Steady-state limiting currents at finite conical microelectrodes.

The investigation of steady-state diffusion-limiting currents at finite conical microelectrodes is reported. Such electrodes are of particular interest as probes in studies of kinetic reactions, measurements in microenvironments, and high-resolution electrochemical imaging. The diffusion-limiting currents were calculated using numerical (finite element) analysis and compared to those obtained at inlaid disk and hemispheroidal microelectrodes. Time-dependent simulations demonstrating the approach of the diffusion current to a steady-state value are also reported. The steady-state diffusion-limiting currents obtained were found to be a strong function of the electrode geometry, including the aspect ratio of the cone and the thickness of the insulating sheath. Thus, simple, approximate analytical expressions which account for these geometrical dependencies in the simulated steady-state diffusion-limited currents are also reported. As a limiting case, an analytical approximation was obtained for the steady-state current to a microdisk as a function of the insulator thickness. The use of these approximate equations in calculating electrode radii from steady-state diffusion-limiting currents is demonstrated, and good agreement was found with previously reported experimental studies. Use of the frequently implemented hemispherical theory to analyze steady-state diffusion-limiting currents obtained with finite conical microelectrodes is shown to result in an experimentally acceptable underestimation of the electrode radius.