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Soft modes near the buckling transition of icosahedral shells
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.ORCID iD: 0000-0002-9881-7857
2007 (English)In: Physical Review E, ISSN 1539-3755, Vol. 76, no 3Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2007. Vol. 76, no 3
Keyword [en]
mechanical-properties, viral capsids, membranes, dynamics, viruses, symmetry, order
URN: urn:nbn:se:kth:diva-16982DOI: 10.1103/PhysRevE.76.031911ISI: 000249785800091ScopusID: 2-s2.0-34548838615OAI: diva2:335025
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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