Handbook of Solvents - George Wypych - ChemTech - Ventech!

8.9 Liquid surfaces 497
out of equilibrium properties. Some models are old (dating before the introduction of QM),
but still in use.
A more detailed description of molecular interactions may lead to refinements of such
models (this is currently being done), but there is no reasonable prospect of replacing them
with what we have here called the standard approach based on potentials. The standard approach,
even when used, may be not sufficient to satisfactorily describe some phenomena.
We quote two examples drawn from the presentation of liquid surfaces in dispersed systems:
bubbles and solid small particles.
The description of the energetics of a single bubble, and of the density inside and
around it, is not sufficient to describe collective phenomena, such as ebullition or separation
of a bubble layer. The description of a single bubble is at a low level in a ladder of models,
each introducing new concepts and enlarging the space (and time) scale of the model.
The same holds for small solid particles in a liquid. There is a whole section of chemistry,
colloidal chemistry, in which our standard approach gives more basic elements, but
there is here, again, a ladder of models, as in the preceding example.
Our standard model extends its range of applicability towards these more complex
levels of theory. This is a general trend in physics and chemistry: microscopic approaches,
starting from the study of the interaction of few elementary particles, are progressively
gaining more and more importance over the whole range of sciences, from biology to cosmology,
passing through engineering and, in particular, chemistry. In the case of liquids,
this extension of microscopical models is far from covering all the phenomena of interest.
8.9.3 STUDIES ON INTERFACES USING INTERACTION POTENTIALS
To close this section on liquid surfaces, limited to a rapid examination of the several types of
surface of more frequent occurrence, we report some general comments about the use of the
standard approach on liquid surfaces.
The first information coming from the application of the method regards the density
profile across the interface. Density may be assumed to be constant in bulk liquids at the
equilibrium, with local deviations around some solutes (these deviations belong to the family
of cybotactic effects, on which something will be said later). At each type of liquid surface
there will be some deviations in the density, of extent and nature depending on the
system.
A particular case is that of mobile surfaces, i.e., liquid/gas and liquid/liquid surfaces.
Having liquids a molecularly grained structure, there will always be at a high level of spatial
deviation a local deviation of the surface from planarity. If there are no other effects, this deviation
(sometimes called corrugation, but the term is more convenient for other cases, like
liquid/solid surfaces, where corrugation has a more permanent status) averages to zero.
Entropic forces are responsible for other effects on the density profile, giving origin at
a large scale to a smooth behavior of the density profile, connecting the constant values of
the two bulk densities. The most natural length unit in liquids is the bulk correlation length,
ξ, i.e., the distance at which the pair correlation gAB(r) has decayed to 1. For bulk water ξ is
around 5-6 Å. This large scale behavior hides different local behaviors, that range among
two extremes, from capillary waves to van der Waals regime. 127 Capillary waves correspond
to a sharp boundary (corrugation apart) with “fingers” of a liquid protruding out of the bulk.
Capillary waves may happen both at liquid and gas surfaces, in the former, in a more stable
status (i.e., with a large mean life) than in the latter.