The thesis is devoted to development of a quantum-statistical theory of equilibrium characteristics and diffusion processes in spatially limited metal systems by using the reference system approach, Zubarev’s non-equilibrium statistical operator method, and functional integration method.
By using the semi-infinite jellium as a reference system, analytic equations for the thermodynamic potential and the s-particle distribution function of electrons of semi-infinite metal are obtained, taking into account discreteness of ion subsystem. These equations are the power expansions of “the difference potential.” It is shown that the non-locality of pseudopotential leads to the need to account for non-diagonal elements of the electron density matrix.
A new analytic equation for the thermodynamic potential of semi-infinite metal is obtained within the jellium model on the basis of which the chemical potential, internal and surface energies are calculated. An influence of the Coulomb interaction between electrons on the chemical potential and surface energy is estimated.
For the first time, the chemical potential and work function for a metal film which is placed either in the vacuum or on a dielectric substrate are calculated with correct accounting of the electroneutrality condition. An effect of the film thickness on the chemical potential and the work function is studied. The calculation of the chemical potential of electrons in a metal film has shown that taking into account the Coulomb interaction between electrons increases the oscillatory quantum size effect and that the correct account for the electroneutrality condition provides a correct behavior of the chemical potential and work function.
The effective potentials of the electron–electron, ion—ion and electron–ion interactions are calculated and an influence of the metal–vacuum separation plane on these potentials and local field correction are investigated.
A quantum-statistical theory of electro-diffusion and viscoelastic electron processes of semi-infinite metal is developed, taking into account the discreteness of the ion subsystem of the metal. The generalized equations are obtained taking into account dynamic screening. A non-equilibrium statistical operator in the Gaussian approximation and in the next approximation using dynamic electron correlations is found. The generalized equations of nonlinear hydrodynamics for non-equilibrium average values of electron density and momentum are obtained, which can be used to describe strongly non-equilibrium processes for the electron subsystem of semi-infinite metal.
A system of Cattaneo-type equations is obtained for the description of interaction of the gas phase with the catalytic metal surface, taking into account adsorption, desorption, and chemical reactions between adsorbed atoms. The generalized transport equations are obtained for the average non-equilibrium values of densities of non-adsorbed and adsorbed atoms for a consistent description of atomic reaction-diffusion processes in the system “metal–adsorbate–gas” within the Rényi statistics. The obtained equations are nonlinear and spatially inhomogeneous, both strong and weak non-equilibrium processes can be described by them.
A mathematical model of reaction-diffusion processes for the Langmuir–Hinshelwood mechanism on the metal catalyst surface is constructed, which enables us to take into account peculiarities of course of the chemical reactions of oxidation-type on the platinum catalyst surface. The mathematical model of reaction-diffusion processes of CO oxidation for the Langmuir–Hinshelwood mechanism on a two-dimensional surface of the platinum catalyst, which takes into account the finiteness of the desorption rate of the oxidation product (CO2) from the catalyst surface, is constructed.
The generalized transport equations are obtained, which consistently describe viscoelastic electron processes with diffusion-electromagnetic processes for atoms-promoters (magnetic dipoles) on the metal surface and with reaction-diffusion processes for the adsorbed atoms on the metal surface in catalytic processes.
An approach is developed for calculating the cross-sectional area of scattering of ionized atoms on the field ionization tip, which is a combination of the classical description of an atom’s approaching the tip and the quantum description of the ionization of an atom. Using this approach, the values of the cross-sectional area of scattering of ionized helium atoms are calculated, which are in satisfactorily agreement with experimental data.
New generalized transport equations with fractional derivatives for a classical system of particles within the Rényi statistics are obtained. In the case of diffusion processes, the generalized diffusion equations with fractional derivatives, in particular, the generalized diffusion equations of the Cattaneo-type, Maxwell–Cattaneo-type for systems with time and spatial nonlocality are obtained.
