Hypemetted chain approximation approximate theories

A fundamental approach to liquids is provided by the integral equation methods (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-Bom-Green), PY (Percus-Yevick), and the HNC (hypemetted chain) approximation, provide the distribution functions directly, and are thus applicable to a wide variety of properties. 

Eq. (5) is useful when analyzing different approximations in the theory of inhomogeneous fluids. In particular, if all the terms involving third- and higher-order correlations in the right-hand side of Eq. (5) are neglected, and if Pi(ro))P2( o)i )Pv( o) are chosen as the densities of species for a uniform system at temperature T and the chemical potentials p,, the singlet hypemetted chain equation (HNCl) [50] results... 

Having at our disposal accurate structural and thermodynamic quantities for HS fluid, the latter has been naturally considered as a RF. Although real molecules are not hard spheres, mapping their properties onto those of an equivalent HS fluid is a desirable goal and a standard procedure in the liquid-state theory, which is known as the modified hypemetted chain (MHNC) approximation. According to Rosenfeld and Ashcroft [27], it is possible to postulate that the bridge function of the actual system of density p reads... 

In the last two decades, new extended laws have been obtained for the concentration dependence of transport properties. It was possible [ 15,16] to use the Fuoss-Onsager theory together with new, more accurate equilibrium pair distribution functions as obtained with the help of the hypemetted chain (HNC) or mean spherical approximation (MSA). 

FH = Flory-Huggins GF = generalized Flory GFD = generalized Flory dimer HNC = hypemetted chain HTA = high temperature approximation IFJC = ideal freely joined chain ISM = interaction site model LCT = lattice cluster theory MS = Martynov-Sarkisov PMMA = polymethyl methacrylate PRISM = polymer reference interaction site model PVME = polyvinylmethylether PS = polystyrene PY = Percus-Yevick RMMSA = reference molecule mean spherical approximation RMPY = reference molecular Percus-Yevick SANS = small angle neutron scattering SFC = semiflexible chain TPT = thermodynamic perturbation theory. 

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