Normalized steady-state tip current

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... 

Normalized steady-state tip current (/ = /-p/Z-poo) computed as a function of L for a quasi-reversible substrate reaction with different values of dimensionless rate constant (k = k°a/D) and dimensionless substrate potential = nFf]/RT) (67). The Butler-Volmer relations for the forward (reduction) and backward (oxidation) rate constants are = k txp(—aE ) exp [(1 — a)E ] where a is the transfer coefficient... 

Hitherto, the feedback and TG/SC modes have found exclusive application in the quantitative study of dimerization kinetics under steady-state conditions (4,5,8). Table 2 provides an extensive list of normalized steady-state tip and substrate currents, as a function of K2 and d/a, which can be used for the analysis of experimental data. The characteristics in Table 2 display the general trends already identified for follow-up chemical reactions (Sec. II.A). (1) For a given d/a value, the tip current varies from a limit corresponding to pure positive feedback (as K2 — 0) to one for negative feedback (as K, —> oo), while the collection efficiency varies from unity to zero as K, increases towards infinity. (2) The feedback and collection currents become most sensitive to kinetics, the closer the tip/substrate separation. Additionally, increasingly fast kinetics become accessible as the tip/ substrate separation is minimized. 

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). 

FIG. 18 Normalized steady-state tip feedback current-distance behavior for the reduction of DF at concentrations of 5.15 mM (o) and 11.5 mM ( ), along with the best theoretical fits (solid lines) for K2 = 0.14 and 0.27, respectively. The behavior obtained for simple diffusion-controlled positive feedback measurements on the oxidation of TMPD is also shown ( ). 

For generality, all of the theoretical predictions have been derived assuming a common diffusion coefficient, D, for the species involved in the electrode process. Since the steady-state tip current in bulk solution depends on K (42), the tip and substrate currents are best normalized with respect to the tip current for the reduction of A, with K = 0. Denoted by iT,i .,eo, this has the form of Eq. (20), with n = 1. 

FIG. 25 Variation of the normalized steady-state tip (a) and substrate (b) currents with tip/substrate separation for a DISP1 pathway, in the TG/SC mode, with K = 1 (0), 2 (A), 5 (o), 10 ( ), 20 (V), and 50 ( ). In (a) the upper dotted line represents one-electron pure positive feedback (K = 0) and the lower dotted line is for two-electron pure negative feedback (K — °o). In (b) the dotted line is the substrate current for pure positive feedback. 

Both Eqs. (4 and 5) were derived using the data tabulated in Ref. [6] for RG = 10. Galceran and coworkers have also provided very accurate alternative equations of similar form [76]. Although the effect of RG is often ignored, when RG < 10 it maybe significant, especially with negative feedback. Very small RG values ( 1.1) occur for micropipette-based tips and the appropriate values of the normalized steady state SECM current for various values of RG have been calculated using a finite element technique [30]. 

Experiments were carried out in DMF with 4mM A, and PhOH at concentrations in the range 0.1-0.43 M, with tetrabutylanunonium tetrafluoroborate as a supporting electrolyte. Distances were established using the positive feedback response for the oxidation of decamethylferrocene, which was added to solutions at millimolar levels. A 7 pm diameter C fiber UME was employed as the tip, while the substrate was a 60 pm diameter Au disk electrode. Typical steady-state tip and substrate approach curves for the diffusion-limited reduction of A at the tip and the oxidation of A " at the substrate are shown in Figure 7.22. The tip and substrate currents are normalized by the steady-state tip current for the one-electron reduction of A (without any chanical reaction, i.e with no PhoH) in bulk solution, denoted by tr ie,oo- The tip current showed the features predicted for ECE/DISPl processes, while the substrate current—always of opposite sign to the tip current—indicated a DISPl pathway unambiguously. 

The plot of normalized steady-state current vs. tip-interface distance, shown in Fig. 12, demonstrates that as the tip-interface distance decreases the steady-state current becomes more sensitive to the value of Kg. Under the defined conditions the shape of the approach curve is highly dependent on the concentration in the second phase, for Kg values over a very wide range, with a lower limit less than 0.1 and upper limit greater than 50. This suggests that SECMIT can be used to determine the concentration of a target solute in a phase, without the UME entering that phase, provided that the diffusion coefficients of the solute in the two phases are known. 

The normalized steady-state current vs. tip-interface distance characteristics (Fig. 18) can be explained by a similar rationale. For large K, the steady-state current is controlled by diffusion of the solute in the two phases, and for the specific and y values considered is thus independent of the separation between the tip and the interface. For K = 0, the current-time relationship is identical to that predicted for the approach to an inert substrate. Within these two limits, the steady-state current increases as K increases, and is therefore diagnostic of the interfacial kinetics. 

