Handbook of Solvents - George Wypych - ChemTech - Ventech!

8.9 Liquid surfaces 499
tions) of the components of the liquid system to write the appropriate statistical partition
function. In the case of solvation energies, the rotational component of the factorized solute
partition function gives a not negligible contribution to ΔG solv . The translational component
of the solute partition function can be factorized apart, as first suggested by Ben-Naim, 128
and included in the cratic component of ΔG solv with a small correction (the cratic component
is the numerical factor taking into account the relationships between standard states in a
change of phase).
In the homogeneous bulk liquid we have to explicitly consider orientations for dynamical
relaxation effects. The same holds for translation in other dynamical problems (diffusion,
transport, etc.).
Coming back to the static problems, it turns out that near the limiting surface, the free
energy of the components of the liquid also depends on positions and orientations. A quantity
like ΔG solv for the transfer of M in the solvent S in the bulk must be replaced by ΔG solv (r,
Ω) specifying position and orientation of M with respect to the surface of S.
This effect must not be confused with the cybotactic effects we have mentioned, nor
with the hole in the solute-solvent correlation function g MS(r) (see Figure 8.5). The hole in
the radial correlation function is a consequence of its definition, corresponding to a conditional
property, namely that it gives the radial probability distribution of the solvent S, when
the solute M is kept at the origin of the coordinate system. Cybotactic effects are related to
changes in the correlation function g MS(r) (or better g MS(r,Ω)) with respect to a reference situation.
Surface proximity effects can be derived by the analysis of the g MS(r,Ω) functions, or
directly computed with continuum solvation methods. It must be remarked that the
obtention of g MS(r) functions near the surface is more difficult than for bulk homogeneous
liquids. Reliable descriptions of g MS(r, Ω) are even harder to reach.
Orientational preferences are the origin of many phenomena, especially when at the
surface there are electric charges, mobile or fixed. Outstanding examples occur in biological
systems, but there is a large literature covering other fields. A relatively simple case that
has been abundantly studied is the electric potential difference across the surface. 129
We have not considered yet the behavior of solutes near the interface. The special, but
quite important, case of the charged components of a salt solution near a charged boundary
is widely known, and it is simply mentioned here.
More generally, the behavior of solutes largely depends on the chemical composition
of the system. Small ions are repelled at the air/gas interface, hydrophobic molecules are attracted
to the interface. Even the presence of a simple CH 3 group has some effect: the air interface
of dilute solutions of methanol is saturated in CH 3OH over a sizeable molar fraction
range. 130 At the liquid/liquid interface between water and hydrocarbon solvents, solutes
with a polar head and an alkylic chain tend to find an equilibrium position, with the polar
head in water, at a distance from the surface depending on the chain length. 131
All the quoted results have been obtained at the static level, employing a mean force
potential, obtained in some cases with inexpensive continuum models; in other cases, with
computer demanding simulations of the free energy profile.
Simulations can give more details than continuum methods, which exploit a simplified
and averaged model of the medium. Among the simulation results we quote the recognition
that small cations, exhibiting strong interactions with water molecules, tend to keep
bound the first solvation layer when forced to pass from water to another solvent. Analogous
effects are under examination for neutral polar solutes at water/liquid interfaces in case