**3. Experimental methods for measuring thermodynamic and kinetic solubilities**

Recent advances in automated chemical synthesis and combinatorial chemistry have generated large numbers of new chemical compounds that need to be screened for possible biological activity and desired ADMET properties. The conventional experimental methods that were once used in the pharmaceutical industry to measure solubility and water-toorganic solvent partition coefficients are inadequate to handle large numbers of new compound because of low throughput capacity and the amount of compound required for the experimental determination. Large quantities of highly purified compounds are not usually available in the initial stages of drug discovery and drug testing. To meet the demands imposed by the increased compound numbers, the pharmaceutical industry has developed miniaturized and automated sample preparation platforms, combined with rapid chemical analysis methods based on nephelometric, uv/visible absorption and/or chromatographic measurements. The experimental protocol used depends on whether one needs to measure the kinetic or thermodynamic solubility.

High throughput kinetic aqueous solubility assays are based on the detection of precipitation of compounds in aqueous or aqueous buffered solutions. Typically, small known aliquots of the stock solution are added incrementally to the aqueous (or aqueous buffered solution) at predetermined time intervals until the solubility limit is reached. The resulting precipitation can be detected optically by nephlometric or laser monitoring methods, and the kinetic solubility is defined as the solute concentration immediately preceding the point at which precipitation was first detected. Kinetic solubility thus represents the maximum solubility of the fastest precipitation species of the given compound into the desired solubilizing solvent media. Numerous modifications of kinetic assays have been suggested in recent years. The suggested modifications differ in the dilution and detection method. For example, Lipinski *et al*. (2001) added small aliquots of a

Prediction of Partition Coefficients and Permeability of Drug Molecules in Biological

compounds studied.

crystalline phase, PAo.

that have been reported to date.

and 2 to give the following mathematical correlations:

Systems with Abraham Model Solute Descriptors Derived from Measured Solubilities and… 99

achieved. Thermodynamic solubility is defined as the concentration in solution of a compound in equilibrium with an excess of solid material being present in solution at the conclusion of the dissolution process. Thermodynamic solubility is considered the "true" solubility of a compound. Experimental methods for determining thermodynamic solubility may be grouped into categories, one that extends the experimental protocols of exiting kinetic solubility determinations to longer "equilibration times" and the other that conducts solubility studies on solid compounds obtained from dried stock solutions to remove the enhancement effects caused by having the added dimethyl sulfoxide present in the final equilibrated solution. The rationale behind the longer equilibration times is that sufficient time will now be afforded for the first-precipitated crystalline phase to convert to the more thermodynamically stable crystalline phase. Sugano and coworkers (2006) reported a significant decrease in solubility with equilibration time for more than half of the 26 model

The preceding discussion focused on aqueous kinetic and thermodynamic solubility measurements. There is no reason that the basic high throughput experimental methodologies cannot be applied to organic solvents and to aqueous-organic solvent mixtures. Measured drug solubility in organic solvents, in combination with the Abraham general solvation model, provides valuable information in regarding the molecule's hydrogen-bonding character and dipolarity. Solubility ratios are substituted into Eqns. 1

where CA,organic and CA,water denote the molar solubility of the solute (component A) in the anhydrous "dry" organic solvent and in water, respectively, and CA,gas is the molar gas phase concentration of the solute above the crystalline phase at the system temperature. This later quantity is calculable as CA,gas = PAo V/RT, from the solute's vapor pressure above the

The solubility ratio in Eqn. 5 represents a hypothetical partitioning process for transferring the solute from water to the anhydrous organic solvent as depicted in Figure 4. Also depicted in Figure 4 are the gas-to-water and gas-to-organic solvent partitioning processes, along with their respective concentration ratios. The hypothetical water-to-organic solvent partitioning process should not be confused with the direct practical organic solvent/water partitioning system that corresponds to the equilibrium solute partitioning between a watersaturated organic phase and an aqueous phase saturated with the organic solvent. For solvents that are partially miscible with water, such as 1-butanol and ethyl acetate, partition coefficients calculated as the ratio of the molar solute solubilities in the organic solvent and water are not the same as those obtained from direct partition between water (saturated with the organic solvent) and organic solvent (saturated with water). Solubility ratios and practical partition coefficients, however, are nearly identical for solvents like linear alkanes, cycloalkanes, chloroform, carbon tetrachloride and dichloromethane, which are almost "completely" immiscible with water. Tables 1 and 2 give the equation coefficients for the Abraham model solubility ratio correlations (Eqns. 5 and 6) for the different organic solvents

log C /C c e · s · a · b · v · A,organic A,water **ESA B V** (5)

log C /C c e · s · a · b · l · A,organic A,gas **E S A BL** (6)

stock solution of the drug (dissolved in dimethyl sulfoxide, DMSO) to the aqueous solvent media every minute until precipitation occurred. The DMSO in solution did increase with each added aliquot and may result in a higher measured aqueous solubility. Dimethyl sulfoxide is known to increase the solubility by helping to solvate the more lipophilic drug compounds. Solubility enhancement by dimethyl sulfoxide can be reduced if the samples are first serially diluted in dimethyl sulfoxide before the aliquots are added to the aqueous solvent system. Special 96-well plates have been designed to facilitate high throughput solubility measurements. The method depicted in Figure 3 allows one to quickly measure the aqueous solubility and aqueous-buffered solubility of 12 different drug candidates. The eight DMSO-diluted concentrations (1 mM to 100 mM) of each drug candidate are placed in the specified well of the drug's respective column. In the 12 x 9 cell matrix, the drug is identified by column number and the concentration is identified by row number. A predetermined aliquot volume from each of the DMSO diluted sample wells is transferred to the corresponding cell in the aqueous plate and aqueous-buffered plate. The volume of DMSO-diluted sample is the same for each transferred aliquot. Each cell in the aqueous plate and aqueous-buffered plate contains an identical volume of solvent. The cell contents are examined for precipitation immediately after the passage of the defined time interview, or alternatively, one can remove the solid and determine the concentration of dissolved drug by standard spectroscopic and/or chromatographic methods.

Fig. 3. Outline of a high throughput method for measuring drug solubility in water and in an aqueous-buffered solution using a 96-well plate.

Kinetic methods often overestimate the thermodynamic drug solubility because of the increased solubilization effect caused by the presence of dimethyl sulfoxide in the aqueous solvent and by the fact that one has not allowed sufficient time for equilibrium to be

stock solution of the drug (dissolved in dimethyl sulfoxide, DMSO) to the aqueous solvent media every minute until precipitation occurred. The DMSO in solution did increase with each added aliquot and may result in a higher measured aqueous solubility. Dimethyl sulfoxide is known to increase the solubility by helping to solvate the more lipophilic drug compounds. Solubility enhancement by dimethyl sulfoxide can be reduced if the samples are first serially diluted in dimethyl sulfoxide before the aliquots are added to the aqueous solvent system. Special 96-well plates have been designed to facilitate high throughput solubility measurements. The method depicted in Figure 3 allows one to quickly measure the aqueous solubility and aqueous-buffered solubility of 12 different drug candidates. The eight DMSO-diluted concentrations (1 mM to 100 mM) of each drug candidate are placed in the specified well of the drug's respective column. In the 12 x 9 cell matrix, the drug is identified by column number and the concentration is identified by row number. A predetermined aliquot volume from each of the DMSO diluted sample wells is transferred to the corresponding cell in the aqueous plate and aqueous-buffered plate. The volume of DMSO-diluted sample is the same for each transferred aliquot. Each cell in the aqueous plate and aqueous-buffered plate contains an identical volume of solvent. The cell contents are examined for precipitation immediately after the passage of the defined time interview, or alternatively, one can remove the solid and determine the concentration of dissolved

drug by standard spectroscopic and/or chromatographic methods.

