Modeling of processes in the surface nanolayers of solids for interfacial interactions
Yuzevych V. M.1, Koman B. P.2

 1 Grygoryi Karpenko Physicomechanical Institute National Academy of Science of Ukraine, 5, Naukova Str., 79601 Lviv, Ukraine
2 Franko Lviv National University, faculty of electronics and computer technologies, 50, Dragomanova Str., 79005 Lviv, Ukraine
E-mail of corresponding: sonce_28@ukr.net 
The traditional approach of quantitative description of the interfacial interactions usually involves finding energy options of the interfacial interaction and calculation physical characteristics of surface layers. These physical characteristics are characterize the spatial (coordinate) distribution of charges, mechanical stress inside double layer, thickness of interacting phases, surface charge, etc. Also they interconnect state parameters in the relevant state equations. It is clear that adequate values of the such type of characteristics should match the main real energy characteristics of the surface layers, such as the surface tension h and the surface energy.
The aim of this work is to develop a mathematical model to determine the physical constants of materials in state equations, taking into account internal mechanical stresses caused by the redistribution of the conduction electrons. This model based on the principles of surface physics and thermodynamics of nonequilibrium processes without the use of cumbersome approaches of statistical physics.
 As the model object of research we choose a defect-free uniform metallic deformed elastic sphere of radius R. The research subject is the macroscopic correlations of surface physics and thermodynamics of nonequilibrium processes, which used to determine surface tension and energy.
 We formulate one-dimensional correlations for modeling mechanical stress and redistribution of electric charges (free for metals and related to semiconductor or insulator) with r coordinate, where r - radius vector of a point in a spherical coordinate system. The sphere (Vm area, r < R) is placed in a uniform inert gas environment (Vc area, r > R), which pressure is equal p = 100 kPa. The electric double layer generated conduction electrons and metal ions and located on the sphere surface on the spherical ring, which thickness h (R > r > R-h) [1].
 We simulate the metal sphere using two-component homogeneous solid environment consisting of two continuous continuums: the conduction electrons and grid ions, for which carried out the hypothesis of continuity and local thermodynamic equilibrium [2,3].The electric double layer is formed on the border of metal (the sphere) and external inert environment. This layer corresponds to the gradient of the electron density in the small border layer (thickness is less than 20 nm) [1]. During this process the electric shells of the thin border atoms are deformed. These deformations are manifested in the change of grid parameters. Based general ideas surface physics and continuum mechanics we put the deformations of atoms in correspondence to the mechanical stresses. Also we consider the distribution of electrical charges and mechanical stress are interrelated. To find the distribution of electrical charges and mechanical stress in a thin surface layer of metal we use Poisson's equation (for electrical charges) of the balance of items of solids and determination of surface tension and energy.
 Using basic equations of surface physics and thermodynamics of nonequilibrium processes we developed a mathematical model to determine the physical quantities characterizing the redistribution of conduction electrons (related charges) and mechanical stress in the surface layer of metal (semiconductor) which correspond them. The presented model takes into account the condition of the dynamic quasiequilibrium of conduction electrons (related charges) in the double electric layer on the metal surface (semiconductor). On the basis of the proposed model we developed the method of determining the physical characteristics of the material which including in the linear state equation (physical equation), the boundary conditions for the chemical potential F0(Zc) and mechanical stress x. Also we determined the most important physical quantities for metal surface - capacitance of the double layer С and the Galvani potential , which can be used to diagnose structural elements in aggressive environments, as well as to determine the energy characteristics of the surface and interphase layers.

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