Anomalous diffusion for active Brownian particles cross-linked to a networked polymer: Langevin dynamics simulation and theory

TL;DR

This paper investigates the subdiffusive behavior of active Brownian particles in viscoelastic polymer networks using Langevin dynamics simulations and theory, revealing how activity influences anomalous diffusion and correlations.

Contribution

It introduces an exact theoretical framework describing active particle dynamics in viscoelastic media, highlighting the impact of propulsion velocity on anomalous diffusion.

Findings

Active Brownian particles exhibit subdiffusion with an exponent ≤ 1/2.

Higher propulsion velocities lead to smaller anomalous diffusion exponents.

The motion is characterized by a fractional Langevin equation with two noise sources.

Abstract

Quantitatively understanding of the dynamics of an active Brownian particle (ABP) interacting with a viscoelastic polymer environment is a scientific challenge. It is intimately related to several interdisciplinary topics such as the microrheology of active colloids in a polymer matrix and the athermal dynamics of the in vivo chromosome or cytoskeletal networks. Based on Langevin dynamics simulation and analytic theory, here we explore such a viscoelastic active system in depth using a star polymer of functionality $f$ with the center cross-linker particle being ABP. We observe that the ABP cross-linker, despite its self-propelled movement, attains an active subdiffusion with the scaling $\langle\Delta \mathbf{R}^2(t)\rangle\sim t^\alpha$ with $\alpha\leq 1/2$, through the viscoelastic feedback from the polymer. Counter-intuitively, the apparent anomaly exponent $\alpha$ becomes smaller as the ABP is driven by a larger propulsion velocity, but is independent of the functionality $f$ or the boundary conditions of the polymer. We set forth an exact theory, and show that the motion of the active cross-linker is a gaussian non-Markovian process characterized by two distinct power-law displacement correlations. At a moderate P{\'e}clet number, it seemingly behaves as fractional Brownian motion with a Hurst exponent $H=\alpha/2$, whereas, at a high P{\'e}clet number, the self-propelled noise in the polymer environment leads to a logarithmic growth of the mean squared displacement ($\sim \ln t$) and a velocity autocorrelation decaying as $-t^{-2}$. We demonstrate that the anomalous diffusion of the active cross-linker is precisely described by a fractional Langevin equation with two distinct random noises.