Self-Coiling Filaments Stabilized by their Shape

Coiled filaments, ranging from nanoscopic biomolecular aggregates (e.g. amyloid) to macro-materials (e.g. ropes), derive emergent structure and mechanics from single filament properties and inter-filament coupling.

Recent experiments on mesoscale filaments (Barber, et. al., Nat. Comm. 2023) present a novel route to generate bundled assemblies, where the filament’s helical elastic ground state (preference for non-zero bend and twist) yield self-coiling single- and multi-filament assemblies. Unlike mechanically assembled structures of straight filaments (e.g. cables, yarns), self-coiling assemblies can also be held together by their intrinsic mechanical state.

Using continuum elasticity theory, geometric packing models, and particle-based simulation, we study optimal shapes of dense self-coiling structures where the target elasticity is incompatible (e.g. not embeddable due to excluded volume) and survey the morphological space of these frustrated materials. We analyze how the structure and mechanics of the assembly depend on the mismatch between target and realizable geometry. We report how assembly size (length and number of filaments) influences the structural response to elastic misfit, which in some cases promotes stronger self-locking internal stresses or alternativley drives bundles to unwind. We anticipate that these results shed light on design parameters for engineering and aid understanding of complex structure and mechanics in self-linking assemblies more broadly.