Instrumental Measurements with Carbon Paste Electrodes, Sensors, and Detectors - Electroanalysis with Carbon Paste Electrodes - page 127

log i

Cathodic
branch

Anodic
branch

-4

-5

α C n
59

α A n
59

Slope - ———

Slope ———

-6

log i 0

E - E eq

-300 -200 -100 100 200 300 mV

FIGURE 6.3 Tafel.plot.for.symmetric.cathodic.and.anodic.branches.(with. C O .=. C R .and. α .=.0.5).

size,. i 0 ,.but.of.different.sign),.the.counter.reaction.can.be.neglected..Thus,.the.logarithmation.of.the.
corresponding.term.of.the.Butler-Volmer.equation.yields.the.Tafel.equation.(Equation.6.6):

a ⋅ n F

R T

⋅ ⋅ h

ln i = ln 0 i − . (6.6)

⋅

.

where.“ α ”.means.the.transfer.coeficient,.either.for.the.reduction.( α C ).or.for.the.oxidation.( α A ).with.
α C .+. α A .=.1..An.example.of.a.Tafel.plot.is.shown.in.Figure.6.3..The.product. α ·. n .can.be.evaluated.
from.the.slope,. i 0 ,.from.the.extrapolated.intercept.

6.1.4 d iFFusion l ayer

6.1.4.1 Diffusion Coeficients
Diffusion.can.be.described.by.the.Fick.laws.(see.Equation.6.2),.where. D .represents.the.diffusion.
coeficient..In.aqueous.solutions.at.room.temperature,.it.is.very.similar.for.common.ions.and.ranges.
between.6.×.10 −10 .and.2.×.10 −9 .m 2 .s −1 ..Biological.molecules,.which.are.usually.larger.and.clumsier,.
show. D -values.of.10 −11 .to.10 −10 .m 2 .s −1 .

6.1.4.2 Macrosized Stationary Electrodes
In.case.the.electrode.surface.is.large.with.respect.to.the.solution.volume,.a.diffusion.layer.is.formed.
increasing.with.time..With.disk-shaped.electrodes,.planar.diffusion.with.a.direction.perpendicular.
to.the.electrode.surface.is.the.dominating.type.
When.applying.a.potential.to.macroelectrodes,.where.a.diffusion-controlled.faradic.process.occurs.
to.its.full.extent.(potential.step.experiment),.the.measured.current.(chronoamperometry;.i.e.,.measure-
ment.of.current.in.dependence.of.time).decreases.according.to.the.Cottrell.equation.(Equation.6.7):

D

*

O

− 1 2 . /

i t ( ) = ⋅ n F A C ⋅ ⋅ = const ⋅ t (6.7)

O

⋅ t

p

.

Here,.the.subscript.“ O ”.stands.for.the.oxidized.species.in.case.of.a.reduction,.and.the.asterisk.means.
the.bulk.concentration..With.suficiently.long.periods,.the.current.will.drop.to.neglectible.values,.
which.means.practically.to.0..Cottrell.behavior.can.be.exploited.for.estimating.“ D ”.with.known.“ n ”.
or.vice.versa.