Quantitative characterization of uniform density, electrochemically inert films on electrodes is achieved by cyclic voltammetry (CV) of a redox probe that partitions from electrolyte into the film. Electrochemically inert films generate no faradaic current in the voltammetric window of the probe. In simulation models, probes pre-equilibrate into films, electrolyze at electrodes, diffuse in film and solution, and extract across film solution interfaces. Film thickness is ℓ. Diffusion length δ approximates distance from the electrode where voltammetry perturbs probe concentration; δ∝ν− 1/2 for scan rate ν. At high ν, δ < ℓ and voltammetric morphologies are typical of semi-infinite linear diffusion. As ν slows, δ ≳ ℓ and CV morphologies can change with relative probe flux in the film and solution. For higher solution flux, voltammograms assume sigmoidal (S-shaped) characteristics; higher film flux generates gaussian (thin layer CV) characteristics. For film and solution diffusion coefficients Df and Ds and κ the equilibrium ratio of probe concentration in film to solution, diagnostics yield κ√(Df/Ds) and ℓ2/Df. Because diagnostics apply for all ν, films are fully parameterized by CV alone. Without these diagnostics, full characterization requires a second, steady state voltammetric measurement. Diagnostics are vetted with [Ru(bpy)3]2 + (probe) in inert polymer films of Nafion and of poly(styrenesulfonate).

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Simulations of cyclic voltammograms for a system with a spatially variant diffusion profile are presented. An expanded version of Fick’s Second Law is used to account for a diffusion coefficient that varies with x, distance normal to the electrode surface. Parameters to define the slope and magnitude of a linearly graded diffusion profile are described. A one dimensional explicit finite difference simulation method is used and parameters are made to be dimensionless. The simulation is vetted by comparison with Nicholson and Shain simulations and determination of the resolution limits. Morphological changes in cyclic voltammograms are observed that indicate an approach to steady state diffusion.

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