Bistability induced by a spontaneous twisting rate for a two-dimensional intrinsically curved filament

Bistability of a helical filament confined on a cylinder

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∼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.