Minimal Bending Energies of Bilayer Polyhedra

TL;DR

This paper investigates the elastic bending energies of bilayer polyhedra, revealing that certain polyhedral shapes are energetically more favorable than spheres, with the snub dodecahedron often being the most stable shape.

Contribution

It introduces a model considering amphiphile segregation along ridges, showing that bilayer polyhedra can have lower energies than spherical vesicles and identifying the most stable polyhedral shape.

Findings

Bilayer polyhedra can have lower bending energies than spherical vesicles.

The snub dodecahedron is generally more energetically favorable than the icosahedron.

Segregation of amphiphiles along ridges influences shape stability.

Abstract

Motivated by recent experiments on bilayer polyhedra composed of amphiphilic molecules, we study the elastic bending energies of bilayer vesicles forming polyhedral shapes. Allowing for segregation of excess amphiphiles along the ridges of polyhedra, we find that bilayer polyhedra can indeed have lower bending energies than spherical bilayer vesicles. However, our analysis also implies that, contrary to what has been suggested on the basis of experiments, the snub dodecahedron, rather than the icosahedron, generally represents the energetically favorable shape of bilayer polyhedra.