FREE-VOLUME IN THE HARD-SPHERE LIQUID

A method is developed for the efficient calculation of free volumes an d corresponding surface areas in the hard sphere system by extending a previous method for calculating, exactly, cavity volumes in sphere pa ckings. This method is used for the first time to evaluate the free-vo lume distribution of the hard sphere liquid over a range of densities near the freezing transition. From the distribution of free volumes, t he equation of state can be obtained from a purely geometric analysis, which permits the calculation of pressure in Monte Carlo simulations where the dynamic definition cannot be employed. Furthermore, the cavi ty-volume distributions are obtained indirectly from the free-volume d istributions in a density range where direct measurement is inadequate . Direct measurement of the first moment of the cavity-volume distribu tion makes it possible to calculate the chemical potential in the vici nity of the freezing transition.