War. Res. Vol. 20, No. 11, pp. 1433-1442, 1986 0043-1354/86 $3.00+0.00 Printed in Great Britain Pergamon Journals Ltd DETERMINATION OF PARTITION COEFFICIENTS AND AQUEOUS SOLUBILITIES BY REVERSE PHASE CHROMATOGRAPHY--I THEORY AND BACKGROUND WALTER J. WEBER JR*, Yu-PING CHINt and CLIFFORD P. RICE~ Water Resources and Environmental Engineering Program, 181 Engineering Building l-A, The University of Michigan, Ann Arbor, MI 48109, U.S.A. (Received January 1986) Abstract--Water solubilities and octanol/water partition coefficients are widely used to predict par- titioning and bioconcentration phenomena for hydrophobic organic pollutants in aqueous systems. This paper is the first in a two part series describing the application of high performance reverse phase liquid chromatography (HPRPLC) for indirect estimation of these two physicochemical parameters to facilitate environmental fate and transport predictions for organic compounds. In the first part, thermodynamic factors which control partitioning processes, water solubilities, and reverse phase retention behavior are discussed, and models for interlinking these three properties are summarized. The second part presents the results of aqueous solubility and octanol/water partition coefficient predictions for a number of organic contaminants from measurements of their HPRPLC behavior, and compares the modeling capabilities of some of the theoretical partitioning/solubility equations developed in the first paper. Key words--organic pollutants, soil/sediment sorption, bioconcentration, activity coefficient, solubility, octanol/water partition coefficient, high performance reverse phase liquid chromatography NOMENCLATURE AHm = enthalpy of mixing Roman symbols AH/= enthalpy of fusion AH v = enthalpy of vaporization A and C = regression coefficients correlating reten- Ko~ = octanol/water partition coefficient tion times and octanol/water partition Kp = partition coefficient coefficients KRp = reverse phase partition coefficient a and b = regression coefficients correlating par- k' = capacity factor tition coefficients for different organic MW = molecular weight solvent/water systems ni = moles of solute aX; a,y = solute activity in phases x and y p = organic modifier proportionality constant b(T) and C(T) = regression coefficients correlating the free R = universal gas constant energy of transfer to the solute cavity RM=thin layer chromatography retention surface area factor b'= coefficient correlating the free energy of S~ = molar solubility transfer to retention time AS/= entropy of fusion C, = molar concentration (tool 1- ~) T = temperature (°K) CSA = solute cavity surface area T,, = solute melting point temperature ACp = change in solute heat capacity during t, = solute retention time phase transition to = mobile phase retention time d = regression coefficient correlating organic tc = corrected retention time solvent/water and hypothetical pure t7 = hypothetical pure water corrected reten- water retention times tion time AE = cohesive energy t~/°rg=corrected retention time in a binary AEm = cohesive energy of mixing water/organic solvent mobile phase f~ = fugacity of crystalline organic solid V = volume f0 = pure liquid component standard state 17 = molar volume fugacity 17~ = solute molar volume 17o = octanol molar volume 17ow = water saturated oetanol molar volume V, = stationary phase volume *Professor of Environmental Engineering and Chairman of Vt = total volume of mobile phase required to the University Water Resources Program. elute a solute 1"Graduate Research Assistant in the Water Resources V~ = void space volume Program. XX; X,Y = solute mole fraction in x and y :~Research Associate in the Great Lakes Research Division. X,~ = mole fraction solubility in water. 1433 1434 WALTER J. WEBER JR et aL Greek synlhols phase liquid chromatography (HPRPLC) to indi- :t and fl = regression constants which correlate rectly estimate n-octanol/water partition coefficients. activity coefficient to retention time Major advantages of this approach include ease of 7, = activity coefficient :,',' = saturation limit solute activity coefficient analysis, speed, precision, and accuracy. Several in water workers (Locke, 1974; Hakfenschied and Tomlinson, /i'= solute activity coefficient in octanol 1981) have also explored the possibility of indirectly 77" =solute activity coefficient in octanol estimating water solubility values using HPRPLC. saturated with water ,) = solubility parameter The bulk of this work to date, however, has treated 6,, = solubility parameter of octanol predictions of S," and K,,,, from HPRPLC mea- ,S' = solubility parameter of octanol saturated surements in terms of purely empirical correlations, with water thus providing no insight to processes which may