Equation of state of inverse power fluids

A new equation of state for the inverse power, r ^{? n} potential, fluid is proposed. It is derived on the basis of the local scaling behaviour of its structural properties, without referring to any perturbative scheme, and therefore recourse to an effective hard sphere diameter. It is shown that the general formula for the compressibility factor can be expressed as the product of three functions. The first represents the hard-sphere equation of state at the same packing fraction, and the other two incorporate the effects of the potential softness, again as functions of density. Using computer simulation results, explicit forms for these soft parts have been established, to give an approximate analytic expression for the r ^{? n} fluid equation of state. Two different regions, characterized by positive and negative softness ‘compressibility’ have been found.