Fig. 3. Outline of a high throughput method for measuring drug solubility in water and in

Kinetic methods often overestimate the thermodynamic drug solubility because of the increased solubilization effect caused by the presence of dimethyl sulfoxide in the aqueous solvent and by the fact that one has not allowed sufficient time for equilibrium to be

an aqueous-buffered solution using a 96-well plate.

achieved. Thermodynamic solubility is defined as the concentration in solution of a compound in equilibrium with an excess of solid material being present in solution at the conclusion of the dissolution process. Thermodynamic solubility is considered the "true" solubility of a compound. Experimental methods for determining thermodynamic solubility may be grouped into categories, one that extends the experimental protocols of exiting kinetic solubility determinations to longer "equilibration times" and the other that conducts solubility studies on solid compounds obtained from dried stock solutions to remove the enhancement effects caused by having the added dimethyl sulfoxide present in the final equilibrated solution. The rationale behind the longer equilibration times is that sufficient time will now be afforded for the first-precipitated crystalline phase to convert to the more thermodynamically stable crystalline phase. Sugano and coworkers (2006) reported a significant decrease in solubility with equilibration time for more than half of the 26 model compounds studied.

The preceding discussion focused on aqueous kinetic and thermodynamic solubility measurements. There is no reason that the basic high throughput experimental methodologies cannot be applied to organic solvents and to aqueous-organic solvent mixtures. Measured drug solubility in organic solvents, in combination with the Abraham general solvation model, provides valuable information in regarding the molecule's hydrogen-bonding character and dipolarity. Solubility ratios are substituted into Eqns. 1 and 2 to give the following mathematical correlations:

$$\log\left(\mathbf{C}\_{\text{A,organic}} / \mathbf{C}\_{\text{A,water}}\right) = \mathbf{c} + \mathbf{e} \cdot \mathbf{E} + \mathbf{s} \cdot \mathbf{S} + \mathbf{a} \cdot \mathbf{A} + \mathbf{b} \cdot \mathbf{B} + \mathbf{v} \cdot \mathbf{V} \tag{5}$$

$$\log\left(\mathbf{C}\_{\text{A,organic}} / \mathbf{C}\_{\text{A,gas}}\right) = \mathbf{c} + \mathbf{e} \cdot \mathbf{E} + \mathbf{s} \cdot \mathbf{S} + \mathbf{a} \cdot \mathbf{A} + \mathbf{b} \cdot \mathbf{B} + \mathbf{l} \cdot \mathbf{L} \tag{6}$$

where CA,organic and CA,water denote the molar solubility of the solute (component A) in the anhydrous "dry" organic solvent and in water, respectively, and CA,gas is the molar gas phase concentration of the solute above the crystalline phase at the system temperature. This later quantity is calculable as CA,gas = PAo V/RT, from the solute's vapor pressure above the crystalline phase, PAo.

The solubility ratio in Eqn. 5 represents a hypothetical partitioning process for transferring the solute from water to the anhydrous organic solvent as depicted in Figure 4. Also depicted in Figure 4 are the gas-to-water and gas-to-organic solvent partitioning processes, along with their respective concentration ratios. The hypothetical water-to-organic solvent partitioning process should not be confused with the direct practical organic solvent/water partitioning system that corresponds to the equilibrium solute partitioning between a watersaturated organic phase and an aqueous phase saturated with the organic solvent. For solvents that are partially miscible with water, such as 1-butanol and ethyl acetate, partition coefficients calculated as the ratio of the molar solute solubilities in the organic solvent and water are not the same as those obtained from direct partition between water (saturated with the organic solvent) and organic solvent (saturated with water). Solubility ratios and practical partition coefficients, however, are nearly identical for solvents like linear alkanes, cycloalkanes, chloroform, carbon tetrachloride and dichloromethane, which are almost "completely" immiscible with water. Tables 1 and 2 give the equation coefficients for the Abraham model solubility ratio correlations (Eqns. 5 and 6) for the different organic solvents that have been reported to date.

Prediction of Partition Coefficients and Permeability of Drug Molecules in Biological

Systems with Abraham Model Solute Descriptors Derived from Measured Solubilities and… 101

Dry Solvent c e s a b v Methanol 0.276 0.334 -0.714 0.243 -3.320 3.549 Ethanol 0.222 0.471 -1.035 0.326 -3.596 3.857 Propan-1-ol 0.139 0.405 -1.029 0.247 -3.767 3.986 Butan-1-ol 0.165 0.401 -1.011 0.056 -3.958 4.044 Pentan-1-ol 0.150 0.536 -1.229 0.141 -3.864 4.077 Hexan-1-ol 0.115 0.492 -1.164 0.054 -3.978 4.131 Heptan-1-ol 0.035 0.398 -1.063 0.002 -4.343 4.317 Octan-1-ol -0.034 0.489 -1.044 -0.024 -4.235 4.218 Decan-1-ol -0.058 0.616 -1.319 0.026 -4.153 4.279 Propan-2-ol 0.099 0.343 -1.049 0.406 -3.827 4.033 Isobutanol 0.127 0.253 -0.976 0.158 -3.882 4.114 sec-Butanol 0.188 0.354 -1.127 0.016 -3.568 3.968 *tert*-Butanol 0.211 0.171 -0.947 0.331 -4.085 4.109 3-Methyl-1-butanol 0.073 0.360 -1.273 0.090 -3.770 4.273 Pentan-2-ol 0.115 0.455 -1.331 0.206 -3.745 4.201 Ethylene glycol -0.270 0.578 -0.511 0.715 -2.619 2.729 2,2,2 -Trifluoroethanol 0.395 -0.094 -0.594 -1.280 -1.274 3.088 Diethyl ether 0.350 0.358 -0.820 -0.588 -4.956 4.350 Tetrahydrofuran 0.207 0.372 -0.392 -0.236 -4.934 4.447 1,4-Dioxane 0.098 0.350 -0.083 -0.556 -4.826 4.172 Dibutyl ether 0.176 0.394 -0.985 -1.414 -5.357 4.524 Methyl *tert*-butyl ether 0.341 0.307 -0.817 -0.618 -5.097 4.425 Methyl acetate 0.351 0.223 -0.150 -1.035 -4.527 3.972 Ethyl acetate 0.328 0.369 -0.446 -0.700 -4.904 4.150 Butyl acetate 0.248 0.356 -0.501 -0.867 -4.973 4.281 Propanone 0.313 0.312 -0.121 -0.608 -4.753 3.942 Butanone 0.246 0.256 -0.080 -0.767 -4.855 4.148 Cyclohexanone 0.038 0.225 0.058 -0.976 -4.842 4.315 Dimethylformamide -0.305 -0.058 0.343 0.358 -4.865 4.486 Dimethylacetamide -0.271 0.084 0.209 0.915 -5.003 4.557 Diethylacetamide 0.213 0.034 0.089 1.342 -5.084 4.088 Dibutylformamide 0.332 0.302 -0.436 0.358 -4.902 3.952 N-Methylpyrolidinone 0.147 0.532 0.225 0.840 -4.794 3.674 N-Methyl-2-piperidone 0.056 0.332 0.257 1.556 -5.035 3.983 N-Formylmorpholine -0.032 0.696 -0.062 0.014 -4.092 3.405 N-Methylformamide 0.114 0.407 -0.287 0.542 -4.085 3.471 N-Ethylformamide 0.220 0.034 -0.166 0.935 -4.589 3.730 N-Methylacetamide 0.090 0.205 -0.172 1.305 -4.589 3.833 N-Ethylacetamide 0.284 0.128 -0.442 1.180 -4.728 3.856 Formamide -0.171 0.070 0.308 0.589 -3.152 2.432 Acetonitrile 0.413 0.077 0.326 -1.566 4.391 3.364 Nitromethane 0.023 -0.091 0.793 -1.463 -4.364 3.460 Dimethylsulfoxide -0.194 0.327 0.791 -1.260 -4.540 3.361 Tributylphosphate 0.327 0.570 -0.837 -1.069 -4.333 3.919

