War. Res. Vol. 20, No. 11, pp. 1433-1442, 1986 0043-1354/86 $3.00+0.00 Printed in Great Britain Pergamon Journals Ltd
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 (1951) observed that good log-linear cor- standard state extrapolated from the solute in an relations exist between the Kr values of a hydro- infiitely dilute solution (Karger et al., 1973). For phobic compound for different organic solvent/water purpose of this discussion the former standard state mixtures if all the organic phases contain the same conditions will be specified; that is the solute activity functional groups. Leo and Hansch (1971) expanded in the region near that of pure component (Xi = 1) upon the work of Collander, and were able to has a constant value of unity and obeys Raoult's law. correlate Kp values for different organic solvent/water In a nonideal aqueous solution, X~ approaches zero partition coefficients using the relationship (the region of infinite dilution), in which case log(gow) = a(log Kp) + b (7) the activity coefficient is greater than unity. The "saturation-limit" solute activity coefficient is used to where a and b are empirical constants. They cau- define the aqueous solubility of hydrophobic organic tioned that this correlation does not necessarily apply compounds, and this value differs from those at to all organic solvent/water mixtures. This is particu- infinite dilution and near the pure component con- larly true when comparing systems involving solutes dition (Tsonopoulos and Prausnitz, 1971). which may specifically interact with the organic phase For the condition of equilibrium, equations (2) and through polar and/or hydrogen bonding to systems in (3) combine to yield which most of the solute-organic solvent interactions are controlled by physical dispersion forces (Leo and (7,X,) ~ = (7,Xi) r. (4) Hansch, 1971; Campbell et al., 1983). If the concentration of a solute is very low in each phase, its respective mole fractions are given by AQUEOUS SOLUBILITYAND ACTIVITYCOEFFICIENTS X: = (C,V )x; X y = (C,V ) ~ (5) The aqueous solubilities of liquid hydrophobic where I7 is the molar volume of the solvent. The organic compounds (for which the solute melting above equations can then be combined to yield an point temperature, T,,, is < 25°C) can be approxi- expression for the partition coefficient in terms of the mated directly from their activity coefficients. Further solute activity coefficients in each phase thermodynamic considerations are required to esti- mate "supercooled" solute activities for substances K, = (Y, 17 )x (6) that are crystalline solids (Tin > 25°C). A good first approximation of the liquid solute activity for a (Chiou et al., 1982; Campbell et al., 1983). This sparingly soluble hydrophobic compound is unity, expression is rigorously correct only for totally im- that is, the same as its pure component activity as miscible phases (i.e. when the respective solubility of specified by the standard state (because of the limited each phase in the other is insignificant). The solubility solubility of water in the organic compound). Solu- of octanol in water (4.5 x 10 -3 M), however, may bility in terms of mole fractions is merely the recipro- significantly alter an organic solute's activity cal of the "saturation limit" aqueous solute activity coefficient, and hence its aqueous solubility. Chiou et coeffÉcient al. (1982) observed that the presence of octanol X,= 1/~7 (8) dissolved in water enhances the aqueous solubilities of DDT and hexachlorobenzene by 160 and 80% and the molar solubility, $7, is simply the product of respectively. The high solubility of water in octanol the mole fraction solubility and the molarity of water (2.6 M) can also cause deviations from equation (6) (55.5mol 1-1) (Yalkowski and Valvani, 1980). The by changing the properties and altering the molar relationship between S~ and X~ is thus log linear volume of pure octanol (17o= 157.7cm 3 mol -l) to log(S~) = log(XT) + 1.74. (9) that of a binary octanol-water solution (17ow = 120 cm 3 mol -~) (Arbuckle, 1983; Chiou et al., Estimation of the aqueous solubility of crystalline 1982; Miller et al., 1985). This combined "mutual organic solids (high T,,) requires a more rigorous solubility" effect offers a potential explanation for the thermodynamic treatment. Since the pure liquid was differences between experimentally observed specified as the standard state, the activity of an octanoi/water partition coefficients and those derived organic solute is defined as from activity coefficients and equation (6). a, =f,/fo (10) The partitioning behavior of a hydrophobic or- ganic substance between water and an organic sol- where f~ and f0 are the fugacities of the crystalline vent is controlled largely by the thermodynamic solid and the pure liquid standard state respectively. behavior of the solute in the aqueous phase (this will The solubility of the solid can be determined by be demonstrated in subsequent sections). It is possi- estimating