Unusual, Non‐Cottrell Behavior of Ionic Transport in Thin Cells and in Films

Abstract

Transport of a single‐salt MX across thin‐layer solid/liquid electrolyte cells and corresponding membranes is treated with consideration of the bulk resistance and the resulting bulk voltage drop. The interfaces are reversible ionic or M/M+zcharacter, and X−z is blocked. The analysis uses floating boundary conditions but linearizes the nonlinear, implicit equations describing current, voltage, and transport parameters. Bulk resistance causes a major distribution of applied voltage between interfacial and bulk components. Modified Cottrell current‐time responses appear, in time‐region sequence, with ohmic, normal Cottrell, exponential, and steady‐state characteristics. Closely related problems are treated approximately, including impedances, e.g., small‐amplitude ac responses, of resistive films with simultaneous dc voltage applied and with simultaneous dc current flow; analysis of passive networks with dc‐voltage‐dependent circuit elements; and distribution of resistivity across small and large levels of concentration‐polarized thin‐layer films and cells.