Solutions of the Yvon-Born-Green equation for a system of square-well molecules at a temperature below the triple point

Abstract

The Yvon-Born-Green equation (with superposition approximation) is solved numerically for the pair correlation function for a system of molecules interacting via the square-well potential (with σ₂/σ₁ = 1·85), for an isotherm below the triple point, and over a broad range of densities. The correlation function data and attendant thermodynamics generated for this isotherm are compared with results reported previously by the authors for several supercritical and subcritical isotherms of the square-well fluid. To facilitate the interpretation of these results, particularly in those regions of (T, ρ) space where phase transitions may occur, a geometrical representation of the data is presented (motivated, in part, by recent work by René Thom), and the location of the triple point is discussed in terms of this construction. The differences anticipated between results reported here and those that would be obtained in an exact statistical mechanical analysis, are identified.