Steady state and potential step techniques

As will now be clear from the first Chapter, electrochemical processes can be rather complex. In addition to the electron transfer step, coupled homogeneous chemical reactions are frequently involved and surface processes such as adsorption must often be considered. Also, since electrode reactions are heterogeneous by nature, mass transport always plays an important and frequently dominant role. A complete analysis of any electrochemical process therefore requires the identification of all the individual steps and, where possible, their quantification. Such a description requires at least the determination of the standard rate constant, k, and the transfer coefficients, and ac, for the electron transfer step, or steps, the determination of the number of electrons involved and of the diffusion coefficients of the oxidised and reduced species (if they are soluble in either the solution or the electrode). It may also require the determination of the rate constants of coupled chemical reactions and of nucleation and growth processes, as well as the elucidation of adsorption isotherms. A complete description of this type is, however, only ever achieved for very simple systems, as it is generally only possible to obtain reliable quantitative data about the slowest step in the overall reaction scheme (or of two such steps if their rates are comparable). 

A fairly wide range of techniques is now available to electrochemists to enable the determination of kinetic and thermodynamic data related to electrode processes. The application of these techniques is the subject of this and subsequent chapters. Throughout the emphasis will be placed on 

Under steady state conditions electron transfer processes with values less than about 5 X lO cm s are regarded as irreversible, i.e. when current flows the electron transfer is insufficiently fast to maintain Nernstian equilibrium at the electrode surface. In such cases kinetic data can be obtained directly from steady state current-voltage measurements analysed on the basis of the Tafel equations (see Fig. 1.4). For a cathodic reaction 

The type of analysis described above requires that both halves of the redox couple are stable and available (a known finite concentration of each must be present in solution to define an equilibrium potential), and that the equilibrium potential can either be measured, or calculated from the Nernst equation (i.e. the standard potential is known). This is often not the case, e.g. particularly in organic electrochemistry, one half of the redox couple may be unstable. However, Tafel type plots may still prove useful. Current-potential data are analysed using the Tafel equation in the fonn 

From the above discussion it will be seen that steady state techniques can only obtain kinetic data for slow processes. Faster reactions are studied by nonsteady state techniques, but before discussing these, a steady state technique that is particularly useful in mechanism elucidation will be described. 

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In single step voltammetry, the existence of chemical reactions coupled to the charge transfer can affect the half-wave potential Ey2 and the limiting current l. For an in-depth characterization of these processes, we will study them more extensively under planar diffusion and, then, under spherical diffusion and so their characteristic steady state current potential curves. These are applicable to any electrochemical technique as previously discussed (see Sect. 2.7). In order to distinguish the different behavior of catalytic, CE, and EC mechanisms (the ECE process will be analyzed later), the boundary conditions of the three processes will be given first in a comparative way to facilitate the understanding of their similarities and differences, and then they will be analyzed and solved one by one. The first-order catalytic mechanism will be described first, because its particular reaction scheme makes it easier to study. 

As for the permeability measurements, most techniques based on the analysis of transient behavior of a mixed conducting material [iii, iv, vii, viii] make it possible to determine the ambipolar diffusion coefficients (- ambipolar conductivity). The transient methods analyze the kinetics of weight relaxation (gravimetry), composition (e.g. coulometric -> titration), or electrical response (e.g. conductivity -> relaxation or potential step techniques) after a definite change in the - chemical potential of a component or/and an -> electrical potential difference between electrodes. In selected cases, the use of blocking electrodes is possible, with the limitations similar to steady-state methods. See also - relaxation techniques. 

The applications of the RDE presented so far all relate to operation under steady-state conditions. However, it has been shown that the possibility of discriminating between closely related mechanisms, such as the eCe and the eCeh, may be improved considerably by using a potential-step technique together with the RDE. The reader interested in the details is referred to the original literature [256,262,263]. 

Two of the electrochemical techniques used in protein film voltammetry are shown in Fig. 4-3. In cyclic voltammetry the electrode potential is swept in a linear manner back and forth between two limits. The rate at which the potential is scanned defines the time scale of the experiment and this can be varied from < 1 mV s to > 1000 V s . This is a very large dynamic range, and it is possible to carry out both steady-state and transient experiments on the same sample of enzyme. " Cyclic voltammetry is important because it provides the big picture and produces a signal that links the reaction or active site of interest to a particular potential. In chronoamperometry, the current is monitored at a constant potential following a perturbation such as a step to this potential or addition of a substrate. This experiment is important because it separates the potential and time dependencies of a response. In both types of experiment, it is usually important to be able to rotate the electrode in order to control transport of the substrate and product to and from the enzyme film. 

