Chalyy K. Equilibrium and non-equilibrium properties of mesoscale liquid systems in the critical region

The thesis presents studies of finite-size effects on the critical behavior of equilibrium and non-equilibrium properties of mesoscale liquid systems. The topics under consideration are as follows: (a) equilibrium critical phenomena in finite-size liquid systems; (b) non-equilibrium critical phenomena in finite-size liquid systems; (c) heat capacity of mesoscale confined liquids; (d) neutron optics of liquids in restricted geometry in the critical region; (e) medical and biological applications of critical phenomena in finite-size liquids. There are five chapters in the thesis in accordance with these topics. A new generalized hypothesis of the static scaling is formulated for confined binary liquid mixtures near the critical liquid-liquid and liquid-vapor states. A general scaling approach to the dynamical properties of finite-size mesoscale one- and two-component liquids is presented. It gives a reliable background to study the peculiarities of critical opalescence spectra (namely, the spectral widthГс of the central Rayleigh component). The problem of the analytical description of the heat capacity of liquid 4He near the ?-point is studied with effects of gravity and confinement taken into account. It is proved that the proposed theoretical approach to finite-size effects on the heat capacity of liquid 4He near the ?-point gives results which are in a good quantitive accordance with the high-resolution experimental data for a broad interval of diameters ranged from 30 nm to 8.17 ?m in cylinder geometry of mesopores and for thin helium films ranged in thickness from 48 nm to 57 ?m. The neutron optics methods are applied to theoretical studies of the critical properties of confined liquids. The problem of propagation of the neutron beam in a non-uniform liquid at restricted geometry is solved. The form of refractive index ellipsoid is studied and possible experimental consequences of neutron refraction in confined liquids are discussed. A general approach to the notion of the universality classes is presented for confined systems of different nature. The following applications to medical and biological systems are studied: (a) the model of the choline receptor being of a great importance for a deeper understanding the process of cell-to-cell communication (synaptic transmission of information); (b) the dependence of the light molecular scattering spectrum (namely, the widths of the central Rayleigh line and Mandelstam-Brillouin components, the Landau-Placzek relation) on the temperature variable and geometrical factor in water suspensions of plasmatic membranes as well as (с) the temperature and size dependence of the width of quasi-elastic peak in neutron scattering data and the diffusion coefficient obtained for membrane structures.