From self-locking entanglement to spontaneous unwinding in coiled filament assembly

Assemblies of flexible filaments are ubiquitous in nature and engineering. From biomolecules to woven textiles and bird nests, flexibility allows filaments to deform and entangle, where elastic shape misfit between the stress-free subunit geometry and the realized assembly yields emergent structure and mechanics. Motivated by recent experiments on self-coiling mesoscale filaments, we describe how shape misfit can either stabilize self-locking multi-filament structures or else drive spontaneous disassembly.

We focus on a prototypical morphology – helical filament bundles – and use elasticity theory, packing models, discrete element simulations, and experiments to study how shape misfit, controlled by the preferred filament shape (e.g. straight, helical, toroidal) and the crowding in the assembly (e.g. number of bundled filaments) influences structure and mechanics. When shape misfit is small, internal stresses generated by bundling are stabilizing, thereby “self-locking” the structure and resisting disassembly. Remarkably, this phenomenon occurs even in the absence of friction and attractive interactions, generating an effective structural cohesion from shape misfit alone. However, structural cohesion is not without bounds – when shape misfit is significant, the bundled state becomes unstable to disassembly through spontaneous fraying. We describe the self-locking/unwinding transition as a competition between two intensive energetic terms: an energy barrier to nucleate detangling and energy release by untangling. While both terms grow with shape misfit, the barrier term initially dominates, yielding maximal self-locking at finite misfit. We show that self-locking stresses generated by shape misfit also yield exotic packing as well as emergent (and tunable) mechanical properties. Fundamentally, we determine an optimal range for internal self-stress in stabilizing coiled filament assembly, where less or more than this “goldilocks” shape misfit yields decreased or (in)stability, which we expect applies to a broader class of material systems.