Computer simulation of the chemical potentials of binary hard-sphere mixtures

An efficient, recently proposed, method for calculating the chemical potentials of hard-sphere fluids up to very high densities by computer simulation is applied to the case of binary additive hard-sphere mixtures. Mixtures are studied with diameter ratios 0.9, 0.6, and 0.3 at packing fractions up to eta = 0.49, for several mole fractions. This paper is believed to give the first direct calculation of the chemical potentials of such mixtures by computer simulation techniques. In addition, pair distribution functions are simulated and compressibility factors calculated from the contact values of these. More particles are used than in earlier works and many more configurations generated. The results are used to test the BMCSL equation of state and systematic deviations are found whose magnitudes increase in systems with large sphere size ratios at small concentrations of the larger component. Two additional routes are explored for calculating the chemical potentials. One is based on a new version of the Gibbs-Duhem equation that relates mole fraction derivatives of the chemical potentials at constant packing fraction. The other route utilizes only the contact values of the pair distribution functions. All three methods are in excellent mutual agreement.