Fig. 4. Solubility ratios describing the various solute transfer processes.



Fig. 4. Solubility ratios describing the various solute transfer processes.

Dry Solvent c e s a b v Olely alcohol -0.096 0.148 -0.841 -0.438 -4.040 4.125 Dichloromethane 0.319 0.102 -0.187 -3.058 -4.090 4.324 Trichloromethane 0.191 0.105 -0.403 -3.112 -3.514 4.395 Tetrachloromethane 0.199 0.523 -1.159 -3.560 -4.594 4.618 1,2-Dichloroethane 0.183 0.294 -0.134 -2.801 -4.291 4.180 1-Chlorobutane 0.222 0.273 -0.569 -2.918 -4.883 4.456 Butane 0.297 -0.005 -1.584 -3.188 -4.567 4.562 Pentane 0.369 0.386 -1.568 -3.535 -5.215 4.514 Hexane 0.361 0.579 -1.723 -3.599 -4.764 4.344 Heptane 0.325 0.670 -2.061 -3.317 -4.733 4.543 Octane 0.223 0.642 -1.647 -3.480 -5.067 4.526 Nonane 0.240 0.619 -1.713 -3.532 -4.921 4.482 Decane 0.160 0.585 -1.734 -3.435 -5.078 4.582 Undecane 0.058 0.603 -1.661 -3.421 -5.120 4.619 Dodecane 0.114 0.668 -1.664 -3.545 -5.006 4.459 Hexadecane 0.087 0.667 -1.617 -3.587 -4.869 4.433 Cyclohexane 0.159 0.784 -1.678 -3.740 -4.929 4.577 Methylcyclohexane 0.246 0.782 -1.982 -3.517 -4.293 4.528 Isooctane 0.318 0.555 -1.737 -3.677 -4.864 4.417 Benzene 0.142 0.464 -0.588 -3.099 -4.625 4.491 Toluene 0.143 0.527 -0.720 -3.010 -4.824 4.545 Fluorobenzene 0.139 0.152 -0.374 -3.030 -4.601 4.540 Chlorobenzene 0.065 0.381 -0.521 -3.183 -4.700 4.614 Bromobenzene -0.017 0.436 -0.424 -3.174 -4.558 4.445 Iodobenzene -0.192 0.298 -0.308 -3.213 -4.653 4.588 Nitrobenzene -0.152 0.525 0.081 -2.332 -4.494 4.187 Benzonitrile 0.155 0.337 -0.036 -1.544 -4.614 3.990 Olive oil -0.035 0.574 -0.798 -1.422 -4.984 4.210 Carbon disulfide 0.047 0.686 -0.943 -3.603 -5.818 4.921 Isopropyl myristate -0.605 0.930 -1.153 -1.682 -4.093 4.249 Triolein 0.385 0.983 -2.083 -2.007 -3.452 4.072


Prediction of Partition Coefficients and Permeability of Drug Molecules in Biological

Systems with Abraham Model Solute Descriptors Derived from Measured Solubilities and… 103

Dry Solvent c e s a b l Heptan-1-ol -0.056 -0.216 0.554 3.596 0.803 0.933 Octan-1-ol -0.147 -0.214 0.561 3.507 0.749 0.943 Decan-1-ol -0.139 -0.090 0.356 3.547 0.727 0.958 Propan-2-ol -0.048 -0.324 0.713 4.036 1.055 0.884 Isobutanol -0.034 -0.387 0.719 3.736 1.088 0.905 sec-Butanol -0.003 -0.357 0.699 3.595 1.247 0.881 *tert*-Butanol 0.053 -0.443 0.699 4.026 0.882 0.907 3-Methyl-1-butanol -0.052 -0.430 0.628 3.661 0.932 0.937 Pentan-2-ol -0.031 -0.325 0.496 3.792 1.024 0.934 Ethylene glycol -0.887 0.132 1.657 4.457 2.355 0.565 2,2,2-Trifluoroethanol -0.092 -0.547 1.339 2.213 3.807 0.645 Diethyl ether 0.288 -0.379 0.904 2.937 0.000 0.963 Tetrahydrofuran 0.189 -0.347 1.238 3.289 0.000 0.982 1,4-Dioxane -0.034 -0.354 1.674 3.021 0.000 0.919 Dibutyl ether 0.153 -0.406 0.758 2.152 -0.610 1.008 Methyl *tert*-butyl ether 0.231 -0.536 0.890 2.623 0.000 0.999 Methyl acetate 0.129 -0.447 1.675 2.625 0.213 0.874 Ethyl acetate 0.182 -0.352 1.316 2.891 0.000 0.916 Butyl acetate 0.147 -0.414 1.212 2.623 0.000 0.954 Propanone 0.127 -0.387 1.733 3.060 0.000 0.866 Butanone 0.112 -0.474 1.671 2.878 0.000 0.916 Cyclohexanone -0.086 -0.441 1.725 2.786 0.000 0.957 Dimethylformamide -0.391 -0.869 2.107 3.774 0.000 1.011 Dimethylacetamide -0.308 -0.736 1.802 4.361 0.000 1.028 Diethylacetamide -0.075 -0.434 1.911 4.801 0.000 0.899 Dibutylformamide -0.002 -0.239 1.402 4.029 0.000 0.900 N-Methylpyrolidinone -0.128 -0.029 2.217 4.429 0.000 0.777 N-Methyl-2-piperidone -0.264 -0.171 2.086 5.056 0.000 0.883 N-Formylmorpholine -0.437 0.024 2.631 4.318 0.000 0.712 N-Methylformamide -0.249 -0.142 1.661 4.147 0.817 0.739 N-Ethylformamide -0.220 -0.302 1.743 4.498 0.480 0.824 N-Methylacetamide -0.197 -0.175 1.608 4.867 0.375 0.837 N-Ethylacetamide -0.018 -0.157 1.352 4.588 0.357 0.824 Formamide -0.800 0.310 2.292 4.130 1.933 0.442 Acetonitrile -0.007 -0.595 2.461 2.085 0.418 0.934 Nitromethane -0.340 -0.297 2.689 2.193 0.514 0.728 Dimethylsulfoxide -0.556 -0.223 2.903 5.036 0.000 0.719 Tributylphosphate 0.097 -0.098 1.103 2.411 0.588 0.844 Propylene carbonate -0.356 -0.413 2.587 2.207 0.455 0.719 Gas-water -1.271 0.822 2.743 3.904 4.814 -0.213

