4476
Ind. Eng. Chem. Res. 1998, 37, 4476-4480
Predicting Cosolvency. 2. Correlation with Solvent Physicochemical Properties An Li*,† and Samuel H. Yalkowsky‡ Environmental and Occupational Health Sciences, School of Public Health, University of Illinois at Chicago, Chicago, Illinois 60612, and Department of Pharmaceutical Sciences, College of Pharmacy, University of Arizona, Tucson, Arizona 85721
In the preceding paper (Ind. Eng. Chem. Res. 1998, 37, xxxx), linear regressions of the solubility ratio σ with the solute log Kow were examined for 15 water/cosolvent systems and the slopes of the regressions, M or M0.5, were reported. In this paper, the dependence of M and M0.5 on the molecular structures and physicochemical properties of cosolvents is investigated. The octanolwater partition coefficient, interfacial tension, and solubility parameter are superior to other properties in correlating with M and M0.5. Multiple linear regression results show that the combination of log Kow and hydrogen-bond-donor density of the cosolvent is the best. Estimation equations for M developed in this study, along with the N values given in the preceding paper, will enable one to estimate the log-linear solubilization of organic chemicals in the 15 binary cosolvent-water mixtures from the chemical structure of the cosolvent and a minimal number of easily available property data which include only the Kow’s of both the solute and cosolvent as well as the solubility of the solute in water. Introduction The effect on the water solubility of organic compounds of adding one or more completely water-miscible organic cosolvents is defined as cosolvency. Cosolvency is a phenomenon which can be applied for many purposes in various scientific and engineering fields. It is also of significance in theoretical research regarding solution thermodynamics, intermolecular forces, and liquid structure. For a particular cosolvent, the strong dependence of cosolvency on the solute hydrophobicity has been manifested by the results of ref 1 and many other papers. However, dependence of cosolvency on the properties of cosolvents is less understood. In practice, selection of the cosolvent is often critical to a successful application. Initial cosolvent screening often starts with measuring the solute solubility in various cosolvent or cosolvent-water mixtures, which is often costly and time-consuming. The dependence of cosolvency on the properties of cosolvents has been the subject of much research. In the pharmaceutical field, the dielectric constant has been used as a polarity index for solvent blending.2,3 The solubility parameter of a solvent mixture has also been found in a number of studies to correlate with the solubility of solutes.4,5 Yalkowsky and Roseman6 showed that the relative cosolvency power for propylene glycol, poly(ethylene glycol), ethanol, and glycerin is about 1:1: 2:0.5. Yalkowsky et al.7 further showed that the twodimensional interfacial tension at the solvent-solute interface could be used, along with the solute surface area, to predict the slope of the solubilization curve. Rubino and Yalkowsky8 demonstrated moderately satisfactory correlations between cosolvency and various polarity indices of 15 cosolvents for three drugs. Li et * To whom all correspondence should be addressed. Phone: 312-996-9597. Fax: 312-413-9898. E-mail:
[email protected]. † University of Illinois at Chicago. ‡ University of Arizona.
