Structure and dynamics of a self-propelled semiflexible filament

Abstract

We investigate structural and dynamical properties of a self-propelled filament using coarse-grained Brownian dynamics simulations. A self-propulsion force is applied along the bond vectors, i.e., tangent to the filament and their locations are considered in two different manners. In case one, force is applied to all beads of the filament, which is termed as homogeneous self-propulsion. Here we obtain a monotonic decrease in the stiffness of the filament with P\'eclet number, hence, radius of gyration also displays the same trend. Moreover, the radius of gyration of the filament shows universal dependence for various bending rigidities with flexure number. The effective diffusivity of the filament shows enhancement with the active force, and it increases linearly with force, and bending rigidity. In case two, self-propulsion force is applied only to a few bond vectors. The location of active forces is chosen in a periodic manner starting from the tail of the filament and leaving the front end without force. In this case, the filament acquires various structures such as the rodlike, helical, circular, and folded states. The transition from several states is understood in terms of tangent-tangent correlation, bending energy, and torsional order parameter. The helical state is identified through a crossover from exponential to oscillatory behavior of the tangent-tangent correlation. A sudden increase in the bending energy separates a helical state to a folded state of the filament.