Department of Mathematical Sciences
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 expression for the excess electrochemical potential which combines electrostatic and entropic effects. We present applications to network bifurcation and membrane casting.
Variational models of network formation and ion transport: Applications to perfluorosulfonate ionomer membranes.
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