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

TL;DR

This paper develops a new equation of state for the hard disk fluid using molecular dynamics data and virial coefficients, predicting higher-order coefficients and explaining phase transition phenomena.

Contribution

It introduces a simulation-based equation of state for hard disks, estimates higher-order virial coefficients, and clarifies the origin of the van der Waals-like loop near the fluid/hexatic transition.

Findings

New molecular dynamics data up to the hexatic transition density.

Estimated higher-order virial coefficients beyond B10.

Predicted inflection point in pressure-density relation.

Abstract

We present new molecular dynamics results for the pressure of the pure hard disk fluid up to the hexatic transition (about reduced density 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 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.