Biomedical Engineering Reference
In-Depth Information
1
1
∫
k
Idt
=
zF
0
Since a constant current is required,
I
is independent of time and the equation re-
duces to
1
1
k
It
k
0.05[ ] * 1[hr] * 3,600[s/hr]
A
=
=
zF
2 * 96, 484.5[C/mol]
+
3
n
0.933
10
−
moles or 0.933 mmole
=
×
With most redox reactions, the rate of electron transfer can be accelerated by
increasing the potential at which the electrode is poised. Thus, the quality of reac-
tion rate is less important than in potentiometric bioelectrodes as sluggish electrode
reactions are switched on via the applied electrode potential. Typically the rate
constant for ET increases by a factor of 10 for every 120-mV increase in electrode
potential. As the potential is increased, the reaction reaches the point where the
rate is limited by the mass transport of reactant to the electrode. When the reac-
tion at the electrode surface is sufficiently fast, the concentration of analyte at the
electrode is zero, and a maximum overall rate of reaction is reached. This overall
rate is limited by the rate of mass transfer and can be obtained by combining Fick's
law of diffusion:
dC
InAFD
dx
⎛
⎞
=
(9.7)
⎜
⎟
⎝
⎠
x
=
0
where
C
is the concentration of the electroactive species,
A
is the electrode area,
D
is the diffusion coefficient, and
x
is the thickness through which diffusion has
to occur. Furthermore, zero thickness (
x
0) represents the electrode surface. The
rate of mass transport to the electrode surface depends on the bulk concentration of
analyte, the electrode shape and area, and diffusion conditions. The use of ampero-
metric electrodes is complicated by the regeneration of the electroactive component
from the analyte. The concentration of the electroactive component at the surface
of the electrode is affected by diffusion of the product through the enzyme layer, the
activity of the enzyme, and diffusion of analyte. Potentiometric sensors do not per-
turb the analyte concentration at the interface since there is no net consumption of
the latter. Hence, the mass transfer of analyte is not important. The potentiometric
signal can be corrupted by electronic noise. However, amperometric sensors have a
significant depletion of the analyte next to the sensor surface so the mass transfer
of analyte to the sensor from the bulk solution must be controlled.
=
