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This article based on the archival documents and scientific periodicals, for the first time reveals a discoverer of so called transitional phase of the substance from the solid state to liquid – the liquid crystals. This fundamental discovery has been made by the Austrian scientist Julius Planer at the Lviv University in 1861.

Microscopic equations for the coefficients of the effective Landau-Ginzburg-Wilson (LGW) fluid Hamiltonian are presented in the case of the reference system that consists of hard spheres with a short-range Yukawa attraction. The mean-field level analysis of the critical parameters of the Sutherland fluid, based on the effective LGW fluid Hamiltonian with two different reference systems, namely, widely used pure hard spheres and hard spheres with the short-range Yukawa attraction, is performed. From the comparison with computer simulation data, the superiority of the reference system that incorporates the short-range attraction is shown.

A convenient approximation is proposed for the correlation function of a pair of large hard-sphere particles in a bidisperse or binary hard-sphere mixture. This approximation is based on the solution of the Ornstein–Zernike/Percus–Yevick integral equations for a hard-sphere mixture. From this result, we obtain the potential of mean force and interaction force for a pair of colloidal spheres in a bidisperse hard-sphere fluid.

The analytic solution of the Poisson equation for a system of two identical charges near a uniformly charged plane is used to understand the phenomenon of an attraction between a pair of charged particles next to an oppositely charged surface that has been observed recently. We found that there is no direct attractive interaction between like charges. We have shown that what is observed experimentally could be interpreted as the ‘apparent attraction’ resulting from the extra force experienced by each charge being in the non-zero plane parallel electric field due to the charged surface. This surface-induced electric field and force are directed to the center of the surface and can oppose the direct Coulomb repulsion between like charges. Both the field and force can be obtained naturally within the framework of classical electrodynamics if the effects of the finite size of a charged surface are taken into account.

The approach to treat the strong attractive interaction between fluid particles adsorbed into porous media is reported. Results are illustrated by the calculations of liquid/vapor phase diagrams for Lennard-Jones fluid in the presence of quenched disorder. Perspectives of the approach from the comparison with computer simulation data available from the literature are discussed.

The molecular dynamics (MD) simulations and replica integral equation theory are employed for the study of the structure and dynamical properties of Kaminsky-Monson molecular model of Lennard-Jones fluid in contact with an adsorbing porous medium. Both theory and MD simulations predict quite similar results for the radial distributions of the fluid-fluid and fluid-matrix correlations which agree well with the Monte Carlo data already reported in the papers. The mean-square displacement and the velocity autocorrelation functions of fluid particles are calculated from the MD simulations and are used to analyze their self-diffusion coefficients. It is shown that the presence of porous media reduces the mobility of fluid particles and hence decreases the self-difussion coefficient.

A two-dimensional model for a chemically associating fluid adsorbed in a disordered porous media has been investigated. The model is studied by means of the associative Replica Ornstein-Zernike equations, with Perens-Yevick and hypernetted chain approximations, extended for associating fluids. The effects of disordered media density and strength of association interaction on the adsorption isotherms and structural properties of adsorbed fluid are explored. To investigate the effect of association interaction on the liquid-gas phase transition, the additional out-core interparticle interaction in the form of square-well attraction is included. This term is considered in the mean field approximation. It permits us to analyze qualitative trends of the behavior of the critical density and temperature dependence on the combined effect of association and of quenched disorder in the model of dimerizing discs with square-well attraction. Our preliminary conclusion concerning this unexplored problem is that the presence of disorder and of association have opposite effect on the critical temperature. Manipulating the matrix density and bonding between particles may keep almost unaltered the critical temperature.