Free volume in the hard sphere liquid
A method is developed for the efficient calculation of free volumes and corresponding surface areas in the hard sphere system by extending a previous method for calculating, exactly, cavity volumes in sphere packings. This method is used for the first time to evaluate the free-volume distribution of the hard sphere liquid over a range of densities near the freezing transition. From the distribution of free volumes, the 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 cavity-volume distributions are obtained indirectly from the free-volume distributions in a density range where direct measurement is inadequate. Direct measurement of the first moment of the cavity-volume distribution makes it possible to calculate the chemical potential in the vicinity of the freezing transition.
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