Competition and complexity in amphiphilic polymer morphology

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. (C) 2019 Elsevier B.V. All rights reserved.