol/water system, the small size and statistical significance of this term suggests that there is little difference in hydrogen-bond basicity between the solvent and water phases of the system (Table 4).53,58 The hydrogen-bond acceptor abilities of the two phases are about the same. PEG/salt ABSs show a slight difference in hydrogen-bond basicity between the phases; however, this descriptor appears to be relatively insignificant in the partitioning of solutes in these systems, contributing little or nothing to the overall quality of the regression (Table 3). In contrast, the a coefficients for the chloroform/water and hexane/ water systems are significantly large and negative, and as a result, both solvents do not favor the partitioning of hydrogen-bond-donor solutes (Table 4). The same is true for the propyleneglycol dipelargolate (PGDP)/water system, although a is not as significantly large and negative.37,58 The s coefficient reflects the relative strengths of dipolar and polarization interactions in the solvents comprising the equilibrium phases. For a PEG/salt ABS, this descriptor is relatively insignificant in describing solute partitioning in these systems (Table 3), and thus, the coefficient suggests that the polymer-rich and saltrich phases have similar polarities that are likely close to that of water. This can be accounted for by the fact that both phases of the system contain substantial amounts of water [PEG-2000/(NH4)SO4 at ∆EO ) 16.0 m contains 70% (w/w) H2O]. The remaining parameter r contributes a small but significant amount (4%) to the final regression. The small positive value for the r coefficient obtained from solute partitioning in PEG/salt ABSs coincides with similar small positive values of this parameter found for nearly all partitioning systems listed in Table 4. This coefficient appears to represent the relative strength of interactions between solute and solvent arising from πand nonbonding electron pairs.49,52,54 The coefficients for this PEG/salt ABS and the 1-octanol/water system are similar (Table 4) and indicate a stronger interaction between the solute and solvent through π- and nelectron pairs as compared to other solvent water systems such as chloroform/water and PGDP/water. This suggests that, in these systems, the solvent- or polymer-rich phases have a modest preference for the partitioning of aromatic and halogenated solutes. Table 4 also contains solvent descriptors measured for various aqueous micellar systems. These systems were formed with anionic (sodium dodecyl sulfate, sodium decyl sulfate, and sodium octyl sulfate), nonionic (Brij-35), and cationic (hexadecyltrimethylammonium and dodecyltrimethylammonium bromide) micelles. The characterization of these systems by LSERs is relevant to the mechanistic study of organic solute solubilization in these systems38,39 and their use in micellar electrokinetic capillary chromatography (MECK).40 It must be recognized that such phases might not be homogeneous with regard to the molecular locus of partitioning, as it is possible that solutes might partition to the micellar core or to some region of the micellar corona. By the same token, similar molecular inhomogeneities have been proposed to exist in the 1-octanol/water system.60 Such structural features have never been suggested for ABSs, but it is not impossible that they could exist. The solvent descriptors for the anionic surfactants in Table 4 appear to be quite similar to those of 1-octanol/ water and ABSs. The v coefficient is reduced because

Ind. Eng. Chem. Res., Vol. 41, No. 11, 2002 2597 Table 4. Abraham’s Solvent Descriptors for Various Partitioning Systems Solvent

c

r(R2)

s(π2H)

PEG-2000/(NH4)2SO4 (full LSER eq 6) PEG-2000/(NH4)2SO4 (reduced LSER eq 10) sodium dodecyl sulfate (SDS) (MECK) sodium decyl sulfate (SDecS) (MECK) sodium octyl sulfate (SOS) (MECK) sodium dodecyl sulfate (SDS) cationic hexadecyltrimethylammonium bromide (CTAB) dodecyltrimethylammonium bromide (DTAB) nonionic Brij-35 1-octanol chloroform hexane di-n-butyl ether (dbe) propyleneglycol dipelargolate (PGDP)

-0.05

0.65

-0.21

a(ΣR2H) 0.21

0.50

V(Vx)

