Analysis of simulated reversible cyclic voltammetric responses for a charged redox species in the absence of added electrolyte

We present an analysis of simulated cyclic voltammetric responses of a dissolved redox salt with no added supporting electrolyte. The redox system of interest is a reversible one electron transfer: A(zA) + e = BzA-1 Only the charged, oxidized species A(zA) and counterion X-zx are initially present in solution (analogous systems where the reduced species and counterion are initially present are not explicitly discussed); their relative concentrations are dictated by Z(A), Z(X), and the constraint of electroneutrality (systems where z(A) = 0 or 1 are not considered). Cyclic voltammetric responses are simulated assuming Nernst-Planck transport, and electroneutrality with perfect IR compensation (easily simulated but experimentally unattainable) and with partial IR compensation. Simulations assuming perfect compensation allow us to elucidate the change in the resistance, R-ref between the working and reference electrodes effected by changes in the depletion layer during the course of the cyclic voltammetric perturbation. Simulation of systems with (more realistic) partial compensation leads to an empirical linear equation which correlates E degrees with cathodic peak potential, E-pc: E-pc = E degrees + (RT/F)[b(z) - 1.347((F/RT)I-pc(1 - gamma)R-ref(0) )(0.929)], where I-pc is the cathodic peak current, R-ref(0) is the resistance of the bulk solution (prior to the CV perturbation) between the working and reference electrodes, and gamma is the fraction of that resistance compensated (by positive feedback) during the perturbation. The constant b(z) is a function of Z(A) (range -1000 to +1000) and z(x) (+/-1, +/-2) with weak dependence on D-X/D-A (range 0.5-2) when D-A = D-B (D-X, D-A, and D-B are the diffusion coefficients of species X, A, and B, respectively). The numerical parameters 1.347 and 0.929 remain constant for the ranges of charges and diffusion coefficients studied.