Simulation of the double hemicylinder generator–collector assembly through conformal mapping technique

Abstract

A conformal mapping technique ideally suited for the numerical simulation of double hemicylinder parallel-electrode assemblies is presented. This transform is shown to allow precise and fast simulations of their behavior when they perform in the generator–collector mode. This is thoroughly established for chronoamperometric experiments but the slight modifications required to treat voltammetry are also presented. Furthermore it permits the derivation of an analytical formulation of the generator and collector currents under steady-state. This allows one to compare the response at double-hemicylinder and double-band generator–collector assemblies, and hence to evaluate the effect of electrode protuberance on the electrochemical response. The same conformal transform is also used for the simulation of the single hemicylindrical electrode chronoamperometric behavior. The ensuing results are tested against Szabo's empirical analytical expression and the agreement found to be excellent.