Perturbation theory interaction site fluids

As we mentioned in the opening paragraph, thermodynamic perturbation theory has been used in two contexts in applications to interaction site fluids. In this section, we will describe efforts to treat the thermodynamics and structure of interaction site fluids in terms of a perturbation expansion where the reference system is a fluid in which the intermolecular forces are spherically symmetric. In developing thermodynamic perturbation theories, it is generally necessary to choose both a reference system and a function for describing the path between the reference fluid and the fluid of interest. The latter choice is usually made between the pair potential and its Boltzmann factor. Thus one writes either... 

We turn now to a discussion of perturbation theories based upon extensions of the Barker-Henderson and Weeks-Chandler-Anderson theories to interaction site potentials. Such theories seek to treat the properties of the fluid as a perturbation about a reference fluid with anisotropic repulsive forces only. The theories have been formulated both explicitly in terms of division of the site-site potential into reference and perturbation potentials (Tildesley, Lombardero et al. )... 

Orientational structure at a liquid vapor-interface of diatomic interaction site fluids has been studied extensively by Gubbins and Thompson using both thermodynamic perturbation theory and molecular dynamics simulation, and by Tarazona and Navascues using perturbation theory. Chacon et al. have applied density-functional theories to these systems. The theoretical methodology and results are reviewed in a comprehensive article by Gubbins, to which the reader is directed for more complete details. 

The formal treatment describing the extension of perturbation theory to polar interaction site systems and to other situations where the perturbative forces are structure-determining is available and has been applied with some success to some simple models of polar diatomics. More quantitative comparisons with computer simulations need to be made. Of course, qualitatively accurate information about the structure of polar interaction site fluids has been available for some time through solutions of the SSOZ-HNC equations. However, this approach does not seem to be useful in the context of thermodynamics. Rather little attention has been paid to polarizable molecules, although these can be treated within the context of the interaction site formalism (see, for example, Chandler and, more recently, Sprik and Klein ). Although the formal treatment of the dielectric constant within the interaction site formalism is now well established, no quantitative approximations seem to emerge from any of the theories available. 

More modem approaches borrow ideas from the liquid state theory of small molecule fluids to develop a theory for polymers. The most popular of these is the polymer reference interaction site model (PRISM) theory " which is based on the RISM theory of Chandler and Andersen. More recent studies include the Kirkwood hierarchy, the Bom-Green-Yvon hierarchy, and the perturbation density functional theory of Kierlik and Rosinbeig. The latter is based on the thermodynamic perturbation theory of Wertheim " where the polymeric system is composed of very sticky spheres that assemble to form chains. For polymer melts all these liquid state approaches are in quantitative agreement with simulations for the pair correlation functions in short chain fluids. With the exception of the PRISM theory, these liquid state theories are in their infancy, and have not been applied to realistic models of polymers. 

The Sanchez-Lacombe model [48-50] is a lattice fluid model in which each component is divided into parts that are placed in a lattice. The different parts are allowed to interact with a mean-field intermolecular potential. By introducing an appropriate number of vacant sites (holes) in the lattice, the correct solution density can be obtained. SAFT [51-53] is based on the perturbation theory. The principle of perturbation theory is that first a model is derived for some idealized fluid with accurately known properties, called the reference fluid . Subsequently, the properties of this model are related to those of a real dense fluid. By expanding this reference fluid into power series over a specified parameter, the power terms can be regarded as corrections or "perturbations for the reference fluid as compared to reality. Obviously, the more the reference model approaches reality, the smaller the corrections are. Therefore, the key issue for applying perturbation theory is deriving the most suitable reference fluid. 

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