ref

-1.31

1.71

this study

-1.22

1.70

this study

-1.72

2.90

40

-1.60

2.69

40

-2.16

0.42

-0.34

-2.43

0.32

-0.24

-1.97

0.45

-0.31

-0.12

-1.87

2.85

40

-0.62 -0.57

0.32 0.57

-0.57 -0.15

-0.08 0.85

-1.84 -3.61

3.25 3.36

39 39

-0.87

0.57

-0.40

0.28

-1.82

2.98

38

-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

39 37, 51, 53, 54, 58 56 58 36, 58 36, 58

of their aqueous nature, and they do not favor the partitioning of hydrogen-bond acceptors. On the other hand, the s coefficient is of negative sign and of significant magnitude when compared to the value for ABSs, but it is smaller than that found in the 1-octanol/ water system. This indicates that polar solutes prefer the aqueous phase in these 1-octanol/water and anionic micellar systems and that there is little such distinction in ABSs. The cationic and nonionic surfactants, however, seem to favor the partitioning of hydrogen-bond-donor solutes, as shown by the significant and positive value for the a coefficient. However, most aqueous/organic systems, with the exception of 1-octanol/water (which is “neutral” in this regard), do not favor the partitioning of hydrogenbond donors. Like ABSs and some aqueous/organic systems, aqueous micellar systems have a significant r coefficient, and as a result, the micelles are presumed to interact more strongly with solutes having π- and n-electron pairs than with water. The nonionic surfactant Brij-35 appears to have a much stronger ability to bond through π- and n-electron pairs than any of the other systems compared. The magnitude of the constant c is also of some concern when examining the coefficients of the aqueous micellar systems. The constant should be very close to zero, as shown for the ABSs and aqueous/organic systems in Table 4, indicating a close relationship between the observed values of the measured parameter (log P) and those predicted by the descriptors. For the aqueous micellar systems, c is often greater than (0.5. It has been suggested that this could result if the descriptors of the solutes do not cover a large enough range, resulting in extrapolation of the regression to the origin.63 However, the magnitude of the constant c in examinations of the coefficients of various aqueous micellar, aqueous/organic, and ABSs also takes into account the scaling factor for converting between different expressions for the equilibrium constant. When the equilibrium constant is expressed as a partition ratio and is dimensionless, as for ABSs and aqueous/organic systems, the constant should be zero. The partition coefficients measured for the aqueous micellar systems used in Quina’s study39 have the units of L mol.-1 In Vitha’s

-0.11

b(Σβ2H)

Figure 4. Logarithm of the distribution ratio (D) for a series of small organic molecules [1 (1) methanol, (2) ethanol, (3) 2-propanol, (4) n-propanol, (5) n-butanol, (6) n-pentanol, (7) benzyl alcohol, (8) phenol, (9) n-octanol; 0 (10) acetic acid, (11) 4-hydroxybenzoic acid, (12) benzoic acid, (13) p-toluic acid; 9 (14) acetonitrile, (15) ethyl acetate, (16) methyl iodide, (17) 1,2-dichloroethane; 4 (18) aniline, (19) p-chloroaniline; O (20) benzamide, (22) acetophenone, (23) nitrobenzene, (24) benzene, (25) anisole, (26) toluene, (27) chlorobenzene, (28) 1,4-dichlorobenzene, (29) 1,2,4-trichlorobenzene, (30) 4,4-dichlorobyphenyl] in a PEG-2000/(NH4)2SO4 ABS at a defined difference in PEG concentration (∆EO ) 16.0 m) between the phases vs values predicted by the calculated regression coefficients (Table 4) and the solute descriptors (Table 2) utilizing eq 6.

study, the chromatographic capacity factor k′ of the solutes in the micelles is measured by MEKC, and this factor is used to determine the LSER for the aqueous micellar systems.40 The capacity factor is dimensionless and is related to the solutes partition coefficient by

log k′ ) log K + log φ

(7)

In these cases, the values of the regression coefficients are independent of how the partition coefficients are expressed, thus allowing for a direct comparison of the regression coefficients of LSERs. Figure 4 illustrates the correlation between the actual distribution ratios measured in the PEG/salt ABSs and the predicted solute distribution ratios obtained from

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Ind. Eng. Chem. Res., Vol. 41, No. 11, 2002

Table 5. Relative Contributiosn of the Descriptors for Octanol/Water Biphasic System coefficients

adjusted R2 for PEG/salt solute set (29)

adjusted R2 for training set (33)

v b+v s+b+v s+b+v+r s+a+b+v+r F statistic

0.69 0.98 0.99 0.99 0.99 1214.08

0.57 0.93 0.97 0.99 0.99 489.81

the calculated regression coefficients and the solute descriptors via eq 6. The correlation coefficient (r2) obtained from the regression was 97%, and the F statistic was 172.17. Although the regression coefficients (c, r, s, a, b, and v) shown in Table 4 for a PEG/salt ABS were for a small set of solutes, the results suggest a plausible way to predict small organic solute partitioning in ABSs. However, when the LSER for the same set of 29 solutes was calculated using published values of their 1-octanol/water partition coefficients

log P(29 solutes) ) -0.07 + (0.58)R2 + (-0.96)π2H + (0.09)ΣR2H + (-3.64)Σβ2H + (3.96)Vx (8) differences in the relative contributions of the regression coefficients were observed between this solute set and a set of 33 compounds obtained from an optimal solute training set36

log P(33 solutes) ) -0.10 + (0.48)R2 + (-0.88)π2H + (0.06)ΣR2H + (-3.50)Σβ2H + (3.92)Vx (9) Table 5 shows that the largest discrepancies lie in the relative contributions of the v, b, and s coefficients, suggesting that our solute set could be improved to achieve an LSER model with a better balance of intermolecular forces that describe solute partitioning, thus resulting in a more accurate prediction of a solute’s distribution ratio in a PEG/salt ABS. Although the LSER model for the 1-octanol/water system utilizing the same solute set as for the PEG/ salt ABSs (eq 8) might not be complete, the relative magnitudes of the regression coefficients as compared to those found for the optimal training set (eq 9) and the full 1-octanol/water LSER model in Table 4 suggest that the solute set used for the PEG/salt ABS LSER model will provide a qualitative determination of the solute-solvent interactions that govern solute partitioning in ABSs. Although the current LSER describing partition in the PEG-salt ABSs might not be complete in every detail, it should have considerable utility in aiding the prediction of solute partitioning in these systems. In addition, the molecular design of ligands for use as extractants or of catalysts for use in aqueous biphasic catalysis can be furthered, as can the design of affinity ligands employed to enhance specific protein partitioning in ABSs. Unfortunately, the form of the current LSER is designed to define the solvation properties of solvents and processes (such as partition) and requires that the molecular solute descriptors be known, although these descriptors are available for limited numbers of solutes (