Absence of Enhanced Diffusion in the Dynamics of a Thick Needle through Three-Dimensional Fixed Spherical Scatterers

Abstract

The existence of three regimes in the dynamics of a thin needle-like particle diffusing through a two-dimensional random array of scatterers as the needle length is varied relative to the scatterer density was previously seen in a series of simulations. The first regime occurs at low density when the needle's diffusion follows the expected Enskog behavior. An intermediate regime gives rise to enhanced diffusion after a critical density of scatterers is reached, a manifestation of the suppression of librational motion as the needle is confined to effectively thinner but longer tubes. The third regime occurs at high scatterer density with the particle dynamics characteristic of a glass. In this article, we investigate whether the tubes seen in the second regime persist in a three-dimensional array of scatterers. The fact that the enhanced regime is not observed in a three-dimensional random array of scatterers suggests that the effective tubes formed by the moving needle are fragile structures highly dependent on dimensionality.

Diffusion of a nanowire rod through an obstacle field

“…The aforementioned results apply to an infinitely thin rod, point-like obstacles, and motion in two dimensions. If the rod thickness is finite a new confinement regime [10] appears, and if the rod is allowed to move in three dimensions the enhanced diffusion regime disappears [11].The entire density dependence of the rod center-ofmass diffusion coefficient, D cm , changes if the underlying motion of the rod between collisions is Brownian instead of ballistic [12]. In this case D cm is constant at very low densities and decreases to a lower constant at high densities.…”

Order parameters in the diffusion of rods through two- and three-dimensional fixed scatterers

“…The algorithm used here is time-step based, evolving the system forward in time in successive steps at constant velocity and correcting those steps which involved a scatterer-tracer collision through a careful accounting of the collision event. [7,8] Even at the highest densities explored in this work, the frequency of these collisions, relative to our time step, were sufficiently low that the calculations could be performed in reasonable time.…”

“…[1,2] We, and others, have used the Lorentz gas (LG) model to describe the solvent as a set of fixed scatterers. [3][4][5][6][7][8] The LG model was originally introduced by Lorentz in 1905 to model the transport of electrons in a metal and from which he derived a linear Boltzmann equation. [9] The model was used to elaborate the diffusion of light fast particles -the wind-across heavy immovable particles -the trees-so to rigorously construct correlation functions for the corresponding kinetic gas systems.…”

“…[6] An enhanced diffusion regime was also seen for a dense solution of infinitely thin rods due to confinement, [23] though absent in the case of thick scatterers. [8] Moreno and Kob [3,4] addressed a thick rod LG model with thick (and non-overlapping) spheres that led to glassy dynamics with increasing density. Tucker and Hernandez [7] addressed a thick rod with point scatterers in two dimensions; finding that both enhanced diffusion and glassy regimes were accessible.…”

Tube Concept for Entangled Stiff Fibers Predicts Their Dynamics in Space and Time

“…Most prominently, it predicts a drastic suppression of the rotational diffusion coefficient [10,[12][13][14] as well as of the translational diffusion coefficient perpendicular to the orientation of the stiff filament [15,16].Rod and needle systems have been studied in simulations and theory extensively [17][18][19][20], differing in the underlying dynamics and aspect ratio of the constituents. For Newtonian dynamics, the transport coefficients behave rather differently [21][22][23][24][25], characterized by an increase in the center of mass diffusion coefficient, first observed by Frenkel and Maguire [21]. A long-standing debate how a finite aspect ratio or a small flexibility of the stiff Brownian rods affects the Doi-Edwards scaling [12,26], has been resolved only recently [13,14,27,28], pointing out, that the densities considered so far just reach the onset of the asymptotic regime and corrections to scaling are relevant [14].…”