its hypothetical "supercooled liquid" i436 WALTER J. WEaER JR et al. activity (Hildebrand et al., 1970; Yalkowski and solvent, and solute-solvent) in solutions which Valvani, 1980; Chiou et al., 1982). The activity of the behave ideally are assumed to be equal. The RST "supercooled solute" is no longer unity and is esti- predicts deviations from ideal solution behavior by mated from the enthalpy of fusion, AHI, estimating the changes in system enthalpy which occur upon mixing, AH,,. A property termed the r 1 "cohesive energy density" of a pure substance is used log(a,) 2.3R [_T,,(T)J to quantify the enthalpy of mixing term. This property is the energy required to vaporize 1 mole of (lla) +-K -R T pure liquid; that is, the energy per unit molar volume (AE/~'). The familiar solubility parameter, 6, is given where R is the universal gas constant, T is the by the square root of the "cohesive energy density" equilibrium temperature (K), and ACp is the change <~ = (AE/P) '>. (15) in the solute heat capacity upon melting. The change in heat capacity for many crystalline solid organic The solubility parameter of a substance can be esti- compounds is small, and as a first approximation mated with reasonable accuracy from the substance's may be considered negligible (Yalkowski and heat of vaporization, AH, Valvani, 1980). This simplifies equation (lla) to = [ p(A/-/,~_-_ RT)1 °' : --mnf~Tm-Z- ] '5 L MW l (16) log(a;) 2.3R 1_ T~T J' (lib) where p is the density o1 the compound, MW its The mole fraction aqueous solubility of solid organic molecular weight, and all other terms are as pre- solutes can be determined from the relationship viously defined (Hildebrand et al., 1970; Barton. 1975). Values for the heat of vaporization can be log(X w) = log(a) - Iog(7~ ) (12) found in chemical handbooks for many compounds, Combination of equations (1 lb) and (12) yields or estimated from known vapor pressure values using the Clausius-Clapeyron equation. -AHt ( T~ - T'~ log(Xi") = ~ \ T--T-~ / -- log(71' ). (13) The regular solution theory, like many conceptual models, is based upon several assumptions: namely Molar aqueous solubility can be estimated by com- (1) no volume change occurs upon mixing; (2) the bining equations (9) and (13) entropy of mixing is ideal: and (3) all molecular interactions in solution are attributable to -AH, (Tm- T~_ tog(S?)=~ \ T~-J--J log(y)*')+ 1.74. (14) London/Van der Waals forces. The last assumption severely limits the applicability of the model to the It is evident that accurate determination of the aque- dissolution of organic solutes in apolar solvents. ous solubility of an organic compound is strongly For dissolution of solute i in solvent s, the chemical dependent upon reliable estimates of the saturation potential of i,/~i, is defined in terms of its standard limit activity coefficient and the heat of fusion state partial molal free energy,/~i', and its activity, ai, (Yalkowski and Valvani, 1979, 1980). While the as change in heat capacity during the solute phase ~, =/(+ RT ln(ai) (17) transition may be insignificant for many compounds, or, from equation (3) the solute heat capacity term should be incorporated if available. Tsonopoulos and Prausnitz (1971) ob- #; = ~'.'-+- RT ln(y,X,), (18) served that the difference between including and Deviations from ideal behavior in regular solutions excluding the heat capacity term for 4-chlorobenzoic are quantified by changes in the enthalpy of a system acid altered its activity coefficient by over a half order upon the mixing of i and s to form an infinitely dilute of magnitude. Subsequent sections present methods solution (Hildebrand et al., 1970; Karger et al., 1973) which can be used to estimate heats of fusion and activity coefficients in apolar solvents and water. 1~ - Ig/ = AH., + RT In(X;) (19)
ESTIMATING ACTIVITY COEFFICIENTS The combination of equations (18) and (19) yields an expression which approximates the solute activity Regular solution theory coefficient It is apparent from the foregoing analysis that both AH,, ln(7,) = R---T-' (20) the solubility and the phase partitioning character- istics of an organic compound can be related to its If it is assumed that no volume change occurs upon activity coefficients in the phase of interest. The mixing, the cohesive energy of mixing, AE,,, for a regular solution theory (RST) provides a reasonably liquid solution can be taken as equal to the enthalpy accurate means for predicting activity coefficients for of mixing term organic solutes in apolar solvents, Molecular interactions (solute-solute, solvent- AH,, = AE,,. (21) Reverse phase chromatography--I 1437
