On the applicability of the van der Waals potential E=−η/Vm to chain molecule liquids

A modified form of the van der Waals expression for the attractive intermolecular potential E=−η/Vm has often been used to take account of the acentric character of the potential function, where V is the volume, η a mean-field parameter representing the strength of the interaction field, and m an empirical parameter, usually a constant in the range 1-2. In this article, we have attempted to examine the validity or limitation of this expression in terms of the relevant equation of state terms such as pressure, volume, temperature, and thermal pressure coefficient. The parameters m and η in the equation were estimated separately. A series of n-alkanes including polyethylene, polyoxyethylene, and a segmented dimer compound capable of forming a liquid crystal were investigated. Strictly speaking, the accuracy of the expression was found to be guaranteed only in a limited range of temperature and volume. An interesting behavior was found for m and η in the LC state. Importance of the analysis on anisotropic liquids such as LCs is emphasized.