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Table of Content Interface structure Two-electrode cells and three-electrode cells Cyclic voltammetry Diffusion Convection Migration
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Electrochemistry MAE-212
Dr. Marc Madou, UCI, Winter 2016 Class III Transport in
Electrochemistry (I) Table of Content Interface structure
Two-electrode cells and three-electrode cells Cyclic voltammetry
Diffusion Convection Migration Interface structure IHL OHL l l l l
l l 1-10 nm
Solvated ions Electrode surface 1-10 nm The double-layer region is:
Where the truncation of the metals Electronic structure is
compensated for in the electrolyte. 1-10 nm in thickness ~1 volt is
dropped across this region Which means fields of order V/m The
effect of this enormous field at the electrode-electrolyte
interface is, in a sense, the essence of electrochemistry.
Two-electrode and three-electrode cells
Electrolytic cell (example): Au cathode (inert surface for e.g.
Nideposition) Graphite anode (not attacked by Cl2) Two electrode
cells (anode, cathode, workingand reference or counter electrode)
e.g. forpotentiometric measurements (voltagemeasurements) (A) Three
electrode cells (working, reference andcounter electrode) e.g. for
amperometricmeasurements (current measurements)(B). Non-polarizable
electrodes: their potentialonly slightly changes when a current
passesthrough them. Such as calomel and H2/Ptelectrodes Polarizable
electrodes: those with stronglycurrent-dependent potentials. A
criterion forlow polarizability is high exchange currentdensity
Two-electrode and three-electrode cells Two-electrode and
three-electrode cells
Inert metals (Hg, Pt, Au) Polycrystalline Monocrystals Carbon
electrodes Glassy carbon reticulated Pyrrolytic graphite Highly
oriented (edge plane, ) Wax impregnated Carbon paste Carbon fiber
Diamond (boron doped) Semiconductor electrodes (ITO) Modified
electrodes Potential window available for experiments is determined
by destruction of electrode material or by decomposition of solvent
(or dissolved electrolyte) Two-electrode and three-electrode cells:
activation control
At equilibrium the exchange currentdensity is given by: The
reaction polarization is then given by: The measurable current
density is thengiven by: For large enough negative overpotential:
(Butler-Volmer) (Tafel law) Two-electrode and three-electrode
cells: activation control
With a symmetry coefficient a >0.5the activation energy for the
reductionprocess is decreased while theactivation energy for the
oxidationprocess is increased. At a=0.5 the curve is symmetrical
inthat the anodic and cathodic portionsare equivalent.The dotted
blue curve isthe result of the same equation but witha=0.6. The
dashed green curve hasa=0.7. Two-electrode and three-electrode
cells: activation control
Tafel plot: the plot of logarithm of thecurrent density against the
overpotential. Example: The following data are thecathodic current
through a platinumelectrode of area 2.0 cm2 in contactwith an Fe
3+, Fe 2+ aqueous solution at298K. Calculate the exchange
currentdensity and the transfer coefficient forthe process. Slope
is a and intercept isa (=ln ie). In general exchange currents are
largewhen the redox process involves nobond breaking or if only
weak bondsare broken. Exchange currents are generally smallwhen
more than one electron needs tobe transferred, or multiple or
strongbonds are broken. Transport in Electrochemistry
The rate of redoxreactions isinfluenced by the cell
potentialdifference. However, the rate of transport tothe surface
can also effect or evendominate the overall reaction rateand in
this class we look at thedifferent forms of mass transportthat can
influence electrolysisreactions. There are three forms of
masstransport which can influence anelectrolysis reaction:
Diffusion Convection Migration Diffusion In essence, any electrode
reaction is aheterogeneous redox reaction. If its rate
dependsexclusively on the rate of mass transfer, then wehave a
mass-transfer controlled electrode reaction.If the only mechanism
of mass transfer is diffusion(i.e. the spontaneous transfer of the
electroactivespecies from regions of higher concentrations
toregions of lower concentrations), then we have adiffusion
controlled electrode reaction. Diffusion occurs in all solutions
and arises fromlocal uneven concentrations of reagents.
