Stability of uniform electrode states in the presence of ohmic drop compensation

Abstract

It is known that the compensation of the ohmic solution resistance by means of a Haber–Luggin capillary (i.e. a reference electrode (RE) that probes the solution potential close to the working electrode (WE)) causes a global feedback that might destabilize the uniform electrode state. In this paper we demonstrate that the cell resistance which is compensated when placing the reference electrode (RE) on the axis of the cell and close to a ring-shaped working electrode (WE) manifests itself in the evolution equation of the local electrode potential in exactly the same way an external series resistor of the same magnitude but negative impedance would do. This implies not only that the strength of the global feedback can easily be measured and thus its impact on the system’s behavior predicted but also that any external electronic cell compensation exerts the same destabilizing global coupling on the system, independent of relative arrangement and geometry of the electrodes. Evidence of this statement is given in three steps: First, a general formulation of the global coupling for the mentioned electrode geometry in terms of the cell resistance and the compensated resistance is derived. Then the spatio-temporal dynamics of electrochemical systems in which the cell resistance is compensated (a) by a close RE and (b) by an external negative impedance are compared in realistic three-dimensional simulations as well as in experiments.