Numerical Simulations of Complex Nonsymmetrical 3D Systems for Scanning Electrochemical Microscopy Using the Boundary Element Method

Abstract

Quantitative treatment of the problems related to scanning electrochemical microscopy (SECM) is performed by means of numerical simulations using the boundary element method (BEM). The method is used to calculate the amperometric steady-state response of a microelectrode or nanoelectrode of a given arbitrary geometry in the SECM feedback mode above surfaces with ideal negative feedback or diffusion-controlled positive feedback. By changing the problem setup from the interior to the exterior Laplace formalism, the precision of the calculation could be improved significantly because the exterior formulation does not require any assumptions about the extension of the diffusion layer at infinite time. The improved precision was demonstrated by simulations of standard problems that have been treated before by finite difference methods. Subsequently a series of simulations is presented that explores the effects of deviations from idealized SECM geometries used in many available finite difference simulations. Such deviations from ideal geometries are frequently encountered in routine SECM experiments and exert a varying influence on the precision of the obtained data and derived physicochemical parameters. Because of the speed of calculation and the flexibility of the geometric arrangements, entire SECM line scans were simulated and used to analyze some issues of recently introduced SECM instruments with integrated distance control mechanisms.

Shearforce positioning of nanoprobe electrode arrays for scanning electrochemical microscopy experiments

“…3D modeling of nonsymmetrical SECM problems has been obtained by boundary element method by Sklyar and Wittstock [55]. It is also amenable to finite elements methods using COMSOL environment.…”

Advective and transient effects in combined AFM/SECM operation

“…The boundary element method has already been used for complex SECM geometries [24,41], and, with some modifications presented in Appendix B, it can be made even more efficient. One potential area for immediate impact of this simulation method is development of an independent frame electrode theory analogous to those available for other useful electrode geometries [20,29,36,42].…”

“…As the location of the computational boundary is moved further and further away from the electrode, the contribution of that portion of the integral become more negligible. It is this fact that leads to the success of one approach to reducing the size of the bounding surface oX, the so called ''exterior formulation [41]''.…”

“…The heavy dashed lines show a path for a typical formulation, in which the boundary is closed at some finite distance [25]. The dotted lines show the path adopted by the ''exterior formulation [41]''. The heavy line on the right side of the symmetric domain, bordering the electrode and a portion of the insulating sheath, shows the abbreviated integration path made possible by use of images in the fundamental solution formulation, and by neglecting the contribution of the line integral very far from the electrode, where the concentration and its gradient are vanishing.…”

Diffusional interactions at dual disk microelectrodes: comparison of experiment with three-dimensional random walk simulations

“…The boundary element method (BEM) [19][20][21][22][23][24][25] is becoming increasingly popular for modeling electrochemical systems, and has recently been applied to three-dimensional simulations of nonsymmetrical geometries [19,21,24,25]. Qiu and Fisher [24] recently used the BEM to model chronoamperometry at dual disk electrodes but they did not address shielding or correlate the simulation results with experimental data.…”