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

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.

arXiv comment9 pages, 8 figures

References in corpus (7)

• Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
• Phase diagram for diblock copolymer melts under cylindrical confinement
• Construction of a pathway map on a complicated energy landscape
• Finding All the Stationary Points of a Potential Energy Landscape via Numerical Polynomial Homotopy Continuation Method
• Searching the solution landscape by generalized high-index saddle dynamics
• Solution landscape of a reduced Landau-de Gennes model on a hexagon
• Pathways connecting two opposed bilayers with a fusion pore: A molecularly-informed phase field approach

Cited by in corpus (2)

• Transition pathways in Cylinder-Gyroid interface
• Spectral Deferred Correction Method for Landau-Brazovskii Model with Convex Splitting Technique