Microscopic surface tension down to molecular dimensions and microthermodynamic surface areas of molecules or clusters

Abstract

Surface tension, surface energy, and entropy of small droplets, n clusters, and of cavities in liquids for sizes down to a single molecule are obtained. Rigourous relations are derived that relate microsurface properties to the usual handbook properties of bulk liquids. The microvalues and their dependence on the ratio of the cluster, droplet, or cavity size to the average liquid molecular size are given for common solvents, polar and nonpolar, including alcohols, water, hydrocarbons, rare gas liquids, and liquid (or solid) metals. Microscopic values are less than bulk-planar values by around 40% for nonpolar liquids, and greater for polar liquids by around 60%. The n-cluster (or cavity) sizes ? at which the microsurface properties approach the bulk values within a desired percentage, e.g., 5%, are given. The ordinary, bulk thermodynamic properties of liquids are also related to new useful quantities: ’’microthermodynamic surface areas’’ of molecules from which, using the equations given, ’’experimental’’ geometric (van der Waals) surface areas of molecules are calculated. The molecular surface properties introduced in the theory of ’’solvophobic forces’’ by this author earlier are finding applications presently in areas like HPLC (’’high pressure liquid chromatogrphy’’), multicomponent adsorption from solution phase (e.g., purification of waters from trace carcinogens), large ion association, protein structure, and drug–biopolymer binding, as well as the earlier ones for the prediction of rates and equilibria in diverse solvents in physical organic chemistry. The microsurface properties given now apply also to the convex case, e.g., the n clusters in nucleation and in metal cluster phenomena.