Fickian Diffusion Constrained on Spherical Surfaces: Voltammetry

Abstract

A model is developed for the voltammetric response due to surface charge injection at a single point on the surface of a sphere on whose surface the electroactive material is confined. Accordingly, charge diffusion is constrained to the spherical surface and thus mimicks the voltammetric response of immobilised microparticles derivatised with electroactive material. The full cyclic voltammetric response is investigated, and the peak currents, the peak-to-peak separation and the symmetry of the voltammetric wave are shown to be indicative of the heterogeneous kinetics and the geometry of the adsorbed microparticle. The results show strong deviations from the responses expected for planar diffusion.

Solid‐State Electrochemical Reactions of Electroactive Microparticles and Nanoparticles in a Liquid Electrolyte Environment

“…For many other cases of functionalized carbon nanotubes (or modified graphite electrodes), Compton et al also identified a square root of scan rate dependency of peak currents [31,32]. These findings have been explained on a theoretical basis by the (non-Cottrellian) propagation of charge on the carbon particle surface [33,34], whereby electrons are assumed to hop from one chemical moiety to another, all being attached to the particle surface, as depicted in Figure 6.7.…”

“…Thompson and Compton investigated, from a theoretical standpoint, the case of a spherical microparticle with an electroactive compound on its surface and attached to a solid electrode surface [33,34]. The movement of charge was assumed to start exclusively from the contact point (or line) between the microparticle and electrode (i.e., at the three-phase boundary, if an electrolyte phase is considered) and to proceed over the particle surface only (see also Section 6.3.1).…”

“…In Ref. [33], the idealized microparticle geometries of a full sphere, a hemisphere, and an inverted hemisphere have been considered (cf. Figure 6.8).…”

“…The inverted hemisphere geometry shows near-identical responses as for the sphere, Figure 6.10 Plots of peak-to-peak separation against log v norm for k 0 ¼ 1 Â 10 À5 and different sphere radii. Results for spheres and hemispheres are compared with the case for planar diffusion only [33].…”

Electrochemistry of Metal Nanoparticles and Quantum Dots

“…10 can be constructed [67]. Compton et al have provided theoretical modeling of charge diffusion on the surface of immobilized spherical particles [67], voltammetry at random microparticle arrays [68], and dissolution of microparticle arrays [69] and nanoparticle detection [70]. Direct oxidation of the Ag nanoparticles during collision events was monitored by the presence of a spike under oxidative current.…”