Ultramicroelectrode diffusion

Aqueous diffusion coefficients are usually on the order of 5 x 10 cm /s. A second is typically a long time to an electrochemist, so 6 = 30 fim. The definition of far is then 30 ]lni. Short is less than a second, perhaps a few milliseconds. Microseconds are not uncommon. Small, referring to the diameter of the electrode, is about a millimeter for microelectrodes, or perhaps only a few micrometers for ultramicroelectrodes (13). 

Auother uauostructuriug techuique shares some commou features with that described above and is shown in Fig. 36.3. A polymer-coated Pt ultramicroelectrode is used as the tip of a STM, and graphite is used as substrate. Ag atoms are deposited on the tip at underpotentials, so that approximately one atomic monolayer is deposited on the tip. After this, a first bias pulse is applied to the tip, causing the formation of a shallow pit. Then a second bias pulse with a smaller amplitude is applied to cause the desorption of silver from the tip. The silver ions desorbed diffuse aud migrate across the tip-sample gap aud deposit ou the high coordiuatiou sites preseut... 

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,... 

However, advantageous applications of micro- and ultramicroelectrodes are not limited to fundamental investigations. Such electrodes open up possibilities for work in very low concentrations of solute. Whatever can be done at a planar electrode can be done at a concentration about a thousand times lower by using an ultramicroelectrode without reaching the limiting diffusion current. This means that one could even obtain responses from solutes of 1 ppb (assuming a measured current density of 1 pA cm-2). 

Earlier it was pointed out that the use of ultramicroelectrodes could also give a several hundred times increase in iL compared with the diffusion-free currents at planar electrodes. The advantage of increasing the ability to measure at higher current densities by using short times in a transient technique with a planar electrode is that the magnitude of the currents is normal and is not forced down to the difficult-to-measure picoampere region that microelectrodes require. 

In Chapter 21, Hawley has formulated a series of questions about the mechanism of an electrode reaction. Complete diagnosis of the mechanism includes knowledge of the electrode reaction products and the sequential steps (E and/ or C) by which they are formed. If a chemical reaction follows rapidly upon an electron transfer, the new (secondary) product may be produced close to the electrode, and may be subject to further electrochemistry. If the secondary products are formed slowly, after the primary electrolysis product has diffused away from the electrode, their formation will ordinarily not influence the electrode mechanism, except in bulk electrolysis. We limit our treatment to reactions occurring on the CV time scale, approximately 20 s to 10 ms for routine technology. Ultramicroelectrode technology (Chap. 12) extends the short-time limit to below 1 ps. 

The mathematical treatment of hemi-spherical diffusion, as encountered in work with ultramicroelectrodes at long experiment times (Section 6.7.3), includes the convenient... 

In order to establish the most appropriate conditions for the determination of the diffusion coefficients of both electroactive species by using Eqs. (4.38) and (4.39), it has been reported that when the reaction product is absent (i.e., cR = 0) neither planar electrodes nor ultramicroelectrodes can be used in DPC for determining diffusion coefficients (see Eqs. (4.48) and (4.50)) because in these situations the anodic limiting current is either independent of DR or null, respectively. 

So, it can be concluded that, when reaction product is not initially present, DPC of limiting currents can only be used for determining both diffusion coefficients when spherical electrodes are used. The use of planar electrodes or ultramicroelectrodes for calculating DR needs species R to be initially present. 

When the diffusion coefficients of both electroactive species are assumed as different, a general solution for the RPV response at any electrode geometry has not been found. In the case of spherical electrodes, the response is rather complex and it can be found in reference [33] (see also Eq. (F.42) in Appendix F). From this solution, the particular cases of planar and spherical ultramicroelectrodes can be directly obtained,... 

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... 

Scanning electrochemical microscopy (SECM the same abbreviation is also used for the device, i.e., the microscope) is often compared (and sometimes confused) with scanning tunneling microscopy (STM), which was pioneered by Binning and Rohrer in the early 1980s [1]. While both techniques make use of a mobile conductive microprobe, their principles and capabilities are totally different. The most widely used SECM probes are micrometer-sized ampero-metric ultramicroelectrodes (UMEs), which were introduced by Wightman and co-workers 1980 [2]. They are suitable for quantitative electrochemical experiments, and the well-developed theory is available for data analysis. Several groups employed small and mobile electrochemical probes to make measurements within the diffusion layer [3], to examine and modify electrode surfaces [4, 5], However, the SECM technique, as we know it, only became possible after the introduction of the feedback concept [6, 7],... 

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]... 

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