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Variational Models of Network Formation and Ion Transport: Applications to Perfluorosulfonate Ionomer Membranes
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Department of Mathematics, Michigan Technological University, Houghton, MI 49931, USA
* Author to whom correspondence should be addressed.
Received: 31 December 2011; in revised form: 13 February 2012 / Accepted: 15 February 2012 / Published: 24 February 2012
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.
Keywords: ionomer membrane; functionalized cahn-hilliard; network morphology; ionic transport
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Gavish, N.; Jones, J.; Xu, Z.; Christlieb, A.; Promislow, K. Variational Models of Network Formation and Ion Transport: Applications to Perfluorosulfonate Ionomer Membranes. Polymers 2012, 4, 630-655.
Gavish N, Jones J, Xu Z, Christlieb A, Promislow K. Variational Models of Network Formation and Ion Transport: Applications to Perfluorosulfonate Ionomer Membranes. Polymers. 2012; 4(1):630-655.
Gavish, Nir; Jones, Jaylan; Xu, Zhengfu; Christlieb, Andrew; Promislow, Keith. 2012. "Variational Models of Network Formation and Ion Transport: Applications to Perfluorosulfonate Ionomer Membranes." Polymers 4, no. 1: 630-655.