Pathways to faceting of vesicles

Abstract

The interplay between geometry, topology and order can lead to geometric frustration that profoundly affects the shape and structure of a curved surface. In this commentary we show how frustration in this context can result in the faceting of elastic vesicles. We show that, under the right conditions, an assortment of regular and irregular polyhedral structures may be the low energy states of elastic membranes with spherical topology. In particular, we show how topological defects, necessarily present in any crystalline lattice confined to spherical topology, naturally lead to the formation of icosahedra in a homogeneous elastic vesicle. Furthermore, we show that introducing heterogeneities in the elastic properties, or allowing for non-linear bending response of a homogeneous system, opens non-trivial pathways to the formation of faceted, yet non-icosahedral, structures.

References in corpus (9)

• Virus shapes and buckling transitions in spherical shells
• Elastic theory of unconstrained non-Euclidean plates
• Smectic Polymer Vesicles
• Buckling transition in icosahedral shells subjected to volume conservation constraint and pressure: relations to virus maturation
• Universal formulae for the limiting elastic energy of membrane networks
• Self-assembly of liquid crystal block copolymer PEG-b-smectic polymer in pure state and in dilute aqueous solution
• Nonlinear elastic model for faceting of vesicles with soft grain boundaries
• Minimal Bending Energies of Bilayer Polyhedra
• A curvature-driven effective attraction in multicomponent membranes

Cited by in corpus (5)

• A Theory of Shape-Shifting Droplets
• Formation of polyhedral vesicles and polygonal membrane tubes induced by banana-shaped proteins
• Shape-Shifting Polyhedral Droplets
• Complex Self-Assembly from Simple Interaction Rules in Model Colloidal Mixtures
• Geometry and dynamics of spring networks of spherical topology