A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 91
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This effect can be attributed tothe large instantaneous current that flows at the disk electrode when the potential isstepped (Figure 9.5.1).An approximate value for the transit time can be obtained by the method suggestedby Bruckenstein and Feldman (24). The radial velocity near the electrode surface is givenby (9.3.10), which can be written(9.5.6)A molecule of R generated at the edge of the disk (r = rx) must diffuse normal tothe disk to reach the ring, since vT is zero at у = 0.
It is then swept in a radial direction and then moves by diffusion and convection in the у direction to reach theinner edge of the ring. This path can be described by some average trajectory andsome time-dependent distance у from the electrode surface. Integration of (9.5.6)yields3/l n f ^ l = 0.51w V 1/21.02.03.0co*p/v)1/3(0.51)2/34.0[ ydt(9.5.7)Figure 9.5.2 Simulated ring-currenttransients. Curve a: Potential step atthe disk. Curve b: Current step at thedisk. [From K.
B. Prater and A. J.Bard, J. Electrochem. Soc, 117, 207(1970), with permission of thepublisher, The ElectrochemicalSociety, Inc.]356 I Chapter 9. Methods Involving Forced Convection—Hydrodynamic MethodsIf one uses the approximation у ~ (Dt)l/2, substitutes this value in (9.5.7), and carries outthe integration, the result iscof = 3.58(*VZ))1/3| l o g f e2/3(9.5.8)With (D/v)l/3> = 0.1, (o = 100 s \ and an electrode with vjr\ = 1.07 (representing arather narrow gap), the transit time from (9.5.8) is about 30 ms. Simulated ring transientsfor electrodes of different geometries are shown in Figure 9.5.3; the points on the curvesrepresent the f values calculated from (9.5.8).
This f more closely represents the time required for the ring current to attain about 2% of the steady value.A study of ring-current transients can be useful in determining adsorption of a diskgenerated intermediate at the disk, since this will cause a delay in the appearance of thisspecies at the ring (25). The transients can also be used in a qualitative way to study electrode processes.
Consider a "shielding transient" experiment described by Bruckensteinand Miller (26) concerning the reduction of oxygen at a copper-ring/platinum-disk electrode (Figure 9.5.4). Oxygen is reduced more readily on Pt than on Cu. If the electrode isimmersed in an air-saturated solution containing 0.2 M H 2 SO 4 and 2 X 10~~5 M Cu(II), noreaction occurs at the disk with ED at 1.00 V vs. SCE. If ER is held at -0.25 V vs. SCE,there is a cathodic ring current of about 11 дА due to the reaction Cu(II) + 2e —> Cu.Oxygen is not reduced at the copper ring at this potential (even though the reversible potential for the reaction O 2 + 4 H + + 4e -> H 2 O is much more positive), because the kinetics are very slow.
If £ D is now stepped to 0.0V, a cathodic disk current of about 700 /xAflows. This current represents reduction of oxygen at the platinum disk and also plating ofcopper by reduction of the Cu(II). This plating of copper on the platinum substrate occursat potentials more positive than those where copper would deposit on bulk copper and iscalled underpotential deposition (Section 11.2.1). The reduction of Cu(II) at the diskshields the ring, so that a drop in / R is observed. As copper deposits on the disk, however,the reduction of oxygen is hindered, and the disk current falls.
After about a monolayer ofcopper has deposited on the disk, further underpotential deposition is no longer possible,Cu(II) reduction at the disk ceases, and the ring current returns to its unshielded value.1.00.51/3cot(D/t>) (0.51)42/3Figure 9.5.3 Simulated ringtransients for electrodes of differentgeometries (r2/r\, гъ1г{). Curve a:1.02, 1.04. Curve b: 1.05, 1.07.Curve c: 1.07, 1.48. Curve d: 1.09,1.52. Curve e: 1.13, 1.92.
Pointsshow transit times, t', calculatedfrom (9.5.8). [From К. В. Prater andA. J. Bard, /. Electrochem. Soc,117, 207 (1970), with permission ofthe publisher, The ElectrochemicalSociety, Inc.]Different choices of у [e.g., 2(Dt)l/2] or a different method of carrying out the integration will result in analternative value of the constant. For example, Bruckenstein and Feldman (24) considered the case in which thespecies diffuses outward for t < t'/2, then back toward the surface for t'/2 < r < r'.
