V
oltammetry permits the mechanistic and kinetic
study of systems in which electron transfers are coupled to chemical reactions. This article out-
lines how reaction rates can be measured by using electrochemical techniques that are becoming more accessible to the nonspecialist. These methods are due partly to the evolution of new types of electrodes and partly to the increasing availability of user-friendly software for mathematical modeling, which is used to extract quantitative information from raw data. The mathematical models may also help the chemist who must choose among a bewildering range of electrode “types”. In this article, we show how simulated responses of various electrode types can be used to compare the range of rate constants that may be measured with them, focusing in particular on applications of steadystate voltammetry.
tus is also designed so that the mass transport is well defined and may be easily modeled. For Fast flow Slow flow example, in the channel flow-cell, k k the electrode stops short at the A B A B C C D edges, so the flow profile is parae e e bolic. One significant advantage of hydrodynamic electrodes is that the system reaches a steady state at a fixed flow rate—that is, FIGURE 1. Mass transport and electrode kinetics. when the consumption of reactants at the electrode is balanced (a) When mass transport is slow, reactants and products remain in the vicinity of the electrode longer, and there is a greater chance that a second electrode reaction will occur. by the continual supply of fresh (b) When mass transport is fast, products formed at the electrode are swept away. reactants. A practical disadvantage of hydrodynamic electrodes is that a greater volume of soluing currents at different potentials for such a system is tion is required than with a stationary electrode. known as steady-state voltammetry, which offers good In the 1970s and 1980s, microelectrodes (8) became reproducibility and eliminates capacitive currents associwidely available as microfabrication technologies matured. ated with reorganizing the layer of ions at the electrode Microwires and foils can be sealed in epoxy or glass, and surface. However, mass transport is typically slowest with the edge is polished to form an electrode flush with the steady-state methods, so time-dependent methods, such as insulating surround. Alternatively, photolithography, fast-scan or short time-step, have traditionally been used screen printing, or even painting can be used to lay down to study fast reactions (4, 5). If the rate of mass transport thin strips or layers. Their small size has made them suitcan, however, be increased, steady-state voltammetry can able for medical applications and studies in small solution be used to study faster reactions. (Cyclic voltammetry, in volumes. which the potential sweep rate is varied as a kinetic probe, The microelectrodes turn out to have several interesting is also extensively used for the qualitative and quantitative properties. As the size of the electrode decreases, so does exploration of electrode reaction mechanisms [4, 5], but is the rate at which reactants are consumed by the electrode not discussed here.) and hence, the current drops. However, the reduced depletion of reactants means that the concentration gradient Hydrodynamic electrodes is steeper at the electrode surface, and hence the rate of By setting a metal rod in an insulator, polishing the end to mass transport per unit area increases. The convergent difform a disc electrode, and fusion shown in Figure 4 rotating it, the rate of mass implies a vastly increased rate transport can be accelerated of mass transport compared owing to the “screwlike” conwith linear diffusion at planar 2.0 vection profile at the electrode electrodes. The two most comsurface. The rotating disc elecmon microelectrode geometries 1.8 trode (6) shown in Figure 3 are microdisc and microband. 1.6 dates back several decades and In the microdisc electrode, the is still the most popular hydrocurrent reaches a steady state in 1.4 dynamic electrode. Other the absence of convection. hydrodynamic electrodes have Recently, researchers have 1.2 since appeared, such as the explored hydrodynamic micro1.0 channel (7) and the wall-jet electrodes, which are hydrodyRate of mass transport (6), which are also shown in namic electrodes that have Figure 3. In both cases, the been miniaturized in the direcrate of mass transport can be FIGURE 2. Number of electrons transferred per reacting moletion of the flow, so that the cule varies sigmoidally with the mass-transport rate. changed by varying the flow time taken for electroactive rate and the cell geometry. As species to flow over them is The middle of the curve has the greatest variation for a given change in an example, mass transport can mass transport and, therefore, the experimental conditions are most sendramatically reduced. Channel sitive. The window, marked in blue, is the region in which accurate measbe increased by using a narmicroband electrodes were the urements can be recorded. rower duct or jet. The apparafirst to be developed, providing (b)
