Ultramicroelectrodes steady state

Selzer Y and Manler D 2000 Scanning electrochemical microscopy. Theory of the feedback mode for hemispherical ultramicroelectrodes steady-state and transient behavior Anal. Chem. 72 2383... 

Figure Bl.19.12. Basic principles of SECM. (a) With ultramicroelectrode (UME) far from substrate, diflfiision leads to a steady-state current, ij, (b) UME near an insulating substrate. Flindered diflhision leads to < ij, 3D. (c) UME near a conductive substrate. Positive feedback leads to go. (Taken from [62],...

Electrode processes are often studied under steady-state conditions, for example at a rotating disk electrode or at a ultramicroelectrode. Polarog-raphy with dropping electrode where average currents during the droptime are often measured shows similar features as steady-state methods. The distribution of the concentrations of the oxidized and reduced forms at the surface of the electrode under steady-state conditions is shown in Fig. 5.12. For the current density we have (cf. Eq. (2.7.13))... 

The properties of the voltammetric ultramicroelectrode (UME) were discussed in Sections 2.5.1 and 5.5.1 (Fig. 5.19). The steady-state limiting diffusion current to a spherical UME is... 

The UMEs used in bioarrays can be divided into three types disk, ring, and strip electrodes. The theory of the disk, ring, and strip UMEs has been extensively studied [97-100], Due to the edge effect, the profile of the mass diffusion to the ultramicroelectrode surface is three dimensional, and can significantly enhance the mass transportation in comparison to the conventional large electrode with one-dimensional mass transportation. The steady-state measurement at a planar UME can be expressed as... 

Diffusion of electroactive species to the surface of conventional disk (macro-) electrodes is mainly planar. When the electrode diameter is decreased the edge effects of hemi-spherical diffusion become significant. In 1964 Lingane derived the corrective term bearing in mind the edge effects for the Cotrell equation [129, 130], confirmed later on analytically and by numerical calculation [131,132], In the case of ultramicroelectrodes this term becomes dominant, which makes steady-state current proportional to the electrode radius [133-135], Since capacitive and other diffusion-unrelated currents are proportional to the square of electrode radius, the signal-to-noise ratio is increased as the electrode radius is decreased. 

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.

Applications have been reported for photoelectrochemical experiments, for example, splitting of water [11], local generation of photoelectrodes by spatially selective laser excitation [12], and steady-state electrochemiluminescence at a band electrode array [13,14]. Band electrodes prepared from very thin films approaching molecular dimensions have been used to assess the limits of theory describing electrode kinetics at ultramicroelectrodes [9]. Spectroelectrochemical applications have been extensively reviewed [1], In an intriguing approach, thin, discontinuous metal films have been prepared on a transparent semiconductor substrate they are essentially transparent under conditions in which a continuous metal film containing the same quantity of metal would be expected to substantially absorb [15]. 

At spherical and disc ultramicroelectrodes under steady-state conditions the peak potential coincides with the reversible half-wave potential ( j lcro),... 

It is evident that the square wave charge-potential curves corresponding to surface-bound molecules behave in a similar way to the normalized current-potential ones observed for a soluble solution reversible redox process in SWV when an ultramicroelectrode is used (i.e., when steady-state conditions are attained), providing the analogous role played by 2sw (surface-bound species) and (soluble solution species), and also 2f (Eq- (7.93)) and the steady-state diffusion-limited current (7 css), see Sect. 2.7. This analogy can be made because the normalized converted charge in a surface reversible electrode process is proportional to the difference between the initial surface concentration (I ) and that... 

Unlike feedback mode of the SECM operation, where the overall redox process is essentially confined to the thin layer between the tip and the substrate, in SG/TC experiments the tip travels within a thick diffusion layer produced by the large substrate. The system reaches a true steady state if the substrate is an ultramicroelectrode (e.g., a microdisk or a spherical cap) that generates or consumes the species of interest. The concentration of such species can be measured by an ion-selective (potentiometric) microprobe as a function of the tip position. The concentration at any point can be related to that at the source surface. For a microdisk substrate the dimensionless expression is [74, 75]... 

