Critical parameters of a Lennard-Jones gas

Abstract

The critical parameters of a gas with molecules interacting via the Lennard-Jones (6, 12) potential are calculated by analyzing the irreducible cluster integrals b, of the fugacity expansions. The method used here has earlier been successfully applied to the Ising model, and locates the critical temperature T, as the limit of the zeros of the cluster integrals bi. The asymptotic behavior of b, at T, is numerically found, and from the fugacity series the critical pressure p, and the critical density p, are calculated. One can then deduce the correct shape of the critical isotherm pp, 0: sgn(pp, )~pp,~s and determine the reiated critical index 8. The ratio p, /p, k~T, is found to be g(2+5 ')/g(1+8 '), where g(x) is the Riemann zeta function, and its universality is thus related to that of 5. 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, and the asymptotic behavior of b, (T,).

100 Years of the Lennard-Jones Potential

“…A comprehensive review on the performance of the LJ potential for the rare gases is provided by Rutkai et al Belov discusses the different approximations for the compressibility factor Z using the (12, 6)-LJ potential, including higher-order contributions in the virial expansion . For the critical parameters of an LJ gas, see Majumdar and RamaRao . It is clear that any improvement on EOS simulations relies on more realistic interaction potentials including higher than two-body terms, such as the Axilrod–Teller–Muto potential. , …”

“…66 For the critical parameters of an LJ gas, see Majumdar and RamaRao. 67 It is clear that any improvement on EOS simulations relies on more realistic interaction potentials including higher than two-body terms, such as the Axilrod− Teller−Muto potential. 68,69 Concerning the EOS for mixtures of gases, as early as in 1927, Lennard-Jones and Cook considered a few atomic and molecular gas mixtures where experimental data were available.…”