Scanning Electrochemical Microscopy. Theory of the Feedback Mode for Hemispherical Ultramicroelectrodes: Steady-State and Transient Behavior

This contribution represents the first comprehensive attempt to treat complex geometry configurations of the scanning electrochemical microscope (SECM) using the alternating direction implicit finite difference method (ADIFDM). Specifically, ADIFDM is used to simulate the steady-state as well as the transient (chronoamperometric) behavior of a hemispherical ultramicroelectrode (UME) tip of the SECM. The feedback effect in this configuration is less pronounced as compared with a disk-shaped UME system. The differences between the two systems are discussed. Analytical approximations for the steady-state behavior and for characteristic features of the transient behavior are suggested. Finally, experimental feedback currents measured above a conductor and an insulator are in excellent agreement with the theory.