Chemistry Reference
In-Depth Information
Velocity
Concentration
δ
H
V
max
C
*
Distance from surface
δ
FIGURE 6.6
Diffusion.layer.(
δ
).and.hydrodynamic.(Prandtl).boundary.layer.(
δ
H
),.at.a.rotating.electrode.
In.fact,.the.hydrodynamic.boundary.layer,.
δ
H
,.also.called.Prandtl.layer,.that.is,.the.layer.with.a.
velocity.gradient,.is.connected.with.the.diffusion.layer.
δ
.(Equation.6.10):
1 3
/
D
v
d
≈
2
d
.
(6.10)
H
.
where. “
v
”. means. the. kinematic. viscosity. in. this. formula.. Assuming. some. standard. values. (
D
. =.
10
−5
cm
2
.s
−1
,.
v
.=.10
−2
.cm
2
.s
−1
),.the.formula.gives.an.estimation.of.
δ
H
.≈.5
δ
.(see.Figure.6.6).
When.performing.DC.voltammetry.at.a.rotating.electrode,.the.limiting.current.of.a.mass.transport-
controlled.system.depends.on.the.angular.velocity,.
ω
.=.2
πN
.(where.
N
.is.the.number.of.revolutions.per.
second).as.expressed.in.the.Levich.equation,.which.is.given.here.for.a.reduction.process.(Equation.6.11):
*
2 3
/
−
1 6
/
1 2
/
i
=
0 620
.
⋅
n F A C D
⋅
⋅
⋅
⋅
⋅
v
⋅
w
.
(6.11)
.
l c
,
O
O
In.this.equation,.“
v
”.is.the.kinematic.viscosity.
6.1.4.4 Microelectrodes
Microelectrodes. are. electrodes. where. the. diffusion. layer. thickness. (
Dt
)
1/2
. is. much. larger. than. the.
radius.
r
o
.of.the.electrode..As.a.consequence,.the.electrode.area.is.too.small.to.produce.a.continuously.
increasing.depletion.of.its.surrounding.and.therefore.leads.to.steady-state.conditions.where.the.cur-
rent.does.not.drop.to.zero.but.to.a.constant.value..Typical.microelectrode.diameters.are.in.the.rang.
of. 2-10.μm.. When. applying. a. constant. potential. (potential. step. experiment). to. a. microelectrode,.
chronoamperometric.measurements.show.current.decays.at.the.beginning.with.a.constant.value.after.
some.time.(Equation.6.12)..The.term.1/
r
o
.that.is.responsible.for.this.is.called.spherical.correction:
1
1
*
i
t
= ⋅
n F A D C
⋅
⋅
⋅
+
.
(6.12)
r
p
⋅
D t
⋅
.
o
For.hemispherical.electrodes,.Equation.6.13.is.valid,.and.for.planar.disks,.the.factor.2
π
.has.to.be.
replaced.by.number.4:
*
i
t
→∞
=
2
p
⋅
n F D C r
⋅
⋅
⋅
⋅
o
.
(6.13)
.
Microelectrodes.with.small.diffusion.layers.allow.voltammetry,.with.rapid.scan.rates.still.providing.
sigmoidal.curves.rather.than.peak.shapes..Very.fast.scan.rates.(usually.larger.than.a.few.hundred.
V s
−1
).will.eventually.produce.peak-type.curves..As.the.ohmic.drop.is.of.small.inluence.only.(usu-
ally.less.than.1.mV.for.1.mM.of.electroactive.species),.the.use.of.a.supporting.electrolyte.is.often.
obsolete..For.similar.reasons,.even.the.use.of.a.reference.electrode.can.be.avoided.
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