2007/06/28 by Michael Widom, M. Widom, Jack Lidmar +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Environmental Science · Materials Science · Physics and Astronomy · #Bacteriophages and microbial interactions #Lipid Membrane Structure and Behavior #Supramolecular Self-Assembly in Materials #physics.bio-ph
paper · pdf · doi:10.1103/physreve.76.031911
28 pages, 6 figures
arxiv created 2007/06/28 · openalex publication_date 2007/09/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Icosahedral shells undergo a buckling transition as the ratio of Young's modulus to bending stiffness increases. Strong bending stiffness favors smooth, nearly spherical shapes, while weak bending stiffness leads to a sharply faceted icosahedral shape. Based on the phonon spectrum of a simplified mass-and-spring model of the shell, we interpret the transition from smooth to faceted as a soft-mode transition. In contrast to the case of a disclinated planar network where the transition is sharply defined, the mean curvature of the sphere smooths the transition. We define elastic susceptibilities as the response to forces applied at vertices, edges, and faces of an icosahedron. At the soft-mode transition the vertex susceptibility is the largest, but as the shell becomes more faceted the edge and face susceptibilities greatly exceed the vertex susceptibility. Limiting behaviors of the susceptibilities are analyzed and related to the ridge-scaling behavior of elastic sheets. Our results apply to virus capsids, liposomes with crystalline order, and other shell-like structures with icosahedral symmetry.