al.9 examined the relationship of the solubilization of naphthalene and nine commonly used polarity indices of 21 cosolvents. In both refs 8 and 9, the end-to-end slope of the solubilization curves, σ, was used as the indicator of the cosolvent solubilization power. σ is essentially the ratio of solubilities of the organic solute in pure cosolvent and in pure water. Similarly, an end-to-half slope, σ0.5, was defined as the solubility ratio of the solute in a 50:50 cosolvent-water mixture and in pure water. Since σ and σ0.5 are specific for each solute-cosolvent-water system, the resulting equations relating σ or σ0.5 with cosolvent properties are specific for each solute. In the preceding paper, we examined the σ and σ0.5 of organic chemicals as related to their octanol/water partition coefficient (log Kow). The log Kow was estimated by Hansch and Leo fragment method. Linear regression equations relating σ and σ0.5 and solute log Kow were reported for 15 cosolvents. The slopes of these regressions, M and M0.5, which reflect the power of cosolvency of a cosolvent toward all organic solutes, can be therefore considered properties of the cosolvent. It was found that values of M deviate from its ideal value of unity, which is based on the linear free energy relationship, with different extents for different cosolvents. On the basis of previous studies8,9 on the correlations of σ with cosolvent properties, it would be interesting to see if M is similarly related to any physicochemical properties of the cosolvents. In this paper, we look further into the nature of M by searching for properties which are best correlated with the M values of various organic cosolvents. The objective is to provide a simple method for cosolvent screening. Methods Selected properties of the 15 cosolvents were collected from literature sources and are listed in Table 1. Kow is the octanol-water partition coefficient estimated using the DayMenus computer program.10 The values
10.1021/ie980233n CCC: $15.00 © 1998 American Chemical Society Published on Web 10/07/1998
Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4477 Table 1. Values of M and M0.5 and Properties of Selected Cosolvents
cosolvent
Ma
M0.5a
log Kowb
methanol ethanol 1-propanol 2-propanol acetone acetonitrile dioxane dimethylacetamide dimethylformamide dimethyl sulfoxide glycerin ethylene glycol propylene glycol PEG 400 n-butylamine
0.89 0.95 1.09 1.11 1.14 1.16 1.08 0.96 0.83 0.79 0.35 0.68 0.78 0.88 0.64
0.73 0.81 1.03 0.96 1.25 1.04 0.99 0.89 0.65 0.72 0.38 0.52 0.55 0.78 0.67
-0.764 -0.235 0.294 0.074 -0.208 -0.394 -0.492 -0.802 -1.038 -1.378 -2.194 -1.369 -1.060
a
b
c
0.923
surface tensionc (103N m-1) 21.9 21.8 23.1 20.7 24.0 28.6 32.8 35.7 36.8 44.0 60.6 47.8 37.1 46.0 23.4
dielec constd 32.6 24.3 20.1 18.3 20.7 36.2 2.2 37.8 36.7 45.0 42.5 37.7 32.0 13.6
d
interfacial tensione (103 N m-1)
solub paramf (MPa1/2)
0.7 0.5
29.7 26.1 24.9 23.5 19.7 24.8 20.7 22.7 24.8 26.7 36.2 34.9 30.7 23.9 18.6
0.0 4.6 6.9 0.9 32.7 12.4 11.7 e
ET(30)g (kJ mol-1) 232 217 212 203 177 191 151 183 183 169 239 236 226
f
HBDh
HBAh
24.70 17.13 13.40 13.06 0.00 0.00 0.00 0.00 0.00 0.00 41.08 35.73 27.23 5.63 20.27
49.40 34.27 26.80 26.12 27.20 76.56 46.89 21.65 25.84 28.16 82.16 71.45 54.47 50.64 20.27
viscosityi (Cp; 25 °C) 0.544 1.074 1.945 2.038 0.306 0.369 1.177 1.956 0.794 1.987 934 16.1 40.4 0.574
g
Reference 1. Reference 10. References 8 and 11. References 12 and 13. Reference 8. References 14 and 15. References 13 and 16. h HBD ) (number of proton donor groups) × density × 1000/molecular weight; HBA ) (number of nonbonding electron pairs) × density × 1000/molecular weight. i Reference 17.
Figure 1. Regression of M (filled symbols and solid lines) and M0.5 (empty symbols and dashed lines) against various properties of selected cosolvents. Symbols for cosolvents: circles, aprotic cosolvents; squares, alcohols; diamonds, glycols; triangles, amines.
