CAVITY FORMATION ENERGY IN HARD-SPHERE FLUIDS - AN ASYMPTOTICALLY CORRECT EXPRESSION

Exact geometrical relations valid for hard sphere (HS) fluids are used to derive analytical expressions for the cavity formation energy equa l to the free energy cost of insertion of a HS solute into a HS solven t and the contact value of the solute-solvent pair distribution functi on (PDF) in the limit of the infinite solute dilution. In contrast to existing relations from the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state, the derived expressions are self-consistent and result in correct asymptotics when the solute size goes to infini ty. The proposed equations are tested against Monte Carlo simulations at diameter ratios d in the range 1 less than or equal to d less than or equal to 3.5 and three reduced densities 0.7, 0.8, and 0.9. The BMC SL theory is shown to systematically underestimate contact PDF values as compared to simulations both for finite solute concentrations and i n the infinite dilution limit calculated by extrapolation of the resul ts obtained at several concentrations. These infinite-dilution values of the solute-solvent PDF at contact calculated from simulations are i n excellent agreement with the analytical expression derived in the pa per. An analogy to the BMCSL equation for HS mixtures is used to exten d this equation into the range of finite concentrations of the solute. The proposed equation is found to agree well with our simulation resu lts. (C) 1997 American Institute of Physics.