An analytical model of the random distribution of two varieties objects of on a two-dimensional plane with a hexagonal structure

Abstract

This work is devoted to the study of the equilibrium states of abstract two-phase systems taking into
account symmetries using the example of sorption of objects of two types on the hexagonal plane. To a first
approximation, such processes are controlled by a certain distribution coefficient, which can be easily measured
experimentally. However, the determination of the likelihood of the formation of conglomerates of the
same type of objects in this case cannot be so easily determined. This paper gives an exact solution to this
probabilistic problem, and also discusses the violation of statistical laws that can occur as a result of the interaction
of sorbed objects. The proposed method for constructing formulas can easily be generalized to other
symmetrical structures other than hexagonal, as well as to a different structure of sorption centers other than
the plane. The results of the work can be used to study exchange reactions in the problems of adsorption and
chemical equilibrium in the presence of certain symmetries in combination with a probability distribution.