A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 78
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In the middle of the figure, the staircase has moved into theregion of E°\ so that the rate of electrolysis is a strong function of potential. The forwardpulse significantly amplifies the rate of reduction of O, and the reverse pulse actually reverses that reduction, so that an anodic current flows. The right side of the figure corresponds to cycles in which the staircase potential has become considerably negative of E° ,and electrolysis begins to occur at the diffusion-controlled rate regardless of potential.Then neither the forward pulse nor the reverse affects the current much, and the samplesbecome similar.
The sampled current in the forward pulses is smaller than in the middle of2.0 i—-1.0Figure 7.3.14 Dimensionless current response throughout an SWV experiment for thereversible O/R system with R absent from the bulk and with the scan beginning well positive ofE°'. Cathodic currents are upward. The time axis corresponds to the half-cycle index m, and thestaircase potential reaches E0' near m = 15. Sampled currents are shown as points. nAEp = 50mV and nkEs = 30 mV.
[Reprinted from J. Osteryoung and J. J. O'Dea, Electroanal. С hem., 14,209 (1986), by courtesy of Marcel Dekker, Inc.]7.3 Pulse Voltammetry < 2971.0 i—0.50.0I-0.50.20.0-0.2п(Е-ЕУ2),У-0.4Figure 7.3.15 Dimensionlesssquare wave voltammograms forthe reversible O/R case with Rabsent from the bulk. nAEp = 50mV and яД£ 8 = 10 mV. Forwardcurrents (i/ff), reverse currents(i/rr), and difference currents(A«/r) vs.
a potential axis referredto the "reversible" Ещ = £ 0 ' +(/?r/nf) ln(Z)R/Z)o)1/2. Note that" ( £ m - £ 1 / 2 ) = (/mF) in f<9m.[Reprinted from J. Osteryoung andJ. J. O'Dea, Electroanal. Chem.,14, 209 (1986), by courtesy ofMarcel Dekker, Inc.]the diagram because the cumulative effect of electrolysis through many cycles is to depletethe diffusion layer and to slow the rate at which О arrives. The continued falloff of sampled current at the right extreme of the figure is caused by this effect. It is clear that the difference current reaches a peak near E° and is small on either side.Figure 7.3.15 contains a dimensionless representation of the voltammograms thatwould be derived from an experiment like that just described.
The forward and reverse currents resemble a cyclic voltammogram and have much of the same diagnostic value, whilethe difference current resembles the response from DPV and has similar sensitivity.The difference current voltammogram reaches a peak at Ещ = E0' + (RT/nF)ln(D R /D o ) 1 / 2 and has a dimensionless peak current, Д^ р , that depends on n, Д£ р , and AESas presented in Table 7.3.2. The actual peak current, Д/р, is therefore(7.3.33)Since the Cottrell factor is the plateau current in an NPV experiment having the samepulse width, Д ^ р gauges the peak height in SWV relative to the limiting response inNPV, just as the ratio (1 - a)l{\ + a) does for DPV [see (7.3.21)]. For the normal operating conditions of Д£ р = 50/л mV and AES = 10/n mV, the SWV peak is 93% of the corresponding NPV plateau height. For DPV, the comparable figure is only about 45%TABLE 7.3.2 Dimensionless Peak Current(фр) vs.
SWV Operating Parameters'*nAEs/mVn/±Ep/mV&102050100a1510200.00530.23760.45310.90981.16190.02380.25490.46860.91861.16430.04370.27260.48450.92811.16750.07740.29980.50770.94321.1745Data from reference 50.hAEp = 0 corresponds to staircase voltammetry.298 • Chapter 7. Polarography and Pulse Voltammetry(Table 7.3.1), so the SWV method is slightly more sensitive than DPV. This is true because the reverse pulses near Eo> produce an anodic current, which enlarges A/.More complicated systems, involving slow heterogeneous kinetics, coupled homogeneous reactions or equilibria (e.g., as in Chapter 12), or more complex forms of mass transfer(e.g., at a UME, Section 5.3), are most easily treated by digital simulation. Osteryoung andO'Dea (50) discuss the application of SWV to a wide range of such phenomena.Figure 7.3.16 contains data for a system involving the oxidation of Fe(CN)5~ in a positive-going scan at a small Pt disk.
