The analytical determination of kinetic parameters for a bimolecular EC mechanism from chronoamperometric data

Abstract

We study the dependence of chronoamperometric data on the kinetic parameters for a bimolecular reaction, characterizing the behavior of an electrochemical mechanism that pertains to lithium/sulfur dioxide batteries. The reaction entails first the reduction of a reactant O to a product R by an instantaneous charge transfer, followed by a homogeneous chemical reaction between O and R to produce an electrochemically inert product P. We model this by a semilinear reaction-diffusion system with discontinuous initial conditions and mixed Dirichlet and Neumann boundary conditions, and develop a procedure to extract from a single potential step experiment the forward and reverse rate constants for the reaction. To do so we define a function ${\mathcal{J}(t):=j(t)\sqrt{t}}$ , where j(t) is the current density from the chronoamperometric output, and use maximum principle and scaling arguments to exploit the location of the minimum of ${\mathcal{J}(t)}$ versus t.