Numerical calculations are performed on a dilute electrolyte solution in equilibrium with a charged surface, using the theory developed by Buff and Stillinger. The concentrations of adsorbed cations in the double layer (in the case of a negatively charged surface) are computed as a function of the electrostatic potential in the adsorption zone. It is found that a critical value of the potential exists, such that, for values of the potential more negative than the critical value, a phase transition in the double layer occurs to yield an almost closehyphen;packed layer of counterions. The results are discussed in the light of similar effects found in polyelectrolyte theory as well as of experimental results from nuclear relaxation studies. It is demonstrated that in the case of a mixed electrolyte solution (two monovalent cations and a common monovalent anion) the adsorbing surface will selectively adsorb the smallest cation below the threshold potential, even though the larger ion may predominate in the bulk phase. This effect is due largely to the short range (hard sphere) interactions.
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