915
Ind. Eng. Chem. Res. 1995,34, 915-920
Estimation of Solubility of Organic Compounds in LOctanol An Li, Sirirat Pinsuwan, and Samuel H. Yalkowsky* Department of Pharmaceutical Sciences, University of Arizona, Tucson, Arizona 85721
Five methods were evaluated for their ability to estimate the solubility of organic compounds in l-octanol. OCTASOL is a modified group contribution method developed in this study. Another and water solubility proposed method uses the product of octanol-water partition coefficient (KO,) (S,) as the approximate of octanol solubility. The average absolute error of the estimate obtained from using OCTASOL is 0.25 log units for the training set (N = 180), and 0.29 log units for a test set (N = 10). When the KO,$,method is used, the error is 0.29 log units (N = 124). Three other approaches (ideal solubility, regular solution theory, and UNIFAC) are also evaluated. Their average absolute errors are 0.85 (N = 209), 0.58 (N = 174), and 0.31 (N = 131)log units, respectively.
Introduction l-Octanol is generally considered a satisfactory surrogate for the lipid phase of biological organisms. The l-octanol-water partition coefficient (KO,)has found numerous applications in various fields. Large amount of experimental data and several estimation methods are available (Hansch and Leo, 1979; Rekker et al., 1993). By contrast, the solubility of organic chemicals in octanol has received much less attention. Experimental data are sparse, and estimation techniques for this property have not been well studied. It was shown that chemicals with similar aqueous solubility can greatly differ in their octanol solubility (Ellgehausen et al., 1981). The activity coefficient of a solute in octanol plays an important role in the correlation between KO, and aqueous solubility, especially for solutes of large molecular size. Thus, prediction of KO, based on aqueous solubility alone or vice versa may be misleading. It was also reported (Banerjee and Baughman, 1991) that incorporation of an octanol solubility term can significantly improve the quality of the correlation between KO, and the bioconcentration factor (BCF). Since the magnitude of KO,is largely controlled by the solute activity in the aqueous phase, octanol solubility may reflect part of the BCF which is not influenced by the aqueous phase activity coefficient of the solute. Due to the increasing interest in the solubility of organic compounds in octanol, we have experimentally determined (Pinsuwan et al., 1994) and collected from literature octanol solubilities for 190 chemicals of varied structure. In this paper, we present two new approaches to the estimation of octanol solubility for solutes. One is a modified group contribution method named OCTASOL, the other is based on the strong correlation between KO,and the ratio of the solubilities in octanol and in water (Pinsuwan et al., 1994). These methods are compared with three other estimation approaches-ideal solubility, regular solution theory, and UNIFAC.
solid, X,can be expressed by the product of its subcooled liquid (subscript L) solubility and the ratio of fugacities cf) of the pure compounds in its solid and subcooled liquid states: l0gX = log
x, + log(f,/f,)
(1)
If the solute concentration is much lower than the molarity of the solvent, the solute molarity is proportional to the mole fraction. Then, it can be shown that log s = log s,
+ logcf,/f,)
(2)
Equation 3 was used for conversion between the molar (So)and mole fraction (X,) solubilities of organic solute in octanol:
X, = SJS,
+ (827 - S;MW)/130.22]
(3)
where 130.22 is the molecular weight of octanol. In deriving eq 3, the density of the saturated solution was assumed to be the same as density of pure l-octanol at 25 "C, 827 g/L. The fugacity ratio fdfLis determined by the thermodynamics of the melting process and is often approximated by eq 4 with the difference in heat capacities of liquid and solid states being ignored. log(f,lf,) = -AS,(T,
- T)/2.303RT
(4)
The value of AS, depends on the molecular structure. Walden's rule, AS, = 13.5 cal/(K mol) for rigid organic compounds, has recently been modified by adding a term counting for molecular symmetry (Dannenfelser et al., 1993):
AS, = 13.5 - R In o
(5)
where 0 is the molecular rotational symmetry number, which is defined as the number of indistinguishable positions that can be obtained by rigidly rotating the molecule about its center of mass.
