Spatially averaging electrodes.

Both potentiometric and voltammetric measurements report on the concentration of the analyte in the closest layer of the sample solution that is unperturbed by the measurement. Besides this local concentration, the solution composition within the thin boundary layer adjacent to the electrode|solution interface is influenced also by local mass transport and other electrochemical processes necessary for signal transduction. This local perturbation of concentrations is typically corrected for by calibration so that the ultimate output of the measurement is the local concentration, at a distance of a few micrometers to about 100 microm from the electrode surface. In contrast to many optical techniques, the electrochemical approach is therefore only capable of measuring local concentrations but cannot be used to assess three-dimensional (3D)-averaged bulk concentrations of inhomogeneous samples. This may pose a problem in very small samples where homogenization by stirring is difficult. We present here the concept of spatially averaging electrodes that can, due to their special design, report 3D spatially averaged bulk concentration of inhomogeneous samples that have some type of symmetry. Within a given type of symmetry an infinite variation of concentration distribution may exist. We illustrate the concept of spatially averaging electrodes with results obtained in microliter-sized hemispherical samples with a source in the center of the drop.