Dynamically Crowded Solutions of Infinitely Thin Brownian Needles

TL;DR

This study uses Brownian dynamics simulations to analyze the complex entangled motion of infinitely thin needles at high densities, revealing transient dynamic arrest, non-Gaussian displacements, and diffusive rotational behavior, with implications for understanding needle Lorentz systems.

Contribution

It provides a detailed characterization of the entangled dynamics of thin needles, including the geometry of the confining tube and the diffusive behavior at long times, supported by analytical and simulation results.

Findings

Needles exhibit one-dimensional sliding in a confining tube at high densities.

Displacements perpendicular to needles show exponential distribution for large displacements.

Rotational motion becomes diffusive under strong confinement.

Abstract

We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is essentially restricted to a one-dimensional sliding in a confining tube composed of neighboring needles. From the density-dependent behavior of the orientational and translational diffusion, we extract the long-time transport coefficients and the geometry of the confining tube. The sliding motion within the tube becomes visible in the non-Gaussian parameter of the translational motion as an extended plateau at intermediate times and in the intermediate scattering function as an algebraic decay. This transient dynamic arrest is also corroborated by the local exponent of the mean-square displacements perpendicular to the needle axis. Moreover, the probability distribution of the displacements perpendicular to the needle becomes strongly non-Gaussian, rather it displays an exponential distribution for large displacements. On the other hand, based on the analysis of higher-order correlations of the orientation we find that the rotational motion becomes diffusive again for strong confinement. At coarse-grained time and length scales, the spatiotemporal dynamics of the needle for the high entanglement is captured by a single freely diffusing phantom needle with long-time transport coefficients obtained from the needle in solution. The time-dependent dynamics of the phantom needle is also assessed analytically in terms of spheroidal wave functions. The dynamic behavior of the needle in solution is found to be identical to needle Lorentz systems, where a tracer needle explores a quenched disordered array of other needles.