ITIES theory, applications

Small LL interfaces have been used by Girault and co-workers (33-38) and by Senda et al. (39, 40). We have used a small hole formed in a thin glass wall (41-43). Figure 16 shows the voltammetric response of lauryl sulfate anion transport between water and nitrobenzene. Recent analytical applications of these microinterfaces have resulted in construction of gel-solidified probes. The advantage of such a modification is ease of handling (44-47). The immobilization can be extended further to studies of frozen interfaces, or even to solid electrolytes. Significantly, ITIES theory also applies to interfaces that are encountered in ion-doped, conductive, polymer-coated electrodes. 

In this chapter our focus is on principles, theory, and applications of micro-ITIES to quantitative voltammetric measurements of CT processes and ionic reactions in solution. The questions of characterization of the interfacial geometry and surrounding insulator, which are essential for both kinetic measurements and analytical applications of micro-ITIES, will also be discussed. 

Unlike solid electrodes, the shape of the ITIES can be varied by application of an external pressure to the pipette. The shape of the meniscus formed at the pipette tip was studied in situ by video microscopy under controlled pressure [19]. When a negative pressure was applied, the ITIES shape was concave. As expected from the theory [25a], the diffusion current to a recessed ITIES was lower than in absence of negative external pressure. When a positive pressure was applied to the pipette, the solution meniscus became convex, and the diffusion current increased. The diffusion-limiting current increased with increasing height of the spherical segment (up to the complete sphere), as the theory predicts [25b]. Importantly, with no external pressure applied to the pipette, the micro-ITIES was found to be essentially flat. This observation was corroborated by numerous experiments performed with different concentrations of dissolved species and different pipette radii [19]. The measured diffusion current to such an interface agrees quantitatively with Eq. (6) if the outer pipette wall is silanized (see next section). The effective radius of a pipette can be calculated from Eq. (6) and compared to the value found microscopically [19]. 

Various types of research are carried out on ITIESs nowadays. These studies are modeled on electrochemical techniques, theories, and systems. Studies of ion transfer across ITIESs are especially interesting and important because these are the only studies on ITIESs. Many complex ion transfers assisted by some chemical reactions have been studied, to say nothing of single ion transfers. In the world of nature, many types of ion transfer play important roles such as selective ion transfer through biological membranes. Therefore, there are quite a few studies that get ideas from those systems, while many interests from analytical applications motivate those too. Since the ion transfer at an ITIES is closely related with the fields of solvent extraction and ion-selective electrodes, these studies mainly deal with facilitated ion transfer by various kinds of ionophores. Since crown ethers as ionophores show interesting selectivity, a lot of derivatives are synthesized and their selectivities are evaluated in solvent extraction, ion-selective systems, etc. Of course electrochemical studies on ITIESs are also suitable for the systems of ion transfer facilitated by crown ethers and have thrown new light on the mechanisms of selectivity exhibited by crown ethers. 

The formulation of the preceding section is very general. We are interested, however, in rotations and vibrations of polyatomic molecules. We therefore discuss now specific applications of the algebraic method beginning with the simple case of one-dimensional coupled oscillators, presented in Section 3.3 in the Schrodinger picture. In the algebraic theory, as mentioned, one associates to each coordinate, x, and related momentum, px = — iti d/dx, an algebra. For... 

The linear Tafel plots and a values close to 0.5 indicate that conventional ET theory, e.g., Buttler-Volmer model, is applicable to heterogeneous reactions at the ITIES. ... 

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. 

Furthermore, natural bond orbital (NBO) analysis of the first-order density has also been used to quantify aromaticity [73,74]. More recently Boldyrev and Zubarev [75] developed the adaptive natural density partitioning (AdNDP) algorithm attempting to combine the ideas of Lewis theory and aromaticity. The results obtained by the application of the AdNDP algorithm to the systems with non-classical bonding can be readily interpreted from the point of view of aromatic-ity/antiaromaticity concepts. 

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