An integral equation method for computing the transient current at microelectrodes

• Published in: Journal of electroanalytical chemistry (Lausanne, Switzerland) Switzerland), 1995-10, Vol.396 (1), p.265-275
• Main Authors: Cope, Davis K., Tallman, Dennis E.
• Format: Article
• Language: English
• Subjects: Chemistry; Electrochemistry; Electrodes: preparations and properties; Exact sciences and technology; General and physical chemistry; Integral equation method; Microelectrodes; Other electrodes
• ISSN: 1572-6657; 1873-2569
• DOI: 10.1016/0022-0728(95)04022-G

The integral equation method (IEM) is an efficient method for computing the transient current at microelectrodes under conditions of convergent diffusion. The IEM is a hybrid analytical-numerical method consisting of three parts: (1) Laplace transforming the diffusion equation and reducing it to an integral equation, the kernel of which is characterized by the cell geometry and is independent of the electrode geometry; (2) numerical solution of the integral equation for the (Laplace transformed) current î( s); (3) numerical inversion of î( s) for the current i( t). The method is applicable to a wide range of electrode-cell geometries and electrode reactions. Furthermore, calculations are reduced from the cell interior to the electrode surface, and various steps in the calculation can be reduced to a concise explicit form (e.g. kernel calculations). These computational steps have a similar form across all problems which allows the repeated use of the same algorithms. For these reasons, the method shows promise of exceptionally high efficiency. In this paper, we present an overview of the IEM: a theoretical formulation in physical and dimensionless variables for electrode-cell geometries in general; introduction of Neumann kernels and reduction to an integral equation; explicit Neumann kernels for a range of electrode-cell geometries; and some remarks on numerical methods for solution of the integral equation and for Laplace inversion of the transformed current.