The term, AE,,, can be approximated from solubility 1962). This partially accounts for the high surface parameters for the solute and solvent using the tension of water. Water molecules in the bulk phase Hildebrand geometric mean assumption (Hildebrand are more randomly agglomerated, but still interact et al., 1970; Karger et al., 1973) through relatively strong dipole interactions. The introduction of an apolar compound requires the AE,,= 17,(6~-- 26,6, + 62,). (22) formation of a cavity in the solvent to accomodate Substitution of equation (21) into (22), and the solute molecule. This brings about the replace- simplification of the polynomial yields ment of water-water dipole interactions by favorable, but weaker solute-water interactions affected primar- AH, = 17, (6, - 6,) 2 (23) ily by London/Van der Waals forces. These physical Introduction of equation (23) into (20), and con- dispersion interactions decrease sharply with the version to a common logarithm base gives distance of molecular separation (as the sixth power 17, (a, - a,) 2 of distance) and are therefore insignificant beyond log ?, = (24) the first layer of water molecules. The degree of 2.3RT hydrogen bonding between water molecules, how- If the difference between the solvent and solute ever, increases significantly in the immediate vicinity solubility parameters is negligible (6 i = 6s), the solu- of a solute molecule, extending it to form a partial tion approaches ideality. cage of ice-like polyhedral structures. This increased The applicability of this method for estimating ordering of solvent molecules results in a decrease in activity coefficients is restricted by the assumptions system entropy, more than offsetting the modest gain presented earlier. For solutions in which specific of enthalpy from mixing between the solute and solute-solvent or strong solvent-solvent interactions solvent. are operative, the regular solution model is not Nemethy and Scheraga (1962) used partition adequate for prediction of activity coefficients. Hagen functions to estimate differences in the free energy of and Flynn (1983) reported that the regular solution water molecules in bulk phase and those at model prediction for the activity coefficient of hydro- solvent/solute interfaces. They observed that the ac- cortisone in water deviated from an experimentally tivities (and hence solubilities) of hydrocarbons are derived value by nearly 21 orders of magnitude. This dependent upon the number of water molecules in the example clearly illustrates that differences in the solvent layer adjacent to the solute molecules. Several molar cohesive energy densities between the solute workers (Hermann, 1971; Amidon et al., 1975; and solvent cannot adequately account for specific Valvani et al., 1976; Yalkowski and Valvani, 1979) molecular interactions which occur in a solution. have shown that a good correlation exists between Solubility parameters, however, can provide a the surface area of the solvent cavity and the solu- reasonable first approximation of whether a particu- bility of aliphatic and aromatic hydrocarbons. The lar solute and solvent are at all compatible. The RST dissolution of nonelectrolytic organic solutes in water model can also predict with reasonable accuracy the can be conceptualized as involving three processes; activity coefficients of nonelectrolytic organic solutes namely, (1) dissociation of solute from the pure in apolar solvents (Hagen and Flynn, 1983) liquid, (2) the formation of cavities in the solvent to accept solute molecules and (3) insertion of solute The solvophobic theory and solute surface area model into the cavities (Amidon et al., 1975). The free The solvophobic theory provides a conceptual energy of transfer, from the pure solute liquid or basis and predictive method for describing the behav- supercooled liquid to water, A/A..... is given by ior of organic compounds in water or solvents which A#t..... = - RT(ln X~'). (25) may participate in hydrogen bonding. The model recognizes that the solubility of nonelectrolytic or- Combining this expression with equation (8) yields an ganic substances is controlled largely by the thermo- expression for the free energy of transfer as a function dynamic properties of the solvent. Frank and Evans of the activity coefficient (1945) first proposed such a concept when they A#t..... = RT(In ? ~'). (26) observed large decreases in the entropies of apolar solute/water solutions upon mixing. They attributed The free energy of transfer term is linearly correlated this phenomenon to the formation of "iceberg" water to the cavity surface area, CSA, by structures around each apolar solute molecule. A~, ..... = b(r)CSa + C(T) (27) Molecular associations of water can be depicted conceptually as existing in one of two possible struc- where b(T) and C(T) are temperature dependent tural configurations, depending upon the number of coefficients (Hermann, 1971). Substitution of equa- associated hydrogen bonds in which the solvent tion (27) into (26) yields an expression for the activity molecule can participate. Water molecules at inter- coefficient as a function of the CSA faces are bound to each other by hydrogen bonds to four other molecules to form "ice-like" polyhedra Fb(T)CSA + C(T)] log = L j (28) (Voice and Weber, 1983; Nemethy and Scheraga, 1438 WALTER J. WEBER JR et al.
