Biomedical Engineering Reference
In-Depth Information
E
1/2
) and (
E
1/2
-
E
3/4
), where
E
1/4
and
E
3/4
are the potentials where
the current is equal to ¼ and ¾ of the limiting current, respectively.
These parameters are compared to the numerical look-up table in
Ref. 112 to yield corresponding values of
k
0
and Į. Watkins et al.
used this method to determine the rate constant for the oxidation of
the ferrocenylmethyltrimethylammonium cation (TMAFc
+
).
44
Watkins and White
113
also studied the oxidation of hexachloroio-
date (III) anion (IrCl
6
3-
) in either the presence or absence of sup-
porting electrolyte. Interestingly, they found that the heterogene-
ous rate constant increases by an order of magnitude in the pres-
ence of supporting electrolyte compared to the conditions where
no salt is present. In a separate study,
114
they investigated the ki-
netics of ion-pair formation between the IrCl
6
3-
and the cation of
the supporting electrolyte (K
+
, Ca
2+
and tetraethylammonium
(TEA
+
)) and directly observed discrete oxidation waves for free
and ion-paired IrCl
6
3-
. More recently, Li et al.
52
have also used
electrodes as small as 1 - 3 nm to measure the rate constants for Fc,
FcCH
2
OH and IrCl
6
3-
. The values they obtained are in general
agreement with previous studies, although they obtained signifi-
cantly higher values for the transfer coefficient Į. While most
studies have employed Pt nanoelectrodes, Velmurugan et al
115
have also studied fast heterogeneous kinetics on Au nanoelec-
trodes. Their motivation was to probe the extent of adiabaticity of
electron transfer for various redox couples, by probing the effect of
the electrode material (and, hence, the density of states,
ȡ
F
, at the
Fermi level) on the rate. Apart from Ru(NH
3
)
6
3+
in KCl and KF, all
other outer-sphere redox couples (Fc, FcCH
2
OH and tetrathiaful-
valene) had nearly identical rates on both Au and Pt electrodes.
Zevenbergen et al.
116
used nanoscale TLCs with electrode
spacing
z
= 50 nm to determine the rate constant for Fc(CH
2
OH)
2
in KCl and NaClO
4
. The current densities at electrodes in these
TLCs were equivalent to those obtained at a 0.016 ȝm
2
hemispher-
ical electrode.
III. THE MESOSCOPIC REGIME
We have heretofore considered cases in which the concepts and
approximations that are used to describe electrochemistry at UMEs
can be applied without modification to nanoscale electrodes. As
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