Properties of solutions to the Yvon–Born–Green equation for the square-well fluid

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Abstract
The Yvon−Born−Green equation under the superposition approximation was solved numerically for a system of molecules interacting via the square−well potential with σ2/σ1 = 1.85, for a temperature−density range bounded by 0 < ϑ < 0.55 and 0 < λ0 < 13. Solutions of the YBG equation throughout this range were found to be unique, and upon examination of the resulting thermodynamic properties, a gas−liquid coexistence region was located and evidence for a high−density, low temperature fluid transition was found. Relative to the range of ϑ − λ0 considered, the down−range properties of the pair−correlation function were used as a guide in carrying through a formal analysis of the YBG equation using basic theorems on the existence and uniqueness of solutions of nonlinear integral equations. Lower bounds on the limit of stability of the pure gas and liquid phase were identified and correlated with the thermodynamic behavior determined via numerical solution of the YBG equation.