PMID: 22587104May 17, 2012Paper

Defects in crystalline packings of twisted filament bundles. I. Continuum theory of disclinations

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Gregory M Grason

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 nonlinear 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 fivefold disclinations is favored in the elastic energy ground state. We study the structure and energetics of multidisclination packings based on models of equilibrium and nonequilibrium cross-sectional order.

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Citations

Jun 20, 2012·Proceedings of the National Academy of Sciences of the United States of America·Isaac R Bruss, Gregory M Grason
Nov 10, 2014·The Journal of Chemical Physics·Luis Cajamarca, Gregory M Grason
Oct 12, 2018·Proceedings of the National Academy of Sciences of the United States of America·Siyu LiRoya Zandi
Jul 23, 2019·Soft Matter·Lucas Menou, Martin Castelnovo
Jun 18, 2017·Physical Review. E·Martin Castelnovo
Jun 18, 2017·Physical Review. E·Andreea PanaitescuArshad Kudrolli
Jul 25, 2019·Physical Review. E·Siyu LiAlex Travesset
Nov 9, 2019·Physical Review Letters·Siyu LiGregory M Grason
Aug 31, 2016·Physical Review. E·Amir Azadi, Gregory M Grason
Sep 5, 2017·Soft Matter·Zhenwei Yao
May 17, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Amir Azadi, Gregory M Grason
Jun 21, 2014·Physical Review Letters·Amir Azadi, Gregory M Grason

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