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) = -8.71nFDr(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.