Hermann (1971), Amidon et al. (1975), and Valvani the "mutual saturation" of the two partitioning et al. (1976) have used variations of equation (28) phases, equation (31) is used in lieu of equation (30) successfully to predict the aqueous solubilities of a to yield number of hydrocarbons. Calculations for the CSA - ASr values of hydrocarbons are based upon concep- log(S?) = 2.~ (Tu - T) - log(Kow) + 0.92. (35) tualization of a solute molecule as intersecting spheres of carbon, hydrogen, and oxygen atoms, in Equation (34) has been reported to provide good which each atom has a fixed radius. A solvent radius correlation between water solubilities and octanol/ of 1.5 A is added to the radius of each atom, and water partition coefficients for polycyclic aromatic the surface area computed using the combined compounds, halobenzenes, and alkyl p-substituted solvent-solute radii and taking into account intra- benzoates (Yalkowski and Valvani, 1980). The use of moleuclar bond lengths and bond angles for each equation (35) for predicting the solubilities of aro- solute molecule. Thorough treatments of methods for matic compounds from their respective octanol/water calculating CSA values have been given by Herman partition coefficients is considered in Part II of this (1971), and Valvani et al. (1976). series. Many non-electrolyte organic compounds deviate
PARTITION COEFFICIENTS AND SOLUBILITY appreciably from ideal behavior in octanol. The solubility parameter of octanol is 10.3, while com- It has been demonstrated in preceding sections that pounds such as mesitylene, o-xylene, and tri- the solubility, S~", and the partition coefficient, Kow, chlorobenzene, to name a few, have solubility param- of an organic compound are both related to the eters that are < 9.3. The RST model can be applied activity coefficient of that compound in a given phase. to predict activity coefficients for organic solutes It is therefore reasonable to expect a diagonal re- under such circumstances by first considering the lationship between S~" and Ko,. Yalkowski and logarithmic form of equation (6) for an octanol/water Valvani (1980) recognized that many organic sub- partitioning system (in which Kp = K,,,.) with mutual stances behave almost ideally in octanol (7~ = 1). For saturation an octanol/water partitioning system the relationship log(7~") = log(K,,w) + log(T,.'") + 0.82 (36) given in equation (6) becomes w -- where yow is the activity coefficient of the binary water saturated octanol phase and log(Vo~/Vw) is equal to 0.82. Equation (24) (RST) can be used to predict or, in logarithmic form log(7°'), and its subsequent substitution into equa- tion (36) yields log(y,') = log(Kow) + 0.94 (30) Y~ (at - a;,y where log (Vo/ff,,) is equal to 0.94. If the "mutual log(7,~) = log(Kow) + + 0.82 (37) 2.3RT solubility" effect into consideration, the molar vol- ume of the water-saturated octanol phase, ~o,., where 6'° is the solubility parameter of the binary becomes 120 cm 3 tool -t, the equation (30) becomes water/octanol organic phase. Combination of equations (14), (32) and (37) re- log(??') = log(Ko,.) + 0.82. (31) sults in the expression Once the activity coefficient for a compound in a log(S?) = [ - ASf(T,, - T) - if,(6,- 6o) 2] particular solvent has been determined, it is also possible to calculated the ideal solubility because the 2.3RT enthalpy of fusion can be approximated by the - log(Ko~.) + 0.92. (38) entropy of fusion, AS/, from the relationship If the "mutual solubility" effect is not taken into aHf = asfr,~ (32) account, equation (38) becomes Combining equation (1 lb) and (32) yields log(S?) = [- ASf(T.~ - T) - I7,.(b,- 60) 2] -As: 2.3RT Iog(a~) = 2.~( m-- T) (33) - log(Kow) + 0.80 (39) Equations (14), (30) and (32) combine to give an where 6o is the solubility parameter of pure octanol. expression which interrelates the aqueous molar solu- This results in a model quite similiar to the one bility of an organic non-electroyte and its octanol/ developed by Amidon and Williams (1982). The water coefficients predictive capabilities of equation (38) will also be as~ considered in Part II. log(S?) = 2.