Preferential Solvation in Mixed Solvents - Fluctuation Theory of Solutions - page 78

and water-water association is disfavored, δ x ′ WW having two minima of -0.022,
near x S = 0.3 and 0.7. The system is nearly ideal, in view of the small values of the
extrema, for this very hydrophilic solute. For the aqueous acetic acid system, water
self-association is favored, δ x ′ WW (max) = 0.050 near x S = 0.50 and for aqueous propa-
noic acid, δ x ′ WW (max) = 0.020 near x S = 0.25, is smaller than for acetic acid, contrary
to expectations (the reverse ratio is found for the nonvolume-corrected δ x WW values
[Marcus 1990]). The mutual interactions are disfavored: for acetic acid δ x ′ WS (min)
= -0.018 near x S = 0.25 and for aqueous propanoic acid, δ x ′ WS (min) = -0.013 near
x S = 0.15.
Propylene carbonate. This system has a miscibility gap at 298 K, so only the
organic solvent-rich region was dealt with (Marcus 1990). The preferential solvation
of water around propylene carbonate, δ x WS ~ 0 for the homogeneous region x S > 0.68,
but the water-water preference, δ x WW has a maximum of 0.36 near x S = 0.76 and this
preference extends even to the third solvation shell, where δ x WW (max) = 0.040 still.
This preference is expected, in view of the phase separation that takes place.
γ- Butyrolactone . This system was dealt with (Marcus 2002a) at 343 K, for which
data were available (higher temperature data showed unreasonable KBIs at x S ≤
0.35). Only small disfavored mutual association and moderate self-association of
the water were observed for these mixtures: δ x ′ WS (min) = -0.015 near x S = 0.3 and
δ x ′ WW (max) = 0.055 near x S = 0.75.
Di- and triethylamine . For aqueous diethylamine, data were available for 313 K
(Marcus 2002a) and yielded preferred water-water association with a double-humped
curve: δ x ′ WW (max) = 0.14 near x S = 0.20 and δ x ′ WW (max) = 0.08 near x S = 0.80. The
disfavored mutual association has a single extremum: δ x ′ WS (min) = -0.06 near x S =
0.15, whereas at x S ≥ 0.5, δ x ′ WS is only very slightly negative. Triethylamine has a
lower critical consolute temperature of 292 K, and even at 283 K, the excess Gibbs
energy is not sufficiently accurate (see above) at x S ≤ 0.4 to obtain meaningful KBIs
(Marcus 1990). At this temperature, δ x WW (min) = -0.060 at x S = 0.77 and δ x WS (max)
= 0.028 at x S = 0.47. No volume-corrected preferential solvation parameters were
calculated for this system, so it is still an open question why the interactions appear
to be of opposite sign for the di- and triethylamines.
1,2-Diaminoethane (ethylene diamine) . Data at 336 K appear to be unreliable
(Marcus 2002a) and only those at 373 K could be used in a reasonable manner.
These lead to nearly ideal behavior of aqueous ethylene diamine at this high temper-
ature: δ x ′ WS is essentially zero over the entire composition range and δ x ′ WW is slightly
negative with δ x ′ WW (min) = -0.02 at x S = 0.65.
Pyrrolidine, piperidine, morpholine, and pyridine . The aqueous pyrrolidine sys-
tem was studied at 333 K (Marcus 2002a) and showed a double-humped δ x ′ WW curve
and a single trough δ x ′ WS curve approaching zero, similar to the diethylamine case
treated above (having the same number of carbon atoms but two ethyl chains rather
than the tetramethylene chain of pyrrolidine). The extrema are: δ x ′ WW (max) = 0.055
near x S = 0.15 and δ x ′ WW (max) = 0.008 near x S = 0.80 and δ x ′ WS (min) = -0.04 near
x S = 0.10, much smaller for pyrrolidine than for diethylamine. It is interesting that
for the former of these two systems, δ x ′ WW turns slightly negative for 0.40 ≤ x S ≤
0.65, where δ x ′ WS is already very nearly zero. Aqueous piperidine (Marcus 2001),