of M and M0.5, as also listed in Table 1, were taken from the regression results of ref 1. Simple and multiple linear regression analyses were performed with the Regression Analysis Tool of Microsoft Excel at the 95% confidence level. Results and Discussion Simple Linear Regressions. The relationships between M and M0.5 values and various properties of the cosolvent are illustrated in Figure 1. The statistics of the regressions are summarized in Table 2. A brief explanation for each cosolvent property used in this
study can be found in ref 9. Rubino and Yalkowsky8 gave a more detailed discussion on the dielectric constant, solubility parameter, interfacial tension, and partition coefficient as they are used as cosolvent polarity indices. The scattering of the points on most plots of Figure 1 is not unexpected. These plots are the results of “double regression” on the original solubility data from numerous sources. Any discrepancy from the σ ∼ log Kow regression1 will be carried over to these M ∼ property regressions. For example, the range of solute log Kow, as discussed in the preceding paper, varies for different
4478 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 Table 2. Results of Simple Linear Regression of M and M0.5 against Properties of Cosolvents M
M0.5
polarity index
N
slope
intercept
R2
dielec const log Kow surface tension interfacial tension solub param ET(30) log viscosity HBDD HBAD
14 13 15 9 14 13 14 15 15
-0.01 ( 0.00 0.31 ( 0.04 -0.01 ( 0.00 -0.02 ( 0.00 -0.04 ( 0.01 -0.01 ( 0.00 -0.18 ( 0.05 -0.01 ( 0.00 -0.01 ( 0.00
1.20 ( 0.13 1.14 ( 0.04 1.33 ( 0.13 0.97 ( 0.04 1.91 ( 0.18 1.96 ( 0.42 0.96 ( 0.05 1.04 ( 0.06 1.18 ( 0.10
0.33 0.85 0.50 0.81 0.72 0.37 0.54 0.49 0.42
cosolvent systems (see Table 2 of the preceding paper) and will result in uncertainties and inconsistency in the values of M and M0.5 used for property regressions. Nevertheless, the dependence of the M’s on some of the polarity indices is obvious. Standing out from the nine cosolvent properties are the octanol-water partition coefficient, interfacial tension, and solubility parameter. The regressions with these parameters are satisfactory with R2 greater than 0.7 for M and greater than 0.6 for M0.5. These results support the usefulness of these properties in predicting cosolvency. The octanol-water partition coefficient has been the most widely used polarity index. In our previous study with naphthalene being the only solute,9 the log Kow values of cosolvents were found to correlate well with σ0.5 but not with σ. In this study, strong correlations of cosolvent log Kow values with both M and M0.5 are obtained. This result indicates that, overall speaking, the hydrophobicity of a cosolvent is an important factor in determining its solubilization power. Less hydrophilic organic cosolvents would be stronger in enhancing the solubility of hydrophobic solutes and be weaker in reducing the solubility of highly hydrophilic organic solutes. The solubility parameter is another cosolvent property that has been used for decades in correlating with the solubilization potential of organic solvents. The correlations of the solubility parameter with σ and σ0.5 for the solute naphthalene were found excellent.8,9 In this study, the solubility parameter is again proven to be one of the best cosolvent properties in correlating with both M and M0.5. When a nonpolar organic solute dissolves in a solvent, the interactions among solvent molecules often contribute more than solvent-solute interactions to the overall free energy of dissolution. It is noticed, however, that 1-butylamine is an outlier in both Figure 1b and Figure 1e. The limited number of original data sets makes it impossible to draw a conclusion on its outlier behavior. With very comparable qualities of correlation, the interfacial tension of the cosolvent shows promise in predicting M. Interfacial tension, like the solubility parameter, reflects the “total polarity” of the chemical and is directly related to the energy of creating a cavity in the solvent to accommodate a solute molecule. However, experimental interfacial tension data are very limited and may not be consistent among laboratories. This makes it difficult to use interfacial tension as a useful index for cosolvent selection and other purposes. Hydrogen-bonding properties HBDD and HBAD describe the volume-based concentration of proton donor and acceptor groups, respectively. The importance of HBDD in determining the cosolvency power has been recognized; its correlations with σ were found excellent