~ (Tin - T) - log(Ko,.) + 0.80. (34) Thus, by virtue of their mutual dependence on the activity coefficient, the solubility, octanol/water par- This model assumes that "mutual solubility" is negli- titioning, and distribution coefficients of an organic gible (Yalkowski and Valvani, 1980). If one considers compound can be interrelated. It is of interest now to Reverse phase chromatography--I 1439 explore the experimental determination of distribu- solute associated with the stationary phase in a tion coefficients by HPRPLC and the estimation of HPRPLC column, Vt, is related to/(Re; the larger the solubility and octanol/water partition coefficients value of K~, the larger the value Vt of the mobile from such measurements. phase required to elute the solute. Indeed, this vol- ume, corrected for the volume, Vv, retained in the pore spaces of the column, is directly equal to KRe PARTITION CHROMATOGRAPHY AND DISTRIBUTION COEFFICIENTS times the volume of the solid phase, V,; that is I1", -- V~ = K~(Vs) (40) Reverse phase chromatography has become a popular analytical methodology since the relatively (Karger et al., 1973). The most common way of recent advent and refinement of instrumentation for expressing the retention capacity of a column is high performance liquid chromatography. A reverse through the use of a capacity factor, k', which is the phase packings is comprised of a nonpolar stationary equilibrium ratio of the number of moles of solute in phase which is either mechanically held or chemically the stationary and mobile phases i.e. n~/nT'. bonded to an inert support.medium. For measure- Thus, ments of partitioning from aqueous solutions the mobile phase is composed of a fixed ratio (isocratic) (41) of water and organic solvent (methanol or aceto- c7 nfLV,j Lv, J nitrile). The exact ratio of water to organic modifier The combination of equations (40) and (41) yields an and the type of organic solvent used are dependent expression for the capacity factor as a function of 1I, upon the physicochemical properties of the target and Vv compounds. V,-Vv Most modern reverse phase packings are com- k' = -- (42) prised of n-octyldecyl groups chemically bonded to vo a silica support medium. Several investigators The capacity factor thus quantifies the distribution (Horvath et al, 1976; Colin and Guichon, 1977; behavior of an organic compound in a reverse phase Karger et al., 1976) have developed models to describe column. This variable can be related in turn to the the sorptive processes which occur within a bonded solute retention time, t,, by dividing each of the reverse phase column. It has been speculated that volume terms in equation (42) by the flowrate of the solvophobic interactions are primarily responsible for mobile phase to give driving solute molecules out of solution and onto the t,- t o stationary phase. This is no clear consensus, however, k' = -- (43) on whether the process is strictly surface adsorption to or phase partitioning. Horvath and co-workers where to is the retention time of the solvent. It is (1976) have attributed the separation to a combina- theoretically possible, therefore, to determine values tion of partitioning and adsorption. The stationary for the capacity factor from measurements of t, and phase can be envisioned as being covered by a to for a particular solute/solvent combination. How- "molecular fur" of alkyl chains. If the surface of the ever, Krstulovic et aL (1982) have found that different support were covered by a monolayer of these al- "unretained" tracers (~4C-methanol, acetone, uracil, kanes the distances between each hydrocarbon mole- sodium nitrate) commonly used to determine to yield cule would be relatively large, and it is improbable inconsistent results. Different mobile phase com- that such a stationary phase would behave like a true positions have been found to yield different solvent liquid. The alkyl groups would have fewer trans- retention times. Nonetheless, because k' is directly lational and rotational degrees of freedom, which proportional to tr and KRe, it is possible, for purposes would inhibit solute migration within the stationary of quantifying partitioning processes in reverse phase phase, and this would make true partitioning an columns, to employ a "corrected retention time", to, unlikely process. Conversely, separation by true ad- (the solute