The time domain on a window accessed by a given experiment or technique, e.g., femtosecond, picosecond, microsecond, millisecond. The time scale (or domain) is often characterized by a set of physical parameters associated with a given experiment or technique, e.g., r2 ]/1) (for - ultramicroelectrode experiments) - thus if the electrode radius is 10-7 cm and the - diffusion coefficient D = 1 x 10-5 cm2/s-1 the time scale would be 10 9s. Closely related to the operative kinetic term, e.g., the time domain that must be accessed to measure a first-order -> rate constant k (s-1) will be l//ci the time domain that must be accessed to measure a given heterogeneous rate constant, k willbe /)/k2. In - cyclic voltammetry this time domain will be achieved when RT/F v = D/k2 with an ultramicroelectrode this time domain will be achieved (in a steady-state measurement when r /D = D/k2 or ro = D/k at a microelectrode [i-ii]. 

The microelectrode is then replaced by an ultramicroelectrode, and steady-state voltammograms of O and ferrocene are recorded this allows calculation of the ratio between the normalized plateau currents, a (Eq. 45). 

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. 

These methods constitute the frame on which any particular method can be elaborated. Yet in practice, the experimental difficulty is that with standard apparatus, 5 /D cannot be varied over an extremely wide range. For example, with the rotating disk electrode (RDE), which is the most convenient steady-state method (with the exception of ultramicroelectrodes [109]), 8 depends on the rotation frequency w of the electrode (see Chapter 2). Yet to maintain correct hydrodynamic conditions w cannot be varied, with... 

At low V, the transport to and from an ultramicroelectrode is best described as hemispherical diffusion, which results in a faradaic current that greatly exceeds that expected for linear diffusion [142,179] (see Sec. II.D.l. and Fig. 21). An important feature of the voltammogram shown in Fig. 21(d) is the absence of a peak. Instead, the current reaches a plateau indicating that a steady-state has been obtained. The steady-state current for an ultramicroelectrode inserted in a large insulating shaft [Fig. 20(c)] is given by Eq. (61), where r is the radius of the electrode surface [180]. The effective transport resulting from hemispherical diffusion also results in an electrode system that is relatively insensitive to natural convection. 

Although the use of ultramicroelectrodes is not restricted to any specific measurement technique [125,143,178,181], only applications in the context of cyclic voltammetry at high sweep rates are considered here (see also Sec. IV). For the studies of reaction kinetics using ultramicroelectrodes under steady-state conditions the reader is referred to the original literature [182]. 

Scanning electrochemical microscopy (SECM) [196] is a member of the growing family of scanning probe techniques. In SECM the tip serves as an ultramicroelectrode at which, for instance, a radical ion may be generated at very short distances from the counterelectrode under steady-state conditions. The use of SECM for the study of the kinetics of chemical reactions following the electron transfer at an electrode [196] involves the SECM in the so-... 

The origins of SECM homogeneous kinetic measurements can be found in the earliest applications of ultramicroelectrodes (UMEs) to profile concentration gradients at macroscopic (millimeter-sized) electrodes (1,2). The held has since developed considerably, such that short-lived intermediates in electrode reactions can now readily be identified by SECM under steady-state conditions, which would be difficult to characterize by alternative transient UME methods, such as fast scan cyclic voltammetry (8). 

Sometimes one is interested only in the steady-state solution (e.g., with rotating disk electrodes or ultramicroelectrodes). Since dColdt = 0 in such a situation, the diffusion equation simply becomes... 

This approach has been employed, for example, in determining the steady-state uncompensated resistance at an ultramicroelectrode (28) and the solution resistance between an ion-selective electrode tip and a surface in a scanning electrochemical microscope (29, 30). It also is sometimes possible to model the mass transport and kinetics in an electrochemical system by a network of electrical components (31, 32). Since there are a number of computer programs (e.g., SPICE) for the analysis of electric circuits, this approach can be convenient for certain electrochemical problems. 

G. Denault, M. Mirkin, and A. J. Bard [/. Electroanai Chem., 308, 27 (1991)] suggested that by normalizing the diffusion-limited transient current, /, obtained at an ultramicroelectrode at short times, by the steady-state current, one can determine the diffusion coefficient, Z), without knowledge of the number electrons involved in the electrode reaction, n, or the bulk concentration of the reactant, C. ... 

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