Carnahan Starling type equations of state for stable hard disk and hard sphere fluids

TL;DR

This paper extends the Carnahan-Starling equation of state to D-dimensional hard particle fluids, deriving new equations that match recent virial coefficient data and improve accuracy over previous models.

Contribution

It introduces a generalized polynomial-based method to derive Carnahan-Starling type equations for D-dimensional hard particle fluids, including the hard disk and hard sphere cases.

Findings

New EoS for D=2 and D=3 match virial data and simulations

The equations improve upon previous CS-type models in accuracy

All derived EoS diverge at non-physical packing fraction=1

Abstract

The well-known Carnahan-Starling (CS) equation of state (EoS) [1] for the hard sphere (HS) fluid was derived from a quadratic relation between the integer portions of the virial coefficients, Bn, and their orders, n. Here we extend the method to the full virial coefficients Bn for the general D-dimensional case. We assume a polynomial function of (D-1)th order for the virial coefficients starting from n=4 and EoS are derived from it. For the hard rob (D=1) case, the exact solution is obtained. For the stable hard disk fluid (D=2), the most recent virial coefficients up to the 10th [2] and accurate compressibility data[3,4] are employed to construct and test the EoS. For the stable hard sphere (D=3) fluid, a new CS-type EoS is constructed and tested with the most recent virial coefficients [5,2] up to the 11th and with the highly-accurate simulation data for compressibility [6-8]. The simple new EoS turn out to be as accurate as the highest-level Pade approximations based on all available virial coefficients, and significantly improve the CS-type EoS in the hard sphere case. We also shown that as long as the virial coefficients obey a polynomial function any EoS derived from it will diverge at the non-physical packing fraction=1.