A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 72
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Also, it is easily shown that \E3/4 - £ 1/4 | = 51.7/a mV at the sametemperature.6Since a is usually between 0.3 and 0.7, both the wave slope and the Tomes criterionfor a totally irreversible system are normally significantly larger than for a reversible system. These figures of merit are not without ambiguity, however.
Consider the predictedwave slope of 63.8 mV for a = 0.85. Within the precision of normal measurements, onecould diagnose the system as either reversible or irreversible. It is always a good idea toexamine reversibility by a method, such as cyclic voltammetry, that allows a view of theelectrode reaction in both directions.Figure 7.2.1 is a display of actual data reported by Meites and Israel (31) for the polarographic reduction of chromate, which behaves as though it is reduced with a rate-determining initial electron transfer.The shapes and positions of irreversible waves can furnish only kinetic information.One may be able to determine such parameters as &f, &b, k°, or a, but thermodynamic results, such as E0' and free energies, are not available (28, 33, 34).
As a rule of thumb, asystem with k° > 2 X 10~2 cm/s appears reversible on the classical polarographic timescale of a few seconds when D is on the order of 10~5 cm2/s. A heterogeneous chargetransfer with & ° < 3 X 1 O ~ 5 cm/s will behave in a totally irreversible manner under thesame conditions, and one can evaluate the rate parameters as described above.
Systemswith к between these limits are quasireversible, and some kinetic information can be obtained from them through the treatment prescribed by Randies (33, 34). Naturally, the precision of the kinetic information deteriorates as the reversible limit is approached. SeeSection 5.5.4 for much more information about the interpretation of irreversible waves.-1.0log i/{id - i) - 0.546 log tFigure 7.2.1 Wave slope plotfor the reduction of 1.0 mMСЮ4 in0.1AfNaOH.Thedifferent symbols refer to curvesrecorded with different drop timesat -0.80 V vs.
SCE: fmax = 7.5 s(open circles), 5.5 s (triangles),4.1 s (half-filled circles), and 3.4 s(filled circles). See Figure 7.1.4for an actual polarogram forthis system. [Reprinted withpermission from L. Meites andY. Israel, /. Am. Chem. Soc, 83,4903 (1961). Copyright 1961,American Chemical Society.]Corrections for electrode sphericity are available. See the original literature for details (28, 32).7.3 Pulse Voltammetry2757.3 PULSE VOLTAMMETRYThe phrase "pulse voltammetry" encompasses a sizable suite of methods whose practicehas changed substantially since the first edition appeared. The methods originated in aclassical polarographic context and were based on the desire to suppress the charging current arising from continuous expansion of the mercury drop at the DME.
Since 1980,practice has departed from the DME, because the SMDE has become the dominant electrode for practical polarographic work and because the use of these methods at stationaryelectrodes has become more common (35).We will consider five subtopics: tast polarography and staircase voltammetry, normalpulse voltammetry, reverse pulse voltammetry, differential pulse voltammetry, and squarewave voltammetry. Tast polarography, normal pulse voltammetry, and differential pulsevoltammetry form a sequence of development rooted historically in polarography at theDME. To illustrate the motivating concepts, we will introduce each of these methodswithin the polarographic context, but in a general way, applicable to both the DME andSMDE. Then we will turn to the broader uses of pulse methods at other electrodes.
Reverse pulse voltammetry and square wave voltammetry were later innovations and will bediscussed principally outside the polarographic context.7.3.1 Tast Polarography and Staircase VoltammetryThe tast method (6, 36-38) is considered here not because it is widely practiced, for itmakes sense only with the DME and it holds no advantages with respect to more advanced pulse methods, but because this method furnishes a useful starting point for understanding the sampling strategies that are integral to pulse voltammetry.In describing current flow at the DME, we noted that the limiting faradaic current increases monotonically during the life of the drop and is described approximately by theIlkovic equation (Section 7.1.2), whereas the charging current decreases steadily (Section7.1.5).
This contrast is illustrated in Figure 7.3.1. Clearly one can optimize the ratio ofDrop fallCharging currentFaradaic currentDrop fallTotal currentFigure 7.3.1Superposition ofcapacitive and faradaiccurrents of a comparablesize at a DME.v276 P Chapter 7. Polarography and Pulse Voltammetryfaradaic to charging current—and thus the sensitivity—by sampling the current at the instant just before drop fall.Tast polarography features precisely this scheme.
At a fixed time т after the birth of adrop, the current is sampled electronically, and this sample is presented to a recordingsystem (e.g., a computer interface, a recording oscilloscope, or a chart recorder) as a constant readout, until it is replaced at the sampling time during the next drop. The potentiostat is active at all times, and the potential is changed in small steps according to astaircase program (Figure 7.3.2), as in conventional polarography.
