Juhyoun Kwak and Allen J. Bard, "Scanning Electrochemical Microscopy. Theory of the Feedback Mode," Anal. Chem., 61 (11), 1221 - 1227 (1989.06.01.)
The steady-state current that flows between the scanning tip (a disk ultramicroelectrode imbedded in an insulating sheath) and a planar sample substrate in a scanning electrochemical microscope (SECM) operating in the feedback mode is calculated by the finite element method with an exponentially expanding grid, for both conductive and insulating samples. For conductive substrates the tip current, representing, for example, the oxidation of R to O, is enhanced by flow of R generated at the substrate to the tip and is a function of tip/substrate distance, d, but not the radius of the insulating sheath. For insulating substrates, the tip current is decreased by blockage of the diffusion of R to the tip by the substrate and depends upon d and the insulating sheath radius. The theoretical results are compared to experimental studies.