Understanding the critical properties of chain molecules

Abstract

The vapour-liquid equilibrium of n-alkanes is computed from a simple perturbation theory. A very accurate equation of state for the repulsive n-alkane chain is combined with a mean-field term which accounts for the contribution of attractive forces to the free energy. The theory correctly predicts the existence of a maximum in the critical density of n-alkanes. When differences in the energetic interactions between methane, methyl and methylene groups are included, a maximum in the critical pressure is found for ethane, in good agreement with experiment. The simplicity of the perturbation scheme allows for an analysis of the conditions that a chain model should possess in order to present maxima either in critical density or pressure. It is shown that the conditions needed for the existence of a maximum in the critical density are (1) overlaps between contiguous sites and (2) small differences in mass between monomer, exterior and interior sites. The conditions needed for the existence of a maximum in the critical pressure are (1) overlaps between contiguous sites and (2) small differences between the energy parameters of the monomer, exterior and interior sites. The presence of flexibility is not a requirement for the existence of maxima in the critical density or pressure and therefore rigid models may also exhibit them. The proposed theory, whereas quite simple, contains the minimum number of ingredients to explain the appearance of maxima in the critical density or pressure of n-alkanes and of more general chain models.