Variational Models of Network Formation and Ion Transport: Applications to Perfluorosulfonate Ionomer Membranes

Polymers

Nir Gavish¹  Jaylan Jones¹  Zhengfu Xu¹  Andrew Christlieb¹ 

[1] ¹Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA ²Department of Mathematics, Michigan Technological University, Houghton, MI 49931, USA

关键词: ionomer membrane;    functionalized cahn-hilliard;    network morphology;    ionic transport;   

DOI  :  10.3390/polym4010630

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.