Number of electrons transferred
(a)
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an increased rate of mass nomena (14, 15), and its use (a) in electrochemistry has been transport and steady-state reviewed (16). Acoustic conditions. Rees et al. (9, 10) streaming occurs in liquids in used a narrow microband electrode in a high-pressure which ultrasonic energy is Rotation fast-flow channel to achieve attenuated, resulting in conhigh mass-transport rates at vection away from the ultrasteady-state conditions. This sonic source. Ultrasound can Electrode technique included a comalso lead to the formation of Vortex drags puter-controlled apparatus to bubbles, or cavitation, in liqsolution toward translate the desired flow rate uids. The formation and colelectrode into the required driving lapse of bubbles is known as pressure, start the flow, scan “transient cavitation”. When a the voltage, record the curcavitational bubble collapses (b) rent, and then stop the flow asymmetrically at a solid surto conserve solution between face, a microjet of solution is readings. formed. Persistent bubbling Flow Macpherson and Unwin and violent oscillation gives Flow (11, 12) developed a miniarise to another form of mass turized wall-jet electrode transport known as “microElectrode known as the microjet elecstreaming”. Microelectrodes, trode, which achieves masswith their small area and rapid (c) transport rates similar to response times, have been those obtained with Rees’s used to study individual caviapparatus. In this apparatus, tation events (17). the jet was much bigger than Ultrasonic microjets have Nozzle the electrode (often referred the added advantage of to as a wall-tube electrode) scouring the electrode’s surwith an off-center alignment face, preventing any films of that apparently enhanced products or impurities from mass transport, if not the theblocking the conducting surElectrode oretical characterization. face. This advantage has led Recently, Macpherson and to interest in ultrasoundFIGURE 3. Hydrodynamic electrodes. Unwin (13) introduced the enhanced electrochemistry radial flow microring elecfor measuring the amount of (a) Rotating disc electrode, in which all parts of the electrode experience the same rates of mass transport; (b) channel electrode, which features a rectantrode, which is also based on lead (18, 19) in wine, petrol gular duct with a rectangular electrode in one wall; (c) wall-jet electrode, in the wall-jet arrangement (Fig(gasoline), and river sediwhich a jet of solution is directed, through the bulk solution, at the center of ure 3). Rather than firing the ment, and copper in beer a disc electrode set in an insulating “wall”. jet at the center of a disc elec(20). It has also allowed electrode (as in the wall-jet), the trochemistry to be conducted jet is directed at the center of an insulating disc outside of in unconventional solutions, such as blood and homogewhich a thin ring electrode has been embedded. This nized eggs. arrangement is mathematically equivalent to the channel Paradoxically, the ultrasound might also be a disadvanmicroband electrode. Therefore, the channel electrode tage because electrodes must be fabricated from a robust theory can be easily translated for use with this electrode. material such as glassy carbon. Otherwise, the electrodes So far, the microring electrode has been used to study erode and develop an ill-defined electrode geometry (21). fairly simple systems with fast electrode kinetics, such as Perhaps the greatest drawback is the chaotic nature of the ultrasonically induced mass-transport processes, which are the ferri-/ferrocyanide couple, although it is clear that it difficult to model. can be extended to fast homogeneous chemistry. Temperature is another variable that affects the mass Other ways to increase mass transport transport and the kinetics. Electrically heated cylindrical Besides shrinking the electrode and applying convection, microelectrodes have been found to increase the rate of there are other ways to increase the rate of mass transport. mass transport and electrochemical kinetics for redox Ultrasound enhances mass transport through several phecouples studied in organic solution (22). Wall-tube elec-
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trodes have also been used at elevated temperatures (23). For work at high temperatures and pressures, the channel and wall-jet geometries have an added advantage over the rotating disc in that they do not require moving parts. Specific benefits of working at elevated temperatures lie in the areas of mechanistic study and electroanalysis in which the enhancement of coupled homogenous chemistry can be advantageous.
unknown parameters, such as rate constants or diffusion coefficients. By using this data, it is also possible to compare several different electrode types.
