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

TL;DR

This paper develops a continuum elasticity theory for twisted filament bundles, revealing how twist induces stresses that lead to the formation of topological defects like disclinations, similar to curved elastic membranes.

Contribution

It introduces a novel theoretical framework linking twist-induced stresses to defect formation in filament bundles, extending elastic theory to complex geometries.

Findings

Twist induces stresses analogous to spherical curvature in elastic sheets.

Above a critical twist, disclinations become energetically favorable.

Multi-disclination configurations are analyzed for equilibrium and non-equilibrium states.

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.