Relaxation time of memorial diffusion by chronoamperometry at a twin-electrode

The diffusion flux is known to be delayed owing to a finite propagation speed, called the memory effect or the second sound for thermal diffusivity. The delay was evaluated electrochemically at a closed-spaced twin-electrode from the transient current of the ferricinium ion, which was transported by diffusion toward the other facing electrode. The traveling period, t(p), from the one electrode to the other was obtained at various separations, w, between the two electrodes. The square-root of t(p) was linear with w, exhibiting an intercept. It is the intercept that reflects the memory effect. The diffusion equation with the memory, tau(partial derivative(2)c/partial derivative t(2)) + partial derivative c/partial derivative t = D(partial derivative(2)c/partial derivative x(2)), was solved analytically for potential step experiments to yield expressions for currents at the two electrodes, where tau is the relaxation time for the memory effect and D is the diffusion coefficient. The ;propagation period was expressed as t(p)(1/2) = 0.20wD(-1/2) + 0.764 tau(1/2). Applying the data of t(p) versus w allowed us to evaluate tau to be of the order of 1 ms. Values of tau decreased with an increase in concentrations of ferrocene, suggesting a participation in interaction between the redox molecules. The propagation speed defined by (D/tau)(1/2) was 0.03 cm s(-1). Electrochemical responses shorter than tau may be controlled by the finite propagation speed rather than electron-transfer rates.