A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 64
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However, if Ek is at least 35/w mV past the cathodic peak,7 the reversalpeaks all have the same general shape, basically consisting of a curve shaped like the forwardi-E curve plotted in the opposite direction on the current axis, with the decaying current of thecathodic wave used as a baseline. Typical i-t curves for different switching potentials areshown in Figure 6.5.1. This type of presentation would result if the curves were recorded on atime base. The more usual i-E presentation is shown in Figure 6.5.2.Two measured parameters of interest on these i-E curves {cyclic voltammograms) arethe ratio of peak currents, /paApc, and the separation of peak potentials, £ p a - £ p c .
For anernstian wave with stable product, / pa // pc = 1 regardless of scan rate, £ A (for Ex >35/n mV past £ pc ), and diffusion coefficients, when / pa is measured from the decaying cathodic current as a baseline (see Figures 6.5.1 and 6.5.2). This baseline can be determinedby the methods described in Section 6.6.If the cathodic sweep is stopped and the current is allowed to decay to zero (Figure6.5.2, curve 4), the resulting anodic i-E curve is identical in shape to the cathodic one, but isplotted in the opposite direction on both the / and E axes. This is so because allowing the cathodic current to decay to zero results in the diffusion layer being depleted of О and populated with R at a concentration near CQ, SO that the anodic scan is virtually the same as thatwhich would result from an initial anodic scan in a solution containing only R.Deviation of the ratio /pa//pc from unity is indicative of homogeneous kinetic or othercomplications in the electrode process (13), as discussed in more detail in Chapter 12.Nicholson (14) suggested that if the actual baseline for measuring /pa cannot be determined, the ratio can be calculated from (a) the uncorrected anodic peak current, (/pa)o,with respect to the zero current baseline (see Figure 6.5.2, curve 3) and (b) the current atEx, 0Sp)(b by the expression:™(U)n0.485(/,Jn(6.5.4)In real cyclic voltammograms the faradaic response is superimposed on an approximately constant charging current.
The situation for the forward scan was discussed in Section 6.2.4. Upon reversal, the magnitude of dE/dt remains constant but the sign changes;hence the charging current is also of the same size, but opposite in sign. It forms a baseline for the reversal response just as for the forward scan, and both /pc and /pa must be corrected correspondingly.The measurement of peak currents in CV is imprecise because the correction for charging current is typically uncertain. For the reversal peak, the imprecision is increased furtherbecause one cannot readily define the folded faradaic response for the forward process (e.g.,curve Г, 2', or У in Figure 6.5.2) to use as a reference for the measurement.
Consequently,CV is not an ideal method for quantitative evaluation of system properties that must be derived from peak heights, such as the concentration of an electroactive species or the rateconstant of a coupled homogeneous reaction. The method's power lies in its diagnosticstrength, which is derived from the ease of interpreting qualitative and semi-quantitative behavior.
Once a system is understood mechanistically, other methods are often better suitedfor the precise evaluation of parameters.7This condition is based on the assumption that the potentiostat responds ideally and that the effects of Ru arenegligible (see Section 1.2.4). A larger margin between the peak and the switching potential would be needed inless ideal circumstances.6.5 Cyclic Voltammetry2410.5-0.3--0.41000-100-200-300-400tFigure 6.5.1 Cyclic voltammograms for reversal at different £ л values, with presentation on atime base.The difference between £ p a and £ pc , often symbolized by Д£ р , is a useful diagnostictest of a nernstian reaction. Although AEp is slightly a function of £ л , it is always close to23RT/nF (or 59/n mV at 25°C).
Actual values as a function of Ex are shown in Table6.5.1. For repeated cycling the cathodic peak current decreases and the anodic one increases until a steady-state pattern is attained. At steady state AEp = 58/я mV at 25°C (5).-0.4 -0.5+2000-100n(E-EV2)-200-300Figure 6.5.2 Cyclic voltammograms under the same conditions as in Figure 6.5.1, but in an i-Eformat.
Ek of (7) Em - 90/n; (2) El/2 - 130/w; (3) Em - 200/n mV; (4) for potential held at EX4until the cathodic current decays to zero. [Curve 4 results from reflection of the cathodic i-E curvethrough the E axis and then through the vertical line at n(E — £ 1/2 ) = 0. Curves 1, 2, and 3 resultby addition of this curve to the decaying current of the cathodic i-E curve (Г, 2', or 3').]242Chapter 6. Potential Sweep MethodsTable 6.5.1 Variation of AEV with Exfor a Nernstian System at 25°C (3)n(Epc-.E\)(Ep-d — Epc)(mV)(mV)71.5121.5171.5271.560.559.258.357.857.0006.5.2nQuasireversible ReactionsBy using the potential program given by (6.5.1) and (6.5.2) in the equations for linearscan voltammetry in Section 6.4, the i-E curves for the quasireversible one-step, one-electron process can be derived.