Table 2. Coefficients in Eqn. 6 for Correlating Solute Solubility in Dry Organic Solvents at

298 K





Prediction of Partition Coefficients and Permeability of Drug Molecules in Biological Systems with Abraham Model Solute Descriptors Derived from Measured Solubilities and… 103

102 Toxicity and Drug Testing

Dry Solvent c e s a b v Propylene carbonate 0.004 0.168 0.504 -1.283 -4.407 3.421 Gas-water -0.994 0.577 2.549 3.813 4.841 -0.869 Table 1. Coefficients in Eqn. 5 for Correlating Solute Solubility in Dry Organic Solvents at

Dry Solvent c e s a b l Olely alcohol -0.268 -0.392 0.800 3.117 0.978 0.918 Dichloromethane 0.192 -0.572 1.492 0.460 0.847 0.965 Trichloromethane 0.157 -0.560 1.259 0.374 1.333 0.976 Tetrachloromethane 0.217 -0.435 0.554 0.000 0.000 1.069 1,2-Dichloroethane 0.017 -0.337 1.600 0.774 0.637 0.921 1-Chlorobutane 0.130 -0.581 1.114 0.724 0.000 1.016 Butane 0.291 -0.360 0.091 0.000 0.000 0.959 Pentane 0.335 -0.276 0.000 0.000 0.000 0.968 Hexane 0.292 -0.169 0.000 0.000 0.000 0.979 Heptane 0.275 -0.162 0.000 0.000 0.000 0.983 Octane 0.215 -0.049 0.000 0.000 0.000 0.967 Nonane 0.200 -0.145 0.000 0.000 0.000 0.980 Decane 0.156 -0.143 0.000 0.000 0.000 0.989 Undecane 0.113 0.000 0.000 0.000 0.000 0.971 Dodecane 0.053 0.000 0.000 0.000 0.000 0.986 Hexadecane 0.000 0.000 0.000 0.000 0.000 1.000 Cyclohexane 0.163 -0.110 0.000 0.000 0.000 1.013 Methylcyclohexane 0.319 -0.215 0.000 0.000 0.000 1.012 Isooctane 0.264 -0.230 0.000 0.000 0.000 0.975 Benzene 0.107 -0.313 1.053 0.457 0.169 1.020 Toluene 0.121 -0.222 0.938 0.467 0.099 1.012 Fluorobenzene 0.181 -0.621 1.432 0.647 0.000 0.986 Chlorobenzene 0.064 -0.399 1.151 0.313 0.171 1.032 Bromobenzene -0.064 -0.326 1.261 0.323 0.292 1.002 Iodobenzene -0.171 -0.192 1.197 0.245 0.245 1.002 Nitrobenzene -0.275 0.001 1.861 1.119 0.000 0.925 Benzonitrile -0.062 -0.402 1.939 2.007 0.000 0.880 Olive oil -0.159 -0.277 0.904 1.695 -0.090 0.876 Carbon disulfide 0.101 0.251 0.177 0.027 0.095 1.068 Triolein 0.147 0.254 -0.246 1.520 1.473 0.918 Methanol -0.039 -0.338 1.317 3.836 1.396 0.773 Ethanol 0.017 -0.232 0.867 3.894 1.192 0.846 Propan-1-ol -0.042 -0.246 0.749 3.888 1.078 0.874 Butan-1-ol -0.004 -0.285 0.768 3.705 0.879 0.890 Pentan-1-ol -0.002 -0.161 0.535 3.778 0.960 0.900 Hexan-1-ol -0.014 -0.205 0.583 3.621 0.891 0.913

298 K

Table 2. Coefficients in Eqn. 6 for Correlating Solute Solubility in Dry Organic Solvents at 298 K

Acetonitrile -0.007 -0.595 2.461 2.085 0.418 0.934 Nitromethane -0.340 -0.297 2.689 2.193 0.514 0.728 Dimethylsulfoxide -0.556 -0.223 2.903 5.036 0.000 0.719 Tributylphosphate 0.097 -0.098 1.103 2.411 0.588 0.844 Propylene carbonate -0.356 -0.413 2.587 2.207 0.455 0.719 Gas-water -1.271 0.822 2.743 3.904 4.814 -0.213

Prediction of Partition Coefficients and Permeability of Drug Molecules in Biological

*app*

*P*

plates.

Systems with Abraham Model Solute Descriptors Derived from Measured Solubilities and… 105

compartments separated by a thin 1-octanol liquid layer coated on a polycarbonate filter. The apparatus is shown in Figure 5. The molar concentration of the compound in the aqueous acceptor compartment, Cacceptor,end is measured at the end of the defined time endpoint, tend. The apparent membrane permeability, Papp, is calculated from Cacceptor,end by

*V V C*

, ( ) *donor equ donor initial donor acceptor <sup>V</sup> C C*

where Vacceptor and Vdonor denote the aqueous phase volumes in the acceptor and donor compartments, respectively, Cdonor,initial refers to the initial compound concentration in the donor phase, and A is the membrane accessible surface area times porosity. The water-tooctanol partition coefficient, Po/w, is derived from the measured apparent permeability using a calibration curve constructed from measured permeabilities of standard compounds of known Po/w values. The assay has been used to measure water-to-hexadecane partition coefficients (Wohnsland and Faller, 2001) and can be performed using 96-well microtiter

