Dynamically crowded solutions of infinitely thin Brownian needles

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 nonGaussian, 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.

The Role of Rotational Motion in Diffusion NMR Experiments on Supramolecular Assemblies: Application to Sup35NM Fibrils

“…The magnitude of this effect has been previously estimated for samples containing rod‐like particles of the uniform size [24] . In particular, the recent simulation study by Leitmann et al [25] . offers detailed information on this subject.…”

Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

“…Furthermore, the elasticity of a single polymer in free space, as elaborated here, could be used as a reference to study the behavior of a single polymer in crowded environments composed of fixed obstacles [65][66][67], solutions of polymers [68][69][70], or active constituents [8,9,71], as, for example, molecular motors. These give rise to intriguing non-equilibrium physics resembling transport processes inside cells and providing fundamental input for novel active materials [72].…”

Non-Gaussian Normal Diffusion in Low Dimensional Systems

“…Despite their apparent simplicity, the analytical solution of the Langevin Eqs. ( 7)-( 9) is rather cumbersome [35,36]. The diffusion properties of a typical ellipsoidal particle are summarized in Fig.…”