Simulation-based equation of state of the hard disk fluid and prediction of higher-order virial coefficients

Abstract

We present new molecular dynamics results for the pressure of the pure hard disk fluid up to the hexatic transition (reduced density about 0.9). The data, combined with the known virial coefficients (up to B ₁₀), are used to build an equation of state, to estimate higher-order virial coefficients, and also to obtain a better value of B ₁₀. Finite size effects are discussed in detail. The ‘van der Waals-like’ loop reported in the literature in the vicinity of the fluid/hexatic transition is explained by suppressed density fluctuations in the canonical ensemble. The inflection point on the pressure–density dependence is predicted by the equation of state even if the hexatic phase simulation data are not considered.

Keywords:

• Hard disk
• Equation of state
• Virial coefficients
• Fluid phase
• Hexatic phase
• Finite-size effects

Acknowledgements

This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic under project LC512 (Center for Biomolecules and Complex Molecular Systems). This paper was presented at the Seventh Liblice Conference on the Statistical Mechanics of Liquids (Lednice, Czech Republic, June 11–16, 2006).