Handbook of Solvents - George Wypych - ChemTech - Ventech!

14.21.2 Predicting cosolvency 1005
served over a wide range of solutes. Indeed, both a and b were found to be dependent on the
range of the solute log K ow used in the regression. For instance, for solutes with log K ow ≤0,
0.01 to 2.99, and ≥3, the correlation of σversus log K ow for cosolvent ethanol have slopes of
0.84, 0.79, and 0.69, respectively, and the corresponding intercepts increase accordingly;
the slope of the overall correlation, however, is 0.95. Much of the scattering on the σ~log
K ow regression resides on the region of relatively hydrophilic solutes. Most polar solutes
dissociate to some extent in aqueous solutions, and their experimental log K ow values are
less reliable. Even less certain is the extent of specific interactions between these polar solutes
and the solvent components.
According to equation [14.21.2.6], σmay not be a linear function of solute log K ow on a
theoretical basis. However, despite the complexities caused by the activity coefficients,
quality of the regression of σ against log K ow is generally high, as evidenced by the satisfactory
R 2 values in Table 14.21.2.2. This can be explained by the fact that changes in both γ ratios
are much less significant compared with the variations of K ow for different solutes. In
addition, the two γ terms may cancel each other to some degree for many solutes, further reducing
their effects on the correlation between σand log K ow. It is convenient and reliable to
estimate σ from known log K ow of the solute of interest, especially when the log K ow of the
solute of interest falls within the range used in obtaining the values of a and b.
Dependence of σ on the properties of cosolvents has been less investigated than those
of solutes. While hundreds of solutes are involved, only about a dozen organic solvents
have been investigated for their cosolvency potentials. A few researchers examined the correlations
between σ and physicochemical properties of cosolvents for specific solutes, for
instance, Li et al. for naphthelene, 31 and Rubino and Yalkowsky for drugs benzocaine, diazepam,
and phenytoin. 81 In both studies, hydrogen bond donor density (HBD), which is the
volume normalized number of proton donor groups of a pure cosolvent, is best for comparing
cosolvents and predicting σ. Second to HBD are the solubility parameter and interfacial
tension (as well as log viscosity and E T-30 for naphthalene systems), while log K ow, dielectric
constant, and surface tension, correlate poorly with σ. The HBD of a solvent can be
readily calculated from the density and molecular mass with the knowledge of the chemical
structure using equation [14.21.2.7]. The disadvantage of using HBD is that it cannot distinguish
among aprotic solvents which have the same HBD value of zero.
HBD =(number of proton donor groups)(density)/(molecular mass) [14.21.2.7]
In an attempt to generalize over solutes, Li and Yalkowsky 82 investigated the possible
correlations between cosolvent properties and slope of the σ~log K ow regressions (b).
Among the properties tested as a single regression variable, octanol-water partition coefficient,
interfacial tension, and solubility parameter, are superior to others in correlating with
b. Results of multiple linear regression show that the combination of log K ow and HDB of
the cosolvent is best (equation [14.21.2.8]). Adding another variable such as solubility parameter
does not improve the quality of regression.
b = 0.2513 log K ow - 0.0054 HBD + 1.1645 [14.21.2.8]
(N = 13, R 2 = 0.942, SE = 0.060, F = 81.65)
where log K ow (range: -7.6 ~ 0.29) and HBD (range: 0 ~ 41) are those of the cosolvent.