Behavior of passive polymeric tracers of different topologies in a dilute bath of active Brownian particles

TL;DR

The paper investigates how an active bath of ABPs modulates the dynamics and conformations of passive tracers with different topologies in 2D. Using coarse-grained Langevin simulations, it shows that a three-arm star polymer develops an arm-pairing conformation at high activity due to asymmetric ABP accumulation, leading to enhanced persistence and faster center-of-mass diffusion than linear polymers or passive particles. At strong activity, the star polymer's dynamics and structure converge toward those of a linear polymer, though the star maintains a higher temporal correlation and a smaller radius of gyration. These results illuminate topology-induced responses to active environments and suggest routes for activity-directed design of polymer-based transport systems in non-equilibrium media.

Abstract

Using computer simulations in two dimensions we investigate the dynamics and structure of passive polymeric tracer with different topologies immersed in a low-density active particle bath. One of the key observations is that polymer exhibit faster dynamics compared to passive colloidal particles at high activity, for the same particle density, in both linear and star polymer topologies. This enhanced motion is attributed to the accumulation of active particles, which induces prolonged and persistent movement of the polymer. Further analysis reveals that star polymers exhibit more complex and intriguing behavior than their linear counterparts. Notably, the accumulation of active particles promotes the pairing of arms in star polymers. For instance, a three-armed star polymer adopts a conformation similar to a linear polymer with two-arms due to this pairing as a result, at high activity, the dynamics of both the polymers converge. Finally, we explore the dynamics of a linear polymer with the same total number of beads as the star polymer. Interestingly, at high activity -- where arm pairing in the star polymer is significant -- the star polymer demonstrates faster dynamics than the linear polymer, despite having the identical number of beads. These findings contribute to a broader understanding of the interactions between active and passive components of varying topologies in dilute systems and highlight their potential for innovative applications ranging from materials science to biomedicine.

Figures (15)

• Figure 1: Schematic of the model system (not to scale): (a) a single star polymer with three arms (blue). (b) A passive linear polymer (blue). (c) A single passive particle (blue). Each of these systems is simulated separately while immersed in a dilute bath of ABPs (green). The red arrows indicate the instantaneous directions of the ABPs. Pairwise non-bonded interactions among the polymer beads, between the polymer beads and ABPs, between passive particles and ABPs, and among the ABPs themselves are modeled using the Weeks-Chandler-Andersen (WCA) potential, represented by double-headed arrows. Additionally, the neighboring beads of the polymer are connected via the finitely extensible nonlinear elastic (FENE) potential, and a bending potential is applied to restrict polymer bending.
• Figure 2: Probability density functions of (a) the arm-arm separation $\mathrm{R}_{A_i\mathrm{-}A_j}$ and (b) the arm-arm angle $\theta_{A_i\mathrm{ -}A_j}$ for different values of the Péclet number $\mathrm{Pe}$. Panels (c) and (d) show the 1D and 2D probability of $\mathrm{R}_{A_i\mathrm{-}A_j}$ and $\theta_{A_i\mathrm{-}A_j}$ for $\mathrm{Pe}=0$ and $\mathrm{Pe}=50$, respectively. Snapshots of conformations of the star polymer and associated ABPs shown in panels (c) and (d) demonstrate the accumulation of ABPs induced by higher activity.
• Figure 3: Radial distribution function $g(r)$ of ABPs surrounding (a) a star polymer for different $\mathrm{Pe}$. The inset in (a) shows a snapshot of the system with the star polymer immersed in an active bath at $\mathrm{Pe}=50$. (b) Effective interaction potential between a pair of arms (blue) of the star polymer as a function of their separation $\mathrm{ R}_{A_i\mathrm{-}A_j}$ for different values of $\mathrm{Pe}$. The insets in (b) show the conformations of the star polymer for a given separation $\mathrm{R} _{A_i\mathrm{-}A_j}$: (i) $3.0$, (ii) $6.0$, and (iii) $9.0$.
• Figure 4: Log-log plot of the time evolution of (a) the mean TAMSD $\left< \overline{\delta r_i^2(\tau)}\right>$; log-linear plots of (b) the time-local anomalous diffusion exponent $\alpha(\tau)$, along with the (c) VACF of the motion for different values of $\mathrm{Pe}$ and (d) the relative effective persistence time $\tau_p(\mathrm{Pe})/\tau_p(\mathrm{Pe}=0)$ at some value of $\mathrm{Pe}$ divided by its inactive value, as a function of $\mathrm{Pe}$ for the center of mass motion of the star polymer. Inset in panel (c) shows a magnified view of the same.
• Figure 5: Log-linear plots showing the time evolution of the intermediate scattering function (\ref{['intscat']}) for (a) wave number $k=1$. Panel (b) shows the change in the compressed exponential coefficient $\beta$ defined in Eq. (\ref{['eq:fitting2']}) as a function of $\mathrm{Pe}$.