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arXiv · 1112.6049

Defects in Crystalline Packings of Twisted Filament Bundles: I. Continuum Theory of Disclinations

Gregory M. Grason
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Abstract

We develop the theory of the coupling between in-plane order and out-of-plane geometry in twisted, two-dimensionally ordered filament bundles based on the non-linear continuum elasticity theory of columnar materials. We show that twisted textures of filament backbones necessarily introduce stresses into the cross-sectional packing of bundles and that these stresses are formally equivalent to the geometrically-induced stresses generated in thin elastic sheets that are forced to adopt spherical curvature. As in the case of crystalline order on curved membranes, geometrically-induced stresses couple elastically to the presence of topological defects in the in-plane order. We derive the effective theory of multiple disclination defects in the cross section of bundle with a fixed twist and show that above a critical degree of twist, one or more 5-fold disclinations is favored in the elastic energy ground state. We study the structure and energetics of multi-disclination packings based on models of equilibrium and non-equilibrium cross-sectional order.

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Gregory M. Grason. 2011-12-28. Defects in Crystalline Packings of Twisted Filament Bundles: I. Continuum Theory of Disclinations. https://doi.org/10.1103/physreve.85.031603

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