Steady state voltammetry

Unlike transient methods, the theory for steady-state techniqnes is relatively simple. Equation (15.14) describes the shape of a steady-state voltammogram at any uniformly accessible working electrode (i.e., when the surface concentrations and diffusion fluxes of redox species are uniform over the entire electrode surface)  

No general analytical expression similar to equation (15.14) is available for a steady-state current vs. potential curve at an electrode whose surface is not uniformly accessible. An exception is a microdisk electrode for which an analytical approximation (15.15) provides an accurate description of a quasireversible steady-state voltammogram (13) 

If the process is totally irreversible, equation (15.14) is simplified as follows  

The kinetic analysis in this case is rather straightforward. The transfer coefficient can be determined directly from the difference of two quartile potentials 

one can use equation (15.16) to obtain k for a specific potential value and calculate k° = KmQexp[a.nF(E - E° )/RT], To use this approach one needs the formal potential value E°, which may not be readily available for a totally irreversible reaction. 

In the course of their pioneering studies on tubular electrodes, Blaedel and Klatt analysed the form of the current-voltage curves for reversible [65], quasi-reversible [66], and irreversible [66] processes. The theoretical treatment was at the level of the Levich approximation, proceeding exactly as described in Sect. 2.1, with the suitable modification of the boundary conditions appropriate to the case in question. The boundary conditions relevant to these three cases are delineated in Table 2. 

For a reversible process, Blaedel and Klatt deduced the current-voltage relationship as 

For the quasi-reversible case, where the forward and back rate constants are given by 

Extension of the quasi-reversible to the irreversible case is facilitated by simply neglecting the reverse reaction. The half-wave potential for a catho- 

Boundary conditions for reversible, quasi-reversible, and irreversible electrode reactions at channel electrodes 

---

Girault et al. employed steady-state voltammetry and impedance spectroscopy to study the kinetics of simple IT (e.g., transfer of TMA from water to DCE) and facilitated transfer of potassium by DB18C6 at micro-ITIES [18b, 24]. In both cases, the standard... 

By today s standards of surface preparation, Will s procedures for surface preparation were crude, the surface structures were not characterized by use of surface analytical instrumentation (Which was neither widely available nor well developed at that time), and he employed extensive potentiodynamic cycling through the "oxide" formation potential region prior to reporting the quasi-steady state voltammetry curve, i.e., the potentiodynamic I-V curve. The studies employing surface analytical methods made a decade or more later were... 

Oldham, K. B. and Myland, J. C. (1994). Steady-state voltammetry. In Fundamentals of Electrochemical Science. Academic Press, San Diego, pp. 263-308. 

This is a dynamic electrochemical technique, which can be used to study electron transfer reactions with solid electrodes. A voltammo-gram is the electrical current response that is due to applied excitation potential. Chapter 18b describes the origin of the current in steady-state voltammetry, chronoamperometry, cyclic voltammetry, and square wave voltammetry and other pulse voltammetric techniques. 

The redox properties of three pairs of diastereomeric mono-methanoadducts of C76 bearing a bis(phenylbutyl)malonate addend (see 54 in Fig. 22) have been studied by steady-state voltammetry (SSV) [44]. 

It should also be recalled that a full electrochemical, as well as spectroscopic and photophysical, characterization of complex systems such as rotaxanes and catenanes requires the comparison with the behavior of the separated molecular components (ring and thread for rotaxanes and constituting rings in the case of catenanes), or suitable model compounds. As it will appear clearly from the examples reported in the following, this comparison is of fundamental importance to evidence how and to which extent the molecular and supramolecular architecture influences the electronic properties of the component units. An appropriate experimental and theoretical approach comprises the use of several techniques that, as far as electrochemistry is concerned, include cyclic voltammetry, steady-state voltammetry, chronoampero-metry, coulometry, impedance spectroscopy, and spectra- and photoelectrochemistry. 

The evidence that the 1 couple can diffuse freely in the liquid domains entrapped by the three-dimensional network of the gelators has also been found in the case of a PVDF-HFP gel via steady-state voltammetry at ultramicroelectrodes. Quite surprisingly the voltammogramms of the liquid and of the gel are almost perfectly superimposable (Fig. 17.14) and the diffusion coefficient of the redox ions could be calculated to be 3.6 x 10 cm2/s and 4.49 x 10-6 cm2/s for I- and I3, respectively, using Equation 17.15,... 