Several advantages of the inlaid disk-shaped tips (e.g., well-defined thin-layer geometry and high feedback at short tip/substrate distances) make them most useful for SECM measurements. However, the preparation of submicrometer-sized disk-shaped tips is difficult, and some applications may require nondisk microprobes [e.g., conical tips are useful for penetrating thin polymer films (18)]. Two aspects of the related theory are the calculation of the current-distance curves for a specific tip geometry and the evaluation of the UME shape. Approximate expressions were obtained for the steady-state current in a thin-layer cell formed by two electrodes, for example, one a plane and the second a cone or hemisphere (19). It was shown that the normalized steady-state, diffusion-limited current, as a function of the normalized separation for thin-layer electrochemical cells, is fairly sensitive to the geometry of the electrodes. However, the thin-layer theory does not describe accurately the steady-state current between a small disk tip and a planar substrate because the tip steady-state current iT,co was not included in the approximate model (19). 

Since for SG/TC measurements, the substrate is generally (1,2,6,10) [though not always (4,11)] several orders of magnitude larger than the tip, it can usually be assumed that the tip has no effect on the substrate characteristics, a fact that has been confirmed experimentally (4,6). In this situation, only the tip current is of interest for quantitative kinetic measurements of follow-up chemical reactions. After normalization, with respect to the steady-state /(-electron current for the diffusion-controlled reduction of A, with the UME placed at a great distance from the substrate electrode [Eq. (20)], the collector tip current, iTc is given by ... 

The normalized steady-state approach curve of tip current versus tip/sub-strate separation for the reduction of III(BF4) is shown in Figure 14. This was obtained with a 25 pm diameter Pt UME, biased at —0.8 V versus AgQRE to affect the diffusion-controlled reduction of III, as the probe was translated towards a 1 mm diameter Pt disk substrate, biased at 0.0 V versus AgQRE to promote the diffusion-controlled oxidation of IV. When analyzed in terms of EQ theory, the approach curve yielded a value k, = 145 s-1, which was in excellent agreement with that determined by cyclic voltammetry at sweep rates between 10 and 50 V s-1. 

Typical steady-state tip and substrate current approach curves for the oxidation of different concentrations of ArCT are shown in Figure 23. A general observation is that as the concentration of ArCT increases, the tip and substrate currents—at a particular distance—decrease, due to the second-order nature of the follow-up chemical reaction. The experimental approach curves are shown alongside theoretically derived curves for a spread of normalized rate constants, K2, from which it can be seen that there is reasonable agreement between the observed and predicted trends. From measurements of both feedback currents, for all three ArCT concentrations investigated, and collection efficiencies, for the lowest two concentrations, a radical dimerization rate constant of 1.2 ( 0.3) X 10s M 1 s 1 was determined (5), which was in reasonable agreement with that determined earlier using fast scan cyclic voltammetry (36). 

FIG. 23 (a) Normalized tip steady-state feedback current-distance behavior for... 

Figure 7.24 shows simulated normalized steady-state current responses of the tip (a) and substrate (b), and the CE=(c) as a function of og d/a) for various values of K in the range 0.5-50. As for the EQ case considered in Section 7.2.1, the behavior is governed primarily by the relative magnitudes of the tip-substrate diffusion time, compared to the lifetime of species B. 

For the SECMIT mode the tip current response is governed primarily by K, Kg, y, and the dimensionless tip-substrate distance, L. Here, we briefly examine the effects of these parameters on the chronoamperometric and steady-state SECMIT characteristics. All chronoamperometric data are presented as normalized current ratio versus in order to emphasize the short-time characteristics, for the reasons outlined previously [12,14-16]. Steady-state characteristics, derived from the chronoamperometric data in the long-time limit, are considered over the full range of tip-substrate separations generally encountered in SECM. 

The driving force for the transfer process was the enhanced solubility of Br2 in DCE, ca 40 times greater than that in aqueous solution. To probe the transfer processes, Br2 was recollected in the reverse step at the tip UME, by diffusion-limited reduction to Br . The transfer process was found to be controlled exclusively by diffusion in the aqueous phase, but by employing short switching times, tswitch down to 10 ms, it was possible to put a lower limit on the effective interfacial transfer rate constant of 0.5 cm s . Figure 25 shows typical forward and reverse transients from this set of experiments, presented as current (normalized with respect to the steady-state diffusion-limited current, i(oo), for the oxidation of Br ) versus the inverse square-root of time. 

The normalization of the iT and is for two-electron processes is somewhat problematic. In Ref. [85], both quantities are normalized with respect to the one-electrode steady-state current, which flows at infinite tip-substrate separation (ii, e,oo = 4FDac ). However, this value is not equal to experimentally measured tip current at d —> oo, which also includes the contribution from the second ET. Nevertheless, by comparing experimental current-distance curves to the theory one can distinguish between DISP1 and ECE pathways and evaluate the k value [85]. 

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.

FIG. 8 Steady-state current-distance curves for a conical tip over conductive (A) and insulating (B) substrates corresponding to different values of the parameter k = height/base radius. L is the distance between the substrate and the point of tip closest to it normalized by the base radius. (A) k = 3 (curve 1), 2 (curve 2), 1 (curve 3), 0.5 (curve 4), and 0.1 (curve 5). The upper curve was computed for a disk-shaped tip. (B) From top to bottom, k = 3, 2, 0.5, and 0.1 The lower curve was computed for a disk-shaped tip. (Reprinted with permission from Ref. 9. Copyright 1992 Elsevier.)... 

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