UNDULATED BILAYER INTERFACES IN THE PLANAR FUNCTIONALIZED CAHN-HILLIARD EQUATION

Experiments with diblock co-polymer melts display undulated bilayers that emanate from defects such as triple junctions and endcaps, [8]. Undulated bilayers are characterized by oscillatory perturbations of the bilayer width, which decay on a spatial length scale that is long compared to the bilayer width. We mimic defects within the functionalized Cahn-Hillard free energy by introducing spatially localized inhomogeneities within its parameters. For length parameter epsilon << 1, we show that this induces undulated bilayer solutions whose width perturbations decay on an O (epsilon(-1/2)) inner length scale that is long in comparison to the O(1) scale that characterizes the bilayer width.