Diffusion-Limited Currents to Nanoparticles of Various Shapes Supported on an Electrode; Spheres, Hemispheres, and Distorted Spheres and Hemispheres

The finite difference method is used to simulate the current at a spherical nanoparticle sitting upon a planar electrode, assuming electrolysis occurs only at the nanoparticle surface. The accuracy of the simulation technique is confirmed by using the same approach to simulate a hemispherical electrode. Nanoparticles with the geometry of a distorted sphere or hemisphere are also considered. Equations are given for the corresponding mass-transport-limiting current. For the spherical nanoparticle, this expression is i lim = −8.71 nFDr s [A] bulk, where D is the diffusion coefficient, r s is the radius of the particle, [A] bulk is the bulk concentration of the electroactive species, and n is the number of electrons transferred.