Critical Behaviour of Confined Systems

Abstract

The critical phenomena and peculiarities of phase transitions in the confined fluid systems are investigated. A system with the geometry of a planeparallel layer is chosen in order to discuss the influence of the space limitations on the critical characteristics of fluids. The main ideas of the Munster iteration procedure were used to find the pair and the direct correlation functions. Such an important characteristic of the system as the correlation length was found and correspondent results were analyzed in the terms of the scaling theory. Special attention is paid to the calculation of the shifts of the critical parameters (critical temperature and density). The three-moment approximation is used to investigate anisotropic liquids. The system of the Ornstein-Zernike (OZ) integral equations is involved to investigate the correlative properties of the binary fluid mixtures. It is shown for the fluids with the isomorphic character of the interaction that the approximation may be used that makes the system similar to the OZ onecomponent liquid model. The asymptotic formulae for the pair correlation functions are found and the validity of the Munster method for the binary mixtures is considered. The peculiarities of critical light opalescence for the systems with the special geometry are considered.

Thermal fluctuations of director orientation in nematic liquid crystals with inclusions

“…Moreover, to compare the predictions of the model with experimental data we can interpret the above considered system (probably with minor modifications) as the isotropic liquid with mesomorphic inclusions. From this point of view our results are in good agreement with experimental data not only in the part of critical temperature shift but regarding the structure of pair correlation functions as well (see for example [23][24][25]). …”

Critical parameters and pair correlations in confined multicomponent liquids

“…On the other hand, our results in limiting cases, i.e. for simple and binary systems (spatially infinite and finite-size), give a well-known formulae that was previously received for these systems in numerous works (see for example [1,6,7,21]) and we can conclude that they are absolutely realistic.…”

“…First of all, in spite of the availability of plenty of data on critical behavior of simple [1][2][3][4] and binary liquid systems [1,[5][6][7][8], multicomponent mixtures (even spatially infinite) have not been studied well enough at the moment (for most remarkable results one can see for example [5,[9][10][11][12][13]). Moreover, we lack data on the critical correlative behavior of finite-size multicomponent systems.…”

Method for diagonalizing pair correlation functions for a multicomponent liquid system

“…, N, where N is the number of components. Under such a definition, the correlation functions are normalized to the densities [7], [8].…”

“…On one hand, it allows determining important statistical characteristics of a system; on the other hand, it can clarify how the number of components affects the qualitative behavior of a system. For example, in the experimental studies of critical opalescence of light by solutions with different numbers (two, three, or four) of components, the Ornstein-Zernike (OZ) approximation, which is analogous to the one used for one-component systems, is often used [2], [5], [7]. Results in the present paper allow concluding that it is possible in principle to apply this approach to solutions with a large number of components in the case where the system is close to a critical state.…”