Ornstein-Zemike theory

G. Stell, Extension of the Ornstein-Zemike theory of the critical region II, Phys. Rev. Bl, 2265-2270 (1970). 

Moreover the components of vector A change to become Aa = aA/vA, etc. An Ornstein-Zemike (OZ) approach (referred to as the integral equation theory) describing multicomponent compressible polymer blend mixtures has been extensively investigated [35]. The multicomponent OZ equation relates the direct correlations matrix C and the total (i.e., direct and indirect) correlations matrix H as ... 

Here, the unrefined (PY, CHNC, and BGY) and refined (PY2, CHNC2, and BGY2) theories are used in conjunction with the virial theorem or the Ornstein-Zemike (O-Z) relation in order to obtain Bg in units of = 1. See ref. 20. 

The polymer RISM theory relates the set of total correlation functions (r) = g(r)-l to the set of site-site direct correlation functions, (c(r), and the set of intramolecular distribution functions, w(r), via the nonlinear site-site Ornstein-Zemike-like (SSOZ) integral matrix equation [41]... 

Fluctuations in thermodynamics automatically imply the existence of an underlying structure that has created them. We know that such structure is comprised of molecules, and that their large number allows statistical studies, which, in turn, allow one to relate various statistical moments to macroscopic thermodynamic quantities. One of the purposes of the statistical theory of liquids (STL) is to provide such relations for liquids (Frisch and Lebowitz 1964 Gray and Gubbins 1984 Hansen and McDonald 2006). In such theories, many macroscopic quantities appear as limits at zero wave number of the Fourier transforms of statistical correlation functions. For example, the Kirkwood-Buff theory allows one to relate integrals of the pair density correlation functions to various thermo-physical properties such as the isothermal compressibility, the partial molar volumes, and the density derivatives of the chemical potentials (Kirkwood and Buff 1951). If one wants a connection between detailed correlations and integrated moments, one may ask about the nature of the wave-number dependence of these quantities. It turns out that the statistical theory of liquids allows an answer to such a question very precisely, which leads to new types of questions. The Ornstein-Zemike equation (Hansen and McDonald 2006), which is an exact equation of the STL, introduces the concept of correlation length which relates to the spatial extension of the density and/or concentration (the latter in the case of mixtures) fluctuations. This quantity cannot be accessed from pure... 

Richardi J, Fries PH, Fischer R, Rast S, Krienke H Liquid acetone and chloroform a comparison between Monte Carlo simulation, molecular Ornstein-Zernike theory, and site-site Omstein-Zemike theory. Mol Phys 93(6) 925—938, 1998. 

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