Theoretical treatment of the amperometric current response of multiple microelectrode arrays

A theoretical approach to the steady-state limiting current response behavior of multiple microelectrode arrays, consisting of spherical, hemispherical, disk-shaped, or hemicylindrical electrode units, is presented. An approximative treatment is given for realistic arrays that contain microelectrodes of finite size and a rigorous description is offered for hypothetical arrays of point or line electrodes. The theories account for convection influences in the sample solution by restricting the diffusional mass transport of electroactive species between bulk sample and electrodes to a stagnant diffusion layer of variable average thickness. The parameters controlling the current efficiency of different arrays are discussed. The results show that arrays with a very low packing density of microelectrodes ideally yield the multiple response of a single microelectrode. The same behavior is generally found for interdigitated electrode arrays. In contrast, closely packed arrays of uniform electrodes simply mimic the response of a conventional macroelectrode of the same total surface area.