Ohta-Kawasaki energy for amphiphiles: asymptotics and phase-field simulations

Abstract

We study the minimizers of a degenerate case of the Ohta-Kawasaki energy, defined as the sum of the perimeter and a Coulombic nonlocal term. We start by investigating radially symmetric candidates which give us insights into the asymptotic behaviors of energy minimizers in the large mass limit. In order to numerically study the problems that are analytically challenging, we propose a phase-field reformulation which is shown to Gamma-converge to the original sharp interface model. Our phase-field simulations and asymptotic results suggest that the energy minimizers exhibit behaviors similar to the self-assembly of amphiphiles, including the formation of lipid bilayer membranes.

51 pages; 14 figures; minor revisions made

References in corpus (5)

• Pathways connecting two opposed bilayers with a fusion pore: A molecularly-informed phase field approach
• On the Ternary Ohta-Kawasaki Free Energy and Its One-dimensional Global Minimizers
• Lamellar phase solutions for diblock copolymers with nonlocal diffusions
• Nonlocal Effect on a Generalized Ohta-Kawasaki Model
• Bifurcation and fission in the liquid drop model: a phase-field approach