Study of the charge-transfer processes (step 3 above), free of the effects of mass transport, is possible by the use of transient techniques. In the transient techniques the interface at equilibrium is changed from an equilibrium state to a steady state characterized by a new potential difference A(/>. Analysis of the time dependence of this transition is the basis of transient electrochemical techniques. We will discuss galvanostatic and potentiostatic transient techniques for other techniques [e.g., alternating current (ac)], the reader is referred to Refs. 50 to 55. 

Pulsed-current techniques can furnish electrochemical kinetic information and have been used at the RDE. With a pulse duration of 10-4 s and a cycle time of 10-3 s, good agreement was found with steady-state results [144] for the kinetic determination of the ferri-ferrocyanide system [260, 261], Reduction of the pulse duration and cycle time would allow the measurement of larger rate constants. Kinetic parameter extraction has also been discussed for first-order irreversible reactions with two-step cathodic current pulses [262], A generalised theory describing the effect of pulsed current electrolysis on current—potential relations has appeared [263],... 

A single DBP droplet is positioned in the vicinity of the microelectrode by the laser trapping technique, and the droplet-microelectrode (edge-to-edge) distance (L) is controlled arbitrarily in micrometer dimension. Knowing the oxidation potential of PPD in the water phase to be 30 mV, PPD is oxidized by a potential step method (100 mV) to induce the dye formation reaction. The anodic current relevant to oxidation of PPD reaches a steady-state value within a short electrolytic time (t) because of cylindrical diffusion of PPD to the microelectrode. The dye formation in the droplet can be easily confirmed by the color change from transparent to cyan or yellow. The dye formation reaction in a single microdroplet could be... 

As is well known, the steady-state behavior of (spherical and disc) microelectrodes enables the generation of a unique current-potential relationship since the response is independent of the time or frequency variables [43]. This feature allows us to obtain identical I-E responses, independently of the electrochemical technique, when a voltammogram is generated by applying a linear sweep or a sequence of discrete potential steps, or a periodic potential. From the above, it can also be expected that the same behavior will be obtained under chronopotentiometric conditions when any current time function I(t) is applied, i.e., the steady-state I(t) —E curve (with E being the measured potential) will be identical to the voltammogram obtained under controlled potential-time conditions [44, 45]. 

The electrochemical characterization of multi-electron electrochemical reactions involves the determination of the formal potentials of the different steps, as these indicate the thermodynamic stability of the different oxidation states. For this purpose, subtractive multipulse techniques are very valuable since they combine the advantages of differential pulse techniques and scanning voltammetric ones [6, 19, 45-52]. All these techniques lead to peak-shaped voltammograms, even under steady-state conditions. 

All the previous techniques described in this chapter used large perturbations of the system for recording the transient response of the system. It is the case, for instance, with potential sweeps (CV) and potential or current step (PITT and GITT). Another way to characterize an electrochemical system is to perturb the system initially at the steady state by the use of an alternative signal of small amplitude this method is used in EIS. 

The latest contribution to the theory of the EC processes in SECM was the modeling of the SG/TC situation by Martin and Unwin [86]. Both the tip and substrate chronoamperometric responses to the potential step applied to the substrate were calculated. From the tip current transient one can extract the value of the first-order homogeneous rate constant and (if necessary) determine the tip-substrate distance. However, according to the authors, this technique is unlikely to match the TG/SC mode with its high collection efficiency under steady-state conditions. 

The development of ultramicroelectrodes with characteristic physical dimensions below 25 pm has allowed the implementation of faster transients in recent years, as discussed in Section 2.4. For CA and DPSC this means that a smaller step time x can be employed, while there is no advantage to a larger t. Rather, steady-state currents are attained here, owing to the contribution from spherical diffusion for the small electrodes. However, by combination of the use of ultramicroelectrodes and microelectrodes, the useful time window of the techniques is widened considerably. Compared to scanning techniques such as linear sweep voltammetry and cyclic voltammetry, described in the following, the step techniques have the advantage that the responses are independent of heterogeneous kinetics if the potential is properly adjusted. The result is that fewer parameters need to be adjusted for the determination of rate constants. 

Of the three SECM modes that can be used to study electrode reaction mechanisms—the TG/SC, feedback, and SG/TC modes—the former is the most powerful for measuring rapid kinetics. With this approach, fast followup and sandwiched chemical reactions can be characterized under steady-state conditions, which are difficult to study even with rapid transient techniques such as fast scan cyclic voltammetry or double potential step chronoamperometry, where extensive corrections for background currents are often mandatory (44). At present, first- and second-order rate constants up to 105 s 1 and 1010 M 1 s, respectively, should be measurable with SECM. The development of smaller tip and substrate electrodes that can be placed closer together should facilitate the detection and characterization of electrogenerated species with submirosecond lifetimes. In this context, the introduction of a fabrication procedure for spherical UMEs with diameters... 

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