Preferential Solvation in Mixed Solvents - Fluctuation Theory of Solutions - page 91

B = 1,4-dioxane. Association of A and B by Lewis acid-base interactions are evident
but in the presence of small concentrations of C (that self-associates at high contents)
its free molecules compete successfully with A for solvation of B.
Other studies of the preferential solvation for which information can be derived
from KBIs in ternary systems have also been made. The system n- heptane + etha-
nol + 1-propanol at 313 K (Zielkiewicz 1995a) showed that ethanol and 1-propanol
mix in a random manner in the presence of n -heptane with no preferential solva-
tion between these two solvents. The same author studied the solvation of N , N -
dimethylformamide (C) in mixtures of water (A) and each of methanol, ethanol,
and 1-propanol (B) at 313 K (Zielkiewicz 1995b). At x C > 0.8 this component was
solvated equally by A and B, but at x C < 0.15 it was preferentially hydrated, that
is, solvated by A, except when x A > 0.8, where the solvation of C by A and B was
random. N , N -dimethylformamide (C) featured also in the studies (Ruckenstein and
Shulgin 2001a) of it in aqueous (A) methanol (B). The KBIs in the system n - hexane
+ 1-hexanol + methyl benzoate were studied at 298 K (Aparicio et al. 2005). They
calculated the excess (or deficit) number of molecules of, say, A, around molecules
of B in pseudobinary systems at constant mole fraction of C from

( )

id

nc GG
AB A B B

= - (3.12)

as suggested in Ruckenstein and Shulgin (2001a). However, although deduction of
G i ij could be justified regarding the interactions involved, this is questionable when
the composition (number of neighboring molecules of each kind) is to be calculated.

3.5 COMPARISON WITH OTHER APPROACHES TO PREFERENTIAL
SOLVATION IN SOLVENT MIXTURES
The Kirkwood-Buff integrals are obtained rigorously from the thermodynamic data,
but the calculation of the interactions between the components of the solvent mix-
tures as volume-corrected preferential solvation parameters depends on the validity
of the notion that subtraction of G i ij from G ij cancels out the volume size discrepan-
cies between the components (Matteoli 1997). Although endorsed by the present
author and others, this notion has been controversial (Ben-Naim 2007a; Matteoli and
Lepori 2007; Ben-Naim 2008; Matteoli and Lepori 2008; Shulgin and Ruckenstein
2008b) (see also Section 4.5 in Chapter 4). The composition of the environment of
a component is indeed dependent on G ij , but the interactions leading to preferences
depend on Δ G ij = G ij - G i ij . The numerical values for the (volume-corrected) pref-
erential solvation parameters presented in this chapter depend on the estimation of
the correlation volumes by the iterative method proposed (Marcus 1990) that could
possibly be improved on. However, the main difficulty with the KBI approach to the
preferential solvation is the high accuracy demanded for the derivative of the chemi-
cal potential of a component (or for the second derivative of the excess Gibbs energy)
that cannot always be met.
One way around this difficulty is to depend on a model, which although not rigor-
ous does lead to reasonable quantitative results regarding the preferential solvation in