Functionalized polymer membranes have a strong
affinity for solvent, imbibing it to form charge-lined networks which
serve as charge-selective ion conductions in a host of energy conversion
applications. We present a continuum model, based upon a reformulation
of the Cahn-Hilliard free energy, which incorporates solvation energy and
counter-ion
entropy to stabilize a host of network morphologies. We derive geometric
evolution for co-dimension one bilayers and co-dimension two pore
morphologies
and show that the system possesses a simple mechanism for competitive
evolution of co-existing networks through the common far-field chemical
potential.