retention time minus the retention time of sorption might also be excluded on the basis that the a relatively unretained internal standard) in lieu of association of the solute with the bonded phase seems the capacity factor. It can be assumed that any to be solvophobic in nature. Irrespective of the environmental changes (i.e. temperature, flowrate, precise mechanism involved, however, the retention etc.) will affect the solute and internal standard in the time of the compound is directly related to the degree same manner. Again, because of the direct propor- of partitioning that occurs. tionality relationships, t c can be used in lieu of KRe to The degree of partitioning in reverse phase correlate HPRPLC results with the octanol/water chromatography is quantified in terms of a solute partition coefficients in equation (7). Thus distribution coefficient,/(Re, characterizing the equi- log(Kow) = A(log to) + C. (44) librium ratio of solute concentration in the stationary and mobile phase i.e. Ke,e = C~/C7'. This constant is The constants A and C are determined empirically by analogous to the partition coefficient defined in equa- calibrating the HPRPLC instrument to a group of tion (1). The volume of a solvent required to elute a organic substances which have well-defined 1440 WALTER J. WEBER JR et al.
octanol/water partition coefficients, under constant the amount of organic solvent in the mobile phase temperature, flowrate, pressure, and mobile phase (Biagi et al., 1979; Butte et al., 1981; Kringstad et al., concentrations. Target compounds are then analyzed 1984). The hypothetical pure water corrected reten- under identical conditions and their octanol/water tion time, t,"', for a particular organic solute can be partition coefficients are estimated from their reten- determined from the relationship tion times using an appropriately calibrated form of equation (44). log(t~") = log(t`"':°r~) --p(% organic modifier) (47) where p is a proportionality constant. Determining PARTITION CHROMATOGRAPHY AND SOLUBILITY the hypothetical pure water corrected retention time for each solute would be a laborious process; a more The preceding section outlines the conceptual basis direct correlation between C ':°rg for a particular iso- for applying HPRPLC measurements to estimation cratic water/organic solvent mobile phase and the of octanol/water partition coefficients for organic solute's activity coefficient in water is therefore de- compounds. Octanol/water partition coefficients and sirable. Because retention times are simply reflections solubility are both related to the activity coefficient of sorptive processes in HPRPLC, log(ti!') can be and therefore to each other, as developed earlier in correlated to the log(t`"/°rg) by a relationship of the this paper. It is thus reasonable to assume that the form given in equation (7), i.e. activity coefficient and solubility of a compound can log(t`') = ~[log(t,"/"rg)] + d (48) also be related to its HPRPLC retention time. Locke (1974) observed that the elution order of hydro- where ~t and d are empirical coefficients. Using the phobic substances from a reverse phase column can data of Biagi et al. (1979), the hypothetical pure water be correlated to solute solubility. This correlation is retention factors, R~, and experimentally derived based on the assumptions that solvophobic inter- acetone/water (40:60) eluted retention factors, actions are the primary thermodynamic driving R~,last, for the separation of napthol and its deriva- forces, that no stable complexes are formed, that the tives using a silicone oil RPTLC system were calcu- solute/stationary phase interactions are weak and lated; these are presented in Table I and plotted in nonspecific, that the stationary phase surface is rela- Fig. 1 (retention factors are the RPTLC equivalent to tively homogeneous, and that the surface activity the logarithm of HPRPLC capacity factors). The coefficients of all the eluting solutes are similar. linearity between the two parameters is excellent It is possible by applying the assumptions de- (correlation coefficient = 0.99), in accord with the scribed above to derive a thermodynamic model in relationship given in equation (48). Substitution of which the selectivity