Adsorption of large ions from an electrolyte solution: a modified Poisson-Boltzmann equation

The behavior of electrolyte solutions close to a charged surface is studied theoretically. A modified Poisson-Boltzmann equation that takes into accou nt the volume excluded by the ions in addition to the electrostatic interac tions is presented. In a formal lattice gas formalism the modified Poisson- Boltzmann equation can be obtained from a mean-field approximation of the p artition function. In an alternative phenomenological approach, the same eq uation can be derived by including the entropy of the solvent molecules in the free energy. In order to visualize the effect of steric repulsion, a si mple case of a single, highly charged, flat surface is discussed. This situ ation resembles recent adsorption experiments of large ions onto a charged monolayer. A simple criterion for the importance of the steric effects is e xpressed in terms of the surface charge density and the size of the ions. I t is shown that when these effects are important a saturated layer is forme d near the surface. A modified Grahame equation relating the ion concentrat ion at the surface to the surface charge density is obtained. (C) 2000 Else vier Science Ltd. All rights reserved.