Physical Sciences and Mathematics Commons^™

Variational Models Of Network Formation And Ion Transport: Applications To Perfluorosulfonate Ionomer Membranes, Nir Gavish, Jaylan Jones, Zhengfu Xu, Andrew Christlieb, Keith Promislow

Michigan Tech Publications

We present the functionalized Cahn-Hilliard (FCH) energy, a continuum characterization of interfacial energy whose minimizers describe the network morphology of solvated functionalized polymer membranes. With a small set of parameters the FCH characterizes bilayer, pore-like, and micelle network structures. The gradient flows derived from the FCH describe the interactions between these structures, including the merging and pinch-off of endcaps and formation of junctions central to the generation of network morphologies. We couple the FCH gradient flow to a model of ionic transport which incorporates entropic effects to localize counter-ions, yielding a flow which dissipates a total free energy, and an …