MODIFIED COTTRELL BEHAVIOR IN THIN-LAYERS - APPLIED VOLTAGE STEPS UNDER DIFFUSION CONTROL FOR CONSTANT-RESISTANCE SYSTEMS

Electrochemical systems that exhibit bulk ohmic resistances cannot be characterized accurately using the Cottrell equation. Under constant applied voltages, a gradual change in the reactant surface concentration from the initial bulk concentration to a final value, often approximately zero for large oxidizing or reducing potential differences, is noted at one interface. For the special case of a thin film with constant bulk resistance and reversible interfacial reactions, the potential drop across the system is given as a sum of the bulk (ohmic) contribution and the concentration overpotentials. For semi-infinite geometry, this condition replaces the traditional c(reactant) (interface, t = 0+) = 0 boundary condition, and a new set of equations has to be solved. Theoretical solutions, a digital simulation and an experimental verification are presented for the experimentally well known case of a fixed-site plasticized PVC membrane containing valinomycin. The results include expressions for current vs. time responses to applied voltage steps across the whole system, and corresponding concentration profiles within the cell or membrane.