Fig. 5. High throughput experimental method for measuring water-to- octanol partition coefficients based on the diffusion of a solute betweentwo aqueous phase compartments. Gao *et al*. (2005) developed a miniaturized method involving the dispersion of colloidal stable porous silica-encapsulated magnetic nanoparticles into water and/or an aqueous-buffered solution. Prior to dispersion, the nanoparticles are preloaded with a known amount of 1 octanol. Equilibrium is quickly established between the drug dissolved in the aqueous (or aqueous-buffered) solution and the small octanol droplets on the nanoparticles. The paramagnetic properties of the nanoparticles facilitate magnetic-induced phase separation. Once the magnetic particles are removed, the uv/visible absorbance of the solution is

recorded. The log Po/w (or log Do/w in the case of an ionic solute) is calculated as

log log [( )( )] *before after aqueous*

*Abs Abs V*

*Abs V*

/

*P*

*o w*

<sup>1</sup> , ( )( )ln(1 ) *acceptor donor acceptor end*

*V V At <sup>C</sup>* (7)

*V V* (8)

tan

(9)

*after oc ol*

*acceptor donor end equ*

Three specific conditions must be met in order to use the Abraham solvation parameter model to predict saturation solubilities. First, the same solid phase must be in equilibrium with the saturation solutions in the organic solvent and in water (i.e., there should be no solvate or hydrate formation). Second, the secondary medium activity coefficient of the solid in the saturated solutions must be unity (or near unity). This condition generally restricts the method to those solutes that are sparingly soluble in water and nonaqueous solvents. Finally, for solutes that are ionized in aqueous solution, CA,water, refers to the solubility of the neutral form. The second restriction may not be as important as initially believed. The Abraham solvation parameter model has shown remarkable success in correlating the solubility of several very soluble crystalline solutes. For example, Eqns 5 and 6 described the molar solubility of benzil in 24 organic solvents to within overall standard deviations of 0.124 and 0.109 log units, respectively. Standard deviations for acetylsalicylic acid dissolved in 13 alcohols, 4 ethers and ethyl acetate were 0.123 and 0.138 log units. Benzil (Acree and Abraham, 2002) and acetylsalicylic acid (Charlton *et al*., 2003) exhibited solubilities exceeding 1Molar in several of the organic solvents studied. In the case of acetylsalicylic acid it could be argued that the model's success relates back to when the equation coefficients were originally calculated for the dry solvents. The databases used in the regression analyses contained very few carboxylic acid solutes (benzoic acid, 2-hydroxybenzoic acid and 4-hydroxybenzoic acid). Most of the experimental data for carboxylic acids and other very acidic solutes was in the form of saturation solubilities, which were also in the 1 to 3 Molar range. Such arguments do not explain why equations (5) and (6) described the measured benzil solubility data. The benzil solubilities were measured after most of the equation coefficients were first determined.

### **4. High throughput experimental methods for measuring water-to-octanol partition coefficients**

Each administered drug has to pass several membrane barriers in order to be delivered to the desired target site for therapeutic action. Orally administered drugs have to be absorbed into the intestine. Transdermally administered drugs need to penetrate human skin. Drugs intended to act in the central nervous system must cross the blood-brain brain barrier (BBB). This barrier is formed by the endothelial cells of the cerebral capillaries and restricts the transport of many compounds into the brain from the blood stream. The cellular architecture of the human intestine, human skin and human brain are quite different; however, the principle of transcellular absorption is the same. The dissolved drug must be transferred from an aqueous environment into the membrane phase, must diffuse across the membrane, and afterwards must partition back into an aqueous-phase compartment. The water-to-octanol partition coefficient, Po/w, is widely regarded in the pharmaceutical industry as a quantitative measure for assessing a drug molecule's affinity for the membrane phase. Considerable attention has been afforded to developing high throughput experimental methodologies that either directly measure Po/w values, or that enable accurate estimation of Po/w from other conveniently measured properties. Poole and Poole (2003) reviewed the direct and indirect separation for obtaining water-to-octanol partition coefficients, with emphasis on the high throughput methods.

As selected examples of experimental methods that have been developed in recent years, Faller and coworkers (2005) designed a rather novel high throughput method to measure lipophilicity based on the diffusion of organic compounds between to aqueous phase

Three specific conditions must be met in order to use the Abraham solvation parameter model to predict saturation solubilities. First, the same solid phase must be in equilibrium with the saturation solutions in the organic solvent and in water (i.e., there should be no solvate or hydrate formation). Second, the secondary medium activity coefficient of the solid in the saturated solutions must be unity (or near unity). This condition generally restricts the method to those solutes that are sparingly soluble in water and nonaqueous solvents. Finally, for solutes that are ionized in aqueous solution, CA,water, refers to the solubility of the neutral form. The second restriction may not be as important as initially believed. The Abraham solvation parameter model has shown remarkable success in correlating the solubility of several very soluble crystalline solutes. For example, Eqns 5 and 6 described the molar solubility of benzil in 24 organic solvents to within overall standard deviations of 0.124 and 0.109 log units, respectively. Standard deviations for acetylsalicylic acid dissolved in 13 alcohols, 4 ethers and ethyl acetate were 0.123 and 0.138 log units. Benzil (Acree and Abraham, 2002) and acetylsalicylic acid (Charlton *et al*., 2003) exhibited solubilities exceeding 1Molar in several of the organic solvents studied. In the case of acetylsalicylic acid it could be argued that the model's success relates back to when the equation coefficients were originally calculated for the dry solvents. The databases used in the regression analyses contained very few carboxylic acid solutes (benzoic acid, 2-hydroxybenzoic acid and 4-hydroxybenzoic acid). Most of the experimental data for carboxylic acids and other very acidic solutes was in the form of saturation solubilities, which were also in the 1 to 3 Molar range. Such arguments do not explain why equations (5) and (6) described the measured benzil solubility data. The benzil solubilities were measured after most of the

**4. High throughput experimental methods for measuring water-to-octanol** 

Each administered drug has to pass several membrane barriers in order to be delivered to the desired target site for therapeutic action. Orally administered drugs have to be absorbed into the intestine. Transdermally administered drugs need to penetrate human skin. Drugs intended to act in the central nervous system must cross the blood-brain brain barrier (BBB). This barrier is formed by the endothelial cells of the cerebral capillaries and restricts the transport of many compounds into the brain from the blood stream. The cellular architecture of the human intestine, human skin and human brain are quite different; however, the principle of transcellular absorption is the same. The dissolved drug must be transferred from an aqueous environment into the membrane phase, must diffuse across the membrane, and afterwards must partition back into an aqueous-phase compartment. The water-to-octanol partition coefficient, Po/w, is widely regarded in the pharmaceutical industry as a quantitative measure for assessing a drug molecule's affinity for the membrane phase. Considerable attention has been afforded to developing high throughput experimental methodologies that either directly measure Po/w values, or that enable accurate estimation of Po/w from other conveniently measured properties. Poole and Poole (2003) reviewed the direct and indirect separation for obtaining water-to-octanol partition

As selected examples of experimental methods that have been developed in recent years, Faller and coworkers (2005) designed a rather novel high throughput method to measure lipophilicity based on the diffusion of organic compounds between to aqueous phase

equation coefficients were first determined.

coefficients, with emphasis on the high throughput methods.

