Kaytlin Brinker modeled proton exchange membrane fuel cells by developing equations to describe the charge distribution in the Stern layer and diffuse layer of the membrane. Her results showed that including the charge imbalance in the membrane is important for calculating fuel cell properties accurately. For future work, she plans to use molecular modeling software to simulate proton diffusion in Nafion under varying hydration conditions and predict transport properties from a theoretical diffusion model.

1. KAYTLIN BRINKER ADVISOR: PROFESSOR PHILIP TAYLOR CASE WESTERN RESERVE UNIVERSITY Computer Modeling of Proton Exchange Membrane Fuel Cells August 4, 2009 Physics REU 2009 Final Presentation

13. model In determining the charge distribution, we first modeled the kinetics of the Stern layer with the Butler-Volmer equation for electrochemical reactions, Next, the diffuse layer is represented by equations for the relation between field and charge density, Poisson’s equation, and the movement of ions across the membrane including the concentration gradient and electric potential, Nernst-Planck equation, Figure 5: First fuel cell developed in 1839 by Sir William Grove. NASA was the first to use fuel cells, installing them for the generation of electricity on Gemini and Apollo spacecraft in the 1960s. http://www.energysolutionscenter.org/distgen/Tutorial/Cogeneration.htm

14. model The field in the electrolyte for the Stern layer is derived from the BV equation , Since an electric field must be continuous, the field from the Stern layer must match the field in the diffuse layer. The Poisson and NP equation can be solved simultaneously for a function of the potential, Here the fractional surface charge density change is, Figure 6: Platinum nanoparticles (gold) with long chains of Nafion (green, blue red, and yellow) where some become adsorbed over the metallic clusters. The background contains water molecules (red and white). http://www.nersc.gov/news/annual_reports/annrep03/advances/4.1.fuelcells.html

17. results Figures 7, 8, & 9: The potential gradient in the Stern layer depends on the charge density in the membrane. The charge density in the diffuse layer depends on the potential gradient in the diffuse layer. Because the electric field must be continuous we can self-consistently determine these quantities. By graphing the potential gradient from both the diffuse and Stern layers, we can obtain a value for the position, r s , where they cross. From this we know the entire charge distribution in the membrane. Stern Layer Diffuse Layer Stern and Diffuse Layers

28. questions?