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.

Integrated submicroelectrodes for combined AFM-SECM measurements are characterized with numerical simulations using the boundary element method. SECM approach curves and SECM images are calculated and analyzed for a model substrate containing pronounced topographical and electrochemical features. The theoretically calculated image has been compared to the experimental data and shows excellent quantitative agreement. Hence, the applicability of integrated AFM-SECM electrodes for combined electrochemical and topographical imaging and a profound theoretical description including quantification of the obtained results are demonstrated.

The BEM algorithm developed earlier for steady-state experiments in the scanning electrochemical microscopy (SECM) feedback mode has been expanded to allow for the treatment of more than one independently diffusing species. This allows the treatment of substrate-generation/tip-collection SECM experiments. The simulations revealed the interrelation of sample layout, local kinetics, imaging conditions, and the quality of the obtained SECM images. Resolution in the SECM SG/TC images has been evaluated, and it depends on several factors. For most practical situations, the resolution is limited by the diffusion profiles of the sample. When a dissolved compound is converted at the sample (e.g., oxygen reduction or enzymatic reaction at the sample), the working distance should be significantly larger than in SECM feedback experiments (ca. 3 r(T) for RG = 5) in order to avoid diffusional shielding of the active regions on the sample by the UME body. The resolution ability also depends on the kinetics of the active regions. The best resolution can be expected if all the active regions cause the same flux. In one simulated example, which might mimic a possible scenario of a low-density protein array, considerable compromises in the resolving power, were noted when the flux from two neighboring spots differs by more than a factor of 2.