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The characterization of quasi-hemispherical Pt electrodes of nanometer dimensions (radius 2-150 nm), prepared by electrophoretic coating of etched Pt wires with poly(acrylic acid), is described. The goals of these experiments are to estimate the accuracy of using steady-state voltammetric limiting currents ([i.sub.lim]) in determining the true electrode area and to develop new electrochemical methods for rapidly screening individual electrodes for nonideal geometries. Electrochemical active areas were determined by measuring the electrical charge (Q) associated with oxidation of adsorbed bis (2,2'-bipyridine)chloro(4,4'-trimethylenedipyridine)osmium(II) in fast-scan voltammetric measurements (scan rate 1000 V/s). Voltammetric peaks corresponding to oxidation of as few as ~7000 molecules (~11 zmol) at individual electrodes are reported, allowing precise measurement of electrode areas as small as [~10.sub.-10] [cm.sub.2]. A plot of [i.sup.lim] (for a soluble redox species) versus [Q.sup.1/2] (for an adsorbed redox species), constructed from [i.sub.lim]-[Q.sup.1/2] data pairs obtained as a function of the electrode radius, is shown to be linear if the electrode geometry is independent of electrode radius; departure of experimental values from the straight-line plot is a diagnostic indicator of a nonideal electrode geometry. The results indicate that ~50% of the electrodes prepared by the electrophoretic polymer-coating procedure are quasi-hemispherical, the remaining being recessed slightly below the polymer coating. The heterogeneous electron-transfer rate constant for the oxidation of the ferrocenylmethyltrimethylammonium cation in [H.sub.2]O/ 0.2 M KCI was also determined from steady-state voltammetry using the method of Mirkin and Bard and found to be [4.sub.8][+ or -] 3.2 cm/s with [alpha]=0.[6.sub.4] [+ or -] [0.1.sub.5].