and retention of an organic equation (48) into equation (46) yields compound are strictly dependent upon its solvation in a polar solvent. If water is used as the mobile log(~i' ) = ~ log(ti! ~'rg) + [3 (49l phase, then, for a given solute, the free energy of where/3 is equal to (d - b'). Equation (49) allows one transfer term defined previously can be linearly cor- to directly correlate the aqueous activity coefficients related to the logarithm of the corrected retention of organic compounds to their water/organic solvent time, C' eluted HPRPLC t, values. This simplifies things [Ata~ ..... ] greatly by circumventing the extrapolation of log(t,"). log(t~) = 1_2"3RT J + b' (45) The determination of aqueous solubilities is done by combining equations (49), (32) and (14) to yield where b' is a constant (Hakfenschied and Tomlinson, 1981). Substitution of equation (26) into equation log(S~') = 1.74-AS/(7",, .- 7") (45) after conversion to base 10 logarithmic form 2.3RT yields - ~t log(t?:°rg) --/L (50) log(t`') = log(?,)") + b '. (46) The constants ct and fl must be determined empir- Because it is not feasible to elute hydrophobic sub- stances with pure water in reverse phase chromatog- Table 1. Hypothetical pure water and experimental acetone/wate~ (40/60) reverse phase thin layer chromatography retention factors raphy, it is necessary to develop a correlation between for napthol and its derivatives the hypothetical water eluent C value and that of a Compound R~ :~'¢'* RT,, water/organic modifier eluent, C '/°~g. Soczewinski and 1. 2. 3, 4-tetrahydrol- 0.28 0.75 Wachtmeister (1962) determined theoretically and 1-napthol verified experimentally that the logarithm of reten- 2-methyl-l-napthol 0.03 1.67 I-bromo-2-napthol 0.08 1.86 tion factor, R~, for a solute in paper chromatography 4-chloro-1 -napthot 0.24 2.08 changed linearly with the amount of organic modifier 2-napthol - 0.14 1.28 present in the mobile phase. Several subsequent 1. 6-dibromo-2-napthol 0.42 2.50 5, 6, 7, 8-tetrahydro-l-napthol 0.01 1.52 workers have shown that log retention factors in 6-bromo-2-napthol 0.21 2.08 reverse phase thin layer chromatography (RPTLC) *R~ :'~ =logO~R/ I). and HPRPLC retention times may vary linearly with From Biagi et al. (1979). Reverse phase chromatography--I 1441
3.0 coefficient; (2) organic solutes may behave like regu- lar solutions in apolar solvents; (3) organic solutes are 25 strongly influenced by solvophobic interactions in water; (4) HPRPLC retention times can be used to quantify the distribution behavior of a solute in reverse phase systems; (5) the distribution coefficients ~ 1.5 of a solute for partitioning from water into different organic solvent systems can be correlated to each ~1.0 other, provided that no specific molecular inter- ,x actions occur between the solute and the organic 0.5 solvents; and, (6) the retention and selectivity of a solute in a reverse phase system appears to be de- 0.0 I I I I I pendent upon its mobile phase activity coefficient. -04 -02 0.0 0.2 0.4 0.6 Rid ocetone / woter Acknowledgements--The authors thank Dr Norman Wiener and Dr Gordon Flynn of the University of Michigan Fig. 1. Correlation between experimentally determined College of Pharmacy for their helpful comments. The work acetone/water and hypothetical pure water reverse phase presented in this two part series has been supported in part thin layer chromatography retention factors for napthol and by the Michigan Sea Grant Program, and in part by the its derivatives. Cooperative Program between the Great Lakes Environ- mental Research Laboratory of the National Oceanic and Atmospheric Administration and the University of icaily by calibrating the HPRPLC instrument to the Michigan. aqueous activity coefficients of several organic com- pounds under constant temperature, flowrate, and mobile phase composition. The retention times for a REFERENCES target compound are then determined under identical conditions. Caution should be exercised regarding Amidon G. L. and Williams N. A. (1982) A solubility equation for nonelectrolytes. Int. J. Pharm. 11, 249-256. selection of the organic solutes used for calibration, Amidon G. L., Yalkowski S. H., Anik S. 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