In typical applications of electrochemistry, Fick's second law for diffusion is established with spatially invariant diffusion coefficients. However, when the diffusion coefficient is spatially dependent, D(x), Fick's second law in one dimension, as shown below, introduces opportunities to control transport.

When the diffusion coefficient varies spatially and the solution is quiescent, steady state flux of the diffusant is possible. Films of nonuniform density and viscosity on electrodes provide a matrix to establish domains with spatially varying diffusion coefficients. To explore impacts of D(x) on probe transport through films under voltammetric perturbation, several inquiries were undertaken.
The impact of spatially varying diffusion coefficients is simulated by explicit finite difference for a redox probe moving through a graded film on an electrode. Voltammetric morphologies vary with the structucture of the gradient. Sigmoidal voltammograms result as cyclic voltammetric scan rate slows.
Graded diffusion coefficients are established on electrodes by modification of density gradient polymers such as Ficoll^{®}. Sigmoidal voltammograms with limiting currents independent of scan rate are observed at slow scan rates, consistent with steady state transport in a domain where the diffusion coefficient is spatially varying.
Ion exchange polymer Nafion cocast with a graded density polymer similarly impacts transport of a probe through the graded Nafion film and sigmoidal voltammograms are observed.
The interplay between Fick's second law with spatially varying diffusion coefficients; simulation of voltammetry with D(x); and implementation of graded diffusion coefficients on electrode modification by Ficoll and by Ficoll-Nafion composites will be presented.