Analytical solutions of integral equations for modelling of reversible electrode processes under voltammetric conditions

Mathematical procedure for analytical solutions of integral equations referring to a voltammetric experiment at a stationary planar electrode of reversible electrode processes is described. The procedure is based upon Laplace transforms and definition of an auxiliary function q(t)=∫0tI(τ)dτ, where I(t) is the faradaic current–time function. The auxiliary function q(t  ) represents the charge consumed in the course of the voltammetric experiment. The methodology is exemplified by considering simple charge transfer reaction, an ECi′ catalytic mechanism, and an electrode mechanism involving partial adsorption of both components of the redox couple. All solutions are derived in terms of integrals that need to be further numerically evaluated.