A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 8
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Its rate depends on mass transfer to the electrode and various surface effects, in addition to the usual kinetic variables. Since electrode reactions are heterogeneous, theirreaction rates are usually described in units of mol/s per unit area; that is,(1.3.4)where у is the current density (A/cm2).Information about an electrode reaction is often gained by determining current as afunction of potential (by obtaining i-E curves). Certain terms are sometimes associatedwith features of the curves.8 If a cell has a defined equilibrium potential (Section 1.1.1),that potential is an important reference point of the system.
The departure of the electrodepotential (or cell potential) from the equilibrium value upon passage of faradaic current istermed polarization. The extent of polarization is measured by the overpotential, rj,rj = E - E{eq(1.3.5)Current-potential curves, particularly those obtained under steady-state conditions, aresometimes called polarization curves. We have seen that an ideal polarized electrode(Section 1.2.1) shows a very large change in potential upon the passage of an infinitesimalcurrent; thus ideal polarizability is characterized by a horizontal region of an i-E curve(Figure 1.3.5a). A substance that tends to cause the potential of an electrode to be nearerto its equilibrium value by virtue of being oxidized or reduced is called a depolarizer? An{a) Ideal polarizable electrode(b) Ideal nonpolarizable electrodeFigure 1.3.5 Current-potential curves for ideal (a) polarizable and (b) nonpolarizable electrodes.Dashed lines show behavior of actual electrodes that approach the ideal behavior over limitedranges of current or potential.8These terms are carryovers from older electrochemical studies and models and, indeed, do not always representthe best possible terminology.
However, their use is so ingrained in electrochemical jargon that it seems wisestto keep them and to define them as precisely as possible.9The term depolarizer is also frequently used to denote a substance that is preferentially oxidized or reduced, toprevent an undesirable electrode reaction. Sometimes it is simply another name for an electroactive substance.1.3 Faradaic Processes and Factors Affecting Rates of Electrode ReactionsI 23ideal nonpolarizable electrode (or ideal depolarized electrode) is thus an electrode whosepotential does not change upon passage of current, that is, an electrode of fixed potential.Nonpolarizability is characterized by a vertical region on an i-E curve (Figure 1.3.5b).
AnSCE constructed with a large-area mercury pool would approach ideal nonpolarizabilityat small currents.1.3.3Factors Affecting Electrode Reaction Rate and CurrentConsider an overall electrode reaction, О + ne ^ R, composed of a series of steps thatcause the conversion of the dissolved oxidized species, O, to a reduced form, R, also insolution (Figure 1.3.6).
In general, the current (or electrode reaction rate) is governed bythe rates of processes such as (1, 2):1.Mass transfer (e.g., of О from the bulk solution to the electrode surface).2.Electron transfer at the electrode surface.3.Chemical reactions preceding or following the electron transfer. These might behomogeneous processes (e.g., protonation or dimerization) or heterogeneousones (e.g., catalytic decomposition) on the electrode surface.4.Other surface reactions, such as adsorption, desorption, or crystallization (electrodeposition).The rate constants for some of these processes (e.g., electron transfer at the electrode surface or adsorption) depend upon the potential.The simplest reactions involve only mass transfer of a reactant to the electrode, heterogeneous electron transfer involving nonadsorbed species, and mass transfer of theproduct to the bulk solution.
A representative reaction of this sort is the reduction of thearomatic hydrocarbon 9,10-diphenylanthracene (DPA) to the radical anion (DPAT) in anaprotic solvent (e.g., N Д-dimethylformamide). More complex reaction sequences involving a series of electron transfers and protonations, branching mechanisms, parallel paths,or modifications of the electrode surface are quite common. When a steady-state current isobtained, the rates of all reaction steps in a series are the same.
The magnitude of this current is often limited by the inherent sluggishness of one or more reactions called ratedetermining steps. The more facile reactions are held back from their maximum rates byElectrode surface regionBulk solutionElectrodeFigure 1.3.6 Pathway of ageneral electrode reaction.24Chapter 1. Introduction and Overview of Electrode Processesrlmtr'HctlrxnFigure 1.3.7 Processes in anelectrode reaction represented asresistances.the slowness with which a rate-determining step disposes of their products or creates theirreactants.Each value of current density, j , is driven by a certain overpotential, 77. This overpotential can be considered as a sum of terms associated with the different reaction steps: Tjmt(the mass-transfer overpotential), r)ct (the charge-transfer overpotential), r]rxn (the overpotential associated with a preceding reaction), etc.
