A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 59
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With r 0 = 1 mm, the cell time constant is about 30 ^s and thelower limit of time scale in step experiments (defined as a minimum step width equal to10/?uC(j) is about 0.3 ms. This result is consistent with the general experience that experiments with electrodes of "normal" size need to be limited to the millisecond time domain218 v Chapter 5. Basic Potential Step Methodsor longer.
However, with r 0 = 5 fxm the cell time constant becomes about 170 ns, so thatthe lower limit of time scale drops to about 1.7 ^s. Before UMEs were understood andreadily available, the microsecond regime was very difficult to reach in electrochemicalstudies. However, UMEs have opened it to relatively convenient investigation (10, 11),not only by potential step methods, but also by other experimental approaches coveredlater in this book.UMEs even allow access to the nanosecond domain, although not yet with routineease or convenience.
To reach it, one must reduce the electrode size further and work withsolutions having high conductivity. For example, by using a disk UME with r 0 = 0.5 /xmand by working in 1 M H 2 SO 4 , one can, in principle, achieve a cell time constant below1 ns, so that the lower limit of time scale could be smaller than 10 ns.
However, experimental work in this range is complicated by serious instrumental problems and by fundamental issues related to the availability of molecules when the diffusion layer thicknessbecomes comparable to the molecular size (12, 14, 15, 48). For a step lasting 10 ns,{Di)112 is only about 3 nm; hence very few solute molecules are close enough to the electrode to react if they must reach it by diffusion. As this book is written, the fastest experiments conducted with diffusing species have been in the time scale range of 500 ns.Faster experiments, with step widths in the range of 100 ns, have been conducted withsystems having the electroactive species attached to the electrode, so that they are presentin large numbers and diffusion is not required (49, 50).
Examples of such systems are discussed in Chapter 14.5.9.2 Voltammetry in Media of Low ConductivityThe uncompensated resistance creates a control error in any potentiostatic experimentsuch that the true potential at the working electrode differs from the apparent (or applied)potential by iRu (Sections 1.3.4 and 15.6).
The true potential is more positive than the apparent value if a cathodic current is flowing, but more negative if the net current is anodic.As recorded with conventional instrumentation, voltammograms are plots of recordedcurrent vs. apparent potential; thus the waves incorporate effects of iRu, which generallymimic the effects of quasireversibility.
That is, they cause a displacement of the voltammogram toward more extreme apparent potentials, and they cause a broadening of thevoltammogram along the axis of apparent potential. Obviously, these effects can causemisinterpretation of data, so it is important to understand when they are significant andhow to minimize or correct for them. The topic is discussed in various contexts in laterchapters, especially in Section 15.6.If one is using a diagnostic electrode of conventional size in a highly conductivemedium, such as an aqueous electrolyte with a concentration of 0.1 M or more, Ru is typically only a few ohms, and iRu is always smaller than a few mV unless currents exceed1 mA, which they rarely do for voltammetry of the type discussed in this chapter.On the other hand, if work is being carried out in a nonaqueous or viscous medium,especially in one of moderate or low polarity, Ru can be large enough to cause substantialerrors.
In a medium such as methylene chloride containing 0.1 M TBABF4, it is not uncommon to have Ru in the range of several Ш , so that iRu exceeds a few mV for any current larger than 1 дА, which it normally does in voltammetry at a conventional electrode.For solvents of genuinely low polarity, such as toluene, Ru is very high even with addedsupporting electrolytes, because the electrolytes do not dissociate. The potential-controlerror is so large at a conventional electrode that the waves are broadened and shifted tothe point of invisibility.5.9 Special Applications of Ultramicroelectrodes219At UMEs, the picture is quite different, because the currents are extremely small;consequently, the error in potential control in a voltammetric experiment is often muchsmaller than in the same experiment with an electrode of conventional size.
Consider, forexample, a disk UME with radius r 0 at which we desire to carry out sampled-currentvoltammetry. What are the conditions that will allow the recording of a voltammogram inwhich the half-wave potential is shifted less than 5 mV by the effect of uncompensated resistance?This condition implies that iRu < 5 mV, where / = ///2 and Ru is given by the limitingform of (5.9.2). If the sampled-current voltammetry is based on semi-infinite linear diffusion (i.e., on early transients), then / is half of the Cottrell current for sampling time r, andthe condition becomesД ^ 5 Х , О - 3У(5.9.4)Thus the error decreases with TQ, and one can improve the accuracy of the voltammogramby using a smaller electrode.On the other hand, if the voltammetry is based on steady-state currents, / is half of thediffusion-limited steady-state current for a disk, which is inFDoC^r^ and the conditionisnFDoC%ITTK< 5 X 10~3\/(5.9.5)In this experimental mode, the error is independent of the size of the disk, but of coursesteady-state currents are generally achievable only at UMEs.
