The natural configuration of an intrinsically curved and twisted filament is uniquely a helix so that it can be referred to as a helical filament. We find that confining a helical filament on a cylinder can create a bistable state. When $c_{0}R=0.5$, where $c_0$ is the intrinsic curvature of filament and $R$ is the radius of cylinder, the phase diagram for the stability of a helix contains three regimes. Regime $I$ has a small intrinsic twisting rate (ITR) and exhibits a bistable state which consists of two isoenergic helices. In regime $II$, the filament has a moderate ITR and the bistable state consists of a metastable low-pitch helix and a stable nonhelix. In regime $III$, the helix is unstable, owing to a large ITR. A similar phenomenon occurs when $c_{0}R\sim 0.5$. Monte Carlo simulation confirms these conclusions and indicates further that there are bistable nonhelices in regime $III$. This bistable system offers a prospective green material since the wide range of parameters and distinctive configurations for bistable states favor its realization and application.

• Received 8 September 2021
• Revised 30 December 2021
• Accepted 31 January 2022

DOI:https://doi.org/10.1103/PhysRevE.105.024502