Theory When a solid organic chemical is placed into a solvent, the solubility of the solid solute in the solvent is reached at equilibrium. Assuming that the solvent does not dissolve in the solute, the mole fraction solubility of a
* To whom correspondence should be addressed. 0888-588519512634-0915$09.00/0
Experimental Data A total of 222 experimental solubility data points for 190 organic chemicals in octanol were compiled fi-om our previous work (Pinsuwan et al., 1994) and other publications (Ellgehausen et al., 1981; Anliker and Moser, 1987; Gobas et al., 1988; Miller et al., 1985; Niimi, 1991;
0 1995 American Chemical Society
916 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995
Sloan, 1992; Yalkowsky et al., 1983; Chiou et al., 1981; Mishra, 1988; Kasting et al., 1992; Ruelle et al., 1992; Kristl et al., 1993; Leung et al., 1989). The solutes in the data set range from simple aromatics to organic pigments and dyes of complex structure. The molar solubilities of these compounds range over 7 orders of magnitude. Experimental temperatures are from 15 t o 30 “C. The melting point temperatures of the solutes were obtained from literature or chemical manufactures’ specifications.
Methods Ideal Solubility, Ideal solubility was considered as an approximate to octanol solubility for some nonpolar and semipolar solutes (Yalkowsky et al., 1983). For solids, Xdeal is equal to the fugacity ratio calculated by eq 4. For solutes which are liquid at solution temperature, Xdeal = 1. Regular Solution Approach. Regular solution theory (Hildebrand et al., 1970) accounts for nonideality of mixing by adding the enthalpy of mixing, which is reflected by the activity coefficient y : log y = v@;(d
- d,)2/2.303RT
(6)
If the volume of solute in solution is negligible compared with that of solvent, CP, = 1. If not, iteration is needed for accurate calculations, since the @, and thus y , depends on X. In this study, @, was set to 1 because a preliminary study showed that CP, = 1 resulted in a better overall estimation than @, less than 1. For many chemicals, values of 6 are not directly available. In this study, 6’s of solutes were estimated by Fedors’ method (Barton, 1983; Fedors, 19741, which is based on the additivity of group contributions to the energy of vaporization and molar volume. For the solvent octanol, 6, = 21.1 MPa1’2 (Barton, 1983). UNIFAC Approach. The UNIQUAC functionalgroup activity coefficient (UNIFAC)model developed by Fredenslund et al. (1975) divides the activity coefficient into a combinatorial part, yc, and a residual part yr:
In y = In yc + In yr
(7)
In this study, computer software PC-UNIFAC (1993) was used to calculate yc and yr. The group interaction parameter incorporated in this program is based on Hansen et a1.k table (Hansen et al., 1991) with some modifications as indicated in the manual of PC-UNIFAC version 4.0. As in the case of regular solution theory, iteration is needed if the solution is not dilute because the y’s are functions of X. In this study, mole fraction of solute was set t o 0.01 when performing UNIFAC. To calculate solute solubility, the activity coefficients obtained from regular solution method (eq 6) and UNIFAC (eq 7) are substituted into eq 8, which assumes that octanol does not dissolve in solute, thus log XL = -log y .
