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Title: 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 \begin{document}$ \varepsilon\ll1 $\end{document}, we show that this induces undulated bilayer solutions whose width perturbations decay on an \begin{document}$ O\!\left( \varepsilon^{-1/2}\right) $\end{document} inner length scale that is long in comparison to the \begin{document}$ O(1) $\end{document} scale that characterizes the bilayer width.

 
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Award ID(s):
1815079
NSF-PAR ID:
10382648
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Discrete and Continuous Dynamical Systems - S
Volume:
15
Issue:
9
ISSN:
1937-1632
Page Range / eLocation ID:
2633
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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