A Green function for the equilateral triangle

Using the image method, a diffusional Green function has been derived analytically for a triangle, when its three sides, all of equal length, have zero intensity. Because many image sites are involved, computational assistance is employed both to construct the Green function and to use it in solving practical problems. An alternative procedure based on eigenfunctions is also summarized.Received: November 18, 2003; revised: April 6, 2004     

The electrochemistry of electrode edges and its relevance to partially blocked voltammetric electrodes

Analytical mathematics and digital simulation are used to predict the response, to a potential jump, of the junction between insulating and conducting regions of an electrode. The simulation is carried out differentially and employs other novel features. Concentrations in the vicinity of edges of positive and negative curvatures, as well as straight edges, are analyzed by the model and thereby the faradaic current densities and currents are predicted. It is shown that, in addition to the well-understood cottrellian current arising from the surface of the conducting electrode, currents are generated that are proportional to the length of the edge and to its curvature. These results are then applied to inlaid disks and to partially blocked electrodes. The possibility is explored of using the response to a potential step to gain information on the geometry of a partially blocked electrode.