l0gX = -log y
&aw
+ log(f&)
(8)
Method. It has been shown that the ratio of molar solubility in octanol (So) to that in water (S,) correlates strongly with the octanol-water partition coefficient (Pinsuwan et al., 1994). Thus, we suppose that Socan be readily estimated by eq 9 if reliable data for S, and KO, are available:
+
log So = log KO, log S,
(9)
This approach is based on the assumption that the solubility ratio of a chemical in octanol and in water is equal to its octanol-water partition coefficient. This assumption implies that the solute is dilute in both phases or the interactions between solute molecules are of the same type and extent in octanol and in water, that no strong specific interactions between solute and solvent occur, and that the mutual saturation of water and octanol in KO,determination has little influence on the solute concentrations in both phases. The experimental data for log KO,were collected from the database section of DayMenus computer program (1991). Experimental S, data were obtained from the AQUASOL dATAbASE (Yalkowsky and Dannenfelser, 1994). The average value was used if more than one datum was available for a compound. DayMenus VAX computer program was used to obtain the calculated KO,,or C log P, based on Hansch and Leo fragment method. C log P was tested to replace experimental KO, in using eq 9. OCTASOL. A group contribution method, OCTASOL, is developed in this study to estimate the solubility of organic solutes in l-octanol. The development of the mothod is based on eq 2. In OCTASOL, solutes are fragmented into functional groups. The aromatic carbon and aromatic CH group are called CAR and CHAR, respectively. In preliminary studies, it was found that for functional groups with carbon as the center atom, including CH3, CH2, CH, C, CH2=, CH=, and C=, their contributions to solute solubility in octanol are significantly different depending on whether or not the group is attached to an aromatic ring. Therefore, these groups are further classified according to the existence of an adjacent aromatic ring. For example, CH2 attached to one or two aromatic rings is called YCH2, while those which do not have adjacent aromatic rings are called XCH2. Functional groups with heteroatoms (halogens, N, 0, S) were not further classified because no statistical justification for such distinction was observed, and the occurrence frequencies of these functional groups are low due t o the limited number of experimental data. The OCTASOL parameters (oil for all functional groups were obtained via a linear no-intercept regression of log SLversus the number of each of the functional groups in the corresponding solute over all the solutes. Functional groups with less than three host chemicals were not included in the regression. The analysis was performed using the Statistical Analysis Systems (SAS) subroutine PROC REG. Experimental SI, were calculated from solubility data using eq 2 and were used in developing the OCTASOL parameters. Of the 222 solubility data collected, 12 were not used because melting point temperature data were not found or because decompositiodsublimation of the chemical occurs at a lower temperature than melting point temperature. Another 14 data were not included because some functional groups of these solutes have frequencies of occurrence less than three. Experimental data of 10 solid chemicals determined in this lab were deliberately set aside and used as a test set for the model. Only one datum for coronene was deleted when performing the regression. This point is an extreme outliner and differs from another datum of coronene by more than 2 orders of magnitude. After obtaining OCTASOL parameters, the molar
Ind. Eng. Chem. Res., Vol. 34,No. 3,1995 917 2 ,
1
g
.OI tt
i
$ -2 6 -3 Y
8,:/ -6
-7 Y
-7
-6
-5
-4
-3 -2 log So, exp'l
-1
0
-7
1
-6
-5
Y -4
-2
-3
-1
1
0
log S,exp'l
Figure 1. Estimation of solubility of organic compounds in odanol by ideal solubility. The line shows the perfect fit.
Figure 4. Estimation of solubility of organic compounds in octanol by K,d&+ The line shows the perfect fit.
I
2 ,
2
N . m
a
. ./
.
-
I
-1
_-
-2
--
; -8
1
-7 -7
-6
-5
-3
-4
-2
-1
0
1
log So, exp'l Figure 2. Estimation of solubility of organic compounds in octanol by regular solution theory. The line shows the perfect fit. 2 ,
-6 -7 -7
-6
-5
-3
-4
-2
-1
0
1
log So, exp'l
Figure 3. Estimation of solubility of organic compounds in odanol by UNIFAC. The line shows the perfect fit.
octanol solubility of the solute was calculated using eq
10:
Results and Discussion Estimates using the ideal solubility approach, regular solution theory, UNIFAC, K o a , method, and OCTASOL are compared to experimental values in Figures 1-5, respectively. The lines in these figures show the perfect fit. Table 1 summarizes the results of the regression analysis. A better fit would have a slope closer to unity and an intercept closer to zero. The
2 '. . . 0.
/
.
--
-3 -. -4
-5
A
t I -7
-6
-5
-4
-3 -2 log So, exp'l
-1
0
1
Figure 6. Estimation of solubility of organic compounds in octanol by OCTASOL. Legends: H, training set; 0, test set; 0 , outliner that was not included in regression. The line shows the perfect fit.
