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Theory is presented for cyclic voltammetry at a hemispherical electrode under conditions where the electric field is nonzero and migration is significant to mass transport. The nonlinear set of differential equations formed by combining the Nernst-Planck equation and the Poisson equation are solved numerically, subject to a zero-field approximation at the electrode surface. The effects on the observed voltammetry of the electrode size, scan rate, diffusion coefficient of electroactive and supporting species, and quantity of supporting electrolyte are noted. Comparison is drawn with experimental voltammetry for the aqueous system [Ru(NH 3 ) 6 ] 3+/2+ at a Pt macroelectrode with varying levels of supporting electrolyte KCl. The approximations concerned are shown to be applicable where the ratio of supporting (background) electrolyte to bulk concentration of electroactive species (support ratio) exceeds 30, and general advice is given concerning the quantity of supporting electrolyte required for quantitatively diffusion-only behavior in macroelectrode cyclic voltammetry. In particular, support ratios are generally required to be greater than 100 and certainly substantially greater than 26, as has been suggested for the steady-state case.

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The reduction of oxygen was studied over a range of temperatures (298−318 K) in n -hexyltriethylammonium bis(trifluoromethanesulfonyl)imide, [N6,2,2,2][NTf2], and 1-butyl-2,3-methylimidazolium bis(trifluoromethanesulfonyl)imide, [C4dmim][NTf2] on both gold and platinum microdisk electrodes, and the mechanism and electrode kinetics of the reaction investigated. Three different models were used to simulate the CVs, based on a simple electron transfer (‘E’), an electron transfer coupled with a reversible homogeneous chemical step (‘ECrev’) and an electron transfer followed by adsorption of the reduction product (‘EC(ads)’), and where appropriate, best fit parameters deduced, including the heterogeneous rate constant, formal electrode potential, transfer coefficient, and homogeneous rate constants for the ECrev mechanism, and adsorption/desorption rate constants for the EC(ads) mechanism. It was concluded from the good simulation fits on gold that a simple E process operates for the reduction of oxygen in [N6,2,2,2][NTf2], and an ECrev process for [C4dmim][NTf2], with the chemical step involving the reversible formation of the O2 •−··· [C4dmim]+ ion-pair. The E mechanism was found to loosely describe the reduction of oxygen in [N6,2,2,2][NTf2] on platinum as the simulation fits were reasonable although not perfect, especially for the reverse wave. The electrochemical kinetics are slower on Pt, and observed broadening of the oxidation peak is likely due to the adsorption of superoxide on the electrode surface in a process more complex than simple Langmuirian. In [C4dmim][NTf2] the O2 •− predominantly ion-pairs with the solvent rather than adsorbs on the surface, and an ECrev quantitatively describes the reduction of oxygen on Pt also.

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Numerical solution of the equilibrium Poisson−Boltzmann equation for hemispherical electrodes of vanishing size reveals that the effects of curvature on the diffuse double layer become significant for electrodes with radii less than 50 nm. These effects include dramatically enhanced capacitance and hence more a rapid potential drop from the outer Helmholtz plane as far as the characteristic tunnelling length for electron transfer. An enhanced driving force is therefore expected for nanoelectrodes as compared to electrodes larger than 50−100 nm, especially at low concentrations of supporting electrolyte.

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