Tangentially driven active polar linear polymers-An analytical study.

The conformational and dynamical properties of isolated flexible active polar linear polymers (APLPs) are studied analytically. The APLPs are modeled as Gaussian bead-spring linear chains augmented by tangential active forces, both in a discrete and continuous representation. The polar forces lead to linear non-Hermitian equations of motion, which are solved by an eigenfunction expansion in terms of a biorthogonal basis set. Our calculations show that the polymer conformations are independent of activity. However, tangential propulsion strongly impacts the polymer dynamics and yields an active ballistic regime as well as an activity-enhanced long-time diffusive regime, which are both absent in passive systems. The polar forces imply a coupling of modes in the eigenfunction representation, in particular with the translational mode, with a respective strong influence on the polymer dynamics. The total polymer mean-square displacement on scales smaller than the radius of gyration is determined by the active internal dynamics rather than the collective center-of-mass motion, in contrast to active Brownian polymers at large Péclet numbers, reflecting the distinct difference in the propulsion mechanism.

Dynamics of active polar ring polymers.

The conformational and dynamical properties of isolated semiflexible active polar ring polymers are investigated analytically. A ring is modeled as a continuous Gaussian polymer exposed to tangential active forces. The analytical solution of the linear non-Hermitian equation of motion in terms of an eigenfunction expansion shows that ring conformations are independent of activity. In contrast, activity strongly affects the internal ring dynamics and yields characteristic time regimes, which are absent in passive rings. On intermediate timescales, flexible rings show an activity-enhanced diffusive regime, while semiflexible rings exhibit ballistic motion. Moreover, a second active time regime emerges on longer timescales, where rings display a snake-like motion, which is reminiscent to a tank-treading rotational dynamics in shear flow, dominated by the mode with the longest relaxation time.