Comparing electrode geometries
In the past, the choice of electrode for a kinetic task was often limited by theory. Because working curves and surfaces are available for all of the electrode types described in this article, the best choice for studying a given reaction Working curves and surfaces mechanism can be selected. By using typical experimental The coupling between mass transport parameters—such as diffusion coeffiand kinetics means that for anything cients, cell geometries, electrode sizes, other than very simple systems, the parand flow rates—and data from numerical (a) tial differential equations that make up simulations (26), it is possible to calcuthe mathematical model are analytically late the range of rate constants that can intractable. Therefore, numerical (finite be measured (within the 10–90% window difference and finite element) methods discussed earlier) by steady-state voltamhave been used to solve them (24). metry for several electrode types. The Because experimentalists were forced to results are shown in Figure 5. delve into numerical analysis and the The microdisc, wall-jet, and channel (b) writing of computer programs to interelectrodes may be used to span a broad range of rate constants, ~8 orders of pret their experiments, adoption of these magnitude. The geometries obviously electrochemical techniques was limited offer more convenience and reproducibilto experts. ity because the apparatus need not be For each experimental mechanism at disassembled, and the working electrode each electrode type, however, it is possineed not be changed to modulate the ble to generate a unique response curve FIGURE 4. Diffusion to micro- and macroelectrodes. mass-transport rate. or surface, known as a “working curve” Hydrodynamic microelectrodes are or “working surface” (depending on the (a) For a macroelectrode, linear diffusion into the plane swamps edge effects. (b) For a the obvious choice for studying fast number of unknown parameters), which microelectrode, edge effects are comparable kinetics by using steady-state experican be used to predict the responses for with diffusion into the plane, and the diffuany set of experimental conditions. ments. Of these, the fast-flow channel sion is convergent. These curves and surfaces have been and radial-flow microring electrode published for several different mecha(RFMRE) offer approximately the same nisms at different electrode types, and they free the exper- timescale for a given electrode size. That result is because imentalist from mathematical modeling. the height of the gap between the electrode and the nozFor steady-state voltammetry, a number of common zle in a RFMRE is about one-tenth of the same height in electrochemical reaction mechanisms have been simulated the fast-flow channel flow cell, and this height difference at a range of electrode types, and the working curves have offsets the higher flow rates of the fast-flow channel been stored in electronic format (24). With an appropriate design. For both these cells, the timescale decreases lininterpolation method, values may be read off at any point early with increasing flow rate, but quadratically with along the working curve. Software has been written to decreasing electrode size. Of the hydrodynamic microelecmake this process more convenient (25), which is freely trodes, the RFMRE has so far been used with the narrowavailable at http://physchem.ox.ac.uk:8000/wwwda. est microelectrode, about one-tenth of a micrometer The user selects an electrode type and mechanism and across, which allows measurements of rate constants up to enters the cell parameters, the limiting current, and the 108 s–1! If the reaction rate for a system under investigation is half-wave potential as a function of radius, rotation speed, and flow rate. Data can be entered directly via the Internet known to be in a reasonably narrow range, the choice of a suitable electrode type may be straightforward. Moreover, or uploaded as a file. For each experimental data set, the theoretical response is predicted for the chosen mechanism with a few simple calculations, the electrode size (and cell geometry and flow rate, in the case of hydrodynamic elecand plotted as a function of mass transport appropriate to trodes) may be optimized to provide the maximum sensithe electrode geometry. A measure of the error is comtivity for studying a particular reaction. puted between the experimental and theoretical sets of There are even ways to study systems in which nothing data. This error may be minimized to “fit” (i.e., optimize)
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References RFMRE Fast-flow channel Microband channel Channel Wall jet Rotating disc Microdisc
(1) (2) (3) (4) (5)
–2
0
2 4 6 log10 k ECE
8
FIGURE 5. Range of rate constants that can be measured with various electrode types. The ranges are for the reaction outlined in eqs 1–3. The measured response falls within the 10–90% window, as shown in Figure 2.
(6) (7) (8) (9) (10) (11)
is known about the reaction rate. Compton et al. devised a channel microband array (27–29) in which each of the band electrodes doubles in width (in the direction of flow) along the channel. Thus, each electrode has its own timescale and associated rate constant window. Slow reaction rates (down to 10–2 s–1) are elucidated best on the large electrodes at slower flow rates, while the smallest electrode (2 µm) measures rate constants of up to 105 s–1. The computer-controlled apparatus automatically varies the flow rate and takes measurements at each electrode. The result is a scan through a wide range of kinetic timescales, yet with enough resolution to allow quantitative analysis. This approach has been used to study the thermal and photochemical reaction of radical ions in nonaqueous solution and the oxidation of ascorbic acid in water (30). Electrochemical methods for studying reaction kinetics have now “matured” to a state in which they can be more widely adopted. Microelectrodes and hydrodynamic electrodes are available commercially, along with computer software for data acquisition. The theory has been know for awhile, but more general simulation techniques have recently emerged that allow a virtually unlimited range of reaction mechanisms to be studied (31, 32). Some of the simulation software is also available commercially or for free on the Internet. For some of the more complex problems, the simulations can consume a large amount of computer memory and processing time, although the steadily increasing power of computer hardware is beginning to render this concern insignificant. However, the electronic storage of data at a high enough resolution, together with an appropriate interpolation algorithm, means that simulations have to be conducted only once to generate the working curve or surface. The Internet provides the ideal means of pooling these resources and will improve accessibility to these powerful tools for mechanistic analysis.
