Calculating the state equation of the cell fluid model

M. P. Kozlovskii, O. A. Dobush

Published 2016-04-28Version 1

We propose the method of calculating the grand partition function of multiparticle system, in which constituents interact with each other via potential, that include repulsive and attractive components. The cell model, which was introduced to describe critical phenomena and phase transitions, is used to provide calculations. According to this model, total volume $V$ of a system, is divided into $N_{v}$ elementary cells of volume $v = V / N_{v}$, each of which can host an arbitrary number of particles. Only a form of interaction potential as well as values of its parameters both with a size of elementary cell are required to make computation within this method. The Morse potential is chosen as an interaction potential to provide estimations. We apply an exact procedure of integration over particles coordinates, that makes it possible to obtain an explicit expression for the grand partition function of the fluid cell model in the form of multiple integral over collective variables. As it can be seen directly from the structure of the transition jacobian, the present multiparticle model appeared to be different from the Ising model, which is widely used to describe fluid systems. The state equation, which is valid for wide temperature ranges both above and below the critical one, is derived in zero-order approximation. The pressure calculated for the cell model at temperatures above the critical one is found to be continuously increasing function of temperature and density. Isotherms of pressure as a function of density have horizontal parts at temperatures below the critical one. This fact states about occurance of the first order phase transition in the present model.