Helical close-packing of anisotropic tubes

TL;DR

This study explores how cross-sectional anisotropy influences the helical close-packing configurations of filaments, revealing complex transitions and optimal packing states that depend on filament shape and anisotropy degree.

Contribution

It introduces an anisotropic generalization of the ideal rope model, demonstrating the nonlinear effects of anisotropy on filament packing configurations and densities.

Findings

Anisotropy causes a transition from straight to helical dense states.

Maximal packing density varies with anisotropy, reaching a lower bound of π/4.

Configurations evolve from spiral tape to spiral screw packings with increasing anisotropy.

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 $\pi/4$ 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.