squared regression coefficient, R2, is a measure of scatter based on each regression equation. The experimental values and estimates from each method for 10 compounds used as a test set for OCTASOL are given in Table 2. Ideal Solubility. The ideal solubilities of the solutes tend to be higher than the observed solubilities in octanol, as illustrated in Figure 1. Only 20 out of 202 data points are exceptions, including several acids, phenols, and benzoates. It was also found that the discrepancy between ideal solubility and solubility in octanol generally increases with increasing molecular weight (MW)of the solute. Errors are mostly within a factor of 10 for almost all solutes having MW below 200 and most solutes with MW below 400. Errors as high as 2-4 orders of magnitude are common for solutes with a M w higher than 400. The solutes having the largest differences between the two solubilities include organic pigments and dyes, polynuclear aromatics, and fully halogenated benzenes and biphenyls. These solutes are either of large molecular size or structurally incompatible with octanol due to a lack of polar functional groups. These observations indicate that octanol is not an ideal solvent for most organic solids. Errors may result when ideal solubilities are used in estimating the solubility of organic compounds in octanol. These errors are most likely for highly nonpolar solutes which have a large molecular size and a high melting point temperature. Regular Solution Theory. Regular solution theory (Hildebrand et al., 1970)accounts to a significant extent
918 Ind. Eng. Chem. Res., Vol. 34,No. 3, 1995 Table 1. Regression Analysis of Estimates Versus Experimental Solubility of Organic Chemicals in Octanol absolute estimation error method N slope intercept R2 av max ideal solubility 209 0.492 0.195 0.821 0.851 4.459 regular solution 174 0.892 0.160 0.722 0.584 2.616 UNIFAC 131 0.941 -0.078 0.781 0.314 1.160 Kowsw 124 0.907 -0.036 0.834 0.288 1.311 OCTASOL training set 180 0.927 -0.087 0.940 0.246 1.151 test set 10 0.294 0.679
min 0.000 0.002 0.003 0.000 0.000 0.116
Table 2. Experimental (22 "C) and Estimated Solubilities in Octanol for 10 Compounds Used as the Test Set in OCTASOL Parameter Estimation (log iM) OCTASOL solute exP ideal reg soln UNIFAC K o d w 1,2,3-trichlorobenzene 0.19 0.443 0.409 0.091 -0.019 -0.102 -0.13 -0.973 -3.655 0.425 -0.149 -0.310 gentisic acid 5-amino-o-cresol -0.76 -0.556 -1.121 0.160 -0.876 -0.253 p-bromoaniline 0.43 0.379 0.304 o -bromobenzoic acid -0.12 -0.445 -0.753 -1.102 -0.076 -0.479 -0.641 -0.415 l-chloro-4-nitrobenzene -0.28 0.226 0.192 -0.409 -0.541 -1.086 hexamethylbenzene -0.89 -0.126 -0.340 -0.586 -0.485 0.184 9-methylanthracene -0.60 0.224 -0.975 -0.239 -0.726 -0.32 -0.797 -0.936 p-toluic acid -1.632 -1.112 -1.315 triphenylene -1.77 -0.509 -0.704 av absolute error 0.55 0.84a 0.47 0.23 0.29 a
If the error for gentisic acid is excluded, the number becomes 0.54.
for the nonideal behavior of the solutes. As shown in Figure 2, the systematic error of the estimates is greatly reduced compared with the results from using the ideal solubility approach. The average absolute error is about 0.6 log unit and was not found to vary much for solutes of different structures. However, when compared with the other methods, regular solution theory has the highest data scatter (see Figure 2). More than 10 estimates differ from the experimental data by more than 1.5 log units, and the greatest difference, for gensitic acid, is more than 3 log units. Also, despite a few surprisingly good estimates for several highly insoluble dyes, the estimation error tends to increase with decreasing solubility. Generally, regular solution theory gives overestimates for compounds having experimental solubility from 0.1 to 1 M (see Figure 2). This is probably because the excess entropy of mixing is not accounted for by this theory. The accuracy of the approach used in this study is largely decided by the accuracy of Fedors' group parameters for molar volume and vaporization energy (Barton, 1983; Fedors, 1974). The accuracy of these parameters is difficult to judge because the experimental data for molar volume and vaporization energy are not available for most of the chemicals used in this study. UNIFAC. The results of the estimation by the UNIFAC model (Fredenslund et al., 1975) are