Two-state model for adsorbed solvent with and without adsorption of a neutral polymer species: a statistical mechanical treatment accounting for local order

Abstract

The implications of the zeroth (random) approximation in the statistical mechanical treatment of an adsorbed monolayer consisting of “up” and “down” solvent molecules, with and without the further presence of the polymer molecules of a neutral solute adsorbed in a single orientation, are briefly examined. Certain inconsistencies in previous work on the subject are thus evidenced. It is concluded that the role played by local order in affecting the inner-layer properties cannot be disregarded. The above model of adsorbed monolayer is therefore re-examined taking local order into account via the quasi-chemical approximation. It is thus shown that an increase in attractive lateral interactions between adsorbed solvent molecules causes the single hump in the curve of the inner-layer capacity versus the charge density on the metal to split into two distinct humps. This may explain the presence of two humps in the differential capacity curves of certain highly polar organic solvents [52,53]. Moreover, it is shown that a Frumkin isotherm behaviour over a wide range of surface coverages is to be expected, provided that solvent-solvent lateral interactions are more attractive than solvent-surfactant and surfactant-surfactant lateral interactions. Noting that the adsorption of several bulky organic molecules from aqueous solutions actually satisfies the Frumkin isotherm, an appreciable hydrogen bonding between adsorbed water molecules is postulated, and a very rough estimate of the effect of such a bonding upon the adsorption behaviour of weakly interacting surfactant molecules is provided.