# Structure and dynamics of a self-propelled semiflexible filament

## TL;DR

This study uses simulations to explore how self-propulsion affects the structure and movement of semiflexible filaments, revealing state transitions and universal behaviors depending on propulsion mode and force application.

## Contribution

It introduces a detailed analysis of self-propelled semiflexible filaments with different force application schemes, uncovering new structural states and universal scaling laws.

## Key findings

- Filament flexibility decreases with increased Péclet number.
- Radius of gyration shows universal dependence across bending rigidities.
- Filament exhibits various structures like rod, helix, and fold depending on force application.

## 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 flexibility 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 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, filament acquires various structures such as rod-like, 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 to a folded states of the filament.