Chemically Modified Carbon Paste Electrodes - Electroanalysis with Carbon Paste Electrodes - page 106

The.thickness.of.the.mean.reaction.(diffusion).layers.inside.the.electrode.bulk.can.be.experimen-
tally.roughly.estimated.by.wiping.off.layers.of.the.carbon.paste.on.paper.until.no.parasitic.signal.
from.the.memory.effect.can.be.monitored..By.determining.the.mass.of.the.stripped.paste.and.via.
the.electrode.surface.and.the.speciic.mass.of.the.paste,.the.diffusion.layer.thickness.can.also.be.
evaluated.

4.4.2.2 Chemically Modiied CPEs
Let.us.consider.the.example.of.the.accumulation.of.mono-.and.divalent.metal.ions.via.ion.exchange.
at. a. vermiculite-modiied. CPE. [1080].. The. concept. developed. in. this. work. is. rather. general. for.
CPEs,.which.have.been.bulk.modiied.with.solid.modiiers.so.that.it.could.be.applied.also.to.other.
systems.accordingly,.as.notably.demonstrated.for.ion.exchange.at.zeolite-modiied.CPEs.[1114],.for.
metal.ions.binding.to.humic.acid-modiied.CPEs.[1694,1701],.or.for.electrodes.containing.function-
alized.silica-based.organic-inorganic.hybrids.[719].
For.the.respective.modeling,.two.distinct.cases.have.to.be.considered:.(i).the.one-to-one.reaction.
(binding.of.monovalent.ions).and.(ii).the.two-to-one.reaction.for.divalent.species..If.a.solid.modi-
ier. M .(i.e.,.vermiculite).is.to.be.added.to.carbon.paste,.it.will.also.appear.on.its.surface.at.a.certain.
surface.concentration,.[ M ] surf ..And.if.the.analyte.“ A ”.reacts.in.a.1:1.ratio.as.(i).with.the.modiier,.the.
reaction.can.be.described.as.shown.in.Equation.4.9:

A + M

surf ↔

AM . (4.9)

.

sol surf

where.the.subscripts.sol.and.surf.designate.the.solution.and.the.electrode.surface,.respectively..The.
corresponding.concentration.equilibrium.constant,. K ′,.is.deined.as

K = [ AM ] /[ ] A /[ M ] . (4.10)

′

.

surf,eq sol surf,eq

The.subscript. surf .indicates.surface.concentrations.and. eq .chemical.equilibrium.
The. dependence. of. the. voltammetric. current. response,. i A , eq ,. on. the. concentration. [ A ] sol . after.
attaining.chemical.equilibrium.(after.long.interaction.time.between.analyte.and.modiier).is.given.
by.Equation.4.11:

=

1 1

K i ′ − K ′ . (4.11)

*

* A max ,

[ A ] i

sol A eq ,

.

where. i A,max .corresponds.to.the.current.with.complete.saturation.of.all.modiier.on.the.surface.with.
the. analyte.. A. plot. of. the. inverse. concentration. of. the. analyte. in. the. solution,. 1/[ A ] sol ,. versus. the.
inverse.voltammetric.current.at.chemical.equilibrium,.1/ i A,eq ,.should.give.a.straight.line.with.inter-
cepts.of. i A,max .on.the.inverse.current.axis.and.− K ′.on.the.inverse.concentration.axis..Thus,. K ′.values.
can.be.estimated.
The.dependence.of.the.current. i A,t .on.the.accumulation.or.reaction.time.t.is.given.by

i = i

* [1 exp(

− − k

*

t * A [ ] )] . (4.12)

.

A,t A,eq v sol

where. k v .represents.the.velocity.constant.for.the.bimolecular.kinetics.of.the.accumulation.or.reac-
tion,.which.can.also.be.expressed.according.to.Equation.4.13:

di
dt

A t ,

= k ∗ [ A ] ∗ ( i − i ) . (4.13)

v sol A eq , A t ,

.