Measuring geometric frustration in twisted inextensible filament bundles

Abstract

We investigate with experiments and novel mapping the structure of a hexagonally ordered filament bundle that is held near its ends and progressively twisted around its central axis. The filaments are free to slide relative to each other and are further held under tension-free boundary conditions. Measuring the bundle packing with micro x-ray imaging, we find that the filaments develop the helical rotation $\Omega$ imposed at the boundaries. We then show that the observed structure is consistent with a mapping of the filament positions to disks packed on a dual non-Euclidean surface with a Gaussian curvature which increases with twist. We further demonstrate that the mean inter-filament distance is minimal on the surface which can be approximated by a hemisphere with an effective curvature $K_{eff}=3{\Omega }^2$. Examining the packing on the dual surface, we analyze the geometric frustration of packing in twisted bundles and find the core to remain relatively hexagonally ordered with inter-filament strains growing from the bundle center, driving the formation of defects at the exterior of highly twisted bundles.

arXiv comment5 figures

References in corpus (6)

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• Geometry and Optimal Packing of Twisted Columns and Filaments
• Emergent structure of multi-dislocation ground states in curved crystals
• Defects in Crystalline Packings of Twisted Filament Bundles: I. Continuum Theory of Disclinations
• The ancient art of laying rope
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Cited by in corpus (6)

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• Mechanics of two filaments in tight contact: The orthogonal clasp
• Persistence of perfect packing in twisted bundles of elastic filaments
• Mechanics of metric frustration in contorted filament bundles: From local symmetry to columnar elasticity
• Twist and Measure: Characterizing the Effective Radius of Strings and Bundles under Twisting Contraction
• Bundling architecture in elastic filaments with applied twist