Interaction site fluids dielectric constant

In this section, we review some of the important formal results in the statistical mechanics of interaction site fluids. These results provide the basis for many of the approximate theories that will be described in Section III, and the calculation of correlation functions to describe the microscopic structure of fluids. We begin with a short review of the theory of the pair correlation function based upon cluster expansions. Although this material is featured in a number of other review articles, we have chosen to include a short account here so that the present article can be reasonably self-contained. Cluster expansion techniques have played an important part in the development of theories of interaction site fluids, and in order to fully grasp the significance of these developments, it is necessary to make contact with the results derived earlier for simple fluids. We will first describe the general cluster expansion theory for fluids, which is directly applicable to rigid nonspherical molecules by a simple addition of orientational coordinates. Next we will focus on the site-site correlation functions and describe the interaction site cluster expansion. After this, we review the calculation of thermodynamic properties from the correlation functions, and then we consider the calculation of the dielectric constant and the Kirkwood orientational correlation parameters. 

Thus, if we know the dielectric constant of the fluid, then Eq. (3.3.15) could be used to improve the results obtained from the SSOZ-MSA approximation, for example. This has been done for dipolar hard dumbbell fluid by Lee and Rasaiah using Monte Carlo simulation results for the dielectric constant (Morriss ), and by Rossky, Pettitt and Stell. However, this approach does not seem to have any value as a predictive tool. Moreover, in the case of some interaction site models, notably hard linear triatomics, the site-site direct correlation function is not a short-range function but in fact increases with increasing r. This notwithstanding, the Cummings-Stell analysis remains an important contribution to our understanding of the SSOZ equation. 

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. 

In this section, we will review some of the results obtained for homogeneous fluids. The focus of the section strongly reflects the author s particular interest rather than a complete review of all work done in this area. To a large extent, we will concentrate on aspects that have not been reviewed previously, or on areas that developed since those reviews. The first section deals with the influence of electrostatic interactions on the structure factor, and we stress the decoupling of dipole-dipole interactions from the structure factor, although there is a strong effect on particular g y r) s. In Section V.B we consider the dielectric constant obtained from the CSL equation with particular reference to the influence of shape forces in the dielectric properties. Section V.C considers the application of interaction site theories to calculate thermodynamic properties and fluid phase equilibria. 

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