Virial coefficients, equation of state, and solid–fluid coexistence for the soft sphere model

Abstract

Virial coefficients up to B ₈ are calculated for the soft-sphere model, with exponents n = 12, 9 and 6. It is demonstrated that for n = 12, the virial series truncated at B ₈ describes well the equation of state (EOS) of the fluid phase up to the freezing density, while for n = 9 and 6 the series departs from the correct behaviour for densities of 75% and 18% of the freezing density, respectively. For these cases Padé approximants provide a much improved description of the equation of state at high density. The EOS for these different exponent-n values are further improved by a one-parameter fit of each to corresponding simulation data, using a form consistent with the known virial coefficients. Fluid–solid coexistence properties are evaluated and the results are in reasonably good agreement with the more-recent literature values.

Keywords:

• virial equation of state
• soft sphere
• Mayer sampling Monte Carlo
• transition properties
• Padé approximation

Acknowledgements

Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for support of this research. Computational resources were provided by the University at Buffalo Center for Computational Research.