This Demonstration focuses on a one-step redox reaction (

) involving two soluble species

and

, taking place at the surface of a planar macroelectrode. Mass transport of both species is characterized as one-dimensional semi-infinite diffusion in the unstirred electrolyte. The initial concentration of species

is null. Because of the uncompensated resistance of the electrolyte, the variation of the electrode potential versus time is not linear, and the cyclic voltammogram differs from the ideal curve plotted without ohmic drop. In addition, correction of voltammetric data,

*a posteriori*, is not the appropriate method to recover the ideal voltammogram.

Dimensionless notation is used for the sake of generality, defining

,

,

and

. Here

is the standard rate constant (

) of the electrochemical reaction

, all symbols having their usual meaning;

is the symmetry factor for electron transfer in the forward direction (here reduction direction);

is the potential scan rate in V/s;

and

are the diffusion coefficients of redox species in

;

is the Faradaic current density in A/

;

is the electrode surface area in

;

is the uncompensated resistance in

;

is the controlled potential (with linear variation with respect to time); and

is the formal potential of redox couple, both potentials being given in V versus the reference electrode. Because of the uncompensated resistance

, the effective potential applied to the electrode is

. Its deviation from the controlled potential

is linearly proportional to the current flowing through the electrode.

The numerical solution of the diffusion equations, together with the boundary condition (electrochemical kinetics) at the electrolyte/electrode interface and the bulk conditions (constant concentrations with respect to time), is readily obtained using the so-called method of lines implemented in the built-in Mathematica function

NDSolve. The dimensionless current density

is computed versus time from the dimensionless flux of redox species at the interface. The cyclic voltammogram is the parametric plot of

versus the dimensionless potential

. You can vary the parameter

, the diffusion coefficient ratio

(in logarithmic scales) and the symmetry factor

, as well as the dimensionless resistance

.

The dimensionless coordinates of voltammetric peaks are evaluated in both the reduction (forward scan) and oxidation (reverse scan) directions, whenever such peaks exist.

[1] A. J. Bard and L. R. Faulkner,

*Electrochemical Methods: Fundamentals and Applications*, 2nd ed., New York: Wiley, 2001.