Diffusion-controlled SECM feedback

Figure 16. (a) The SECM current versus distance curve and a steady-state voltammogram (inset) obtained with a 46-nm radius polished Pt electrode. Aqueous solution contained 1 mM FcCH2OH and 0.2 M NaCl. (a) Theoretical approach curve (solid line) for diffusion-controlled positive feedback was calculated from Eq. (19). Symbols are experimental data. The tip approached the unbiased Au film substrate with a 5-nms-1 speed, (b) Experimental (symbols) and theoretical (sold lines) steady-state voltammograms of 1 mM ferrocenemethanol obtained at different separation distances between a 36-nm Pt tip and a Au substrate, d = oo (1), 54 nm (2), 29 nm (3), and 18 nm (4). v = 50 mV s-1. Theoretical curves were calculated from Eq. (22). Adapted with permission from Ref. [51]. Copyright 2006, American Chemical Society. 

Amphlett and Denuault (11) have formulated a time-dependent SECM problem based on the same ideas (i.e., the simulation space is expanded beyond the edge of the insulating sheath and diffusion from behind the shield is taken into account). The steady-state responses were calculated as a longtime limit of the tip transient currents. These authors also obtained two equations describing SECM approach curves for a pure positive and negative feedback. The equation for a diffusion-controlled positive feedback is identical to Eq. (30) (this is not surprising because both equations are based on the same approximate expression from Ref. 9). The parameters reported in Ref. 11 for RG = 10.2 and 1.51 are quite close to those obtained in Ref. 7... 

Conventional SECM theory is not applicable to micropipet tips because the ratio of the glass radius to the aperture radius (RG) is typically much less than 10 [the typical RG value is 1.1 (52)]. An approach curve for facilitated transfer of potassium could only be fit to the theory for a diffusion-controlled positive feedback assuming a near-hemispherical shape of the meniscus (49). But the later video-microscopic study showed that the ITIES formed at the micropipet tip is flat (52). Neither was it possible to fit an iT — d curve obtained when a micropipet tip approached an insulator (49). Both conductive and insulting curves can be fit to the theory developed recently for small RG (53) (see Chapter 5). The theory accounting for finite kinetics of facilitated IT at the ITIES has yet to be developed. 

The accuracy of the IT kinetic measurements performed with micropipette tips may have been affected by their small RG, that is, the ratio of the outer glass radius to the aperture radius, which is normally <2 [68]. In earlier SECM literature, the theory was developed for RG= 10 that is typical for metal-in-glass tips. Because of this issue, no satisfactory theoretical fit could be obtained for approach curves of facilitated potassium transfer either for the diffusion-controlled positive feedback or pure negative feedback [65]. Both conductive and insulting curves were fitted later to the theory developed for small RG values [69] (see Chapter 5). However, the SECM theory for finite substrate kinetics and small RG was developed much later [70], and to our knowledge has not yet been used in any study of IT at the ITIES. 

The feedback mode [Fig. 2(a)] is one of the most widely used SECM techniques, applicable to the study of interfacial ET processes. The basic idea is to generate a species at the tip in its oxidized or reduced state [generation of Ox] in Fig. 2(a)], typically at a diffusion-controlled rate, by electrolysis of the other half of a redox couple (Redj). The tip-generated species diffuses from the UME to the target interface. If it undergoes a redox... 

Given that, under the defined conditions, there is no interfacial kinetic barrier to transfer from phase 2 to phase 1, the concentrations immediately adjacent to each side of the interface may be considered to be in dynamic equilibrium throughout the course of a chronoamperometric measurement. For high values of Kg the target species in phase 2 is in considerable excess, so that the concentration in phase 1 at the target interface is maintained at a value close to the initial bulk value, with minimal depletion of Red in phase 2. Under these conditions, the response of the tip (Fig. 11, case (a)] is in agreement with that predicted for other SECM diffusion-controlled processes with no interfacial kinetic barrier, such as induced dissolution [12,14—16] and positive feedback [42,43]. A feature of this response is that the current rapidly attains a steady state, the value of which increases... 

Later [24], it was shown that the theory for the ErQ process under SECM conditions can be reduced to a single working curve. To understand this approach, it is useful first to consider a positive feedback situation with a simple redox mediator (i.e., without homogeneous chemistry involved) and with both tip and substrate processes under diffusion control. The normalized steady-state tip current can be presented as the sum of two terms... 

The SG/TC mode of SECM was also applied by Martin et al. [86] to study the oxidation of DMPPD. The generator was a 2-mm2 substrate electrode, and the collector was a 25-pm diameter Pt disk electrode. The substrate potential was stepped from 0 V versus Ag quasi reference electrode, where no Faradic process took place, to +500 mV, where the oxidation of DMPPD was diffusion controlled. The tip potential was held at 0 V, at which the oxidized form of DMPPD could be reduced at a diffusion controlled rate. After the tip-substrate separation was found from the positive feedback current-distance curve, the rate constant was obtained from the current transient at the tip. The feedback and SG/TC modes were also used to study the reduction of... 

