Scaled Particle Theory and the Efficient Calculation of the Chemical Potential of Hard Spheres in the NVT Ensemble

We propose and test a new method for calculating the chemical potential of a hard-sphere fluid using Monte Carlo calculations in the NVT ensemble, which we call the SP-MC method. The method employs ideas from scaled particle theory (SPT), including a recent new SPT result of Smith and Labík for hard-sphere mixtures. The method is based on the calculation of the chemical potential at infinite dilution of a series of hard spheres of smaller diameter than that of the system of interest. Using this easily obtained data in conjunction with theoretical considerations, the chemical potential of the hard-sphere system may be accurately obtained. The SP-MC method is more precise than any other currently available method, and it can be used up to extremely high densities, including into the metastable region.