Theory diffusion-controlled SECM feedback

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. 

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... 

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. 

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). 

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