Then the constant in (9.5.8)is 4.51.9.6 Modulated RDE «1 357600- 12Ring400 -Figure 9.5.4 Time dependence of the oxygenreduction current at the disk and the Cu(II)reduction current at the ring of a platinum ringdisk electrode. Solution: 0.2 M H 2 SO 4 and 2 X10~5 M Cu(II) with air saturation. Rotation speed,2500 rpm. Disk potential held at 0.00 V vs. SCEfor t > 0; ring potential = -0.25 V vs.
SCE at allt. Disk area, 0.458 cm2; £ 2 / 3 = 0.36; collectionefficiency, 0.183. [Reprinted with permission fromS. Bruckenstein, and B. Miller, Accts. Chem. Res.,10, 54 (1977). Copyright 1977, AmericanChemical Society.]- 8\200 - | Disk potentialswitched from1.0 to 0.0 V\- 4\Disk residual currentГT2010Seconds\\4^DiskГ30This rather simple experiment demonstrates quite clearly the "poisoning" of the oxygenreduction process by copper. Incidentally, Cu(II) is a rather common impurity in distilledwater and mineral acids, and this experiment demonstrates that underpotential depositionof a monolayer of copper from solutions containing as little as 1 ppm Cu can drasticallyaffect the behavior of a platinum electrode.
Adsorption of small amounts of other impurities (i.e., organic molecules) can also have an effect on solid-electrode behavior. Thus,electrochemical experiments often require making great efforts to establish and maintainsolution purity.The RRDE can also be used to study electrochemical processes at electrodes modified with thin polymer films (Chapter 14). In this application, the polymer film is preparedon the disk, and the ring monitors the flux of ions from the film during a potential sweep.For example, the flux of the cation, 1,3-dimethylpyridinium, from a film ofpolypyrrole/poly(styrenesulfonate) was monitored at the ring electrode, as the disk wascycled in an acetonitrile solution over the potential region where reduction and oxidationof the film occurred (27).9.6 MODULATED RDE9.6.1 Hydrodynamic ModulationFor all of the methods discussed so far in this chapter, we have assumed that the rotationrate of the electrode is constant and at its steady-state value of со when measurements ofcurrents are carried out.
However, it can also be useful to measure currents under conditions when (o is changing with time.The simplest case involves a mono tonic variation of со as a function of time (e.g.,со ос t2) and an automatic plotting of /D vs. (ol/2. These "automated Levich plots" can beof value compared to manual (and possibly more precise) point-by-point measurements,especially when the electrode surface is changing with time (e.g., during an electrodeposition, or with impurity or product adsorption) and a rapid scan is needed. This technique and related methods have been reviewed (28).Another useful technique features the sinusoidal variation of со112 [called sinusoidalhydrodynamic modulation]. Consider an RDE whose rotation rate is varied sinusoidallyabout a fixed center speed, щ, at a frequency cr, so that the instantaneous value of co1^2 isgiven by112o)l /2= (o 0l/2+ A(osin(o-r)(9.6.1)358Chapter 9. Methods Involving Forced Convection—Hydrodynamic Methods1/22For example, consider the case where o)}j = 19.4 s~ (o>0 = 376 s~\ rotation rate =1/21/23600 rpm), Aw = 1.94 s~ (i.e., Aw = 3.8 s~\ equivalent to 36 rpm), and the modu1lation frequency is 3 Hz [a = 6ir s" ].
In this situation, w varies between 380 and 3721s" (between 3636 and 3564 rpm) three times per second (Figure 9.6.1). Aa> is alwayssmaller than co0, and is usually only about 1% of cu0. The usable modulation frequency depends on the inertia and response of the motor-electrode system and is usually 3 to 6 Hz.If the system follows the Levich equation, (9.3.22), the current is given byl /2/(0 - A'[o) 03l/6112+ Acosin(o-f)](9-6.2)2where A' = 0.62nFAD% v~ C$ = i^/a)}/ . Thus,~u/J(9.6.3)and the amplitude of the modulated current is 5(9.6.4)A/ =This varying component of the disk current is most conveniently recorded after filteringand passage through a lock-in amplifier or full-wave rectifier (Figure 9.6.2).Although the A/ value is much smaller in magnitude than /WQ, it has the very important advantage of being free of contributions from processes that do not depend on themass-transfer rate.
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