Evaluation of the second virial coefficient for the Mie potential using the method of brackets

TL;DR

This paper applies the method of brackets to evaluate the second virial coefficient for the Mie potential, providing a series expansion in temperature and analyzing its asymptotic behavior, consistent with known special cases.

Contribution

It introduces the method of brackets to analytically evaluate the second virial coefficient for the Mie potential, extending the approach to asymptotic limits.

Findings

Results align with the Lenard-Jones potential in special cases.

Provides series expansion of the second virial coefficient in temperature.

Analyzes asymptotic behavior as temperature approaches zero and infinity.

Abstract

The second virial coefficient for the Mie potential is evaluated using the method of brackets. This method converts a definite integral into a series in the parameters of the problem, in this case this is the temperature $T$. The results obtained here are consistent with some known special cases, such as the Lenard-Jones potential. The asymptotic properties of the second virial coefficient in molecular thermodynamic systems and complex fluid modeling are described in the limiting cases of $T \rightarrow 0$ and $T \rightarrow \infty$.