Line of charges in electrolyte solution near a half-space I. Counterion condensation

The effect of a half-space on counterion condensation around a line of charges in electrolyte solution is examined in the framework of Debye-Hückel electrostatics. The half-space substrate is allowed to be a conductor, a dielectric, or a semiconductor. Counterions are predicted to be released completely as the line of charges approaches a conducting substrate. When it approaches a dielectric substrate, depending on the ratio of solvent to substrate dielectric constant, there are three possibilities: (1) epsilon(sol)/epsilon(sub) < 1; the counterions are partially (or completely) released; (2) epsilon(sol)/epsilon(sub) = 1; the amount of condensation remains unchanged; and (3) epsilon(sol)/epsilon(sub) > 1; more counterions condense. Depending on the relative magnitude of screening lengths in the semiconductor and in the solution, its effect on condensation follows either that of a metal or that of a dielectric. For the case of a moderately doped silicon substrate, condensation is predicted to be similar to that for a dielectric.