Paired microelectrodes or arrays of mikroelectrodes are often used in modern electrochemistry because they offer a possibility to generate different species at different microelectrodes, including anion and cation radicals, which allows to investigate electrogenerated chemiluminescence (ECL). Recently, we used the conformal transformation for the simulation of the double hemicylinder generator-collector microelectrode assembly [1], which is applied here for investigation of ECL in a cell with two parallel-hemicylindrical microelectrodes. Employment of the conformal mapping techniques for the simulation of two-dimensional electrochemical problems at microelectrodes represents the most efficient and easiest way of obtaining an accurate numerical solution for diffusion at microelectrodes or microelectrode assemblies. Conformal transforms allow mapping of a two-dimensional real space, where the flux lines may be extremely curved or present singularities onto a space in which the flux lines become (almost) parallel [2]. It is probably the best numerical approach for the symmetrical electrode problems.
Furthermore, conformal mappings have the important own properties and often allow obtaining the exact solution of the problem. There are a few analytical solutions for the steady-state current in the double-band and channel-double-band microelectrode generator-collector systems using the conformal mapping [3-6] and ECL steady state intensity for the double-band microelectrode system [3, 4]. The analytical expressions for the steady-state current and ECL intensity in a cell with two microelectrode hemicylinders are presented here. Our next aim is to compare the efficiency of ECL emission in two different microelectrode systems: with two bands [3,4] and two hemicylinders, where the equal conditions have been created for: the ECL excitation (the same reaction scheme), equal electrode surface areas (with the corresponding radii, widths and length of the electrodes) and common numerical approach for the simulations (i.e., the conformal mappings and the ADI method) in both cases.

References
1. C. Amatore, A. I. Oleinick, I.B. Svir, J. Electroanal. Chem. 553 (2003) 49.
2. C. Amatore, in I. Rubinstein (Ed.), Physical Electrochemistry: Principles, Methods and Applications, M. Dekker, New York. (Ch. 4) 1995.
3. B. Fosset, C. A. Amatore, J. E. Bartelt, A.C. Michael, R. M. Wightman, Anal. Chem. 63 (1991) 306.
4. C. A. Amatore, B. Fosset, K. M. Maness, R. M. Wightman, Anal. Chem. 65 (1993) 2311.
5. I. A. Arkoub, C. Amatore, C. Sella, L. Thouin, J.-S. Warkocz, J. Phys. Chem. B 105 (2001) 8694.
6. C. Amatore, C. Sella, L. Thouin, J. Phys. Chem. B 106 (2002) 11565.

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1. Simulation of the Droplet Interior Problem