Course notes
173
limit ourselves in what follows to expressing the overpotential of an electrode
as a function of current density in the electrode and of the kinetic parameters
relevant to each regime.
4.2.2 – Pure-charge-transfer regime (extreme case)
This regime appears when the rate constants of diffusion and adsorption of the
electroactive species are much higher than the rate constant of electronic transfer.
L Exchange-current density
Consider the following electrode reaction at equilibrium:
Ox + ne m Red
The electrode is the site of two opposing reactions, each characterized by a
current density i 0,Red < 0 and i 0,Ox > 0 such that
i 0,Ox = | i 0,Red | = i 0
i 0 denotes the exchange-current density, which is expressed in A cm
−2
.
i 0,Red and i 0,Ox are given by the following expressions:
i
nF k [Red] e
and i
n Fk [Ox] e
0,Ox
Ox
0
E
0,Red
R ed
0
E
RT
n F th
RT
n F th
=
= −
−
a
b
where k Ox and k Red are the respective rate constants for the oxidation and reduction reactions and [Ox] 0 and [Red] 0 are the concentrations of Ox and Red
at the electrode, which are constant in their given phase. α and β denote the
anodic and cathodic transfer coefficients, respectively, with α + β = 1.
L Butler-Volmer equation
The current density i through a polarized electrode subjected to an overpotential η is the sum of the oxidation current i Ox and the reduction current i Red :
i = i Ox + i Red
The Butler-Volmer equation expresses i as a function of the overpotential as
follows:
i i e
e
0
RT
n F
RT
n F
=
−
η
η
−
a
b
`
j
L Electrode impedance Z
The electrode impedance is obtained by expanding the Butler-Volmer equation
in a Taylor series to linearize it and then applying a Laplace transform. We