SE
F
slope
intercept
R2
SE
F
0.19 0.09 0.16 0.09 0.12 0.19 0.16 0.16 0.18
5.88 60.49 13.14 30.57 30.55 6.38 14.18 12.71 9.33
-0.01 ( 0.00 0.31 ( 0.06 -0.01 ( 0.00 -0.02 ( 0.01 -0.04 ( 0.01 -0.01 ( 0.00 -0.19 ( 0.05 -0.01 ( 0.00 -0.01 ( 0.00
1.12 ( 0.14 1.03 ( 0.06 1.23 ( 0.14 0.89 ( 0.07 1.93 ( 0.19 2.05 ( 0.43 0.87 ( 0.05 0.95 ( 0.06 1.11 ( 0.11
0.31 0.70 0.44 0.60 0.75 0.43 0.52 0.51 0.43
0.21 0.14 0.18 0.16 0.12 0.20 0.17 0.17 0.18
5.43 25.81 10.16 10.43 36.32 8.30 13.25 13.54 9.91
for several solutes.8,9 However, neither HBDD nor HBAD was found to strongly correlate with M or M0.5 in this study. The hydrogen-bond capacity of a cosolvent may play an important role in not only the cosolventwater interactions but also the cosolvent-solute interactions, which is not reflected in the M’s. For this reason, HBDD correlates with σ, which is solute-specific, but not with the M’s, which presumably embrace all organic solutes. Surface tension and viscosity are found to only weakly correlate with M and M0.5 values, similar to the observations made with σ and σ0.5.8,9 Among the worst cosolvent properties as a single independent variable are dielectric constant and ET(30). The dielectric constant has been proven a poor property in correlating with cosolvency power σ.8,9 As a single physical characteristic, the dielectric constant may not reflect the major type of molecular interactions in the solutecosolvent-water solution. It might be promising, though, when the solute involved is ionic. ET(30) is among a group of empirical polarity indices based on the solvent effect on shifting the maximum in the light absorption spectrum of a solute.13 Its failure to correlate with M may lie in the differences in solvent-solute interactions between most organic solutes covered in this study and pyridinium N-phenolbetaine, upon which ET(30) is based. Multiple Linear Regressions. Cosolvency is a complex function of more than one type of molecular interactions and may not be predicted accurately from a single cosolvent property. It is noticed from the M ∼ log Kow simple linear correlation that glycols and alcohols are all below the regression line, while aprotic cosolvents are all above the line. Similar observations were made for the regressions of σ with log Kow for selected solutes.9 This implies that the hydrogenbonding properties of the cosolvent are important in determining M but may not be appropriately reflected in the octanol-water partition coefficient. Thus, we used a multiply linear regression with both log Kow and hydrogen-bond-donor density (HBDD) as independent variables. The solubility parameter is also tested as one of the independent variables. Poly(ethylene glycol) and n-butylamine are excluded in the regressions. The results are summarized in Table 3. The M and M0.5 values predicted using log Kow and HBDD are plotted against the “experimental” values in Figure 2. Multiple linear regressions have been shown to produce much improved correlations between cosolvent properties and the cosolvency power σ or σ0.5.8 The regression of M and M0.5 with both HBDD and log Kow shows the best results. Adding another independent variable, the solubility parameter, does not further improve the regression. In addition, the combination of HBDD and the solubility parameter seems not to be
Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4479 Table 3. Results of Multiple Linear Regression of M and M0.5 against Properties of Cosolvents coefficients of independent variable log Kow a
0.251 ( 0.030 0.209 ( 0.042 0.255 ( 0.049
b
0.233 ( 0.053 0.158 ( 0.062 0.148 ( 0.081
HBDD -0.005 ( 0.001 0.005 ( 0.005 -0.006 ( 0.004 -0.007 ( 0.0024 0.007 ( 0.005 0.0003 ( 0.006
solub param M -0.053 ( 0.016 -0.0186 ( 0.006 0.0013 ( 0.013 M0.5 -0.061 ( 0.002 -0.028 ( 0.008 -0.030 ( 0.022
intercept
R2
SE
F
1.165 ( 0.026 -3.323 ( 0.008 1.556 ( 0.131 1.136 ( 0.285
0.942 0.769 0.927 0.942
0.060 0.120 0.067 0.063
81.65 16.64 63.94 49.05
1.071 ( 0.047 2.343 ( 0.350 1.676 ( 0.193 1.701 ( 0.473
0.837 0.814 0.865 0.864
0.109 0.117 0.099 0.105
25.62 21.83 32.14 19.02
a
This equation is used to obtain the estimated M values in Figure 2. b This equation is used to obtain the estimated M0.5 values in Figure 2.
