Geometrical Aspects of the Penetrable-Sphere Model

Abstract

It is shown that the potential energy of interaction in the penetrable‐sphere model may be decomposed into negative two‐body, four‐body, ··· potentials corresponding to attractive forces among the molecules, and positive three‐body, five‐body, ··· potentials corresponding to repulsive forces. These and related aspects of the interaction energy imply, via the potential distribution theory, a number of inequalities among the thermodynamic functions of the model fluid. It is also shown that the interaction potential is a homogeneous function of the coordinates of the molecular centers and of the sphere radius, from which there follow two virial‐like relations. The latter yield a geometric criterion for phase equilibrium in the model, as well as additional thermodynamic inequalities.