Theory of ultramicroelectrodes

This review describes the theory of mass transport at ultramicroelectrodes that have broken through several experimental limitations of electrochemical measurements. On the basis of the mathematical miniaturization, the ultramicroelectrode can be classified into a point electrode, a line electrode, and a plane electrode. Electrochemical features of these electrodes are described from a viewpoint of the mass transport, especially due to diffusion. Theoretical difficulty in ultramicroelectrodes is mainly due to nonuniform current distribution on the electrode surface. The expression for the time-dependent diffusion-controlled current at any electrode geometry, which predicts the current responding to any potential variation, is presented. Conditions of the steady-state current are specified. The diffusional characteristic functions at a disk. a cylinder, and a band are presented, from which the theories of various electrochemical techniques can be derived analytically. Voltammetric peak currents at several ultramicroelectrodes are compared in light of the diffusional edge effect. The properties of the steady-state current are described at a disk, a band array, a ring, and a recess electrode. The theory is extended to the current-potential curves complicated by the heterogeneous kinetics at a disk, a cylinder, and a band-array electrode.

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