Entropicforces act to smooth out these uneven distributionsof
concentration and are therefore the main drivingforce for this
process. For a large enough sample statistics can be used topredict
how far material will move in a certain time- and this is often
referred to as a random walkmodel wherethe mean square displacement
interms of the time elapsed and the diffusivity: Diffusion The rate
of movement of material by diffusioncan be predicted mathematically
and Fickproposed two laws to quantify the processes.The first law:
this relates the diffusional flux Jo (ie the rate ofmovement of
material by diffusion) to theconcentration gradient and the
diffusioncoefficient Do. The negative sign simply signifiesthat
material moves down a concentrationgradient i.e. from regions of
high to lowconcentration. However, in many measurementswe need to
know how the concentration ofmaterial varies as a function of time
and this canbe predicted from the first law. The result is Fick's
second law: inthis case we consider diffusion normal toan electrode
surface (x direction). The rate ofchange of the concentration ([O])
as afunction of time (t) can be seen to be relatedto the change in
the concentration gradient. Fick's second law is an important
relationshipsince it permits the prediction of thevariation of
concentration of different speciesas a function of time within
theelectrochemical cell. In order to solve theseexpressions
analytical or computationalmodels are usually employed. Diffusion
The thickness of the Nernst diffusion layervaries within the range
mmdepending on the intensity of convection causedby agitation of
the electrodes or electrolyte. According to the definition of the
Nernstdiffusion layer the concentration gradient maybe determined
as follows: Where: C0 - bulk concentration;Cc -concentration of the
ions at the cathodesurface;c - thickness of the Nernst
diffusionlayer. Therefore the flux of ions toward the
cathodesurface: Each ion possesses an electric charge.The density
of the electric currentformed by the moving ions: Where: F -
Faradays constant, F = Coulombs; z - number ofelementary charges
transferred by eachion. The maximum flux of the ions may beachieved
when Cc=0 therefore theelectric current density is limited by
thevalue: Diffusion Homework II: derive the identity:
From activation control to diffusioncontrol: Concentration
difference leads to anotheroverpotential i.e.
concentrationpolarization: UsingFaradays law we may write also: At
a certain potential C s=0 and then: Cyclic Voltammetry In
voltammetry the potential is continuously changed as a linear
function of time. The rate of change of the potential with time is
referred to as the scan rate (v). In Cyclic voltammetry,the
direction of the potential is reversed at the end of the first
scan. Thus, the waveform is usually of the form of an isosceles
triangle. Cyclic voltammetry is apowerful tool for thedetermination
of formal redoxpotentials, detection of chemicalreactions that
precede or followthe electrochemical reactionand evaluation of
electrontransfer kinetics. An advantage is that theproduct of the
electron transferreaction that occurred in theforward scan can be
probedagain in the reverse scan. Diffusion: Cyclic
voltammetry
Scan the voltage at a given speed (e.g. from+ 1 V vs SCE to -0.1 V
vs SCE and back at100 mV/s) and register the current . At low
current density, the conversion ofthe electroactive species is
negligible. At high current density the consumption ofelectroactive
species close to the electroderesults in a concentration gradient.
