Insights from Single-File Diffusion into Cooperativity in Higher Dimensions
Abstract
Diffusion in colloidal suspensions can be very slow due to the cage effect, which confines each particle within a short radius on one hand, and involves large-scale cooperative motions on the other. In search of insight into this cooperativity, here the authors develop a formalism to calculate the displacement correlation in colloidal systems, mainly in the two-dimensional case. To clarify the idea for it, studies are reviewed on cooperativity among the particles in the one-dimensional case, i.e. the single-file diffusion (SFD). As an improvement over the celebrated formula by Alexander and Pincus on the mean-square displacement (MSD) in SFD, it is shown that the displacement correlation in SFD can be calculated from Lagrangian correlation of the particle interval in the one-dimensional case, and also that the formula can be extended to higher dimensions. The improved formula becomes exact for large systems. By combining the formula with a nonlinear theory for correlation, a correction to the asymptotic law for the MSD in SFD is obtained. In the two-dimensional case, the linear theory gives description of vortical cooperative motion.
Cite
@article{arxiv.1507.05714,
title = {Insights from Single-File Diffusion into Cooperativity in Higher Dimensions},
author = {Takeshi Ooshida and Susumu Goto and Takeshi Matsumoto and Michio Otsuki},
journal= {arXiv preprint arXiv:1507.05714},
year = {2017}
}
Comments
27 pages, 4 figures; "accepted author manuscript" after an embargo of 12 months (http://www.worldscinet.com/authors/authorrights.shtml) following the publication by Biophysical Reviews and Letters, for Special Issue Continuation on Single File Dynamics and Generalizations in Interdisciplinary Sciences