Figure 17.14 Steady-state voltammetry of a liquid and polymer (PVDF-HFP) gel electrolyte at a Pt ultramicroelectrode. Scan speed lOmV/s. Reprinted by permission from Mac Millan Publishers Ltd Nature Materials, 2003, 2, 402.

The final cell design, as in semi-infinite electrochemistry, depends very much on the goals of the experimenter. For example, when one is interested in single-electrode coulometry for n value, concentration, or spectral measurements, the cell requirements are minimal. Potential scan experiments (voltammetry, potential scan coulometry, steady-state voltammetry) or experiments... 

For discs and bands, it is very difficult to obtain analytical expressions for the steady-state current, although at first sight the theory for steady-state voltammetry... 

Other Electrode Geometries Microelectrodes and Steady-State Voltammetry... 

The current-potential relationship of the totally - irreversible electrode reaction Ox + ne - Red in the techniques mentioned above is I = IiKexp(-af)/ (1+ Kexp(-atransfer coefficient, ks is -> standard rate constant, t is a drop life-time, S is a -> diffusion layer thickness, and

logarithmic analysis of this wave is also a straight line E = Eff + 2.303 x (RT/anF) logzc + 2.303 x (RT/anF) log [(fi, - I) /I -The slope of this line is 0.059/a V. It can be used for the determination of transfer coefficients, if the number of electrons is known. The half-wave potential depends on the drop life-time, or the rotation rate, or the microelectrode radius, and this relationship can be used for the determination of the standard rate constant, if the formal potential is known. 

A steady state is independent of the details of the experiment used in attaining it. Thus, under conditions where a steady state is attained, e.g., under convective conditions in an - electrochemical cell, the application of a constant current leads to a constant potential and similarly the application of a constant potential leads to the same constant current. Voltammetric steady states are most commonly reached using linear potential sweeps (or ramps) in a single or cyclic direction at a UME or RDE. A sigmoidally shaped current (l)-potential (E) voltammogram (i.e., a steady-state voltammogram) is recorded in the method known as steady-state voltammetry as shown in the Figure. Characteristics of the... 

Refs. [i] Bard AJ, FaulknerLR (2001) Electrochemical methods, 2nd edn. Wiley, New York, chaps. 5, 6, 9, 11, 12 [ii] Bard AJ, Mirkin MV (eds) (2001) Scanning electrochemical microscopy. Marcel Dekker, New York [Hi] Oldham KB, Myland JC (1994) Fundamentals of electrochemistry. Academic Press, New York, chap. 8 [iv] Zoski CG (1996) Steady-state voltammetry at microelectrodes. In Vanysek P (ed) Modern techniques in electro analysis. Wiley, New York... 

Table 8 A comparison of the kinetic time-scales accessible with steady-state voltammetry using common electrode geometries. 

Fig. 46 Tune-scales accessible by steady-state voltammetry at common electrode...

Fig. 48 Range of rate constants that can be measured by steady-state voltammetry at common electrode geometries for (a) an ECE process and (b) an EQE process.

Figure 20. Example of preparative electrolysis monitored by steady-state voltammetry. The curves shown are constructed but they could have been recorded with RDE, UME, or polarography for a substrate O that is reduced reversible at 5 = l O V to a product that is reducible at -1.6 V. The medium is reduced at E < —2.4 V. The different curves correspond to a) Before the preparative electrolysis, b) after 50 % of O has been electrolyzed to product, and c) after exhaustive electrolysis of O to product.

Libraries were generated from iminoquinol ether and 11,2,4 tria/olo 4,3-a pyridinium perchlorate collections in the wells of a microtiter plate by potentiostatic microelectrolysis.72 The progress of electrolysis was monitored by microelectrode steady-state voltammetry, and product formation was screened by semi-quantitative HPLC/MS. A schematic of the employed four-electrode assembly and a photograph of that bundle in action in the robotic system are shown in Fig. 14.21. 

---