t~, = chemical potential control relationships between reverse phase chro- i~i~ = standard state chemical potential Atz,~,,~= partial molar free energy of transfer matographic behavior and solubility and partitioning /) = density. behavior. The first paper in this two part series summarizes the current level of understanding of concepts underlying solubility and partitioning re- INTRODUCTION lationships, and discusses the relevance of these con- cepts to the selectivity and retention of solutes in The increased presence of anthropogenic organic reverse phase chromatography systems. Part I begins pollutants in surface and subsurface waters raises by examining the relationships of both the phase questions concerning the environmental transport partitioning behavior and solubility characteristics of and distribution of these materials and their effects on a compound to its activity coefficient(s) within a given the aquatic community and human health. The man- system. Methods for estimating activity coefficients ner in which a compound moves and is distributed are then discussed, along with their inherent limi- within an aquatic system and its associated solid tations and inaccuracies. Having established quanti- phases, both inert (soils, sediments, suspended solids) tative relationships between the activity coefficient o1" and living (flora and fauna), is influenced significantly an organic contaminant and its partitioning and by the physicochemical properties of that compound. solubility characteristics and associated parameters, Many organic contaminants are "hydrophobic", and Part I then considers diagonal relationships between tend to sorb from the aqueous phase onto or into solubility and partitioning behavior and their related phases which are thermodynamically more favorable. parameters. Finally, the technique of HPRPLC is The n-octanol/water partition coefficient (K,,,,.) and discussed, its characteristic parameters identified, and water solubility ($7) are two physicochemical par- these parameters then related and correlated to the ameters commonly used to predict soil/sediment characteristic properties of solubility and partition- sorption (Karickhoff et al., 1979, 1984; Briggs, 1973; ing. Emphasis is given to the potential application Means et aL. 1980; Chiou et al., 1982; Voice et aL, of HPRPLC for quantifying the partitioning and 1983) and biosorption or bioconcentration phenom- activity coefficients of organic pollutants in aqueous ena (MacKay, 1982; Chiou et al., 1977; Neely et aL, media. 1974) for lipophilic organic contaminants. Values for these two "predictor" parameters can be determined PHASE PARTITIONING AND ACTIVITY COEFFICIENTS either experimentally (McAuliffe, 1966; Karickhoff and Brown. 1979; Sutton and Calder, 1974; Haque The partition coefficient, Kp, quantifies the equi- and Schmedding, 1975; Chiou et al., 1982) or esti- librium partitioning of a liquid or "supercooled" mated from empirical models (Rekker, 1977; Fujita et organic solute between two phases al., 1964; Leo and Hansch, 1979; Arbuckle, 1983). Direct experimental determinations of n-octanol/ K~=--cC (~) water partition coefficients are laborious, however, and frequently suffer from lack of precision and where Ci~ and C~ are the molar concentrations of accuracy. This is particularly true for very hydro- solute i in phases x and y, respectively. phobic compounds (S~ < 50 ppb and log K,,,. > 6). For conditions of equilibrium between two immis- Conversely, estimates of water solubilities and cible solvent phases, the chemical activity, a, of n-octanol/water partition coefficients using such solute i is equal in each phase empirical models as are available do not account a' = a~ (2l quantitativel~ for steric effects and other consid- erations relating to molecular configuration. Chemically activity is quantified by the expression A number of investigators (Veith et al.. 1979; a, = 7,);'L (3) McCall, 1975: Unger et al., 1978; Eadsforth and Moser, 1983; Renberg et aL, 1980; McDuffie, 1980; where 7~ and X, are the activity coefficient and mole D'Amboise and Hanai, 1982; Rapaport and fraction of the solute, respectively. The activity Eisenreich, 1984) have used high performance reverse coefficient reflects the degree to which a solution Reverse phase chromatography--I 1435 deviates from ideality. It is not a constant, however, ble to develop relationships between a solute's par- and varies with X~ and ai. The two standard states tition coefficients for different organic/water systems commonly employed for defining the activity provided that the solute/organic solvent molecular coefficient are based on (1) the pure liquid or sub- interactions are limited to weak dispersion forces. cooled liquid component and (2) the "hypothetical" Collander