Geometry and mechanics of densely-packed helical filaments

Filament assemblies are of profound importance in structural materials and are ubiquitous in both engineered (cables, ropes, textiles) and natural systems (biopolymers, plant tendrils, muscles and tendons), spanning a huge range of length scales. In densely-packed filaments, structure and mechanics derive from the interplay of both the inherent flexibility of backbones and the local and non-local constraints of contact. Here, we consider a elementary geometry of helical close-packing of a single filament, extending the pioneering study of Pryzbyl and Pieranski (EPJE 2001) on the helical close-packing of the ideal rope model. In particular, inspired by recent experiments on self-coiling, anisotropic microfilaments, we study the helical close-packing of anisotropic rods with eccentric (elliptical) cross-sections. We show that close-packed states of anisotropic rods exhibit a strong sensitivity to tilt of cross-section, leading to a rich spectrum of structural transitions with increasing eccentricity. We compare these in terms of the capillary packing fraction and show that optimally dense states become increasingly helical with rod anisotropy. Next we consider a minimal mechanical model for capillary confinement of elastic filaments, and determine the packing fraction vs. pressure equation of states, which are marked by mechanically driven transitions between distinct states of helical packing.