Omstein-Zemike theory/equation

Onsager coefficient 202-213, 256 Omstein-Zemike theory/equation 204, 214... 

Integral equation theories are widely used in the theoretical study of liquids. There are two broad classes of integral equation theories those based on the Bom-Green-Yvon (BGY) hierarchy and those based on the Omstein-Zemike (OZ) equation [88]. Although the formalism is exact in both classes, it is generally easier to fashion approximations in the case of the OZ-equation-based approach, and this type of theory has therefore been more popular. Surprisingly, the BGY approach has never been implemented for nonuniform polymers, and this section is therefore restricted to a discussion of the OZ-equation-based approach. 

Omstein-Zemike theory of the critical opalescence which operates also with a linear equation for the joint correlation function. 

From the many tools provided by statistical mechanics for determining the EOS [36, 173, 186-188] we consider first integral equation theories for the pair correlation function gxp(ra,rp) of spherical ions which relates the density of ion / at location rp to that of a at ra. In most theories gafi(ra,rp) enters in the form of the total correlation function hxp(rx,rp) = gxp(rx,rp) — 1. The Omstein-Zemike (OZ) equation splits up hap(rx,rp) into the direct correlation function cap(ra, rp) for pair interactions plus an indirect term that reflects these interactions mediated by all other particles y ... 

Theories based on the solution to integral equations for the pair correlation fiinctions are now well developed and widely employed in numerical and analytic studies of simple fluids [6]. Furtlier improvements for simple fluids would require better approximations for the bridge fiinctions B(r). It has been suggested that these fiinctions can be scaled to the same fiinctional fomi for different potentials. The extension of integral equation theories to molecular fluids was first accomplished by Chandler and Andersen [30] through the introduction of the site-site direct correlation fiinction c r) between atoms in each molecule and a site-site Omstein-Zemike relation called the reference interaction site... 

Computer simulations are not the only methods which can be used to calculate the dielectric constant of pure liquids. Other approaches are given by the use of integral equations, in particular, the hypemetted chain (HNC) molecular integral equation and the molecular Omstein-Zemike (OZ) theory (see Section 8.7.1 for details on such methodologies). 

As an example of how to determine compressibilities by mean of integral equations, we would like to quote here the already cited paper of Richardi et al. in which molecular Omstein-Zemike (MOZ) theory and site-site Omstein-Zemike (SSOZ) theory have been exploited. In particular, using the MOZ, the compressibility can be evaluated using the equation ... 

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