LOW DIMENSIONAL STRUCTURES FORMATION ON ENERGETICALLY INHOMOGENEOUS SURFACE OF SEMIPERMEABLE MEMBRANES
The features of the structure of adsorption layers on the energetically inhomogeneous surface of biological membranes and semiconductor sensors are considered. On the basis of fundamental thermodynamic equations, it is shown that in the process of adsorption on an energetically inhomogeneous surface, a heterogeneous adsorption layer with the properties of a two-dimensional gas under constant surface pressure and a coordinatively saturated phase close in properties to the adsorption film are formed. It is shown that the structure of the coordination saturated phase has a fractal character with Hausdorff dimension 1 < H < 2, whereas the properties of the two-dimensional gas phase allow us to consider the phase transition and the formation of the gap line between the surface phases as a process of cluster growth with a fractal boundary in the process of diffusion of excited particles from the two-dimensional gas phase. Diffusion to the fractal boundary of the forming cluster is considered using the fractional diffusion operator, as a result of which the growth equation of a coordinatively saturated cluster of reduced dimension is obtained. On the basis of the obtained equation, the principles of mathematical modeling of transfer processes on the energetically inhomogeneous surface of sensors or biological membranes are developed.
Authors: A. I. Mamykin, M. N. Shishkina
Keywords: Adsorption, cell membrane, phase transition, diffusion layer, coordinatively saturated cluster, energetically inhomogeneous surface, low dimensional structures
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