Estimates of vapor pressure below the triple point for the LJ system

Vapor pressures are estimated for a full Lennard-Jones (LJ) potential system at three temperatures below the triple point. A Bennett Monte Carlo calculation of Helmholtz free energy differences for small LJ $n-$atom clusters is used to predict $\ln (\rho _{liq}/\rho _{1})$, the intercept at $n=\infty $, where $\rho_{liq}$ and $\rho _{1}$ are bulk liquid and monomer vapor number densities. The approximation that the vapor consists of monomers only provides an estimate of $\ln (P)/P_{c})$. The results are presented in a corresponding states plot comparison with experimental data for argon at higher temperatures, the extrapolated vapor pressure formula used by Iland \emph{et al} [K. Lland, J. W\"{o}lk and R. Strey, J. Chem. Phys. \textbf{127}, 54506 (2007)], and Monte Carlo results of Chen \emph{et al.} [B. Chen, J. I. Siepmann, K. J. Oh, M. L. Klein, J. Chem. Phys. \textbf{115}, 10903 (2001)] Such a plot provides a check on vapor pressure expressions extrapolated to low temperatures where no experimental data are available.