The results have been treated theoretically by assumingreversibility at all frequencies and by adjusting two parameters, the radius of the disk, r$,and El/2 = E0' + (RT/nF) ]n(DR/Do)1/2, to provide the best fit. The change in behavior withfrequency is rooted in the fact that the diffusion pattern at a UME can deviate from the semiinfinite linear case, as discussed in Section 5.3.
The validity of the model is supported by theconsistency of these parameters for runs at different frequencies and by the quality of the fit.This example illustrates the typical manner of comparing SWV results with theory.(c) Background CurrentsThe considerations involved in understanding background currents in SWV are exactlythose encountered in the treatment of DPV. If tv is greater than five cell time constants,there is no appreciable charging current contribution, either to the individual current samples or to the differences. Faradaic background processes do contribute and often controlthe detection limits of SWV.
At solid electrodes or near background limits, the effects onthe forward and reverse currents can be sizable, but they are often suppressed effectivelyin the difference currents.100 i—0.000.25POTENTIAL/V(SCE)0.50Figure 7.3.16 Squarewave voltammograms at aPt disk UME in a solutionof20mMFe(CN)£~alsocontaining 2 M KNO3.Each scan was made from0.0 V to 0.50 V with &Ep =50 mV and AES = 10 mVwith frequencies of (a) 5Hz, (b) 60 Hz, (c) 500 Hz.Points are experimental;curves are fitted to give r 0and Ец2, respectively, as:(a) 11.9/^m, 0.2142 V,(b) 12.4 /un, 0.2137 V,(c) 12.2 M m, 0.2147 V.[Reprinted from D.Whelan, J.
J. O'Dea, J.Osteryoung, and K. Aoki,/. Electroanal Chem., 202,23 (1986), with permissionfrom Elsevier Science.]7.3 Pulse Voltammetry299(d) ApplicationsOsteryoung and O'Dea (50) have proposed the broad diagnostic use of SWV in a way similarto that for which cyclic voltammetry (Chapters 6 and 12) has been so successful. IndeedSWV does have a high information content, especially when one considers the voltammograms of forward and reverse currents, and it has the power to interrogate electrode processesover a wide potential span in a reasonable time. Its strengths with respect to CV are derivedespecially from its ability to suppress the background. In general, systems can be examined atsubstantially lower concentrations than with CV.
Moreover, there is normally much less distortion of the response by the background, so that fitting of data to theoretical models can bedone with greater accuracy. On the whole, SWV is better than CV for evaluating quantitativeparameters for systems that are understood mechanistically. SWV also has weaknesses withrespect to CV: For most practitioners CV is more intuitively interpretable in chemical terms.Also, because the reversal in CV covers a large span of potentials, it can more readily highlight linkages between processes occurring at widely separated potentials. Finally, CV offersa considerably wider range of time scales than SWV as presently practiced.For practical analysis, SWV is generally the best choice among all pulse methods, because it offers background suppression with the effectiveness of DPV, sensitivity slightlygreater than that of DPV, much faster scan times, and applicability to a wider range ofelectrode materials and systems.
The most reproducible behavior and lowest detectionlimits are generally found at mercury surfaces, so an SMDE working as an HMDE isquite effective with SWV. In the next section, we will continue this discussion of practicalanalysis in more general terms applicable to pulse methods as a group.7.3.6 Analysis by Pulse VoltammetryThe differential pulse and square wave techniques are among the most sensitive means for thedirect evaluation of concentrations, and they find wide use for trace analysis. When they canbe applied, they are often far more sensitive than molecular or atomic absorption spectroscopyor most chromatographic approaches.
In addition, they can provide information about thechemical form in which an analyte appears. Oxidation states can be defined, complexation canoften be detected, and acid-base chemistry can be characterized. This information is frequentlyoverlooked in competing methods. The chief weakness of pulse analysis, common to mostelectroanalytical techniques, is a limited ability to resolve complex systems. Moreover, analysis time can be fairly long, particularly if deaeration is required.Pulse measurements are sufficiently sensitive that one must pay special attention to impurity levels in solvents and supporting electrolytes.