With n = 1, Do = 10~5cm2/s, and CQ = 1 mM, the conductivity must exceed only 3 X 10~5 fl^cm"1. Thisminimum would characterize 10~4 M HC1 and would be met by all aqueous electrolyteshaving concentrations above that of the electroactive species, as well as by most commonsolvent systems of lower polarity containing weakly dissociated electrolytes.A fascinating empirical aspect of voltammetry at UMEs is that one can often recordvoltammograms in media that would not satisfy even the foregoing condition.
Useful datahave been gathered, for example, in solvents without any added supporting electrolyte orin polymers of very high viscosity. An example of the former is found in Figure 4.3.5.Systems of this kind typically do not adhere to the assumptions that we used to treatvoltammetry in Sections 5.4 and 5.5, because migration becomes an important part of themass transfer, and because the charged species produced or consumed at the electrodesurface affect the local conductivity quite significantly (51). Equations 5.9.2 to 5.9.5 donot apply in that situation. Theory is available for nernstian systems (12, 15, 48, 52).One can often simplify the instrumentation used with UMEs because iRu is veryfrequently negligible and / is very small.
Under these conditions, there is nothing tobe gained by trying to position a separate reference electrode near the working electrode and there is no danger of polarizing the reference by passing the cell currentthrough it. Thus two-electrode cells are often used, especially in high-speed experiments (Chapter 15).5.9.3Applications Based on Spatial ResolutionBecause UMEs are physically small, they can be used to probe small spaces. Single electrodes have been employed frequently in physiological applications, such as the measurement of time-dependent concentrations of neurotransmitters near synapses of neurons (6).220Chapter 5.
Basic Potential Step MethodsSingle electrodes also provide the basis for scanning electrochemical microscopy (SECM,Chapter 16). Groups of microelectrodes can be used in various interesting ways to providea spatially sensitive characterization of a system.Combinations and arrays of UMEs are often made by the microlithographic techniques common to microelectronics, and they frequently consist of parallel bands. If thebands are connected in parallel, they behave as a single segmented electrode and followthe principles outlined in Section 5.2.3. If they are independently addressable, they can beused as separate working electrodes to characterize different regions of a sample, such asa polymer overlayer (53).One can also use the elements of an array to probe chemistry occurring at neighboring elements. The simplest example is a double-band system used in the generator collector mode (Figure 5.9.2).
The two bands are spaced closely enough together to allowthe diffusion fields to overlap, so that events at each electrode can be affected by theother. One of the electrodes, called the generator, is used to drive the experiment, oftenby having its potential scanned slowly enough to produce a steady-state voltammogram.Suppose the double band assembly is immersed in a solution containing only species Оin the bulk. Assume further that the reaction О + ne <=^ R is reversible and that the product R is chemically stable. In the absence of any influence from the second electrode, onewould record, at either of the electrodes, a quasi-steady-state voltammogram characteristic of a single band.
However, in the generator-collector mode, the second electrode isset at a potential in the base region of the reduction wave for O, so that any R arrivingthere is immediately reconverted to O. A current will flow at this collector only when thegenerator is producing R, thus a plot of the current at the collector vs.
the potential of thegenerator should have the same shape as that recorded at the generator, but with the opposite sign. Also, currents at the collector are smaller than corresponding values at thegenerator, because the collector does not collect all of the generated R. This is an example of a reversal experiment implemented in a spatial mode, and it has much in commonwith voltammetry at a rotating ring-disk assembly (Chapter 9) and with generationcollection experiments in scanning electrochemical microscopy (Chapter 16).
Like otherreversal experiments, generation-collection at the double band is sensitive to the chemical stability of species R. If it does not survive long enough to diffuse to the collector, nocurrent will be recorded there, and if only a part survives, then only a part of the expected current will be seen. The kinetics of solution-phase reactions can be diagnosedand quantified in this sort of experiment.An interesting phenomenon in a generation-collection experiment involving a UMEarray is that the current at the generator can be enhanced by the collector through a mechanism called feedback.
Without active collection, all of the R produced at the generator(Feedback)GeneratorCollectorFigure 5.9.2 Schematicrepresentation of twomicroband electrodesoperating in the generatorcollector mode.5.10 References « 221would diffuse into solution and would have no further effect on the experiment at the generator electrode.
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