Competition and Complexity in Amphiphilic Polymer Morphology

TL;DR

This paper investigates the evolution and competition of different morphologies in amphiphilic polymers using a gradient flow model, revealing bifurcations leading to pearling and fingering instabilities, supported by simulations and experiments.

Contribution

It introduces a bifurcation analysis of morphology evolution in the Functionalized Cahn-Hilliard model, connecting theoretical predictions with simulations and experiments.

Findings

Identification of bifurcation types leading to pearling and fingering instabilities.

Quantitative comparison of model predictions with simulations.

Qualitative agreement with laboratory experiments.

Abstract

We analyze the competitive evolution of codimension one and two morphologies within the $H^{-1}$ gradient flow of the strong Functionalized Cahn-Hilliard equation. On a slow time scale a sharp hypersurface reduction yields a degenerate Mullins-Sekerka evolution for both codimension one and two hypersurfaces, leading to a geometric flow that depends locally on curvatures couples to the dynamic value of the spatially constant far-field chemical potential. Both codimension one and two morphologies admit two classes of bifurcations, one leads to pearling, a short-wavelength in-plane modulation of interfacial width, the other flips motion by curvature to the locally-ill posed motion against curvature, which leads to fingering instabilities. We present a bifurcation diagram for the morphological competition, and compare our results quantitatively to simulations of the full system and qualitatively to simulations of self-consistent mean field models and laboratory experiments; illuminating the role of the pearling bifurcation in the development of complex network morphologies.