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  • Letter

Dynamics of active polar ring polymers

Christian A. Philipps, Gerhard Gompper, and Roland G. Winkler
Phys. Rev. E 105, L062501 – Published 15 June 2022
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  • INTRODUCTION
  • MODEL
  • DYNAMICS
  • DISCUSSION
  • ACKNOWLEDGMENTS
    • Supplemental Material
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    Abstract

    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.

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    • Received 31 January 2022
    • Revised 17 March 2022
    • Accepted 23 May 2022

    DOI:https://doi.org/10.1103/PhysRevE.105.L062501

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Anomalous diffusionPersistence lengthPolymer behaviorPolymer conformation changes
    1. Physical Systems
    Living matter & active matter
    Polymers & Soft Matter

    Authors & Affiliations

    Christian A. Philipps1,2,*, Gerhard Gompper1,†, and Roland G. Winkler1,‡

    • 1Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
    • 2Department of Physics, RWTH Aachen University, 52056 Aachen, Germany

    • *c.philipps@fz-juelich.de
    • †g.gompper@fz-juelich.de
    • ‡r.winkler@fz-juelich.de

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    Issue

    Vol. 105, Iss. 6 — June 2022

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    Images

    • Figure 1
      Figure 1

      Illustration of an active polar ring polymer. The arrows indicate the local tangential active force. An arbitrary position vector r(s,t) and the ring diameter vector rd(t) are shown.

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    • Figure 2
      Figure 2

      Normalized mean-square displacement in the center-of-mass reference frame, 〈Δr2(t)〉, of (a) flexible, pL=102, and (b) semiflexible, pL=10−2, APRPs as function of the time t/τ1, where τ1 is the longest relaxation time, for various Péclet numbers Pe (increasing from bottom to top). The black lines show power laws with the indicated time dependence. The insets show subsequent conformations with Δt≈1/ω1 of discrete flexible and semiflexible polymers of length L=50l. To illustrate the clockwise reptation motion, half of the monomers are colored blue and red, respectively.

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    • Figure 3
      Figure 3

      Normalized autocorrelation function of the ring diameter rd(t) as a function of the time ω1t, where ω1=2πfa/(γL), for Pe=103 and various pL values as indicated in the legend (increasing from bottom to top at ω1t=π). The dashed line corresponds to the exponential exp(−t/τ1)=exp(−12πω1t/Pe). Curves for pL<10−2 are indistinguishable from that with pL=10−2.

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