Handbook of Solvents - George Wypych - ChemTech - Ventech!

1004 An Li
partial derivative ∂(log S m)/∂f, 76 or the regressional (not end-to-end) slope of the
solubilization curve. 77 The σ defined in these ways will depend on the range of f and on the
accuracy of all data points over the entire range of f. These definitions are not desirable because
they make σ difficult to predict and interpret in light of the concept of ideal solvent
mixture on which the log-linear model is based. Note also that σis not related to the crystalline
structure of the solute, since the contributions from the free energy of melting to the two
solubilities cancel out. However, it may change if the solute exists in pure cosolvent with a
chemical identity different from that in water, as in the cases where solute degradation, solvation,
or solvent-mediated polymorphic transitions occur in either solvent.
Estimation of σ
Laboratory measurements of S w and S c can be costly and difficult. Various methods, including
group contribution technique and quantitative structure (or property) property relationships
(QSPRs or QPPRs), 78 are available to estimate S w and S c, from which σ values can be
derived. A direct approach of predicting σ has also been established based on the dependence
of cosolvency on solute hydrophobicity. Among a number of polarity indices,
octanol/water partition coefficient, K ow, was initially chosen by Yalkowsky and Roseman 61
for correlation with σ, due mainly to the abundance of available experimental K ow data and
the wide acceptance of the Hansch-Leo fragment method 79 for its estimation. K ow is a macroscopic
property which does not necessarily correlate with micro-scale polarity indices
such as dipole moment, and only in a rank order correlates with other macroscopic polarity
indicators such as surface tension, dielectric constant, and solubility parameter.
Correlation between σ and solute K ow takes the form:
σ= a + blog Kow [14.21.2.5]
where a and b are constants that are specific for the cosolvent but independent of solutes.
Their values have been reported for various cosolvents and are summarized in Table
14.21.2.2.
From Table 14.21.2.2, the slopes of equation [14.21.2.5], b, are generally close to
unity, with few below 0.6 or above 1.2. Most of the intercepts a are less than one, with a few
negative values. In searching for the physical implications of the regression constants a and
b, Li and Yalkowsky 80 derived equation [14.21.2.6]:
∞* ∞*
*
( ) ( ) ( )
σ= logK + log γ / γ + log γ / γ + log V / V
ow 0 c w w 0 c [14.21.2.6]
According to this equation, σ~log Kow correlation will indeed have a slope of one and a
∞* *
predictable intercept of log (Vo*/Vc) if both γ0 / γc
and γw / γw
∞ terms equal unity. Vo*= 0.119 L mol -1 based on a solubility of water in octanol of 2.3 mol L -1 , and Vc ranges from
0.04 to 0.10 L 3 mol -1 , thus log (Vo*/Vc) is in the range of 0.08 to 0.47, for the solvents in-
∞*
cluded in Table 14.21.2.2 with the exclusion of PEG400. However, both γ0 / γc
and
*
γw / γw
∞ are not likely to be unity, and their accurate values are difficult to estimate for many
∞*
solutes. The ratio γ0 / γc
compares the solute behavior in water-saturated octanol under di-
*
lute conditions and in pure cosolvent at saturation, while the γw / γw
∞ term reflects both the
effect of dissolved octanol on the aqueous activity coefficient and the variation of the activity
coefficient with concentration. Furthermore, the magnitudes of both terms will vary
from one solute to another, making it unlikely that a unique regression intercept will be ob-