Comment on "Exact Analytic Second Virial Coefficient for the Lennard-Jones Fluid" (arXiv:0909.3326v1)

TL;DR

This paper corrects a previously published asymptotic expansion for the second virial coefficient of the Lennard-Jones fluid at low temperatures, providing the accurate mathematical expression.

Contribution

It identifies and corrects an error in the asymptotic expansion of the second virial coefficient for the Lennard-Jones fluid at low temperatures.

Findings

The corrected asymptotic expansion differs significantly from the previous one.

The new expression accurately describes the behavior of B_2(T) as T approaches zero.

Clarifies the mathematical form of the virial coefficient in the low-temperature limit.

Abstract

The asymptotic expansion for $T\rightarrow 0$ from Byung Chan Eu of $B_2(T)=-16\sqrt{2\pi}v_0e^{\varepsilon\beta}(\varepsilon\beta)^{3/2} \biggl[ 1+\dfrac{19}{16\epsilon\beta}+\dfrac{105}{512(\epsilon\beta)^2}\dots \biggr]$ is wrong. The correct expression is $B_2(T)=-2\sqrt{2\pi}v_0e^{\varepsilon\beta}(\varepsilon\beta)^{-1/2}\biggl[ 1+\dfrac{15}{16\varepsilon\beta}+\dfrac{945}{512(\varepsilon\beta)^2} +\dots\biggr]$.