Topological defects, surface geometry and cohesive energy of twisted filament bundles

Cohesive assemblies of filaments are a common structural motif found in diverse contexts, ranging from biological materials such as fibrous proteins, to artificial materials such as carbon nanotube ropes and micropatterned filament arrays. In this paper, we analyze the complex dependence of cohesive energy on twist, a key structural parameter of both self-assembled and fabricated filament bundles. Based on the analysis of simulated ground states of cohesive bundles, we show that the non-linear influence of twist derives from two distinct geometric features of twisted bundles: (i) the geometrical frustration of inter-filament packing in the bundle cross-section; and (ii) the evolution of the surface geometry of bundles with twist, which dictates the cohesive cost of non-contacting filaments at the surface. Packing frustration in the bundle core gives rise to the appearance of a universal sequence of topological defects, excess 5-fold disclinations, with increasing twist, while the evolution of filament contact at the surface of the bundle generically favors twisted geometries for sufficiently long filaments. Our analysis of both continuum and discrete models of filament bundles shows that, even in the absence of external torque or intrinsic chirality, cohesive energy universally favors twisted ground states above a critical (length/radius) aspect ratio and below a critical filament stiffness threshold.