Persistence of perfect packing in twisted bundles of elastic filaments

TL;DR

This paper shows that elastic filament bundles can maintain perfect hexagonal packing under high twist due to elastic effects counteracting geometric frustration, which is confirmed through x-ray imaging and modeling.

Contribution

It reveals a mechanism by which elastic filament bundles preserve order under twist, combining experimental imaging with a new elastic model.

Findings

Order persists even above 360 degrees of twist

Elastic contraction counteracts geometric expansion

Model explains preservation of packing order

Abstract

It is generally understood that geometric frustration prevents maximal hexagonal packings in uniform filament bundles upon twist. We demonstrate that a hexagonal packed elastic filament bundle can preserve its order over a wide range of twist due to a subtle counteraction of geometric expansion with elastic contraction. Using x-ray scanning and by locating each filament in the bundle, we show the remarkable persistence of order even as the twist is increased well above 360 degrees, by measuring the spatial correlation function across the bundle crosssection. We introduce a model which analyzes the combined effects of elasticity including filament stretching, and radial and hoop compression necessary to explain this generic preservation of order observed with Hookean filaments.