**partition coefficients** 

compartments separated by a thin 1-octanol liquid layer coated on a polycarbonate filter. The apparatus is shown in Figure 5. The molar concentration of the compound in the aqueous acceptor compartment, Cacceptor,end is measured at the end of the defined time endpoint, tend. The apparent membrane permeability, Papp, is calculated from Cacceptor,end by

$$P\_{app} = -\left(\frac{V\_{aceptor} \, V\_{dorn}}{V\_{aceptor} + V\_{dorn}}\right) \frac{1}{A \, t\_{end}} \text{Im}(1 - \frac{\mathcal{C}\_{aceptor, end}}{\mathcal{C}\_{equ}}) \tag{7}$$

$$\mathbf{C}\_{equ} = \left(\frac{V\_{domor}}{V\_{domor} + V\_{accept}}\right)\mathbf{C}\_{dunor,initial} \tag{8}$$

where Vacceptor and Vdonor denote the aqueous phase volumes in the acceptor and donor compartments, respectively, Cdonor,initial refers to the initial compound concentration in the donor phase, and A is the membrane accessible surface area times porosity. The water-tooctanol partition coefficient, Po/w, is derived from the measured apparent permeability using a calibration curve constructed from measured permeabilities of standard compounds of known Po/w values. The assay has been used to measure water-to-hexadecane partition coefficients (Wohnsland and Faller, 2001) and can be performed using 96-well microtiter plates.

Fig. 5. High throughput experimental method for measuring water-to- octanol partition coefficients based on the diffusion of a solute betweentwo aqueous phase compartments.

Gao *et al*. (2005) developed a miniaturized method involving the dispersion of colloidal stable porous silica-encapsulated magnetic nanoparticles into water and/or an aqueous-buffered solution. Prior to dispersion, the nanoparticles are preloaded with a known amount of 1 octanol. Equilibrium is quickly established between the drug dissolved in the aqueous (or aqueous-buffered) solution and the small octanol droplets on the nanoparticles. The paramagnetic properties of the nanoparticles facilitate magnetic-induced phase separation. Once the magnetic particles are removed, the uv/visible absorbance of the solution is recorded. The log Po/w (or log Do/w in the case of an ionic solute) is calculated as

$$\log P\_{o/w} = \log \left[ (\frac{Abs\_{before} - Abs\_{after}}{Abs\_{after}}) (\frac{V\_{aquous}}{V\_{oc\tan\alpha}}) \right] \tag{9}$$

Prediction of Partition Coefficients and Permeability of Drug Molecules in Biological

Systems with Abraham Model Solute Descriptors Derived from Measured Solubilities and… 107

Wet Solvent c e s a b v Butan-1-ola 0.376 0.434 -0.718 -0.097 -2.350 2.682 Pentan-1-ola 0.185 0.367 -0.732 0.105 -3.100 3.395 Hexan-1-ola -0.006 0.460 -0.940 0.142 -3.284 3.792 Heptan-1-ola 0.041 0.497 -0.976 0.030 -3.438 3.859 Octan-1-ola 0.088 0.562 -1.054 0.034 -3.460 3.814 Nonan-1-ola -0.041 0.562 -1.103 0.090 -3.540 3.922 Decan-1-ola -0.136 0.542 -0.989 0.046 -3.722 3.996 Isobutanola 0.249 0.480 -0.639 -0.050 -2.284 2.758 Olely alcohol a -0.096 0.148 -0.841 -0.438 -4.040 4.125 Dichloromethane 0.319 0.102 -0.187 -3.058 -4.090 4.324 Trichloromethane 0.191 0.105 -0.403 -3.112 -3.514 4.395 Tetrachloromethane 0.199 0.523 -1.159 -3.560 -4.594 4.618 1,2-Dichloroethane 0.183 0.294 -0.134 -2.801 -4.291 4.180 1-Chlorobutane 0.222 0.273 -0.569 -2.918 -4.883 4.456 Butane 0.297 -0.005 -1.584 -3.188 -4.567 4.562 Pentane 0.369 0.386 -1.568 -3.535 -5.215 4.514 Hexane 0.361 0.579 -1.723 -3.599 -4.764 4.344 Heptane 0.325 0.670 -2.061 -3.317 -4.733 4.543 Octane 0.223 0.642 -1.647 -3.480 -5.067 4.526 Nonane 0.240 0.619 -1.713 -3.532 -4.921 4.482 Decane 0.160 0.585 -1.734 -3.435 -5.078 4.582 Undecane 0.058 0.603 -1.661 -3.421 -5.120 4.619 Dodecane 0.114 0.668 -1.664 -3.545 -5.006 4.459 Hexadecane 0.087 0.667 -1.617 -3.587 -4.869 4.433 Cyclohexane 0.159 0.784 -1.678 -3.740 -4.929 4.577 Methylcyclohexane 0.246 0.782 -1.982 -3.517 -4.293 4.528 Isooctane 0.318 0.555 -1.737 -3.677 -4.864 4.417 Benzene 0.142 0.464 -0.588 -3.099 -4.625 4.491 Toluene 0.143 0.527 -0.720 -3.010 -4.824 4.545 Fluorobenzene 0.139 0.152 -0.374 -3.030 -4.601 4.540 Chlorobenzene 0.065 0.381 -0.521 -3.183 -4.700 4.614 Bromobenzene -0.017 0.436 -0.424 -3.174 -4.558 4.445 Iodobenzene -0.192 0.298 -0.308 -3.213 -4.653 4.588 Nitrobenzene -0.152 0.525 0.081 -2.332 -4.494 4.187 Diethyl ethera 0.248 0.561 -1.016 -0.226 -4.553 4.075 Diisopropyl ethera 0.472 0.413 -0.745 -0.632 -5.251 4.059 Dibutyl ether 0.252 0.677 -1.506 -0.807 -5.249 4.815 o-Nitrophenyl octyl ether 0.121 0.600 -0.459 -2.246 -3.879 3.574 Ethyl acetatea 0.441 0.591 -0.699 -0.325 -4.261 3.666 Butyl acetatea -0.475 0.428 -0.094 -0.241 -4.151 4.046 PGDPb 0.256 0.501 -0.828 -1.022 -4.640 4.033 Methyl isobutyl ketone 0.383 0.801 -0.831 -0.121 -4.441 3.876 Olive oil -0.035 0.574 -0.798 -1.422 -4.984 4.210

where Absbefore and Absafter refer to the measured uv/visible absorbance of the aqueous solution prior and after partitioning, respectively, and Vaqueous/Voctanol is the ratio of the aqueous phase volume divided by the volume of the octanol phase.