as good a choice as the combination of HBDD and log Kow. The predominant influence of log Kow on cosolvency has thus been clearly proven. In addition, the results of this study may be indicative of the fact that the ability to donate a proton to form a hydrogen bond can be very important in deciding the solubilizing potential of a cosolvent toward organic solutes. Although HBDD alone does not seem to work, it complements the general lipophobicity, expressed by the octanol-water partition coefficient, of the cosolvent in determining the overall solubilizing potential of a cosolvent. Predicting Organic Solubility in Mixed Solvents. Many publications, including the preceding paper, have examined the dependence of the solubility ratio σ on solute properties. In this paper, we expanded the cosolvent studies by looking at the correlations between cosolvent properties and M, which is the slope of regression of σ with a solute property. The difference between σ and M is that, while σ is specific for each ternary solute/cosolvent/water system, M can be considered as a property of the cosolvent. By expanding our research from σ to M, we should be able to see the possibility of predicting the solubilization of organic chemicals by cosolvents. On the basis of the results of this and many other studies, minimal information will, presumably, be required to estimate the solubility of an organic chemical in the 15 selected mixed-solvent systems. The essential information includes Kow (and HBDD) of the cosolvent, Kow of the solute, and solubility of the solute in pure water. Three sets of equations will be involved. The first is
M ) 0.2513 log Kow - 0.0054 HBDD + 1.1645 (1a) M0.5 ) 0.2327 log Kow - 0.0068 HBDD + 1.0713 (1b) where log Kow and HBDD are those of the cosolvent and the constants are from Table 3. The second set is
σ ) M log Kow + N
(2a)
σ0.5 ) M0.5 log Kow + N0.5
(2b)
where log Kow is that of the solute and N’s can be found in Table 2 of ref 1. And the third set is
log Sm ) log Sw + σf
(3a)
log Sm ) log Sw + σ0.5f
(3b)
where S’s are the solute solubilities in the cosolvent-
Figure 2. Regression of estimated M (filled diamonds and solid line, using eq 1a) and M0.5 (empty diamonds and dashed line, using eq 1b) against M and M0.5 listed in Table 2. Symbols for cosolvents: circles, aprotic cosolvents; squares, alcohols; diamonds, glycols.
water mixture (m) and in pure water (w) and f is the volume fraction of the cosolvent in the solvent mixture. Large databases and reliable estimation techniques are readily available for both Kow and Sw. The hydrogenbonding-donor density, HBDD, is directly obtained from the molecular weight, density, and structure of the cosolvent. Thus, estimation of the solubility of organic chemicals in cosolvent-water mixed solvents can be much easier than any other methods published previously. Predicted and experimental solubilities for 3, out of 79, randomly selected solutes in methanol/water systems are plotted in Figure 3. Where the solvent mixture is around 50:50 for water:cosolvent, the b-set of the above equations for M0.5 and σ0.5 would result in more accurate estimates than the a-set. The approach presented above has its limitations. First, it should result in acceptable estimates of log Sm only if the solubilization follows a log-linear manner, i.e., if eq 3 holds. Such a log-linear solubilization requires that the solvent mixture be an ideal solution. The example shown in Figure 3 is for the water/ methanol system, which is the closest to the ideal mixture among the 15 water/cosolvent systems investigated in this work. For highly nonideal solvent mixtures, where the solubilization deviates severely from the log-linear pattern, the approach elucidated here may not provide accurate estimates. Second, the accuracy of the solubility estimates can be affected severely by the uncertainties associated with the M and N values, as discussed in the preceding paper. The values of M and N are less reliable for cosolvents DMA, DMSO, DMF, acetonitrile, 1-butylamine, and polypropylene glycol because of limited data sets and relatively poor regression coefficients (see Table 2 in ref 1). Third,
4480 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998
Literature Cited
Figure 3. Estimated versus experimental solubilities of randomly selected solutes in methanol-water mixtures. Symbols: b, solubilities estimated using eqs 1a, 2a, and 3a (methanol volume fraction 0-1); ], solubilities estimated using eqs 1b, 2b, and 3b (methanol volume fraction 0-0.6).
it is important to limit the use of the estimation equations (1) and (2) within the ranges of log Kow used in this work. The log Kow ranges for solutes can be found in Table 2 of the preceding paper, and that for cosolvents is from -2.2 to +0.3 with the exclusion of that for 1-butylamine. Acknowledgment This work is supported by the Dean’s Office, School of Public Health, University of Illinois at Chicago.
