On the Surface Tension of Chain-Molecular Melts: Relation to Bulk Properties

The existence of formal relations between functions describing equilibrium bulk and surface properties is well established. We consider this question in terms of the Simha–Somcynsky hole theory and the extensive experimental information on the equation of state and surface tension of chain-molecular fluids presented recently by Dee and Sauer, with some additions from the earlier literature. The scaled surface tension–temperature function is very well described by Guggenheim's empirical power expression. On the other hand we observe a linear relation between surface tension and the temperature-dependent hole fraction, derived from the equation of state. The coexistence of the ensuing temperature function and Guggenheim's expression leads to significant conclusions regarding the coefficients of the above surface tension–free volume relation, and the scaling temperatures of surface tension and equation of state. The results obtained have implications for predictive purposes based on equation of state information, and as a guide to further theoretical developments.