Solid domains in lipid vesicles and scars

Abstract

The free energy of a crystalline domain coexisting with a liquid phase on a spherical vesicle may be approximated by an elastic or stretching energy and a line tension term. The stretching energy generally grows as the area of the domain, while the line tension term grows with its perimeter. We show that if the crystalline domain contains defect arrays consisting of finite length grain boundaries of dislocations (scars) the stretching energy grows linearly with a characteristic length of the crystalline domain. We show that this result is critical to understand the existence of solid domains in lipid-bilayers in the strongly segregated two phase region even for small relative area coverages. The domains evolve from caps to stripes that become thinner as the line tension is decreased. We also discuss the implications of the results for other experimental systems and for the general problem that consists in finding the ground state of a very large number of particles constrained to move on a fixed geometry and interacting with an isotropic potential.

7 pages, 6 eps figures

References in corpus (6)

• Grain Boundary Scars and Spherical Crystallography
• Virus shapes and buckling transitions in spherical shells
• Interacting Topological Defects on Frozen Topographies
• Direct Visualization of Dislocation Dynamics in Grain Boundary Scars
• Ground state of a large number of particles on a frozen topography
• Universality in the Screening Cloud of Dislocations Surrounding a Disclination

Cited by in corpus (7)

• Perspective: Geometrically-Frustrated Assemblies
• Crystallography on Curved Surfaces
• Crystalline Particle Packings on a Sphere with Long Range Power Law Potentials
• Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary
• Effect of dipolar moments in domain sizes of lipid bilayers and monolayers
• Topological vacancies in spherical crystal clusters
• Crystalline membrane morphology beyond polyhedra