Abstract
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.
Highlights
A central goal of polymer chemistry is the design of materials with novel macroscopic properties by controlling the spontaneous generation of nanoscaled, phase separated networks [1,2]
We present applications of the binary mixture energy to Small Angle X-ray Scattering (SAXS) data for well-hydrated Nafion, and an extension of the energy to incorporate of ionic conduction in a framework that preserves the gradient flow structure
The functionalized Cahn-Hilliard (FCH) modeling framework extends the scope of the continuum variational approach to incorporate the influence of the solvation entropy of ions on the network morphology of phase separated materials
Summary
A central goal of polymer chemistry is the design of materials with novel macroscopic properties by controlling the spontaneous generation of nanoscaled, phase separated networks [1,2]. Continuum models of network formation in Nafion [18,19,20], have successfully predicted geometric features, such as pore radius and overall solvent uptake as a function of ionic group density, liquid phase pressure, and effective elastic response of the polymer phase. Key fuel cell membrane characteristics such as water uptake, gas transport, proton conductivity, and mechanical stability are linked to the presence and organization of the ionic and crystalline domains in PFSAs. Future improvement in PFSA performance requires a fundamental understanding of the formation and function of these essential morphological features.
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