| Electrodes are modified with polymer films to impart novel permeability, sensitivity, and catalytic properties. Often, redox probes partition from solution into films and are electrolyzed at the electrode. Films are assumed to be of uniform density and constant probe diffusion coefficients throughout the films. For uniform diffusion coefficient, Fick's second law describes transport 6cx,t 6t=D62c x,t6x2 where x, t, c(x, t), and D, are distance from the electrode, time, time and space dependent concentration, and probe diffusion coefficient. In some solvents, polymers form non-uniform films on surfaces. Diffusion coefficients are inversely proportional to medium viscosity and density. A more generalized form of Fick's second law describes spatially varying diffusion coefficients 6cx,t 6t=66x Dx6 cx,t6x =Dx 62cx,t 6x2+6D x6x6 cx,t6x .;Here, cyclic voltammetric responses are modeled for three different film structures: uniform, density gradient, and bilayer films. Simulations were developed by dimensionless, explicit finite difference methods. Simulation were validated against existing mathematical and simulation results. Simulation time scales sufficed to ensure probe diffusion lengths exceeded film thicknesses.;Voltammetric responses are characterized by relative fluxes in film and solution phases. For uniform films, when the flux conditions in the film and solution are comparable (Jfilm ≅ Jsolution), voltammograms assume the classical avian shape. When Jfilm > Jsolution, voltammograms become more symmetric or Gaussian, and when Jfilm < Jsolution, voltammograms have sigmoidal character. In graded density films, voltammetric morphology varies from avian to sigmoidal as the density gradient in the film steepens. In bilayer films, all three morphologies, avian, Gaussian, and sigmoidal, are observed, dependent on relative fluxes in the film and solution phases. For uniform and bilayer cases, diagnostic equations are derived.;Experimental data were analyzed for the uniform and density gradient films on glassy carbon electrodes. For the uniform film case, Nafion ® films were evaluated with redox probes of Fe( III) and Rubpy2+3 . For the density gradient case, Ficoll® films were probed with ferrocene. Film parameters were extracted with the derived diagnostic equations and by fitting of experimental voltammograms by simulation. Where two methods were applied, results were in good agreement. |
