A very accurate hard sphere equation of state over the entire stable and metstable region

TL;DR

This paper introduces a simple, highly accurate analytical equation of state that describes the entire stable and metstable regions of hard sphere systems, unifying different amorphous states with a single model.

Contribution

The authors develop a novel analytical EoS based on potential energy landscape analysis that accurately covers both stable and metstable regions, including amorphous states.

Findings

Achieves high accuracy in modeling the entire stable and metstable regions.

Unifies description of gas, liquid, supercooled liquid, and glass states.

Can be extended to real systems using conventional methods.

Abstract

The hard sphere system plays a basic role in condensed matter physics and related fields, and equation of state (EoS) is the ultimate solution to its thermodynamic properties (1-3). Dozens of EoSs have been proposed since van der Waals historic work and many reliable EoSs are available for the stable fluid region (3). For the metstable region, all available EoSs are not accurate enough for various applications. It has been considered impossible to develop an analytical EoS for the entire stable and metstable region 4. By virtue of a potential energy landscape analysis combined with the Woodcock type EoS (2,5), here we show that a fairly simple analytical equation can be obtained to reproduce the compressibility of the entire region with high accuracy. Therefore, all four amorphous states of matter, gas, liquid, supercooled liquid and glass, can be represented with a single EoS. Examples are given to show that highly accurate EoS is necessary for applications in thermodynamic property or liquid structure predictions. By using conventional approaches, such as appending an attractive term of van der Waals type (6) or using the equation within the framework of perturbation theory (1,7), it can be extended to an EoS for various real systems, including supercooled liquids and glasses.