The extension of the replica Ornstein-Zernike (ROZ) equations is applied to the study of the structural properties of a Lennard-Jones fluid confined in an attractive polydisperse disordered matrix. The ROZ equations in combination with the orthogonal polynomial expansions for the correlation functions are used. The radial distribution functions are calculated for the adsorbed fluid at different temperatures. The effect of matrix polydispersity on the excess internal energy is considered in our study as well.

The traditional formalism in liquid state theory based on the calculation of the pair distribution function is generalized and reviewed for nematic fluids. The considered approach is based on the solution of orientationally inhomogeneous Ornstein-Zernike equation in combination with the Triezenberg-Zwanzig-Lovett-Mou-BuffWertheim equation. It is shown that such an approach correctly describes the behavior of correlation functions of anisotropic fluids connected with the presence of Goldstone modes in the ordered phase in the zero-field limit. We focus on the discussions of analytical results obtained in collaboration with T.G. Sokolovska in the framework of the mean spherical approximation for Maier-Saupe nematogenic model. The phase behavior of this model is presented. It is found that in the nematic state the harmonics of the pair distribution function connected with the correlations of the director transverse fluctuations become long-range in the zero-field limit. It is shown that such a behavior of distribution function of nematic fluid leads to dipole-like and quadrupole-like long-range asymptotes for effective interaction between colloids solved in nematic fluids, predicted before by phenomenological theories.

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Selective adsorption from binary polymer mixtures on a crystalline surface is studied in terms of the lattice gas model in conjunction with the results of the association theory. An interplay of the selectivity and the surface induced segregation is shown to result in a variety of competing factors which dominate the adsorption process. The role of the bead diameter, chain length and the surface activity in the preferential adsorption of one component is analyzed. A variation of the selectivity coefficient with the density and composition is also discussed.

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