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arXiv · 2104.06386

Undulated Bilayer Interfaces in the Planar Functionalized Cahn-Hilliard Equation

Keith Promislow·Qiliang Wu
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Abstract

Experiments with diblock co-polymer melts display undulated bilayers that emanate from defects such as triple junctions and endcaps, \cite{batesjain_2004}. 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 $\varepsilon\ll1$, we show that this induces undulated bilayer solutions whose width perturbations decay on an $O\!\left(\varepsilon^{-1/2}\right)$ inner length scale that is long in comparison to the $O(1)$ scale that characterizes the bilayer width.

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Keith Promislow, Qiliang Wu. 2021-04-13. Undulated Bilayer Interfaces in the Planar Functionalized Cahn-Hilliard Equation. https://arxiv.org/abs/2104.06386

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