A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 92
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Thus, A/ is essentially independent of double-layer charging and isunaffected by oxidation and reduction of the electrode or of adsorbed species. More-3803763,33727\\JГ\/ЛV7/Vt2Aco-^- t, S~Г\ Г\V/\JГ\\J/\I2Д i = 10OnAFigure 9.6.1Representation of Acoand A/ for a sinusoidallyhydrodynamically modulatedRDE.5This equation was derived for limiting-current conditions. It is also valid for currents in the rising portion of areversible wave. It will not be valid if the rate of change in со is comparable to the rate of hydrodynamicrelaxation.
Thus, Ao>/ct>o and cr are usually kept small.9.6 Modulated RDE < 359Full-waverectifier/n amplifierLock-in — Ai-vw-Motor- Sq. - V-Wr-1—v№-TachFigure 9.6.2 Schematic ofspeed control and disk-currentprocessing circuitry. Only thecurrent follower of theconventional three-electrodepotentiostat that controls thedisk electrode is shown.[Reprinted with permission fromB. Miller, and S.
Bruckenstein,Anal Chem., 46, 2026 (1974),Copyright 1974, AmericanChemical Society.]over, it is relatively insensitive to the anodic and cathodic background currents. Sinusoidal hydrodynamic modulation is a useful technique for the determination of very low(submicromolar) concentrations with the RDE, for studies in the presence of surfacecomplications, and for measurements near the background limits of the solvent/supporting-electrolyte system. Shown in Figure 9.6.3 are results from a study in which 0.2 цМT1(I) was reduced at an amalgamated gold RDE (which can be used when a mercurylike surface is desired) (29). Even though the faradaic current for the T1(I) reductioncannot be distinguished from the residual current on the iD-E scan, a clear reductionwave is found by measuring Д/.
It is also possible to obtain kinetic information fromhydrodynamic modulation experiments, by employing a values where deviations fromLevich behavior occur (30).9.6.2Thermal ModulationThe RDE can also be modulated thermally by irradiating the back of the disk electrodewith a laser (Figure 9.6.4) (31). This method is the RDE analog of the temperature jump-0.25-0.50£(V vs. SEC)-0.75-1.00Figure 9.6.3 Controlled-potentialcathodic scans of T1(I) at anamalgamated gold disk. All A traces areRDE curves, all В traces are HMRDEcurves. (A, B) 0.01 M HC1O4; (Л2, ВТ)2.0 X 10~7 M Tl + in 0.01 M HC1O4.Current sensitivities indicated bymarkers; zero current for all curves isthe dashed line.
For all curves, COQ2 = 60rpm1^2. For В curves, Act>^2 = 6 ipm^ 2 ,(J/2TT = 3 Hz, averaging time constant =3 s, and scan rate = 2 mV/s. [Reprintedwith permission from B. Miller, and S.Bruckenstein, Anal. Chem., 46, 2026(1974). Copyright 1974, AmericanChemical Society.]360Chapter 9. Methods Involving Forced Convection—Hydrodynamic Methods- Steel tubeLaser beam• EpoxyQINRDEsystem- Gold shellAbsorptivelayer"FluidFigure 9.6.4 Schematicdiagram of the apparatusemployed for temperaturemodulation of the RDE.The laser pulse irradiatesa disk electrode coatedwith an absorptive layer.[Reprinted withpermission from J. L.Valdes, and B. Miller,/. Phys.
Chem. 92, 525(1988). Copyright 1988,American ChemicalSociety.]experiment discussed in Section 8.7.5. Experiments for both constant and modulated irradiation of the electrode have been carried out. In the constant mode, the irradiating beamrepresents a heat input (on the order of 25-200 mW), while heat is carried away from theelectrode surface by thermal diffusion and convection into the solution.
Eventually, asteady-state disk temperature is attained. This temperature change is proportional to w~ 1/2(since a higher rotation rate results in more heat being carried away from the electrodesurface). The temperature change at the electrode surface will cause a change in a numberof parameters, such as D (see Section 8.7.5), that affect /D; hence the disk current is modulated by the heating of the laser beam. A theoretical analysis shows that the magnitude ofthe current change, Д/г> is proportional to the laser heat input, but is relatively independent of <o (31).In the periodically modulated version of this experiment (32), the laser heating is carried out sinusoidally at a frequency of 5 to 20 Hz, and the resulting sinusoidally varyingcurrent, A/D, is detected with a lock-in amplifier, as in hydrodynamic modulation.
