Accurate prediction of hard-sphere virial coefficients B6 to B12 from a compressibility-based equation of state.

Abstract

We derive an analytical equation of state for the hard-sphere fluid that is within 0.01% of computer simulations for the whole range of the stable fluid phase. In contrast, the commonly used Carnahan-Starling equation of state deviates by up to 0.3% from simulations. The derivation uses the functional form of the isothermal compressibility from the Percus-Yevick closure of the Ornstein-Zernike relation as a starting point. Two additional degrees of freedom are introduced, which are constrained by requiring the equation of state to (i) recover the exact fourth virial coefficient B4 and (ii) involve only integer coefficients on the level of the ideal gas, while providing best possible agreement with the numerical result for B5. Virial coefficients B6 to B10 obtained from the equation of state are within 0.5% of numerical computations, and coefficients B11 and B12 are within the error of numerical results. We conjecture that even higher virial coefficients are reliably predicted.