illustrated in Figure 3. No systematic error is observed and the estimation accuracy is satisfactory, indicating the validity of the UNIFAC method in estimating the octanol solubility of organic chemicals. An apparent advantage of UNIFAC is its wide range of application with respect to different soluteholvent systems. It has been used successfully to estimate the aqueous solubility and octanol-water partition coefficient of organic chemicals (Chen et al., 1993; Li et al., 1994). The major limitation of this method is the absence of interaction parameters for many functional group pairs. For instance, it is at present incapable of estimating the octanol solubility of many drugs containing phosphorus, barbital groups, aromatic rings with more than one nitrogen atom, and >N- or -NHgroups attached to an aromatic ring. Because not all model parameters are available for all the functional
groups presented in these molecules, their activity coefficient in solution cannot be estimated by UNIFAC. KO, and S, Method. If the experimental data for both KO,and S, are available, eq 9 gives good estimates of octanol solubility for the solutes used in this study. When the experimental values for both KO,and S, were used, the average absolute estimation error is only 0.29 log units, corresponding to a factor of 2. The largest errors of estimate are observed for three chlorinated phenols. The behavior of the chlorinated phenols may violate the assumptions of this method discussed previously, due to specific interactions with octanol or between solute molecules. As a result, the estimates calculated from the product of KO, and S, are 8-20 times higher than the experimental octanol solubilities of these chlorophenols. When C log P was used in place of experimental KO, in eq 9, the average error was increased to 0.4 log units over 108 solutes. This error is lower than those obtained from ideal solubility and regular solution methods discussed above. The K,,,S, approach is the easiest of all five methods discussed in this paper since it does not require any fragmentation of the molecule or calculation of the activity coefficient, and the melting point temperature and entropy of melting are not needed. OCTASOL. Values of oi obtained from multiple linear regression are given in Table 3, along with their standard error, number of chemicals having the group, and the number of occurrences over all solutes. The overall statistics are very satisfactory ( n = 180, R2 = 0.833, RMSE = 0.353) considering the structural diversity of the solutes, the different sources of experimental data, and the fact that no correction factor was used in the regression. The results validate the OCTASOL group contribution approach in estimating the solubility of organic chemicals in octanol. The values of oi reflect the contribution of group z to the solubility of the organic solute in octanol. It is noticed that all groups with carbon as the center atom (except CAR and CHAR) have lower oi values when they are adjacent to an aromatic ring than when they are not. Thus, when these groups connected to aromatic ring(s), they may contribute less to the solute octanol
Ind. Eng. Chem. Res., Vol. 34,No. 3, 1995 919 Table 3. OCTASOL Group Parameters oi (26 "C) POUP
CAR CHAR X-CH3 Y-CHn X-CHiY-CH2X-CH< Y-CH
c-
Y>C=
-F -CL -BR -1
-NO2 -CN -OH -COOH
-coo-0-co-
-NH2 -NH-N< -N< or -N= -Ne >NC(=O)=NC(=O)-NHC(=O)-NHC(=O)N(CH3)2 -OCH3 -S(=O)CH3 -C7HzC13a
Oi
std error
no. of chemicals
freq
-0.155 0.073 0.335 0.122" 0.057 -0.034" -0.119 -0.683 -0.085" -0.317 -0.701 0.098" -1.032 0.376" 0.131 0.008" 0.285" -0.008" -0.082" 0.470 0.724 -0.158 -0.188 -0.217 0.095" -0.146" -0.150" -0.076" -0.802 -0.378" -0.002" -0.184' 0.177" 0.066" -0.005" 0.045"
0.024 0.012 0.056 0.126 0.026 0.082 0.037 0.125 0.089 0.072 0.331 0.109 0.294 0.325 0.026 0.040 0.184 0.144 0.221 0.064 0.110 0.107 0.136 0.071 0.142 0.115 0.226 0.073 0.109 0.270 0.308 0.195 0.206 0.136 0.316 0.187
159 146 72 15 59 20 45 34 20 16 5 19 3 3 66 10 4 12 5 36 15 36 9 21 7 6 8 8 15 6 3 10 3 21 3 4
654 908 142 18 199 23 110 34 35 29 5 26 3 3 226 28 4 12 6 46 15 37 10 34 8 10 9 18 33 6 3 13 3 21 3 4
note aromatic C aromatic CH
sp3, not in aromatic ring N in ring, sp3 or sp2 not in aromatic ring not in ring in ring
chlordane nuclear
Parameter values are not significant at a confidence level of 95%.
