Adsorption isitherms for neutral organic compounds—a hierarchy in modelling Part IV. Charge of maximum adsorption—statistical mechanical basis

Abstract

The charge at which adsorption of organic compounds attains a maximum (σ max M ) at an electrochemical interface is analysed using several multi-state models in a hierarchical manner. The analysis is based on statistical mechanical results for the following models: (A) two-state site parity, (B) two-state multi-site, and (C) three-state site parity. The coulombic interactions due to permanent and induced dipole effects (using mean field approximation), electrostatic field effects and specific substrate interactions have been taken into account. The simplest model in the hierarchy (two-state site parity) yields the explicit dependence of σ max M on the permanent dipole moment, polarizability of the solvent and the adsorbate, lattice spacing, effective coordination number, etc. Other models in the hierarchy bring to light the influence of the solvent structure and the role of substrate interactions, etc. As a result of this approach, the “composition” of σ max M in terms of the fundamental molecular constants becomes clear. With a view to use these molecular results to maximum advantage, the derived results for σ max M have been converted into those involving experimentally observable parameters like C 0 , C 1 , E N , etc. Wherever possible, some of the earlier phenomenological relations reported for σ max M , notably by Parsons, Damaskin and Frumkin, and Trasatti, are shown to have a certain molecular basis, viz. a simple two-state site parity model. As a corollary to the hierarchical modelling, σ max M and the potential corresponding to it ( E max ) are shown to be constants independent of θ max or c org for all models. The implication of our analysis for σ max M with respect to that predicted by the generalized surface layer equation (which postulates σ max and E max variation with θ) is discussed in detail. Finally we discuss in passing σ min M and the electrosorption valency in this context.