Defect-Driven Shape Instabilities of Bundles

Topological defects are crucial to the thermodynamics and structure of condensed matter systems. For instance, when incorporated into crystalline membranes like graphene, disclinations with positive and negative topological charge elastically buckle the material into conical and saddlelike shapes, r...

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Autores principales:	Isaac R. Bruss, Gregory M. Grason
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2018
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/b3b7788c884c4e339c3d3f8792596d2a
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spelling	oai:doaj.org-article:b3b7788c884c4e339c3d3f8792596d2a2021-12-02T11:44:12ZDefect-Driven Shape Instabilities of Bundles10.1103/PhysRevX.8.0310462160-3308https://doaj.org/article/b3b7788c884c4e339c3d3f8792596d2a2018-08-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.8.031046http://doi.org/10.1103/PhysRevX.8.031046https://doaj.org/toc/2160-3308Topological defects are crucial to the thermodynamics and structure of condensed matter systems. For instance, when incorporated into crystalline membranes like graphene, disclinations with positive and negative topological charge elastically buckle the material into conical and saddlelike shapes, respectively. A recently uncovered mapping between the interelement spacing in 2D columnar structures and the metric properties of curved surfaces motivates basic questions about the interplay between defects in the cross section of a columnar bundle and its 3D shape. Such questions are critical to the structure of a broad class of filamentous materials, from biological assemblies like protein fibers to nanostructured or microstructured synthetic materials like carbon nanotube bundles. Here, we explore the buckling behavior for elementary disclinations in hexagonal bundles using a combination of continuum elasticity theory and numerical simulations of discrete filaments. We show that shape instabilities are controlled by a single material-dependent parameter that characterizes the ratio of interfilament to intrafilament elastic energies. Along with a host of previously unknown shape equilibria—the filamentous analogs to the conical and saddlelike shapes of defective membranes—we find a profoundly asymmetric response to positive and negative topologically charged defects in the infinite length limit that is without parallel to the membrane analog. The highly nonlinear dependence on the sign of the disclination charge is shown to have a purely geometric origin, stemming from the distinct compatibility (or incompatibility) of effectively positive- (or negative-)curvature geometries with lengthwise-constant filament spacing.Isaac R. BrussGregory M. GrasonAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 8, Iss 3, p 031046 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Isaac R. Bruss Gregory M. Grason Defect-Driven Shape Instabilities of Bundles
description	Topological defects are crucial to the thermodynamics and structure of condensed matter systems. For instance, when incorporated into crystalline membranes like graphene, disclinations with positive and negative topological charge elastically buckle the material into conical and saddlelike shapes, respectively. A recently uncovered mapping between the interelement spacing in 2D columnar structures and the metric properties of curved surfaces motivates basic questions about the interplay between defects in the cross section of a columnar bundle and its 3D shape. Such questions are critical to the structure of a broad class of filamentous materials, from biological assemblies like protein fibers to nanostructured or microstructured synthetic materials like carbon nanotube bundles. Here, we explore the buckling behavior for elementary disclinations in hexagonal bundles using a combination of continuum elasticity theory and numerical simulations of discrete filaments. We show that shape instabilities are controlled by a single material-dependent parameter that characterizes the ratio of interfilament to intrafilament elastic energies. Along with a host of previously unknown shape equilibria—the filamentous analogs to the conical and saddlelike shapes of defective membranes—we find a profoundly asymmetric response to positive and negative topologically charged defects in the infinite length limit that is without parallel to the membrane analog. The highly nonlinear dependence on the sign of the disclination charge is shown to have a purely geometric origin, stemming from the distinct compatibility (or incompatibility) of effectively positive- (or negative-)curvature geometries with lengthwise-constant filament spacing.
format	article
author	Isaac R. Bruss Gregory M. Grason
author_facet	Isaac R. Bruss Gregory M. Grason
author_sort	Isaac R. Bruss
title	Defect-Driven Shape Instabilities of Bundles
title_short	Defect-Driven Shape Instabilities of Bundles
title_full	Defect-Driven Shape Instabilities of Bundles
title_fullStr	Defect-Driven Shape Instabilities of Bundles
title_full_unstemmed	Defect-Driven Shape Instabilities of Bundles
title_sort	defect-driven shape instabilities of bundles
publisher	American Physical Society
publishDate	2018
url	https://doaj.org/article/b3b7788c884c4e339c3d3f8792596d2a
work_keys_str_mv	AT isaacrbruss defectdrivenshapeinstabilitiesofbundles AT gregorymgrason defectdrivenshapeinstabilitiesofbundles
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Defect-Driven Shape Instabilities of Bundles

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