Solution landscapes of the diblock copolymer-homopolymer model under two-dimensional confinement

TL;DR

This paper explores the complex solution landscape of confined diblock copolymer-homopolymer systems in two dimensions using an extended Ohta--Kawasaki model, revealing new stationary solutions and symmetry-breaking phenomena.

Contribution

It introduces a novel computational approach combining saddle dynamics and search algorithms to identify and classify diverse stationary solutions in the model.

Findings

Identification of new stationary solution classes including Flower, Mosaic, Core-shell, and Tai-chi.

Demonstration of symmetry-breaking phenomena with increased solutions at larger domain sizes.

Mapping of transition pathways between stable states via saddle points.

Abstract

We investigate the solution landscapes of the confined diblock copolymer and homopolymer in two-dimensional domain by using the extended Ohta--Kawasaki model. The projected saddle dynamics method is developed to compute the saddle points with mass conservation and construct the solution landscape by coupling with downward/upward search algorithms. A variety of novel stationary solutions are identified and classified in the solution landscape, including Flower class, Mosaic class, Core-shell class, and Tai-chi class. The relationships between different stable states are shown by either transition pathways connected by index-1 saddle points or dynamical pathways connected by a high-index saddle point. The solution landscapes also demonstrate the symmetry-breaking phenomena, in which more solutions with high symmetry are found when the domain size increases.