Critical parameters of a LennardJones gas
Abstract
The critical parameters of a gas with molecules interacting via the LennardJones (6, 12) potential are calculated by analyzing the irreducible cluster integrals b_{l} of the fugacity expansions. The method used here has earlier been successfully applied to the Ising model, and locates the critical temperature T_{c} as the limit of the zeros of the cluster integrals b_{l}. The asymptotic behavior of b_{l} at T_{c} is numerically found, and from the fugacity series the critical pressure p_{c} and the critical density ρ_{c} are calculated. One can then deduce the correct shape of the critical isotherm pp_{c} ~ sgn(ρρ_{c})ρρ_{c}^{δ} and determine the related critical index δ. The ratio p_{c}ρ_{c}k_{B}T_{c} is found to be ζ(2+δ^{1})ζ(1+δ^{1}), where ζ(x) is the Riemann zeta function, and its universality is thus related to that of δ. The numerical values of the critical parameters are then compared with the experimental data on rare gases; the agreement is good and represents an improvement over the methods based on equations of state. This can be taken to be a strong support for the numerical conjectures about the behavior of zeros of b_{l} and the asymptotic behavior of b_{l}(T_{c}).
 Publication:

Physical Review A
 Pub Date:
 October 1976
 DOI:
 10.1103/PhysRevA.14.1542
 Bibcode:
 1976PhRvA..14.1542M