Theory generation/collection mode

A feature of SECM is the quantitative theory available based on reaction-diffusion models (Chapter 5). The SECM may be used for kinetic studies in either the feedback or generation-collection modes. These two possibilities are described below from the point of view of studying immobilized enzyme kinetics. 

Three approaches to kinetic analysis were proposed (1) steady-state measurements in a feedback mode, (2) generation/collection experiments, and (3) analysis of the chronoamperometric SECM response. Unlike the feedback mode, the generation/collection measurements included simultaneous analysis of both IT-L and Is-L curves or the use of the collection efficiency parameter (IS/IT when the tip is a generator and the substrate is a collector). The chronoamperometric measurements were found to be less reliable (5), so only steady-state theory will be discussed here. 

Martin RD, Unwin PR (1998) Theory and experiment for the substrate generation tip collection mode of the scanning electrochemical microscope application as an approach for measuring the diffusion coefficient ratio of a redox couple. Anal Chem 70 (2) 276-284. doi 10.102l/ac97068Ip... 

An observation of general validity that has been made for other polyconjugated systems can be made here for PITN and derivatives. Whenever three conjugated double bonds organized in the trans configuration exist in a molecule, a collective mode of the fl type takes place with the generation of typical Raman scattering, which is the basis of ECC theory. This trans effect may become a useful structural spectroscopic probe. 

The quantitative scanning electrochemical microscopic (SECM) theory has been developed for various regimes of measurements and electrochemical mechanisms. Different operating modes of the SECM, for example, feedback and generation/collection (G/C) modes, steady-state and transient... 

The substrate generation/tip collection (SG/TC) mode with an ampero-metric tip was historically the first SECM-type measurement performed (32). The aim of such experiments was to probe the diffusion layer generated by the large substrate electrode with a much smaller amperometric sensor. A simple approximate theory (32a,b) using the well-known c(z, t) function for a potentiostatic transient at a planar electrode (33) was developed to predict the evolution of the concentration profile following the substrate potential perturbation. A more complicated theory was based on the concept of the impulse response function (32c). While these theories have been successful in calculating concentration profiles, the prediction of the time-de-pendent tip current response is not straightforward because it is a complex function of the concentration distribution. Moreover, these theories do not account for distortions caused by interference of the tip and substrate diffusion layers and feedback effects. 

The latest contribution to the theory of the EC processes in SECM was the modeling of the substrate generation/tip collection (SG/TC) situation by Martin and Unwin (40). Both the tip and substrate chronoamperometric responses to the potential step applied to the substrate were calculated. From the tip current transient one can extract the value of the first-order homogeneous rate constant and (if necessary) determine the tip/substrate distance. However, according to the authors, this technique is unlikely to match the TG/SC mode with its high collection efficiency under steady-state conditions. 

The RMFA is generated by setting the normalized Ith memory function of the time-correlation function of interest equal to the Zth normalized memory function of the time-correlation function of a reference dynamical variable [47, 48]. Specializing this prescription in various ways leads to known approximation schemes, such as the Vineyard and Kerr approximations, and their generalization to molecular liquids. A dielectric form of the RMFA has been applied quite successfully to reproduce the optical mode excitation profiles in liquid water [49, 50]. However, this dielectric approach cannot be applied to the description of another important collective excitation in water, the acoustic mode, and it is desirable to develop a theory that accounts for all the characteristic features of the collective excitations in molecular liquids. 

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