Numerical solution of SECM diffusion

V. NUMERICAL SOLUTION OF SECM DIFFUSION PROBLEMS USING PDEase2 PROGRAM PACKAGE... 

Numerical Solution of SECM Diffusion Problems Using COMSOL Multiphysics.113... 

An alternative electrochemical approach to the measurement of fast interfacial kinetics exploits the use of the scanning electrochemical microscope (SECM). A schematic of this device is shown in Fig. 14 the principle of the method rests on the perturbation of the intrinsic diffusive flux to the microelectrode, described by Eq. (34) above. A number of reviews of the technique exist [109,110]. In the case of the L-L interface, the microelectrode probe is moved toward the interface once the probe-interface separation falls within the diffusion layer, a perturbation of the current-distance response is seen, which can be used to determine the rate of interfacial processes, generally by numerical solution of the mass-transport equations with appropriate interfacial boundary conditions. The method has been... 

Extraction of quantitative chemical information from SECM requires a mathematical model of the interaction of the tip and substrate. Such modeling typically involves numerical solution of a reaction-diffusion equation with the boundary conditions appropriate to the interfacial kinetics. Simulation of SECM experiments is computationally much more demanding than for standard electrochemical experiments (discussed in Chapter 1.3). This is because diffusion in at least two dimensions must be considered and the discontinuity in the boundary condition between the tip metal and insulating sheath necessitates a fine mesh. 

The above SECM theory was developed by solving 2D axisymmetric diffusion problems. Even for an idealized situation (i.e., a flat, planar substrate, strictly perpendicular to the axis of the well-shaped disk tip) only numerical solutions could be obtained. When deviations from this ideal case occur in a real experiment, one has to evaluate the effects of such deviations and check if the available theory can still be used for data analysis. Similar questions arise when the substrate s topography is complicated and/or its surface reactivity is highly non-uniform. 

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