Chronopotentiometry at a microband electrode: simulation study using a Rosenbrock time integration scheme for differential-algebraic equations and a direct sparse solver

Two-dimensional digital simulation of chronopotentiometry at a microband el ectrode cannot be performed by conventional alternating direction implicit finite-difference simulation methods, as a result of non-local boundary con ditions at the electrode. It is also potentially troublesome for iterative Krylov algorithms for solving linear algebraic equations that result from i mplicit temporal integration schemes. These difficulties can be avoided by representing the spatially discretised initial boundary value problem in th e form of a set of differential-algebraic equations, to which a suitable in tegration scheme, such as the Rosenbrock ROWDA3 scheme, can be applied. The resulting linear algebraic equations can be solved unfailingly by a genera l direct sparse algorithm such as Y12M. Using this technique it has been fo und that the chronopotentiometric potential-time curves and transition time characteristics of a single charge transfer reaction at a microband electr ode resemble those for a microhemicylinder electrode of the same surface ar ea, although transition times are somewhat shorter. The simulation reveals also that the assumption of a uniform flux of the concentration at the elec trode, encountered in the literature in the context of the two-dimensional theories of chronopotentiometry at microelectrodes, is not adequate, owing to non-negligible edge effects observed. (C) 2001 Elsevier Science B.V. All rights reserved.