The steady-state voltammetric behavior of spherical electrodes of nanometer dimensions (1 and 10 nm) is computed by numerical solution of the Nernst-Planck and Poisson equations. The results demonstrate that the reversible oxidation or reduction of an electroactive species, assumed to be present in solution at millimolar concentrations, is strongly affected by the electric field from the electrode surface, even in the presence of a large excess quantity of supporting electrolyte (0.5 M). The assumptions of electroneutrality or diffusion-controlled transport are shown to be generally inappropriate for analyzing the voltammetric response (wave shape and limiting current) of electrodes of dimensions less than similar to 0.1 mu m. Transport-limited currents corresponding to the oxidation or reduction of a charged electroactive species are significantly enhanced or depressed relative to values calculated by assuming electroneutrality. When a neutral reactant is oxidized or reduced, the limiting current is unaffected by the electric field, but the voltammetric wave no longer has a classical Nernstian shape and is shifted in potential with respect to a reference electrode. Depending on the relative values of the formal redox potential (E degrees') and the potential of zero charge (PZC), the nonclassical wave shape may lead to situations where a transport-limited electrochemical reaction appears to be limited by the rate of heterogeneous electron transfer. Conversely, it is possible for a kinetically limited oxidation or reduction to appear as a reversible reaction from an analysis of the voltammetric wave shape. The results are discussed in terms of a recent report of unusually large heterogeneous rate constants obtained by steady-state voltammetry at electrodes of nanometer dimensions.
