This Demonstration shows on the dimensionless concentration profile for the species

involved in the electron transfer reaction

. The perturbation signal is a sinusoidal variation of the electrode potential. Two mass transport conditions in the electrolyte are taken into account: (1) finite-length diffusion with constant concentrations of redox species at the distance

from the electrode/electrolyte interface; and (2) restricted diffusion with an impermeable boundary condition (zero flux) at the distance

from the interface.

(i) the electrode is uniformly accessible,

(ii) the electrochemical reaction has reversible kinetics,

(iii) the double-layer charging current is neglected,

(iv) the faradaic impedance is calculated at the equilibrium potential of the electrode and

(v) both redox species

and

have the same initial concentrations and same diffusion coefficients.

Dimensionless quantities are defined for all variables/parameters; that is, the distance from the interface

, the time variable

, the interfacial concentration

, the angular frequency of sinusoidal signal

, its amplitude

and the diffusion impedance

. Here

denotes the initial concentration,

is the diffusion coefficient,

is the diffusion resistance and

is the Nernst constant, with

,

and

having their usual meanings.

Of course, semi-infinite diffusion conditions can be recovered at high frequencies, typically at

, irrespective of the permeable or impermeable boundary at

.

General rules for computing the species concentration versus distance and time are given in [1].

[1] C. Montella, J.-P. Diard and B. Le Gorrec,

*Exercices de cinétique électrochimique : II. Méthode d’impédance*, Paris: Éditions Hermann, 2005 pp. 237.