Typically т is 2-6 s7and AE is a few mV. The record of the experiment is a trace of the sampled currents vs.52+potential, which is equivalent to time. Figure 1.3.3b shows an example for 10~ M Cdin 0.01 M HC1. The drop time is enforced at a fixed value by dislodging each drop mechanically just after the current sample is taken. This procedure allows an even drop timeover the entire potential range.
Figure 7.3.4 is a diagram of the experimental arrangement.Since the potentiostat is always active and the potential is constant during a drop'slifetime, the actual current flow at the electrode is the same as that observed in conventional polarography with a controlled drop time. The difference is that the recording system is fed only signals proportional to the sampled currents.
The faradaic component ofthe limiting sampled current must be'C ^„„2/3 — 1/6Ш=/и о i\whereas the charging component is/ C (T) = 0.00567Ci(£ z -Е)т2/Зт~1/3(7.3.2)The improvements in this method yield detection limits near 10л-6 M, perhapsslightly lower than those of conventional polarography. Since tast measurements are onlysampled-current presentations of conventional polarographic currents, all conclusionsabout the shapes of waves and all diagnostics developed for conventional measurementsof maximum currents apply to the tast technique.Cycle 1 •Cycle 2 •• Cycle 3AEt0itт 0т 0x 0Figure 7.3.2 Staircase waveform and sampling scheme for tast polarography and staircasevoltammetry.
The experiment is a series of cycles in which a potential is established and heldconstant for a period, a current sample is taken at time т after the start of the period, then thepotential is changed by an amount AE. In tast polarography, the mercury drop is dislodged atthe end of each cycle, as indicated by the vertical arrows. In staircase voltammetry, this step isomitted. The time between the current sample, drop dislodgment, and the change in potential isexaggerated here. Usually it is negligible and the cycle period is essentially the same as r.7One can alternatively apply a slow potential ramp to the working electrode, such that the potential changesonly 3-10 mV during the life of the drop.7.3 Pulse Voltammetry-0.6-0.4-0.8-0.6-0.4277-0.8E (V vs.
SCE)ifl)(b)52+Figure 7.3.3 Polarograms at a DME for 10~ M Cd in 0.01 M HC1. {a) Conventionaldc mode, (b) Tast mode. Note that the tast method eliminates the sharp nonfaradaic spikesappearing at each drop fall. The PZC is near —0.5 V in this experiment, hence the charging currentspikes appear "anodic" at more positive potentials and "cathodic" at more negative ones.Tast polarography can also be carried out at an SMDE; however there is no value indoing so. The faradaic current at an SMDE follows a Cottrell-like decay; therefore it is atits lowest value at the end of the drop's life. In the interest of larger signals and a shorterscanning time for the whole polarogram, one needs to use the shortest possible droptime.
Because drop formation proceeds quickly and with some convective disruption, thecurrent-time profile does not adhere precisely to the theory for spherical diffusion, andthe limiting currents are not as interpretable in fundamental terms as at a DME. Discrimination against charging current is automatic, because the electrode does not have achanging area at any time when sampling would occur, so there rarely is an appreciablecharging current with the staircase waveform. This point is discussed in greater detail inSection 7.3.2.The tast method is designed for a periodically renewed electrode, so it is not evenconceptually applicable to a stationary electrode, such as a Pt disk or an HMDE.
However, staircase voltammetry (35), based on closely related concepts, can find use at suchelectrodes. The experiment is outlined in Figure 7.3.2. The sampling time and cycle duration are no longer limited by the growth and fall of a mercury droplet; hence one canvary them over a wide range. Times as short as microseconds are possible. One also hasthe freedom to vary AE considerably. This parameter defines the density of current samples along the potential axis, thus it controls the "resolution" of the voltammetry. Of^el.PotentiostatVp )DropknockerPulsesequencerPotentialprogrammer1HEConverter1Sample/Hold1RecorderFigure 7.3.4 Schematicexperimental arrangement fortast polarography.
Staircasevoltammetry is carried out at astationary electrode with the samesystem except the drop knocker.278 • Chapter 7. Polarography and Pulse Voltammetrycourse, r defines the kinetic time scale. If т is also the cycle period, then the ratio А£/т isa scan rate, y, describing the speed with which the experiment gathers data over a givenpotential range.Since staircase voltammetry does not involve periodic renewal, each cycle inheritsits initial conditions from the preceding cycle, and the response from any sample is generally affected by the prior history of the experiment.
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