Henchoz and coworkers (2010) determined the water-to-octanol partition coefficients of 21 acidic and 29 basic pharmaceutical compounds using microemulsion electrokinetic capillary chromatography (MEEKC) coupled with uv absorption and mass spectrometric detection. The method involves measuring the retention factor of the investigated compound

$$k\_{\text{solute}} = \frac{(t\_{r,\text{solute}} - t\_{r,\text{cof}})}{(1 - \frac{t\_{r,\text{solute}}}{t\_{r,\text{mec}}})t\_{r,\text{cof}}} \tag{10}$$

where tr,solute, tr,eof and tr,mc are the retention/migration times of the investigated drug compound, a highly hydrophilic neutral marker (such as dimethyl sulfoxide) and a highly lipophilic pseudostationary phase marker (such as dodecanophenone or 1-phenyldodecane). The migration times of the two markers define the migration window. The log Po/w of the drug molecules are obtained from a calibration curve

$$
\log \mathbf{k}\_{\text{solute}} = \text{slope} \cdot \log \mathbf{P}\_{\text{o/w}} + \text{intercept} \tag{11}
$$

established with the measured retention factors of standard compounds with known log Po/w values. The proposed method was validated using a set of 35 well-balanced reference compounds that contained neutral, acidic (pKa > 3.6) or basic (pKa < 5.5) compounds with log Po/w values ranging from 0.7 to 4.8. The acidic compounds were analyzed at a pH = 2, while the neutral and basic compounds were analyzed at pH = 10. The authors found that the log Po/w values based on MEEKC method differed by less than 0.5 log units from the log Po/w values determined by the more traditional shake-flask method. The method allowed log Po/w measurement in less than 20 minutes, which is acceptable for quick screening methods. The authors further noted that the MEEKC method could be easily automated, consumed very little sample and solvent, and did not require a highly purified drug sample. Logarithms of the water-to-organic solvent partition coefficients represent another solute property that has been successfully correlated by Eqn. 12 of the Abraham solvation parameter model.

$$\text{Log P} = \text{c} + \text{e} \cdot \text{E} + \text{s} \cdot \text{S} + \text{a} \cdot \text{A} + \text{b} \cdot \text{B} + \text{v} \cdot \text{V} \tag{12}$$

In Table 3 we have compiled the equation coefficients that have been reported describing the various water-to-organic solvent partitioning systems that have been studied. In the case of the alkane and chloroalkane (dichloromethane, trichloromethane, tetrachloromethane, 1,2-dichloroethane and 1-chlorobutane) solvents, one will note that the equation coefficients for describing log P are identical to the coefficients for correlating the log molar solubility ratios, log (CA,organic/CA,water) values. As noted previous the molar solubility ratios describe a "hypothetic partitioning" processes for solute transfer to an anhydrous "dry" organic solvent. Solubility ratios and practical partition coefficients are nearly identical for solvents that are almost "completely" immiscible with water.

Water-organic solvent based biphasic systems are widely used in liquid-liquid extraction and in calculating Abraham model solute descriptors in accordance with Eqn. 12. For compounds that react with water, or for compounds that have very low aqueous solubilities, water-based


where Absbefore and Absafter refer to the measured uv/visible absorbance of the aqueous solution prior and after partitioning, respectively, and Vaqueous/Voctanol is the ratio of the

Henchoz and coworkers (2010) determined the water-to-octanol partition coefficients of 21 acidic and 29 basic pharmaceutical compounds using microemulsion electrokinetic capillary chromatography (MEEKC) coupled with uv absorption and mass spectrometric detection.

> , , ,

*r solute*

( )

*r solute r eof*

,

*r mc*

(1 )

*t*

where tr,solute, tr,eof and tr,mc are the retention/migration times of the investigated drug compound, a highly hydrophilic neutral marker (such as dimethyl sulfoxide) and a highly lipophilic pseudostationary phase marker (such as dodecanophenone or 1-phenyldodecane). The migration times of the two markers define the migration window. The log Po/w of the

established with the measured retention factors of standard compounds with known log Po/w values. The proposed method was validated using a set of 35 well-balanced reference compounds that contained neutral, acidic (pKa > 3.6) or basic (pKa < 5.5) compounds with log Po/w values ranging from 0.7 to 4.8. The acidic compounds were analyzed at a pH = 2, while the neutral and basic compounds were analyzed at pH = 10. The authors found that the log Po/w values based on MEEKC method differed by less than 0.5 log units from the log Po/w values determined by the more traditional shake-flask method. The method allowed log Po/w measurement in less than 20 minutes, which is acceptable for quick screening methods. The authors further noted that the MEEKC method could be easily automated, consumed very little sample and solvent, and did not require a highly purified drug sample. Logarithms of the water-to-organic solvent partition coefficients represent another solute property that has been successfully correlated by Eqn. 12 of the Abraham solvation

In Table 3 we have compiled the equation coefficients that have been reported describing the various water-to-organic solvent partitioning systems that have been studied. In the case of the alkane and chloroalkane (dichloromethane, trichloromethane, tetrachloromethane, 1,2-dichloroethane and 1-chlorobutane) solvents, one will note that the equation coefficients for describing log P are identical to the coefficients for correlating the log molar solubility ratios, log (CA,organic/CA,water) values. As noted previous the molar solubility ratios describe a "hypothetic partitioning" processes for solute transfer to an anhydrous "dry" organic solvent. Solubility ratios and practical partition coefficients are nearly identical for solvents

Water-organic solvent based biphasic systems are widely used in liquid-liquid extraction and in calculating Abraham model solute descriptors in accordance with Eqn. 12. For compounds that react with water, or for compounds that have very low aqueous solubilities, water-based

*t t*

 

,

*t*

*r eof*

log ksolute = slope **·** log Po/w + intercept (11)

Log P = c + e · **E** + s · **S** + a · **A** + b · **B** + v · **V** (12)

(10)

The method involves measuring the retention factor of the investigated compound

*<sup>k</sup> <sup>t</sup>*

*solute*

drug molecules are obtained from a calibration curve

that are almost "completely" immiscible with water.

parameter model.

aqueous phase volume divided by the volume of the octanol phase.


Prediction of Partition Coefficients and Permeability of Drug Molecules in Biological

for seven organic solvent-to-organic solvent partitioning systems.

298 K

log P values at 298 K

**partition coefficient data** 

Systems with Abraham Model Solute Descriptors Derived from Measured Solubilities and… 109

Diethyl ether 0.206 -0.169 0.873 3.402 0.000 0.882 Dipropyl ether 0.065 -0.202 0.776 3.074 0.000 0.948 Diisopropyl ether 0.114 -0.032 0.685 3.108 0.000 0.941 Dibutyl ether 0.369 -0.216 0.026 2.626 -0.499 1.124 Ethyl acetate 0.130 0.031 1.202 3.199 0.463 0.828 Butyl acetate -0.664 0.061 1.671 3.373 0.824 0.832 Methyl isobutyl ketone 0.244 0.183 0.987 3.418 0.323 0.854 Olive oil -0.156 -0.254 0.859 1.656 0.000 0.873 Carbon disulfide 0.101 0.251 0.177 0.027 0.095 1.068 Triolein 0.147 0.254 -0.246 1.520 1.473 0.918 Table 4. Coefficients in Eqn. 2 for Correlating Solute Gas-to-Organic Solvent log K values at

partitioning systems may not be appropriate. Poole and coworkers (Karunasekara and Poole, 2010; Qian and Poole, 2007; Ahmed and Poole, 2006a,b) have reported Abraham model correlations for several totally organic biphasic systems, such as heptane + formamide, hexane + acetonitrile, heptane + methanol, heptane + N,N-dimethylformamide, heptane + 2,2,2 trifluoroethanol, and heptane + 1,1,1,3,3,3-hexafluoroisopropanol. The organic-based biphasic systems allow one to calculate solute descriptors for compounds that might not otherwise be possible with water-based partitioning systems. For example, the biphasic hexane + acetonitrile, heptane + N,N-dimethylformamide, and heptane + 2,2,2-trifluoroethanol systems were used, in combination with chromatographic retention factors, to determine a complete set of descriptors for organosilicon compounds (Atapattu and Poole, 2009; Ahmed *et al*., 2007), many of which react with water. Abraham model equation coefficients are tabulated in Table 5

