When your filaments are fibers: the geometry and elasticity of filament bundles

When your filaments are fibers: the geometry and elasticity of filament bundles
Daria Atkinson, University of Massachusetts Amherst
Picture of Daria Atkinson
Date and time: Thu, Oct 31, 2019 - 11:30am
Refreshments at 11:15am
Location: Lederle1033
Category: Condensed Matter Seminar

Filamentous and columnar assemblies are ubiquitous in physical systems, from microscopic and biological materials, such as discotic liquid crystals and biopolymer bundles, to familiar, macroscopic materials like yarns, cables, and ropes.  Ordered ground states in filament bundles, however, are highly geometrically constrained, and we show that only two families of filament textures permit equidistance between the constituent filaments---the developable domains, which can bend, but not twist, and the helical domains, which can twist uniformly, but not bend.  The elastic response of bent and twisted filament bundles that cannot access equidistant ground states, such as those formed by DNA plasmids under confinement, is then doubly geometrically frustrated---the presence of twist frustrates crystalline order in the bundle cross-section, and the presence of bend couples any compromise structure to the filament texture. Because of this, the global response of non-equidistant filament bundles to deformations cannot adequately be described by a linearized elastic energy. To describe non-equidistant systems, we derive a geometrically nonlinear, coordinate invariant theory for the elasticity of filamentous materials, and discuss the response of hexagonally coordinated domains to the imposition of non-equidistant geometries.