Evaluation of second osmotic virial coefficients from molecular simulation following scaled-particle theory

We report a scaled particle theory-based method for evaluation of second osmotic virial coefficients from molecular simulations of dilute species in solution. In this method, we evaluate the work associated with growing a cavity in solution that is perfectly permeable to the solvent but is completely impermeable to the solutes, thereby establishing an osmotic stress between the cavity interior and exterior. Extrapolating our results to determine the solute concentration in contact with a cavity with an infinite radius, we are able to evaluate the solute osmotic pressure and second osmotic virial coefficient. A finite size correction is introduced to account for the impact of effectively concentrating the solutes in the periphery of the simulation box with increasing cavity size. We demonstrate the utility of the proposed method by evaluating second osmotic virial coefficients for methane in water as a function of temperature. The approach proposed here provides a physically transparent route for calculation of second osmotic virial coefficients by direct interrogation of simulation configurations without having to explicitly evaluate the long-range integral over solute-solute correlations required following McMillan-Mayer theory.