The electrode reaction can then be represented by a resistance, R, composed of a series of resistances (or more exactly,impedances) representing the various steps: Rm, Rct, etc. (Figure 1.3.7). A fast reactionstep is characterized by a small resistance (or impedance), while a slow step is representedby a high resistance. However, except for very small current or potential perturbations,these impedances are functions of E (or /), unlike the analogous actual electrical elements.1.3.4Electrochemical Cells and Cell ResistanceConsider a cell composed of two ideal nonpolarizable electrodes, for example, two SCEsimmersed in a potassium chloride solution: SCE/KC1/SCE.
The i-E characteristic of thiscell would look like that of a pure resistance (Figure 1.3.8), because the only limitation oncurrent flow is imposed by the resistance of the solution. In fact, these conditions (i.e.,paired, nonpolarizable electrodes) are exactly those sought in measurements of solutionconductivity. For any real electrodes (e.g., actual SCEs), mass-transfer and charge-transfer overpotentials would also become important at high enough current densities.When the potential of an electrode is measured against a nonpolarizable referenceelectrode during the passage of current, a voltage drop equal to iRs is always included inthe measured value. Here, Rs is the solution resistance between the electrodes, which, unlike the impedances describing the mass transfer and activation steps in the electrode reaction, actually behaves as a true resistance over a wide range of conditions. For example,consider once again the cell in Figure 1.3.4.
At open circuit (/ = 0), the potential of thecadmium electrode is the equilibrium value, £eq,cd (about —0.64 V vs. SCE). We saw ear-Hg/Hg2CI2/K+, CI7Hg2CI2/Hg©fc0appl1Ideal electrodes• Real electrodesFigure 1.3.8 Current-potential curve for a cell composed of two electrodes approaching idealnonpolarizability.1.3 Faradaic Processes and Factors Affecting Rates of Electrode Reactions. 25Her that with £ app i = —0.64 V (Cd vs. SCE), no current would flow through the ammeter.If £ appl is increased in magnitude to -0.80 V (Cd vs. SCE), current flows. The extra applied voltage is distributed in two parts.
First, to deliver the current, the potential of theCd electrode, Ecd, must shift to a new value, perhaps -0.70 V vs. SCE. The remainder ofthe applied voltage (-0.10 V in this example) represents the ohmic drop caused by current flow in solution. We assume that the SCE is essentially nonpolarizable at the extantcurrent level and does not change its potential. In general,£ appl (vs. SCE) = ECd(vs. SCE) - iRs = £eq,Cd(™.
SCE) + V - iRs(1.3.6)The last two terms of this equation are related to current flow. When there is a cathodiccurrent at the cadmium electrode, both are negative. Conversely, both are positive for ananodic current. In the cathodic case, £ appl must manifest the (negative) overpotential(£ Cd - £eq,cd) needed to support the electrochemical reaction rate corresponding to the current.
(In the example above, r\ = -0.06 V.) In addition £ appl must encompass the ohmicdrop, iRs, required to drive the ionic current in solution (which corresponds to the passage ofnegative charge from the cadmium electrode to the SCE).10 The ohmic potential drop in thesolution should not be regarded as a form of overpotential, because it is characteristic of thebulk solution and not of the electrode reaction. Its contribution to the measured electrodepotential can be minimized by proper cell design and instrumentation.Most of the time, one is interested in reactions that occur at only one electrode. Anexperimental cell could be composed of the electrode system of interest, called theworking (or indicator) electrode, coupled with an electrode of known potential that approaches ideal nonpolarizability (such as an SCE with a large-area mercury pool),called the reference electrode.
If the passage of current does not affect the potential ofthe reference electrode, the E of the working electrode is given by equation 1.3.6.Under conditions when iRs is small (say less than 1-2 mV), this two-electrode cell (Figure 1.3.9) can be used to determine the i-E curve, with E either taken as equal to £ app i orcorrected for the small iRs drop. For example, in classic polarographic experiments inaqueous solutions, two-electrode cells were often used. In these systems, it is often truethat / < 10 /x,A and Rs < 100 П, so that iRs < (10~ 5 A)(100 ft) or iRs < 1 mV, which isnegligible for most purposes.
With more highly resistive solutions, such as those basedon many nonaqueous solvents, a very small electrode (an ultramicr о electrode, Section5.3) must be used if a two-electrode cell is to be employed without serious complica-PowersupplyWorkingelectrodeReferenceelectrode^applFigure 1.3.9Two-electrode cell.10The sign preceding the ohmic drop in (1.3.6) is negative as a consequence of the sign convention adopted herefor currents (cathodic currents taken as positive).26 : Chapter 1.
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