Vapor-phase metastability and condensation via the virial equation of state with extrapolated coefficients

Recently reported virial coefficients for the Lennard-Jones model are extrapolated to very high order, and the results are used to study the behavior of virial equation of state (VEOS). Convergence of the VEOS is examined in the context of gas-phase metastability and condensation. Comparison to molecular simulation data shows that the VEOS can accurately describe the equation of state over much of the metastable region, and the stability limits of very low-order isotherms correspond well with simulation-based estimates of the spinodal densities. However, as higher-order terms are added to the density series, the VEOS becomes less capable of characterizing metastable states, and instead appears to be moving toward a description of condensation. The fully-summed VEOS based on virial coefficients extrapolated to infinite order abruptly ends in the metastable region with a branch-point singularity. This form represents the culmination of a sequence of curves in which the pressure reaches a maximum before turning downward, both more sharply and at lower density with increasing series order; the corresponding sequence of maxima converge to the point where the fully-summed VEOS diverges. Thus, the extrapolation-based fully-summed VEOS exhibits the qualitative features of condensation, but it fails to provide quantitative agreement with condensation densities established by molecular simulation. The shortcomings point to a need to better understand the behavior of the virial coefficients with increasing order, perhaps with consideration of the volume dependence of the cluster integrals on which the VEOS is based.