(1) Li, A.; Yalkowsky, S. H. Predicting Cosolvency. 1. Solubility Ratio and Solute log Kow. Ind. Eng. Chem. Res. 1998, 37, xxxx. (2) Kato, Y.; Ohuchi, T. Solubilizing Agents. IV. Dielectric Constant Correlations with Drug Solubility in the Mixtures of Glycols and Their Derivatives with Water. Yakugaku Zasshi 1972, 92, 257-263. (3) Prakongpan, S.; Nagai, T. Solubility of Acetaminophen in Cosolvents. Chem. Pharm. Bull. 1984, 32, 340-343. (4) Martin, A.; Newburger, J.; Adjei, A. Extended Hildebrand Solubility Approach: Solubility of Theophylline in Polar Binary Solvents. Pharm. Res. 1980, 69, 487-491. (5) Adjei, A.; Newburger, J.; Martin, A. Extended Hildebrand Solubility Approach: Solubility of Caffeine in Dioxane-Water Mixtures. Pharm. Res. 1980, 69, 659-661. (6) Yalkowsky, S. H.; Roseman, T. J. Solubilization of Drugs by Cosolvents. In Techniques of Solubilization of Drugs; Yalkowsky, S. H., Ed.; Dekker: New York, 1981; Chapter 3. (7) Yalkowsky, S. H.; Valvani, S. C.; Amidon, G. L. Solubility of Nonelectrolytes in Polar Solvents. IV. Nonpolar Drugs in Mixed Solvents. J. Pharm. Sci. 1976, 65, 1488-1494. (8) Rubino, J. T.; Yalkowsky, S. H. Cosolvency and Cosolvent Polarity. Pharm. Res. 1987, 4, 220-230. (9) Li, A.; Andren, A. W.; Yalkowsky, S. H. Choosing a Cosolvent: Solubilization of Naphthalene and Cosolvent Property. Environ. Toxicol. Chem. 1996, 15, 2233-2239. (10) DayMenus; Daylight Chemical Information Systems, Inc.: Irvine, CA, 1991. (11) Yaws, C. L.; Yang, H. C.; Pan, X. 633 Organic Chemicals: Surface Tension Data. Chem. Eng. 1991, March, 140-150. (12) Physical Properties of Some Organic Solvents; Eastman Kodak: Rochester, NY, 1975. (13) Reichardt, C. Solvents and Solvent Effects in Organic Chemistry, 2nd ed.; VCH: Weinheim, Germany, 1988. (14) Barton, A. F. M. Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd ed.; CRC Press: Boca Raton, FL, 1991. (15) Barton, A. F. M. Solubility Parameters. Chem. Rev. 1975, 75, 731-753. (16) Connors, K. A. Chemical Kinetics: The Study of Reaction Rates in Solution; VCH: Weinheim, Germany, 1990; Chapter 8. (17) Lide, D. R. Handbook of Chemistry and Physics, 72nd ed.; CRC Press: Boca Raton, FL, 1991-1992. (18) Li, A.; Andren, A. W. Solubility of Polychlorinated Biphenyls in Water/Alcohol Mixtures. 1. Experimental Data. Environ. Sci. Technol. 1994, 28, 47-52. (19) Khossravi, D.; Connors, K. A. Solvent Effects on Chemical Processes. V. Hydrophobic and Solvation Effects on the Solubilities of Substituted Bipenyls in Methanol/Water Mixtures. J. Pharm. Sci. 1993, 82, 817-820. (20) Dey, B. P.; Lahiri, S. C. Solubilities of Amino Acids in Methanol + Water Mixtures at Different Temperatures. Indian J. Chem. 1988, 27A, 297-302.
Received for review April 13, 1998 Revised manuscript received July 17, 1998 Accepted August 3, 1998 IE980233N
