EQUILIBRIUM DOUBLE-LAYER THEORY

Abstract

Those electrolyte double-layer theories are reviewed and compared which involve detailed consideration of charge and potential conditions in the double-layer region. Separate consideration is given to those calculations where it may be a good approximation to treat all charges as continuously distributed and those where discreteness-of-charge effects must be invoked. Three conditions are analyzed: (1) that where there is no specific adsorption and the (solvent) molecules in the mono-molecular inner region of the double layer are all of the same type and close-packed; (2) specific ionic adsorption; and (3) specific adsorption of neutral substances. It is shown how previous treatments of (1) may be improved by including induced molecular polarization and average planar dipolar interaction effects. Careful attention is given to the calculation of the field which orients dipoles in the inner layer, and it is pointed out how the inclusion of planar depolarization alters the approach to dielectric saturation. Errors, defects, and simplifications in earlier continuous-charge treatments of specific ionic adsorption are discussed. Some difficulties arose from failure to distinguish properly mean fields, based on the continuous-charge approximation, and fields derived from the micropotential, a quantity derived from discreteness-of-charge considerations. It is concluded that presently available phenomenological treatments of specific ionic adsorption and the micropotential are inadequate since they generally involve improper calculations of the micropotential, ignore various charge discreteness effects, and employ oversimplified statistical mechanics. Comparison of previous treatments of specific adsorption of neutral substances again shows unwarranted simplification. In particular, it does not appear that the dipole moment and/or dielectric constant of adsorbed molecules can be extracted with any confidence by applying current theory to experimental data. An improved treatment of the problem is outlined which makes use of an approximate formula of Frumkin that treats unadsorbed and adsorbed regions in the double-layer separately but which is here generalized by coupling such regions together by planar interaction. Finally, a statistical treatment of the discrete adsorption problem is briefly described which is more nearly correct than the usual Boltzmann expressions in those situations where competition and saturation effects are important.