The thesis is devoted to the development of theoretical approaches and their application to the description of thermodynamic and structural properties of a confined fluid. The obtained theoretical findings are supplemented by the results of computer simulations performed within this study.
Several basic models of confinement and their modifications are considered. In particular, main attention is paid to disordered porous media modeled by a matrix of randomly distributed hard particles with and without overlapping. Analytical expressions are proposed to describe the thermodynamic properties of the hard-sphere fluid in these models of porous media, which were obtained on the basis of scale particle theory (SPT). This theory was also extended by taking into account more sophisticated models such as a sponge-like matrix and a matrix formed by particles of a non-spherical shape. It is shown that the results of the developed theory are in a good quantitative agreement with the computer simulation data.
The SPT theory of a hard-sphere fluid confined in a hard-sphere matrix is used for the description of the reference system within the perturbation theory to study a liquid-vapour phase transition in a simple fluid and in an associative fluid of patchy colloids with four interacting sites. It was found that both the critical temperature and the critical density decrease with a decrease of the matrix porosity, and simultaneously the coexistence region of phase diagrams gets narrower. Furthermore, it is also shown that an increase of matrix particles size can lead to a growth of the critical temperature.
A further application of the SPT theory concerns the description of the primitive model of an ionic fluid in an uncharged disordered matrix. For this purpose, the method of collective variables was combined with the SPT and the corresponding equations for the main thermodynamic quantities were derived with taking into account the terms higher than the Gaussian approximation. Therefore, the liquid-vapour phase transition of the confined ionic fluid was investigated with the asymmetry of oppositely charged ions, both in charges and sizes. The obtained phase diagrams show that the critical parameters of ionic fluids strongly depend on the matrix porosity and the sizes of matrix particles, and in general have the same trends as in simple fluids. Furthermore, the size asymmetry of oppositely charged ions strengthens this effect. On the contrary, the charge asymmetry significantly suppresses the influence of the matrix presence.
Using the field-theory approach in the mean-field and Gaussian approximations, the structural properties were studied for three qualitatively different fluid models in the confinement formed by two parallel hard walls. Specifically, the model of two-Yukawa pair potential, oscillating Yukawa potential and the model of nematic Maier-Saupe fluid are considered, for which pair correlation functions in the bulk and density profiles in the confinement with respect to the hard wall are obtained. For the nematic fluid, orientation characteristics such as the order parameter and its profile depending on the distance to the wall are also calculated. It is observed that the contact value of the fluid density profile can have a non-monotonous dependence on temperature. In the case of a nematic fluid, a significant disruption of orientational order in the vicinity of hard walls is noticed. To assess an accuracy of the obtained theoretical results, the corresponding computer simulations with the use of Monte-Carlo method were performed. It is shown that the Gaussian approximation provides a much better quantitative description of the fluid density profile than the mean-field approximation.
Using the dissipative dynamics, computer simulations were performed to study the processes of microphase separation in a binary fluid between two hard walls, functionalized with nonostructured polymer brushes in the form of stripes. At a fixed polymer length, the morphology of the obtained phases was investigated depending on the distance between the walls and the width of the stripes, as well as depending on the different compositions of the fluid components, represented by good and bad solvents. The conditions are established under which the phases of different morphology (layered, columnar, mixed, droplets) can be formed. The proposed approach is generalized for the description of swelling processes in a porous membrane, for which the values of pore size and the membrane thickness are obtained depending on the solvent composition. The obtained results agree well with experimental findings at the qualitative level.
