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.

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

References in corpus (13)

• Theoretical perspective on the glass transition and amorphous materials
• Anomalous transport in the crowded world of biological cells
• Geometric interpretation of pre-vitrification in hard sphere liquids
• Langevin formulation for single-file diffusion
• Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: Configuration changes and vibration modes
• Effective Edwards-Wilkinson equation for single-file diffusion
• Dynamics of heterogeneous hard spheres in a file
• A minimal model for kinetic arrest
• Effect of correlated noise on quasi-1D diffusion
• Interacting single-file system: Fractional Langevin formulation versus diffusion-noise approach
• Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids
• Emerging quasi-0D states at vanishing total entropy of the 1D hard sphere system: a coarse-grained similarity to the car parking problem
• Criteria of amorphous solidification

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• Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids
• Single-File Diffusion of Active Brownian Particles
• Langevin analogy between particle trajectories and polymer configurations
• Displacement correlations in a two-dimensional colloidal liquid and their relationship with shear strain correlations