A generalized van der Waals theory of solid-fluid equilibria for non-spherical molecules

Abstract

By making use of recently obtained theoretical and Monte Carlo simulation results for solid state thermodynamics and solid-fluid equilibria for systems of hard dumbbells a generalized van der Waals theory of solid-fluid equilibria has been formulated. The theory predicts how the temperature dependence of the solid-liquid (and vapour-liquid) equilibrium is influenced by non-spherical molecular shape for diatomic molecules. Two regimes of behaviour are identified, depending on whether the underlying hard dumbbell reference system freezes into a plastic crystal or an orientationally ordered crystal. The theory correctly predicts a decrease in the triple point temperature and density change on freezing between spherical molecules, such as argon, and slightly non-spherical molecules which freeze into plastic crystal phases such as nitrogen. An extension of the theory which includes a simplified treatment of the influence of quadrupolar interactions provides a plausible explanation for the relatively high reduced triple point temperature of carbon dioxide.

The phase diagram of the two center Lennard-Jones model as obtained from computer simulation and Wertheim’s thermodynamic perturbation theory

“…7. The results of this work are in line with the predictions of the mean-field theory proposed by Paras et al 63 Let us finish by discussing the phase behavior of the 2CLJ at very low temperatures. For the range of temperatures considered so far ͑above the triple point͒, the disordered solid phase was found to be the stable phase.…”

“…This conclusion holds for systems with bond lengths L*Ͼ0.4 ͑no plastic crystal phases are possible͒. 63 A marked difference is noted in comparison with the T t /T c ratio of the LJ monomer fluid (T t /T c ϭ0.687/1.31ϭ0.52). In summary, the triplepoint temperature is about 0.3 of the critical point in the case of 2CLJ fluids with L*Ͼ0.4, but it is 1/2 of the critical temperature in monomer LJ fluids.…”

“…It seems that in 2CLJ systems, the ratio T t /T c slowly increases with L* in the region where the stable solid phase is ordered, i.e., 0.4рL*Ͻ1, as was predicted some time ago using a mean-field approach. 63 For the model considered here, the 2CLJ with L*ϭ1, the disordered solid was found to be the stable solid phase for most of thermodynamic conditions. However, it has been found that at very low temperatures ͑substantially below the triple point͒, the stable solid phase is an ordered solid.…”

Molecular Modeling of Solid Fluid Phase Behavior

“…We established that this model has both orientationally ordered and orientationally disordered solid phases. Using the free energy of this model system as a reference system in a generalized van der Waals theory of the phase diagram gives a very nice qualitative description of the departures from the principle of corresponding states in the solid-fluid phase behavior of nonspherical molecules [8]. The effect of quadrupolar interactions was also investigated [5,6,9].…”

Solid-fluid equilibrium: new perspectives from molecular theory

“…The properties of hard dumbbells can be used as the reference system for a generalized van der Waals [38,48] treatment of the effect of molecular shape upon solid fluid equilibrium for systems with attractive intermolecular forces. This is accomplished via the following approximation for the Helmholtz free energy per molecule:…”