Nafion is used extensively as a proton exchange membrane in PEM fuel cells. The membrane must be hydrated in order to function properly as an electrolyte and as a physical separation barrier between the anode and the cathode. In this project, potassium ferricyanide is added to the hydrating electrolyte solution and is shown to incorporate into the Nafion membrane. By using hydrodynamic voltammetry, the ferricyanide redox signals can be used as a diagnostic and an investigative tool to study the integrity and swelling properties of the Nafion membrane. When ferricyanide is absent from the hydrating solution, but present in the bulk electrolyte solution during the hydrodynamic voltammetry experiments, the signals produced (or lack thereof) can be used as a diagnostic tool for the physical integrity of the membrane. When ferricyanide is allowed to incorporate into the membrane, the properties of the hydrated membrane can be investigated. An new equation, known as the Tedford equation, was derived to determine the diffusion coefficient of the analyte in the bulk solution and an apparent diffusion of electrons within the membrane itself. The Tedford equation accounts for the dependence on the rotation rate as well as known membrane properties such as thickness and the concentration of the analyte incorporated into the membrane from the bulk solution during hydration.
For a bare rotating disk electrode, the Levich equation can be used to determine the bulk diffusion coefficient (D) by plotting the diffusion limiting current (iL
) against the square root of the rotation rate (ω).
iL=0.62nFAD2/3 ν-1/6 C* ω1/2 (1)
The slope is made up of the known variables where n is the number of electrons in the redox reaction, F is Faraday’s constant, A is the electroactive area of the electrode, ν is the kinematic viscosity of the solution, and C* is the concentration of the analyte in the bulk.
The Dahms-Ruff equation can be used to determine the apparent diffusion coefficient of electrons (DE) and the current due to this apparent diffusion (iE).
DE=D+kφ2 Cp* (π/4) (2)
iE=(FADE Cp*)/δm (3)
where k is the rate constant of the redox reaction, φ is the average distance between the redox centers in the membrane, Cp* is the total amount of analyte in the membrane, and δm is the membrane thickness.
Equations 1 and 3 were combined to derive the Tedford equation in relation to the peak current (ip).
ip=0.62nFAD2/3 v-1/6 ω1/2 (C*-Cm )+(nFADE Cm)/δm (4)
This equation can be used to determine the apparent diffusion coefficient of the electrons with the ferricyanide redox centers in the membrane. It can also be used to compare membranes with differing hydration times and possibly to study hydrating properties.