Chemistry Reference
In-Depth Information
a rotating-disc configuration. Moreover, a transport-determined current is
proportional to the difference between the concentration in solution and
the concentration at the electrode surface. When the latter turns zero, the
current cannot increase any further and this is termed a limiting-current.
This is a simplification arising from the Nernst diffusion-layer concept. Pri-
marily, this applies to transport by diffusion, where the current according
to the first law of Fick is proportional to the concentration gradient of the
reacting component at the electrode surface. Nernst assumes that the con-
centration profile is linear in a large part of the depletion layer, bordering
the electrode surface. By extrapolating the linearised profile, a thickness of
the diffusion layer (depletion layer or enhancement layer for the reacting
component and the reaction product, respectively) can be calculated. This
notion has no real meaning due to the asymptotical extinguishing of the
depletion.
When comparing Equations 1.37 and 1.38, it is clear that it is the relation
of two parameters, namely the transport coefficient, m, and the formal reac-
tion rate constant k
0¢
(incorporated in k(
E
) in Equation 1.37; see also Equa-
tion 1.20), that decides whether the current is determined mainly by the BV
relation or by transport. In a voltammogram, the potential area in which
the BV relation applies decreases when k
0¢
increases relatively in relation
to m. In electrochemical terms, one speaks of an increase in the reversible
character of the voltammetric wave. When having sufficient positive (neg-
ative) potentials for an oxidation (reduction), transport mostly prevails.
Providing that the appropriate cell and/or electrode configuration is
present, transport-determined currents are very reproducible and suitable
for analytical purposes.
When transport is rate determining, the shape of the voltammetric curve
can, in a rather simple way, be deducted by means of the Nernst diffusion-
layer concept
44
. As an example, a solution is considered that contains oxi-
dising and reducing agent of the same redox system and where
n
electrons
intervene in the interconversion. As the potential is varied in a positive or
a negative sense starting from the equilibrium potential, the following can
be stated:
(
)
in
=
Fm
c
•
-
c
[1.39]
RR
(
)
i
=-
n cc
Fm
•
-
[1.40]
0
0
Transport coefficients of components of the same redox couple usually
display only very small differences, hence m
O
= m
R
= m is assumed. It must
be remembered that
c
and m are time-dependent parameters when no
steady-state electrode configuration is used.
When the potential sufficiently deviates from the equilibrium potential,
c
= 0 and the current attains a limiting value:
