Diffusion within a layered, graphite-like, spherical electrode: Theoretical aspects

A method of analysis is presented whereby one may determine from chronocoulometric measurements whether a spherical electrode is isotropic or anisotropic. To be examined theoretically is diffusion of a species within a collection of flat impermeable disks stacked parallel to and at equal distance from each other, forming an enveloping spherical surface. Within this model, which mimics a layered, graphite-like spherical electrode, species can enter (or leave) each of the disks only through the edge, i.e., transport across the faces of the disks is not allowed. The functional form of the transient dimensionless flux for this stratified structure, following a concentration step at the surface, was found to be very similar to that of an isotropic sphere of the same radius subject to otherwise identical conditions. However, the times required for the two types of spheres to achieve a prescribed fraction of their maximum capacity were found to differ, particularly for short times. Provided the number of disks is known, a parameter that can be easily obtained from the size of the particle and the interplanar distance of the layered material, the analysis presented in this work affords means of extracting from the experimental data the correct diffusion coefficient of the species within the stratified lattice, and thus assessing the error involved by assuming the sphere to be isotropic.