Abstract
A solution of the diffusion equation for a reversible redox electrochemical reaction in the presence of only one species (the reactant) and in the absence of products at the initiation of the reaction for a square wave perturbing potential is presented. The solution furnishes the concentration profiles for reactant and product and their dependence on the time elapsed from the initiation of the halfcycle t′, on the frequency of the periodic potential, on the number of cycles, N, and on the symmetry of the signal. In addition, the dependences of the current on t′ and N, and that of the charge density on N, were obtained. Conclusions from the theory are experimentally verified by using the reversible [Fe(CN) 6] 4−/[Fe(CN) 6] 3− redox couple on platinum as a test reaction.
Highlights
INTRODUCTIONThe apphcatlon of periodic perturbmg potentials to electrodes up contact with electrolyte solutions produces different changes at the interphase depending on the potential limits (E, and E,), frequency (f) and time-symmetry of the perturbatlon[l-51 For a simple electrochemical reaction mvolvmg soluble species m solution, these changes can be assigned to modlficatlons of charging of the electrical double layer (nonfaradalc process) and vanatlon of local concentrations of reactant and product m the vlcmlty of the electrode caused by the faradalc process For the sake of slmphclty, one can consider as a first approach that the relative contrlbutlon of non-faradalc to faradalc processes IS negligible When the faradalc process proceeds by applying a penodlc perturbing potential and occurs under either diffusion or mtermedlate kinetics control, concentration gradients at the electrodesolution interphase are established Correspondmgly, pulsating diffusion boundary layers are built up for the concentrations of reactant and product involved m both the anodlc and cathodic reactions, respectively The general behavlour of each one of these layers for a fixed geometry depends on the properties of the solution, kinetic parameters of the electrochemical reaction and perturbing potential condltlons for a particular electrochemical reaction subjected to a time-symmetric square wave perturbing potential, which 1s potential-symmetric with respect to its equlhbrmm potential, the average thicknesses of the dlffuslon boundary layers for a constant number of cycles decrease as f mcreases[S]
When the square wave perturbing potential mvolves the condltlon rJz,> 100, the concentration profiles resulting for re and ox durmg the cathodic halfcycle are smnlar to those already known for reaction (1) proceeding under a constant potential step, le the concentration profile of ox increases monotonously with X* to approach the bulk solution concentration, whereas the opposite trend results for the concentration profile of re For both cases the dlffuslon layer becomes thicker as t’ increases oniy a slight change m the concentration profiles with N can be noticed
The concentratzon profiles of ox and re resulting m the followmg cathodic halfcycles, ze odd values of N, show a maxzmum value of c, and a mzmmum value of c, for small values oft’ The values of c, m the bulk of the solutzon decrease as N increases In thzs case one can observe that the maximal value of c, and the mmzmum value of c, tend to dzsappear as t’ increases
Summary
The apphcatlon of periodic perturbmg potentials to electrodes up contact with electrolyte solutions produces different changes at the interphase depending on the potential limits (E, and E,), frequency (f) and time-symmetry of the perturbatlon[l-51 For a simple electrochemical reaction mvolvmg soluble species m solution, these changes can be assigned to modlficatlons of charging of the electrical double layer (nonfaradalc process) and vanatlon of local concentrations of reactant and product m the vlcmlty of the electrode caused by the faradalc process For the sake of slmphclty, one can consider as a first approach that the relative contrlbutlon of non-faradalc to faradalc processes IS negligible When the faradalc process proceeds by applying a penodlc perturbing potential and occurs under either diffusion or mtermedlate kinetics control, concentration gradients at the electrodesolution interphase are established Correspondmgly, pulsating diffusion boundary layers are built up for the concentrations of reactant and product involved m both the anodlc and cathodic reactions, respectively The general behavlour of each one of these layers for a fixed geometry depends on the properties of the solution, kinetic parameters of the electrochemical reaction and perturbing potential condltlons for a particular electrochemical reaction subjected to a time-symmetric square wave perturbing potential, which 1s potential-symmetric with respect to its equlhbrmm potential, the average thicknesses of the dlffuslon boundary layers for a constant number of cycles decrease as f mcreases[S].
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