Multiscale Model of Proton Transport in Perfluorosulfonic-Acid Membrane
Building on previous multiscale modeling efforts1, we use a resistor-network paradigm to describe ionomers as a network of conductive nodes and throats. The effective network resistance is a function of the connectivity of the network and transport resistance between each neighboring node. We use common imaging methods to extract the network geometry from direct imaging of the ionomer2. Molecular theory and simulations are used to describe and calculate the proton conductivity in throats as a function of size. Kirchhoff's circuit laws are applied on each node in the system and the effective resistance across the membrane is determined for ion conduction. Once designed, a poroelastic model is used to change node and throat sizes and subsequent network connectivity with water content and swelling.
This work was funded by the Assistant Secretary for Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office, of the U. S. Department of Energy under contract number DE-AC02-05CH11231 and by a National Science Foundation Graduate Research Fellowship under Grant No. DGE 1106400
 J. T. Gostick and A. Z. Weber, “Resistor-Network Modeling of Ionic Conduction in Polymer Electrolytes,” Electrochimica Acta.
 F. I. Allen, L. R. Comolli, A. Kusoglu, M. A. Modestino, A. M. Minor, and A. Z. Weber, “Morphology of Hydrated As-Cast Nafion Revealed through Cryo Electron Tomography,” ACS Macro Lett., vol. 4, no. 1, pp. 1–5, Jan. 2015.
Figure 1. 3D projection of pore-network generated from skeletonization of cryo-TEM tomography image of Nafion ionomer. The green cylinders show throats of the hydrophilic network connecting nodes, shown as red balls. The background is a cutaway of the network where blue is the hydrophilic domain and black the hydrophobic backbone.