On extrapolation of virial coefficients of hard spheres

TL;DR

This paper discusses and compares methods for extrapolating virial coefficients of hard spheres, proposing estimates for higher coefficients and exploring their potential behavior beyond known values.

Contribution

It introduces new extrapolation techniques for virial coefficients and provides estimated values for coefficients beyond the 14th, suggesting possible negative values at large n.

Findings

Estimated values for B11 to B15 virial coefficients.

Potential decrease and negativity of virial coefficients beyond B14.

Extrapolation methods applicable to other scientific fields.

Abstract

Several methods of extrapolating the virial coefficients, including those proposed in this work, are discussed. The methods are demonstrated on predicting higher virial coefficients of one-component hard spheres. Estimated values of the eleventh to fifteenth virial coefficients are suggested. It has been speculated that the virial coefficients, B_n, beyond B_{14} may decrease with increasing n, and may reach negative values at large n. The extrapolation techniques may be utilized in other fields of science where the art of extrapolation plays a role.