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?