In this case the wave shape and Д £ р are functions of v, k°, a,and EK. As before, however, if Ek is at least 901 n mV beyond the cathodic peak, the effectof Ek is small. In this case the curves are functions of the dimensionless parameters a andeither Л (see equation 6.4.3) or an equivalent parameter, ф defined by 8(6.5.5)Typical behavior is shown in Figure 6.5.3.For 0.3 < a < 0.7 the Д Ep values are nearly independent of a and depend only on ф.Table 6.5.2, which provides data linking ф to k° in this range (14), is the basis for a widelyused method (often called the method of Nicholson) for estimating k° in quasireversibleО•ил-0.1--0.2--0.3180 120 60 0 -60-120-180E-EV2, mVi-0.1--0.2--0.3"180 120 60 0 -60-120-180£-£ 1 / 2 , mVFigure 6.5.3 Theoretical cyclic voltammograms showing effect of ф and a on curve shapefor a one-step, one-electron reaction.
Curve 1: ф = 0.5, a = 0.7. Curve 2\ф — 0.5, a = 0.3.Curve 3: ф = 7.0, a = 0.5. Curve 4: ф — 0.25, a — 0.5. [Reproduced with permission from R. S.Nicholson, Anal. Chem., 37, 1351 (1965). Copyright 1965, American Chemical Society. Abscissalabel adapted for this text.]8Note that ф in (6.5.5) is not the same as W(E) in (6.4.5).6.6 Multicomponent Systems and Multistep Charge Transfers243Table 6.5.2 VariationofAEpwith<Aat25oC(14)aФ2076543210.750.500.350.250.10F— F-^pa^pcmV616364656668728492105121141212aFor a one-step, one-electronprocess with EA = Ep - 112.5/wmV and a = 0.5.systems. One determines the variation of Д £ р with i>, and from this variation, ф.
The approach is closely related to the determination of the electron-transfer kinetics by the shiftof Ep with v as described in Section 6.4.With both of these approaches one must be sure that the uncompensated resistance,Ru, is sufficiently small that the resulting voltage drops (of the order of /p/?u) are negligible compared to the AEp attributable to kinetic effects. In fact, Nicholson (14) hasshown that resistive effects cannot be readily detected in the AEp-v plot, because the effect of uncompensated resistance on the AEp-v behavior is almost the same as that of ф.The effect of Ru is most important when the currents are large and when k® approachesthe reversible limit (so that) Д £ р differs only slightly from the reversible value).
It isespecially difficult not to have a few ohms of uncompensated resistance in nonaqueoussolvents (such as acetonitrile or tetrahydrofuran), even with positive-feedback circuitry(Chapter 15). Many reported studies made under these conditions have suffered fromthis problem.6.6 MULTICOMPONENT SYSTEMS ANDMULTISTEP CHARGE TRANSFERSThe consecutive reduction of two substances О and O' in a potential scan experiment ismore complicated than in the potential step (or sampled-current voltammetric) experimenttreated in Section 5.6 (15, 16).
As before, we consider that the reactions О + ne —> R andO' + n'e —» R' occur. If the diffusion of О and O' takes place independently, the fluxes areadditive and the i-E curve for the mixture is the sum of the individual i-E curves of О andO' (Figure 6.6.1). Note, however, that the measurement of i'p must be made using the decaying current of the first wave as the baseline.
Usually this baseline is obtained by assuming that the current past the peak potential follows that for the large-amplitude potential2step and decays as t~^ . A better fit based on an equation with two adjustable parameters244Chapter 6. Potential Sweep MethodsO+O' + n'e -> R'100-100-200-300-400 mVFigure 6.6.1Voltammograms forsolutions of (7) О alone; (2)O' alone and, (3) mixture ofО and О', with n = nr,has been suggested by Polcyn and Shain (16); since this fitting procedure depends on the reversibility of the reactions and is a little messy, it is rarely used.An experimental approach to obtaining the baseline was suggested by Reinmuth (unpublished).
Since the concentration of О at the electrode falls essentially to zero at potentials just beyond £p, the current beyond £ p is independent of potential. Thus if thevoltammogram of a single-component system is recorded on a time base (rather than in anX-Y format) and the potential scan is held at about 60/n mV beyond £ p while the timebase continues, the current-time curve that results will be the same as that obtained withthe potential sweep continuing (until a new wave or background reduction occurs). For atwo-component system this technique allows establishing the baseline for the secondFigure 6.6.2 Method forobtaining baseline formeasurement of i'p of secondwave.
Upper curves: potentialprograms. Lower curves:resulting voltammograms with(curve 1) potential stopped atEi and (curve 2) potential scancontinued. System as in Figure6.6.1.6.6 Multicomponent Systems and Multistep Charge Transfers4: 245wave by halting the scan somewhere before the foot of the second wave and recording thei-t curve, and then repeating the experiment (after stirring the solution and allowing it tocome to rest to reestablish the initial conditions). The second run is made at the same rateand continues beyond the second peak (Figure 6.6.2).An alternative experimental approach involves stopping the sweep beyond Ep, as before, and allowing the current to decay to a small value (so that О is depleted in the vicinity of the electrode or the concentration gradient of О is essentially zero near theelectrode).
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