A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 9
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Introduction and Overview of Electrode ProcessesWorking orindicatorтReferenceAuxiliary orcounterelectrodesFigure 1.3.10 Three-electrode cell andnotation for the different electrodes.tions from the ohmic drop in solution. With such electrodes, currents of the order of 1nA are typical; hence Rs values even in the Mft range can be acceptable.In experiments where iRs may be high (e.g., in large-scale electrolytic or galvaniccells or in experiments involving nonaqueous solutions with low conductivities), athree-electrode cell (Figure 1.3.10) is preferable.
In this arrangement, the current ispassed between the working electrode and a counter (or auxiliary) electrode. The auxiliary electrode can be any convenient one, because its electrochemical properties do notVacuumCapillaryN 2 or H 2 inlet29/26HgSaturated KCIMedium-porositysintered-PyrexdiscAuxilliaryelectrodeReferenceelectrode14 cmSolutionlevelHg 2 CI 2 + KCIHg4% agar /saturatedpotassium chlorideCoarse-porosity,sintered-Pyrexgas-dispersioncylinderMedium fritStirring barFigure 1.3.11 Typical two- and three-electrode cells used in electrochemical experiments, (a) Twoelectrode cell for polarography.
The working electrode is a dropping mercury electrode (capillary) and the N2inlet tube is for deaeration of the solution. [From L. Meites, Polarographic Techniques, 2nd ed., WileyInterscience, New York, 1965, with permission.] (b) Three-electrode cell designed for studies withnonaqueous solutions at a platinum-disk working electrode, with provision for attachment to a vacuum line.[Reprinted with permission from A. Demortier and A.
J. Bard, /. Am. С hem. Soc, 95, 3495 (1973). Copyright1973, American Chemical Society.] Three-electrode cells for bulk electrolysis are shown in Figure 11.2.2.1.3 Faradaic Processes and Factors Affecting Rates of Electrode Reactions27affect the behavior of the electrode of interest. It is usually chosen to be an electrodethat does not produce substances by electrolysis that will reach the working electrodesurface and cause interfering reactions there.
Frequently, it is placed in a compartmentseparated from the working electrode by a sintered-glass disk or other separator. Thepotential of the working electrode is monitored relative to a separate reference electrode, positioned with its tip nearby. The device used to measure the potential difference between the working electrode and the reference electrode has a high inputimpedance, so that a negligible current is drawn through the reference electrode.
Consequently, its potential will remain constant and equal to its open-circuit value. Thisthree-electrode arrangement is used in most electrochemical experiments; several practical cells are shown in Figure 1.3.11.Even in this arrangement, not all of the iRs term is removed from the reading madeby the potential-measuring device.
Consider the potential profile in solution betweenthe working and auxiliary electrodes, shown schematically in Figure 1.3.12. (The potential profile in an actual cell depends on the electrode shapes, geometry, solutionconductance, etc.) The solution between the electrodes can be regarded as a potentiometer (but not necessarily a linear one). If the reference electrode is placed anywhere but exactly at the electrode surface, some fraction of iRs, (called iRu, where Ruis the uncompensated resistance) will be included in the measured potential. Evenwhen the tip of the reference electrode is designed for very close placement to theworking electrode by use of a fine tip called a Luggin-Haber capillary, some uncompensated resistance usually remains.
This uncompensated potential drop can sometimes be removed later, for example, from steady-state measurements by measurementof Ru and point-by-point correction of each measured potential. Modern electrochemical instrumentation frequently includes circuitry for electronic compensation of the iRuterm (see Chapter 15).If the reference capillary has a tip diameter d, it can be placed as close as 2d from theworking electrode surface without causing appreciable shielding error. Shielding denotesa blockage of part of the solution current path at the working electrode surface, whichcauses nonuniform current densities to arise at the electrode surface.
For a planar electrode with uniform current density across its surface,Ru =X/KA(1.3.7)WorkingelectrodeAuxiliary electrodesolnfl)Wk•ЛЛЛЛМЛЛЛЛЛЛЛЛЛЛЛ^^Ref(b)Figure 1.3.12 (a) Potentialdrop between working andauxiliary electrodes insolution and iRu measuredat the reference electrode.(b) Representation of the cellas a potentiometer.28Chapter 1. Introduction and Overview of Electrode Processeswhere x is the distance of the capillary tip from the electrode, A is the electrode area, andк is the solution conductivity. The effect of iRu can be particularly serious for sphericalmicroelectrodes, such as the hanging mercury drop electrode or the dropping mercuryelectrode (DME). For a spherical electrode of radius r 0 ,In this case, most of the resistive drop occurs close to the electrode. For a reference electrode tip placed just one electrode radius away (x = r 0 ), Ru * s already half of the value forthe tip placed infinitely far away.
Any resistances in the working electrode itself (e.g., inthin wires used to make ultramicroelectrodes, in semiconductor electrodes, or in resistivefilms on the electrode surface) will also appear in Ru.1.4 INTRODUCTION TO MASS-TRANSFER-CONTROLLEDREACTIONS1.4.1Modes of Mass TransferLet us now be more quantitative about the size and shape of current-potential curves.As shown in equation 1.3.4, if we are to understand /, we must be able to describe therate of the reaction, v, at the electrode surface. The simplest electrode reactions arethose in which the rates of all associated chemical reactions are very rapid compared tothose of the mass-transfer processes. Under these conditions, the chemical reactions canusually be treated in a particularly simple way. If, for example, an electrode process involves only fast heterogeneous charge-transfer kinetics and mobile, reversible homogeneous reactions, we will find below that (a) the homogeneous reactions can be regardedas being at equilibrium and (b) the surface concentrations of species involved in thefaradaic process are related to the electrode potential by an equation of the Nernst form.The net rate of the electrode reaction, i; rxn , is then governed totally by the rate at whichthe electroactive species is brought to the surface by mass transfer, vmt.
Hence, fromequation 1.3.4,^rxn = vmi = i/nFA(1.4.1)Such electrode reactions are often called reversible or nernstian, because the principalspecies obey thermodynamic relationships at the electrode surface. Since mass transferplays a big role in electrochemical dynamics, we review here its three modes and begin aconsideration of mathematical methods for treating them.Mass transfer, that is, the movement of material from one location in solutionto another, arises either from differences in electrical or chemical potential at the twolocations or from movement of a volume element of solution.
The modes of masstransfer are:1. Migration. Movement of a charged body under the influence of an electric field(a gradient of electrical potential).2.Diffusion. Movement of a species under the influence of a gradient of chemicalpotential (i.e., a concentration gradient).3.Convection. Stirring or hydrodynamic transport. Generally fluid flow occurs because of natural convection (convection caused by density gradients) and forcedconvection, and may be characterized by stagnant regions, laminar flow, and turbulent flow.1.4 Introduction to Mass-Transfer-Controlled Reactions < 29Mass transfer to an electrode is governed by the Nernst-Planck equation, written forone-dimensional mass transfer along the x-axis as(1.4.2)where Jx(x) is the flux of species / (mol s xcm 2 ) at distance x from the surface, D\ isthe diffusion coefficient (cm2/s), dC\(x)ldx is the concentration gradient at distance x,дф(х)/дх is the potential gradient, z\ and C\ are the charge (dimensionless) and concentration (mol cm~ 3 ) of species /, respectively, and v(x) is the velocity (cm/s) with whicha volume element in solution moves along the axis.
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