Handbook of Solvents - George Wypych - ChemTech - Ventech!

8.7 Theoretical and computing modeling 461
There is a large critical literature, but two recent reviews (Floris and Tani 40 and
Wallqvist and Mountain, 41 both published in 1999) are here recommended as an excellent
guide to this subject. The two reviews consider and analyze about 100 potentials for pure
water. WM review starts from historical models, FM review pays attention to recent models
(about 70 models, supplemented by ion-water potentials). The two reviews partly overlap,
but they are to a good extent complementary, especially in the analysis of the performances
of such models.
There are, to the best of our knowledge, no reviews of comparable accuracy for the potentials
regarding other liquid systems.
8.7 THEORETICAL AND COMPUTING MODELING OF PURE LIQUIDS
AND SOLUTIONS
8.7.1 PHYSICAL MODELS
In this chapter we shall present a necessarily partial review of the main theoretical approaches
so far developed to treat liquid systems in terms of physical functions. We shall restrict
ourselves to two basic theories, integral equation and perturbation theories, to keep the
chapter within reasonable bounds. In addition, only the basic theoretical principles underlying
the original methods will be discussed, because the progress has been less rapid for theory
than for numerical applications. The latter are in fact developing so fast that it is an
impossible task to try to give an exhaustive view in a few pages.
A fundamental approach to liquids is provided by the integral equation methods 42-44
(sometimes called distribution function methods), initiated by Kirkwood and Yvon in the
1930s. As we shall show below, one starts by writing down an exact equation for the molecular
distribution function of interest, usually the pair function, and then introduces one or
more approximations to solve the problem. These approximations are often motivated by
considerations of mathematical simplicity, so that their validity depends on a posteriori
agreement with computer simulation or experiment. The theories in question, called YBG
(Yvon-Born-Green), PY (Percus-Yevick), and the HNC (hypernetted chain) approximation,
provide the distribution functions directly, and are thus applicable to a wide variety of
properties.
An alternative, and particularly successful, approach to liquids is provided by the thermodynamic
perturbation theories. 42,44 In this approach, the properties of the fluid of interest
are related to those of a reference fluid through a suitable expansion. One attempts to choose
a reference system that is in some sense close to the real system, and whose properties are
well known (e.g., through computer simulation studies or an integral equation theory).
As a last physical approach we mention, but do not further consider, the scaled-particle-theory
(SPT) 38,45 which was developed about the same time as the Percus-Yevick theory.
It gives good results for the thermodynamic properties of hard molecules (spheres or
convex molecules). It is not a complete theory (in contrast to the integral equation and perturbation
theories) since it does not yield the molecular distribution functions (although
they can be obtained for some finite range of intermolecular separations).
Early work on the theory of dense fluids dealt almost exclusively with simple atomic
fluids, in which the intermolecular forces are between the centers of spherical molecules
and depend only on the separation distance r. However, in real fluids the intermolecular
forces depend on the molecular orientations, vibrational coordinates, etc., in addition to r.