Partitioning system c e s a b v Formamide-to-heptane 0.083 0.559 -2.244 -3.250 -1.614 2.384 N,N-Dimethylformamide-to-heptane 0.065 0.030 -1.405 -2.039 -0.806 0.721 2,2,2-Trifluoroethanol-to-heptane 0.160 0.856 -1.538 -1.325 -2.965 1.190 1,1,1,3,3,3-Hexafluoroisopropanol-to-heptane -0.225 0.720 -1.357 -0.577 -2.819 1.161 Methanol-to-heptane -0.056 0.164 -0.620 -1.337 -0.957 0.507 Ethylene glycol-to-heptane 0.343 0.000 -1.247 3.807 -2.194 2.065 Acetonitrile-to-hexane 0.097 0.189 -1.332 -1.649 -0.966 0.773 Table 5. Coefficients in Eqn. 12 for Correlating Solute Organic Solvent-to-Organic Solvent

**5. Calculation of Abraham solute descriptors from measured solubility and** 

The application of Eqn. 1 and Eqn. 2 requires a knowledge of the descriptors (or properties) of the solutes: **E**, **S**, **A**, **B**, **V** and **L**. The descriptors **E** and **V** are quite easily obtained. **V** can be calculated from atom and bond contributions as outlined previously (Abraham and McGowan, 1987). The atom contributions are in Table 6; note that they are in cm3 mol -1. The


b Propylene glycol dipelargonate.

Table 3. Coefficients in Eqn. 12 for Correlating Solute Water-to-Organic Solvent log P values at 298 K


Carbon disulfide 0.047 0.686 -0.943 -3.603 -5.818 4.921 Isopropyl myristate -0.605 0.930 -1.153 -1.682 -4.093 4.249 Triolein 0.385 0.983 -2.083 -2.007 -3.452 4.072 a Correlation uses the Bo solute descriptor.

Table 3. Coefficients in Eqn. 12 for Correlating Solute Water-to-Organic Solvent log P values

Wet Solvent c e s a b l Butan-1-ol -0.095 0.262 1.396 3.405 2.565 0.523 Pentan-1-ol -0.107 -0.001 1.188 3.614 1.671 0.721 Hexan-1-ol -0.302 -0.046 0.880 3.609 1.785 0.824 Heptan-1-ol -0.159 0.018 0.825 3.539 1.425 0.830 Octan-1-ol -0.198 0.002 0.709 3.519 1.429 0.858 Nonan-1-ol -0.197 0.141 0.694 3.616 1.299 0.827 Decan-1-ol -0.302 0.233 0.741 3.531 1.177 0.835 Isobutanol -0.095 0.262 1.396 3.405 2.565 0.523 Olely alcohol -0.268 -0.392 0.800 3.117 0.978 0.918 Dichloromethane 0.192 -0.572 1.492 0.460 0.847 0.965 Trichloromethane 0.157 -0.560 1.259 0.374 1.333 0.976 Tetrachloromethane 0.217 -0.435 0.554 0.000 0.000 1.069 1,2-Dichloroethane 0.017 -0.337 1.600 0.774 0.637 0.921 1-Chlorobutane 0.130 -0.581 1.114 0.724 0.000 1.016 Butane 0.291 -0.360 0.091 0.000 0.000 0.959 Pentane 0.335 -0.276 0.000 0.000 0.000 0.968 Hexane 0.292 -0.169 0.000 0.000 0.000 0.979 Heptane 0.275 -0.162 0.000 0.000 0.000 0.983 Octane 0.215 -0.049 0.000 0.000 0.000 0.967 Nonane 0.200 -0.145 0.000 0.000 0.000 0.980 Decane 0.156 -0.143 0.000 0.000 0.000 0.989 Undecane 0.113 0.000 0.000 0.000 0.000 0.971 Dodecane 0.017 0.000 0.000 0.000 0.000 0.989 Hexadecane 0.000 0.000 0.000 0.000 0.000 1.000 Cyclohexane 0.163 -0.110 0.000 0.000 0.000 1.013 Methylcyclohexane 0.318 -0.215 0.000 0.000 0.000 1.012 Isooctane 0.264 -0.230 0.000 0.000 0.000 0.975 Benzene 0.107 -0.313 1.053 0.457 0.169 1.020 Toluene 0.121 -0.222 0.938 0.467 0.099 1.012 Fluorobenzene 0.181 -0.621 1.432 0.647 0.000 0.986 Chlorobenzene 0.064 -0.399 1.151 0.313 0.171 1.032 Bromobenzene -0.064 -0.326 1.261 0.323 0.292 1.002 Iodobenzene -0.171 -0.192 1.197 0.245 0.245 1.002 Nitrobenzene -0.296 0.092 1.707 1.147 0.443 0.912 Benzonitrile -0.067 -0.257 1.848 2.009 0.227 0.870

b Propylene glycol dipelargonate.

at 298 K


Table 4. Coefficients in Eqn. 2 for Correlating Solute Gas-to-Organic Solvent log K values at 298 K

partitioning systems may not be appropriate. Poole and coworkers (Karunasekara and Poole, 2010; Qian and Poole, 2007; Ahmed and Poole, 2006a,b) have reported Abraham model correlations for several totally organic biphasic systems, such as heptane + formamide, hexane + acetonitrile, heptane + methanol, heptane + N,N-dimethylformamide, heptane + 2,2,2 trifluoroethanol, and heptane + 1,1,1,3,3,3-hexafluoroisopropanol. The organic-based biphasic systems allow one to calculate solute descriptors for compounds that might not otherwise be possible with water-based partitioning systems. For example, the biphasic hexane + acetonitrile, heptane + N,N-dimethylformamide, and heptane + 2,2,2-trifluoroethanol systems were used, in combination with chromatographic retention factors, to determine a complete set of descriptors for organosilicon compounds (Atapattu and Poole, 2009; Ahmed *et al*., 2007), many of which react with water. Abraham model equation coefficients are tabulated in Table 5 for seven organic solvent-to-organic solvent partitioning systems.


Table 5. Coefficients in Eqn. 12 for Correlating Solute Organic Solvent-to-Organic Solvent log P values at 298 K