Thevariation of A/D with E is called thermal modulation voltammetry (TMV). Near E° , A/Dshows a peak whose magnitude for a nernstian reaction is a function of the ratio of the entropic energy of the electrode reaction divided by the activation energy of the mass transport process. While the method is capable of extracting thermodynamic information abouta reaction, both the theory and the experimental set-up is sufficiently complex that it hasnot yet found widespread use.9.7 CONVECTION AT UMEsOne advantage of ultramicroelectrodes (Section 5.3) is that mass transport to the electrodeby radial diffusion is high, even in the absence of convection. For a microdisk electrode ofradius r, the mass-transfer coefficient is:mo = 4D/77T(9.7.1)However, the mass-transfer coefficient can be increased above this level by introducingconvective flow, for example, by rotating the electrode or rapidly flowing a solution to it.This might be useful in measurements of rapid heterogeneous electron-transfer kinetics,where the radial diffusion alone is insufficient to remove mass-transfer limitations.As noted in Section 9.3.6, the theory developed earlier for the RDE does not hold forUMEs where there is significant radial diffusion to the edges of the electrode.
Although no9.7 Convection at Ultramicroelectrodes3610.03r = 5 |im0.0250.020.01510 jim0.0115|im0.00505001000со (rad/s)15002000Figure 9.7.1 The effect ofangular rotation rate, со, on themass-transfer coefficient, m, for anRDE. The horizontal lines indicatethe mass-transfer coefficients forunrotated UMEs of different radii,r. Calculations assume D = 1.0 X1СГ5 cm2/s and v = 0.01 cm2/s.[Adapted from data in X. Gao, andH. S.
White, Anal. Chem., 67, 4057(1995).]theoretical treatments exist for the rotating UME, one can obtain a good concept of the behavior by considering the limiting situations at low and high rotation rates (33, 34). As OJ —> 0, thebehavior approaches that of a stationary UME, while as со —> oo, the usual RDE dependencyon o)l/2 should be observed. Shown in Figure 9.7.1 is the dependency of the mass-transfer coefficient for an RDE on со, along with m for electrodes with radii of 5,10, and 15 jiim. Clearly,for the larger radii, mass transport can be enhanced by rotating the electrode, but the electrodeof 5-fAm radius shows a larger mass-transfer coefficient than can be attained for an RDE atany experimentally accessible rotation rate.
Rotation of UMEs of larger radii (e.g., 15 /im)might be useful, however, when solutions of high resistivity are used (34) or where studies ofpolymer films (Section 14.4.2) are of interest (33). An additional problem that arises with rotating UMEs (33, 34) is that the electrode itself is often offset from the rotation axis duringconstruction and the rotation may cause flexing of the shaft with additional offset, causing theeffect discussed in Section 9.3.6. Note that it is also possible to increase the effective masstransfer rate to a UME by using it in the positive feedback mode with a scanning electrochemical microscope, as discussed in Section 16.4.2.Convective flow to UMEs can also be attained by flowing the solution past a stationary electrode.
For example, flow can be directed normal to the electrode from a nozzle positioned nearby (Figure 9.7.2) (35). This configuration is sometimes called a wall jet orSolution in •"""""OX Silicone rubber^ \ \ connectorCapillary connectedto x, у and z axispositionersReferenceelectrodeSolution outlet(to waste)Stainless steelsupportBreadboardFigure 9.7.2 Schematicdrawing of arrangement forwall jet or microjetelectrode. [Reprinted withpermission from J. V.Macpherson, S. Marcar,and P. R.
Unwin, Anal.Chem., 66, 2175 (1994).Copyright 1994, AmericanChemical Society.]362Chapter 9. Methods Involving Forced Convection—Hydrodynamic Methodsmicrojet electrode. A jet of solution fed by gravity or pumped from a small nozzle (e.g.,50-100 jum diameter) impinges on the uitramicroelectrode (e.g., 25 ^ m diameter). Themass-transfer coefficient for this configuration is proportional to the square root of thevolume flow rate and can be as large as 0.55 cm/s, equivalent to that of an uitramicroelectrode with a radius of 150 nm in the absence of convection (35).
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