Competition and complexity in amphiphilic polymer morphology

• Published in: Physica. D Vol. 400; p. 132144
• Main Authors: Christlieb, Andrew, Kraitzman, Noa, Promislow, Keith
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.12.2019
• Subjects: Amphiphilic interface; Curvature driven flow; Functionalized Cahn–Hilliard energy; Geometric evolution; Multiscale analysis; Network formation; Curvature driven flow; Network formation; Geometric evolution; Functionalized Cahn–Hilliard energy; Amphiphilic interface; Multiscale analysis
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2019.06.010

The strong functionalized Cahn–Hilliard equation models self assembly of amphiphilic polymers in solvent. It supports codimension one and two structures that each admit two classes of bifurcations: pearling, a short-wavelength in-plane modulation of interfacial width, and meandering, a long-wavelength instability that induces a transition to curve-lengthening flow. These two potential instabilities afford distinctive routes to changes in codimension and creation of non-codimensional defects such as end caps and Y-junctions. Prior work has characterized the onset of pearling, showing that it couples strongly to the spatially constant, temporally dynamic, bulk value of the chemical potential. We present a multiscale analysis of the competitive evolution of codimension one and two structures of amphiphilic polymers within the H−1 gradient flow of the strong Functionalized Cahn–Hilliard equation. Specifically we show that structures of each codimension transition from a curve lengthening to a curve shortening flow as the chemical potential falls through a corresponding critical value. The differences in these critical values quantify the competition between the morphologies of differing codimension for the amphiphilic polymer mass. 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. In particular we propose that the experimentally observed onset of morphological complexity arises from a transient passage through pearling instability while the associated flow is in the curve lengthening regime. •Analyze self-assembly of codimension one and two morphologies in amphiphilic castings.•Derivation of regularized curve lengthening equations that drive morphological competition.•Characterize morphological complexity as transient passage through pearling instability.•Comparison of FCH flow with experiment, molecular dynamics, and self-consistent field theory.