Self-Assembly of Triblock Copolymers Under Soft Confinement: Solution Landscape, Bifurcation Diagram, and Heatmap

We investigate the self-assembly of triblock copolymers under soft confinement with a multicomponent triblock homopolymer-copolymer (THC) model. To address computational challenges associated with multiple components and mass conservation, we develop a novel accelerated projection saddle dynamics (A-PSD) method and prove the linear stability theory of the continuous A-PSD rigorously. With this algorithm, we numerically construct solution landscapes, a bifurcation diagram, and heatmaps to systematically study the THC model. First, we derive a multitude of extreme points, which can be categorized into several classes, including Layer class, Flower class, Circle class and Core-Shell class. The connections between these classes are established and some novel structures are observed. Next, we illustrate the emergence of critical points and the impact of domain size with a bifurcation diagram. Finally, we employ heatmaps to visualize the impact of volume fractions on the morphological behavior of the system.