FLUCTUATIONS IN ELECTROCHEMICAL SYSTEMS .1. GENERAL-THEORY ON DIFFUSION-LIMITED ELECTROCHEMICAL REACTIONS

A model of the stochastic behavior of the electrochemical interface is presented when electrochemical reactions limited by diffusion of the reacting species occur on the electrode surface. The random fluctuations of the state variables (concentrations and voltage) are supposed to come from Poisson elementary noise sources which are directly acting on the elementary fluxes, either reactive or diffusive, of the particles. The evolution of the state variables is governed by Langevin equations obtained from the linearization of the nonlinear electrochemical equations deduced from the heterogeneous electrochemical kinetics. The Langevin noise sources are derived from the Poisson elementary noise sources. Their first and second order moments are calculated and appear to be coherent with the master equation approach. Finally, the control and observation variables are defined for the electrochemical interface and the power spectral density of the observable quantity (current or potential) are derived from the Poisson elementary noise sources.