Biomedical Engineering Reference
In-Depth Information
Finally, the heterogeneous kinetics at the electrode surface are
described by the Butler-Volmer (BV) expression
e
e
iFAkC kC
(
)
(3)
f
O
b
R
where
i
is the reduction current at the electrode (using the conven-
tion that
reduction
corresponds to a positive current),
F
is Fara-
day's constant,
A
is the area of the electrode, and the forward and
backward rates are given by
kk
0
exp
DK
f
f
(4)
0
kk
exp (1
D K
)
f
b
In the latter expressions
k
is the standard heterogeneous rate
constant,
D
is the transfer coefficient,
220
K
=
(
E - E
0
) is the over-
potential and
f = F/RT
with
R
the gas constant and
T
the tempera-
ture.
Steady-state requires that the rate of mass transport of O, the
rate of mass transport of R, and the net rate of electron transfer at
the interface be equal:
i
=
FJ
R
=
FJ
O
. Applying this condition turns
Eqs. (1), (2), and (3) into a set of three algebraic equations in three
unknowns (the current
i
and the two surface concentrations
C
O
e
and
C
R
e
). These are easily solved, yielding for the current
b
DK
f
b
(1
DK
)
f
Ce
Ce
i
O
R
ยท
FDb
(5)
DK
f
(1
DK
)
f
0
e
e
b
/
Ak
For the special case of a pure oxidation reaction,
C
O
b
= 0, this ex-
pression takes a simpler form,
i
i
lim
(6)
f
K
0
(1
DK
)
f
1
e
(
b
/
Ak
)
e
Here we also introduced the so-called diffusion-limited cur-
rent,
i
lim
, whose value is given by
i
lim
=
FDC
R
b
b
.
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