(12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32)
Bieniasz, L. K.; Speiser, B. J. Electroanal. Chem. 1998, 441, 271. Gaudello, J. G.; Wright, T. C.; Jones, J. A.; Bard, A. J. J. Am. Chem. Soc. 1985, 107, 888. Compton, R. G.; Dryfe, R. A. W. Prog. React. Kinet. 1995, 20, 245. Bott, A. W. Curr. Separations 1999, 18, 9. Eklund, J. C.; Bond, A. M.; Alden, J. A.; Compton, R. G. Adv. Phys. Org. Chem. 1999, 32, 1. Brett, C. M. A.; Brett, A. M. O. Electrochemistry Principles, Methods, and Applications; Oxford Science Publications, Oxford, 1993. Fisher, A. C. Electrode Dynamics; OUP, Oxford, 1996. Wightman, R. M. Science 1988, 240, 415. Rees, N. V. et al. J. Phys. Chem. 1995, 99, 7096. Rees, N. V.; Alden, J. A.; Dryfe, R. A. W.; Coles, B. A.; Compton, R. G. J. Phys. Chem. 1995, 99, 14813. Macpherson, J. V.; Beaston, M. A.; Unwin, P. R. J. Chem. Soc., Faraday Trans. 1995, 91, 899. Martin, R. D.; Unwin, P. R. J. Electroanal. Chem. 1995, 397, 325. Macpherson, J. V.; Unwin, P. R. Anal. Chem. 1998, 70, 2914. Birkin, P. R., Silva-Matinez, S. J. Electroanal. Chem. 1996, 416, 127. Leighton, T. G. The Acoustic Bubble; Academic Press: New York, 1994. Ball, J. C.; Compton, R. G. Electrochemistry 1999, 67, 912. Birkin, P. R.; O’Connor, R. O.; Rapple, C.; Silva-Martinez, S. J. Chem. Soc., Faraday Trans. 1998, 94, 3365. Akkermans, R. P.; Ball, J. C.; Rebbitt, T. O.; Marken, F.; Compton, R. G. Electrochim. Acta 1998, 43, 3443. Blythe, A.; Akkermans, R. P.; Compton, R. G. Electroanalysis; in press. Agra Gutierrez, C.; Hardcastle, J. L.; Ball, J. C.; Compton, R. G. Analyst 1999, 124, 1053. Compton, R. G.; Eklund, J. C.; Page, S. D.; Sanders, G.H.W.; Booth, J. J. Phys. Chem. 1994, 98, 12410. Beckmann, A.; Schneider, A.; Gründler, P. Electrochemistry Communications 1999, 1, 46. Trevani, L. N.; Calvo, E.; Corti, H. R. J. Chem. Soc., Faraday Trans. 1997, 93, 4319. Alden, J. A. D. Phil. Thesis, Oxford University. http://physchem.ox. ac.uk:8000/john/Thesis, accessed February 7, 2000. Alden, J. A.; Compton, R. G. Electroanalysis 1998, 10, 207. Alden, J. A.; Hakoura, S.; Compton, R. G. Anal. Chem. 1999, 71, 806. Alden, J. A., et al. Anal. Chem. 1998, 70, 1707. Prieto, F.; Oyama, M.; Coles, B. A.; Alden, J. A.; Compton, R. G.; Okazaki, S. Electroanalysis 1998, 10, 685. Cooper, J. A; Compton, R. G. Electroanalysis 1998, 10, 141. Prieto, F.; Coles, B. A.; Compton, R. G. J. Phys. Chem. B. 1998, 102, 7442. Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589. Alden, J. A.; Compton, R. G. J. Phys. Chem. B. 1997, 101, 960.
J. A. Alden is a scientific programmer at Oxford GycoSciences. His research interests include computational electrochemistry. R. G. Compton is a professor at Oxford University. His research interests include physical electrochemistry and electroanalysis. Address correspondence to Compton at Physical and Theoretical Chemistry Laboratory, South Parks Rd., Oxford OX1 3QZ, U.K. (richard.compton@ chemistry.ox.ac.uk).
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