Fig. 10.12. General principles of the SECM feedback mode. The UME, normally a disk electrode of radius r, is used to generate a redox mediator in its oxidised or reduced form (a reduction process is shown here) at a diffusion-controlled rate. As the UME approaches an insulating surface (a) diffusion of Ox to the electrode simply becomes hindered and the recorded limiting current is less than the steady-state value measured when the electrode is placed far from the surface, in the bulk of the solution, /( >). This effect becomes more pronounced as the tip/substrate separation, dKcm, is decreased. As the UME approaches a conducting surface (b) the original form of the redox mediator (Ox) can be regenerated at the substrate establishing a feedback cycle and an additional flux of material to the electrode.

Related to the corrosion problems was a recent SECM study, which demonstrated the possibility of eliminating typical experimental problems encountered in the measurements of heterogeneous electron transfer at semiconductor electrodes (27). In this experiment, the redox reaction of interest (e.g., reduction of Ru(NH3)s+) is driven at a diffusion-controlled rate at the tip. The rate of reaction at the semiconductor substrate is probed by measuring the feedback current as a function of substrate potential. By holding the substrate at a potential where no other species than the tip-generated one would react at the substrate, most irreversible parasitic processes, such as corrosion, did not contribute to the tip current. Thus, separation of the redox reaction of interest from parallel processes at the semiconductor electrode was achieved. 

Feedback theory has been the basis for most quantitative SECM applications reported to date. Historically, the first theoretical treatment of the feedback response was the finite-element simulation of a diffusion-controlled process by Kwak and Bard (1), but we will start from a more general formulation for a quasi-reversible process under non-steady-state conditions and then consider some important special cases. 

In order to explain the effects of irreversible follow-up chemical reactions on the SECM response, it is first useful to briefly review the feedback and TG/SC characteristics under diffusion-controlled conditions, without the... 

Normalized steady-state feedback current-distance approach curves for the diffusion-controlled reduction of DF and the one-electron oxidation of TMPD are shown in Figure 18. The experimental approach curves for the reduction of DF lie just below the curve for the oxidation of TMPD, diagnostic of a follow-up chemical reaction in the reduction of DF, albeit rather slow on the SECM time scale. The reaction is clearly not first-order, as the deviation from positive feedback increases as the concentration of DF is increased. Analysis of the data in terms of EC2i theory yielded values of K2 = 0.14 (5.15 mM) and 0.27 (11.5 mM), and thus fairly consistent k2 values of 180 M s and 160 M 1 s 1, respectively. Due to the relatively slow follow-up chemical reaction, steady-state TG/SC measurements carried out under these conditions yielded collection efficiencies close to unity over the range of tip-substrate separations investigated (-0.5 < log d/a < 0.0) (4). 

SECM is used to study an Ej-Ci reaction (O + R R Z). A 10-/xm tip is used to reduce O while being positioned over a Pt electrode where R is oxidized back to O at a diffusion-controlled rate. When the tip is 0.2 jxm from the surface, the approach curve shows the same feedback current as for a mediator where the product is stable. However, when the tip is 4.0 /xm away, the response is close to that for an insulating substrate. Estimate the rate constant for the decomposition of R to Z. If this reaction were studied by cyclic voltammetry, approximately what scan rates would be needed to find a nernstian response What are the advantages of SECM in studying this kind of reaction compared to CV ... 

Fig. 3.26a-e A scheme representing five stages of the SECM current-distance experiment, a The tip is positioned in the solution close to the Nafion coating on ITO. b The tip has penetrated partially into the film, and the oxidation of Os(bpy)3+ starts at the Pt tip, which was held at 0.8 V vs. SCE, where the electrode reaction is diffusion-controlled. The effective electrode (tip) surface grows with penetration, c The entire tip electrode is immersed in the film, but is still far from the ITO substrate that is biased at 0.2 V vs. SCE, where the reduction of the generated Os(bpy)3+ can take place, d The tip is sufficiently close to the substrate to observe positive SECM feedback, e The tip reaches the surface of ITO (the tunneling region) [15,387]. (Reproduced with the permission of the American Association for the Advancement of Science)... 

Figure 5.14 (a) Schematic illustrating SECM SG-TC mode. The heterogeneously active BDD electrode is biased at a potential to electrolyze the redox couple (Ox to Red or Red to Ox). The tip is biased at a suitable potential to convert the electrogenerated species back to its original form at a diffusion-controlled rate. Variations in tip current reflect variations in the underlying ET capabilities of the surface. In feedback, the tip is biased to electrolyze the redox couple and the substrate left unbiased or biased to turn over the electro-generated form of the redox couple at a diffusion limited rate, (b)... 

SECM with AC impedance relies on measuring the conductance of the solution between the microdisc tip and the counterelectrode in the bulk of the solution. It was shown that the conductance depends on the tip-substrate distance, in the same way as the diffusion-controlled current, and this can be exploited to accurately position the tip [135]. This approach has the merit of being applicable in the absence of a redox mediator, and is convenient when the tip is operated as a passive probe [136]. This methodology has been exploited by Wipf and coworkers to construct an AC-SECM capable of harnessing AC and DC amperometric signals to record feedback images at constant distance with respect to... 

Figure 9 JO Schematics of the feedback SECM for measurements of electrochemical heterogeneous rate constant at semiconductor electrode, (a) UME tip is poised at positive potential, so that R will get oxidized to O at diffusion control rate. When the tip is closed to the snbstrate surface, O may get re-reduced at semiconductor electrode, depending on the potential at which semiconductor electrode is polarized ( j). Thus, 1 depends upon rate of redaction of O on semiconductor surface, (b) A steady-state irreversible voltammogram (/ vs. E ).

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