Phase transition in a cell fluid model

Abstract

We propose a method of describing a phase transition in a cell fluid model with pair interaction potential that includes repulsive and attractive parts. An exact representation of the grand partition function of this model is obtained in the collective variables set. The behavior of the system at temperatures below and above the critical one is explored in the approximation of a mean-field type. An explicit analytic form of the equation of state which is applicable in a wide range of temperatures is derived, taking into account an equation between chemical potential and density. The coexistence curve, the surface of the equation of state and the phase diagram of the cell Morse fluid are plotted.

The equation of state of a cell fluid model in the supercritical region

“…One of the ways to obtain the latter is an analytical calculation of the grand partition function (GPF) of the system. As it had been already shown in [11,12], the GPF of the cell fluid model within the framework of the grand canonical ensemble is of the form…”

“…Clearly, this energy is of a repulsive nature and corresponds to the interaction between particles located in the same cell. In [11,12] we obtained a general functional representation of the grand partition function of the cell fluid model in the set of collective variables in the following form…”

“…In this way, it is possible to take into account the influence of long-range fluctuations, which is necessary for the description of critical behavior. To follow this purpose, we start from the expression of the grand partition function of the cell fluid in ρ 4 -model approximation, which is derived from (2.4) (see [11,12])…”

Using a Cell Fluid Model for the Description of a Phase Transition in Simple Liquid Alkali Metals

“…Here c is the linear size of each cell, N a is the number of cells along each axis. Values ρ j (η) are the occupation numbers of cells [14,10,6]. The interaction potential has the following form 12 is difference between two vectors l 1 and l 2 from a set…”

“…It enable to obtain the equation of state of the cell model in wide range of temperatures below and above the critical point. Particular analytical results were conducted with use of the Morse potential U (r) = e −2(r−R 0 )/α − 2 e −(r−R 0 )/α (1) The consequence of the approach [8,10] is a restriction of the ratio between the coordinate of minimum R 0 and effective reach α of the interaction potential R 0 /α < 4 ln 2. However according to numerical results [4,12] this ratio exceeds R 0 /α = 4 ln 2 for real substances, in particular, for fluid metals.…”