Frumkin-Butler-Volmer theory and mass transfer in electrochemical cells

Abstract

An accurate mathematical description of the charge transfer rate at electrodes due to an electrochemical reaction is an indispensable component of any electrochemical model. In the current work we use the generalized Frumkin-Butler-Volmer (gFBV) equation to describe electrochemical reactions, an equation which, contrary to the classical Butler-Volmer approach, includes the effect of the double layer composition on the charge transfer rate. The gFBV theory is transparently coupled to the Poisson-Nernst-Planck ion transport theory to describe mass transfer in an electrochemical cell that consists of two parallel plate electrodes which sandwich a monovalent electrolyte. Based on this theoretical approach we present analytical relations that describe the complete transient response of the cell potential to a current step, from the first initial capacitive charging of the bulk electrolyte and the double layers all the way up to the steady-state of the system. We show that the transient response is characterized by three distinct time scales, namely; the capacitive charging of the bulk electrolyte at the fastest Debye time scale, and the formation of the double layers and the subsequent redistribution of ions in the bulk electrolyte at the longer harmonic and diffusion time scales, respectively.