Helical close-packing of anisotropic tubes

Abstract

Helically close-packed states of filaments are common in natural and engineered material systems, ranging from nanoscopic biomolecules to macroscopic structural components. While the simplest models of helical close-packing, described by the ideal rope model, neglect anisotropy perpendicular to the backbone, physical filaments are often quite far from circular in their cross-section. Here, we consider an anisotropic generalization of the ideal rope model and show that cross-section anisotropy has a strongly non-linear impact on the helical close-packing configurations of helical filaments. We show that the topology and composition of the close-packing landscape depends on the cross-sectional aspect ratio and is characterized by several distinct states of self-contact. We characterize the local density of these distinct states based on the notion of confinement within a `virtual' cylindrical capillary, and show that states of optimal density vary strongly with the degree of anisotropy. While isotropic filaments are densest in a straight configuration, any measure of anisotropy leads to helicity of the maximal density state. We show the maximally dense states exhibit a sequence of transitions in helical geometry and cross-sectional tilt with increasing anisotropy, from spiral tape to spiral screw packings. Furthermore, we show that maximal capillary density saturates in a lower bound for volume fraction of π/4 in the large-anisotropy, spiral-screw limit. While cross-sectional anisotropy is well-known to impact the mechanical properties of filaments, our study shows its strong effects to shape the configuration space and packing efficiency of this elementary material motif.