solubility than the same group with no adjacent aromatic ring present. This may be the result of differences in the dipole moments of these two types of the same functional group. Due mainly to the limited number of experimental data, some group parameter estimates are not statistically significant. These parameter values should therefore be used with caution at present. They will be improved when more experimental solubility data are available. Compared with the four methods discussed above, OCTASOL has several apparent advantages. First, it does not need experimental data as long as the values of oi are available for all groups in the solute of interest. The chemical structure of the solute is the only input information needed. Second, it is very versatile with respect t o variations in solute molecular structure and capable of estimating the octanol solubility of complex compounds. The good estimates for all dyes and pigments manifest this ability, although the oi value of nitrogen (N group) was determined largely from the solubility data of these dyes and pigments. Third, the estimation accuracy is very satisfactory- the average absolute error is only 0.25 log units for the solute used in developing the model parameters. For the 10 compounds used in the test set, the average error of 0.29 log units was obtained, which is only slightly higher than that of the training set and lower than the errors from most other methods. The K o a , method gives better estimates than OCTASOL for three compounds in this test set, but it is not able to estimate S for four other compounds in the test set due t o lack of experimental data for either KO, or S,. In addition, OCTASOL, although an empirical approach, has the potential
to examine the contributions of different functional groups t o the solute solubility in octanol, thus provides information useful in theoretical studies of solubility phenomena. Summary
A group contribution method, OCTASOL, was developed in this study to estimate the solubility of organic compounds in 1-octanol. It is a modified group contribution method, in which functional groups with carbon as the center atom are subdivided into two types according to whether there is an adjacent aromatic ring. Such a distinction was not made for groups with heteroatoms. The average absolute estimation error from using OCTASOL is 0.25 log units for 180 solutes in the training set and 0.29 log units for 10 solutes in the test set. The values of OCTASOL parameters will be improved as more experimental solubility data become available. Another approach proposed in this paper is to use the product of KO, and S , as the estimate of octanol solubility. This method assumes that KO, is equal to the solubility ratio of the solute in octanol and in water. The average error of estimates is 0.29 log units for 124 compounds. The Ko,S, method is complementary to OCTASOL: the former is simple and easy to use but requires experimental data of KO, and S,, while the latter is able to estimate octanol solubility for complex compounds and compounds whose experimental data of KO, and S, are not available. Three other methods of estimating octanol solubility of organic chemicals were also evaluated. The ideal solubility tends to overestimate the octanol solubility
920 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995
for most chemicals, and the difference between the two solubilities increases as the octanol solubility decreases. Regular solution theory, combined with Fedors' group contribution method to estimate solubility parameter of solutes, compensates significantly for the systematic errors resulted from using the ideal solubility. However, it still results in overestimates for most compounds and errors as large as 2-3 orders of magnitude occur for some solutes. The use of UNIFAC method produces reasonably satisfactory estimates with an average estimation error of 0.31 log units. Lack of the needed group interaction parameters prevents application of UNIFAC to about 50 compounds in the data set used in this study.
Acknowledgment This work is supported by USEPA Grant R817475.
Nomenclature
KO,= octanol-water partition coefficient S = solubility of solid solute, mom SL= solubility of solid solute in subcooled liquid states, mom S, = solubility of solute in water, mom So = solubility of solute in octanol, mom X = mole fraction solubility of solid solute X L = mole fraction solubility of solid solute in subcooled liquid states X o = mole fraction solubility of solute in octanol fs = fugacity of pure compound in its solid state f L = fugacity of pure compound in its subcooled liquid state MW = molecular weight of the solute T = solution temperature, K T , = melting point temperature of solute, K R = gas constant, J/(K mol) ASm = entropy of melting at T,, J/(K mol) oi = OCTASOL parameter for functional group i n, = number of functional group i in molecule
Greek Symbols u = the molecular rotational symmetry number Y = the molar volume of the solute, m3/mol @, = volume fraction of the solvent 6 = solubility parameters of solute, MPa112 6, = solubility parameters of solvent, MPa112 y = activity coefficient yc = combinatorial part of activity coefficient yr = residual part of activity coefficient
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Abstract published i n Advance ACS Abstracts, February 1, 1995. @