Concentration polarization: Theconsumption of electroactive species
closeto the electrode results in a concentrationgradient and
diffusion of the speciestowards the electrode from the bulk
maybecome rate-determining. Therefore, alarge overpotential is
needed to produce agiven current. Polarization overpotential: c
Ferricyanide Diffusion: Cyclic voltammetry
The thickness of the Nernstdiffusion layer (illustratedin previous
slide) istypically 0.1 mm, anddepends strongly on thecondition of
hydrodynamicflow due to such as stirringor convective effects. The
Nernst diffusion layeris different from theelectric double layer,
whichis typically less than 10 nm. Diffusion: Cyclic voltammetry
(also polarography) Diffusion: Microelectrodes
Microelectrode: at least one dimension must be comparable to
diffusion layer thickness (sub m upto ca. 25 m). Produce steady
state voltammograms. Converging diffusional flux Advantages of
microelectrodes: fast mass flux - short response time (e.g. faster
CV) significantly enhanced S/N (IF / IC) ratio high temporal and
spatial resolution measurements in extremely small environments
measurements in highly resistive media Diffusion:
Microelectrodes
Microelectrodes have at least one dimension of the order of microns
In a strict sense, a microelectrode can be defined as an electrode
that has a characteristic surface dimension smaller than the
thickness of the diffusion layer on the timescale of the
electrochemical experiment Small size facilitates their use in very
small sample volumes. - opened up the possibility of in vivo
electrochemistry. This has been a major driving force in the
development of microelectrodes and has received considerable
attention.. Diffusion: Microelectrodes
At very short time scale experiments (e.g., fast-scan cyclic
voltammetry) a microelectrode will exhibit macroelectrode (planar
diffusion) behavior. At longer times, the dimensions of the
diffusion layer exceed those of the microelectrode, and the
diffusion becomes hemispherical. The molecules diffusing to the
electrode surface then come from the hemispherical volume (of the
reactant-depleted region) that increases with time; this is not the
case at macroelectrodes, where planar diffusion dominates At short
times size of the diffusion layer is smaller than that of the
electrode, and planar diffusion dominates--even at microelectrodes.
Convection Convection results from the action of aforce on the
solution. This can be apump, a flow of gas or even gravity.There
are two forms of convection thefirst is termed natural convection
andis present in any solution. This naturalconvection is generated
by small thermalor density differences and acts to mix thesolution
in a random and thereforeunpredictable manner. In the case
ofelectrochemical measurements theseeffects tend to cause problems
if themeasurement time for the experimentexceeds 20 seconds. It is
possible to drown out the naturalconvection effects from
anelectrochemical experiment bydeliberately introducing
convectioninto the cell. This form of convection istermed forced
convection. It istypically several orders of magnitudegreater than
any natural convectioneffects and therefore effectivelyremoves the
random aspect from theexperimental measurements. This ofcourse is
only true if the convection isintroduced in a well defined
andquantitative manner. Convection If the flow is controlled, after
a smalllead in length, the profile will becomestable with no mixing
in the lateraldirection, this is termed laminar flow. For laminar
flow conditions the masstransport equation for (1
dimensional)convection is predicted by: where vx is the velocity of
the solutionwhich can be calculated in manysituations be solving
the appropriateform of the Navier-Stokes equations. Ananalogous
form exists for the threedimensional convective transport. When an
electrochemical cellpossesses forced convection wemust be able to
solve the electrodekinetics, diffusion and convectionsteps, to be
able to predict thecurrent flowing. This can be adifficult problem
to solve even formodern computers. Migration The final form of mass
transportwe need to consider ismigration. This is essentially
anelectrostatic effect which arisesdue the application of a
voltageon the electrodes. Thiseffectively creates a
chargedinterface (the electrodes). Anycharged species near
thatinterface will either be attractedor repelled from it
byelectrostatic forces. Themigratory flux induced can bedescribed
mathematically (in 1dimension) as: The contribution of migration
istypically avoided by adding a lotof indifferent electrolyte. See
example: Nanogen DNAchip. Homework Calculate the potential of a
battery with a Zn bar in a 0.5 M Zn 2+ solutionand Cu bar in a 2 M
Cu 2+ solution. Show in a cyclic voltammogram the transition from
kinetic control todiffusion control and why does it really happen ?
Derive how the capacitive charging of a metal electrode depends on
potentialsweep rate. What do you expect will be the influence of
miniaturization on apotentiometric sensor and on an amperometric
sensor?