Collective Dynamics in Quasi-One-Dimensional Hard Disk System

Adrián Huerta,Victor M Pergamenshchik,Andrij Trokhymchuk,Taras Bryk

doi:10.3389/fphy.2021.636052

Abstract

We present the results of molecular dynamic studies of collective dynamics in a system of hard disks confined to a narrow quasi-one-dimensional (quasi-1D) channel. The computer simulations have been performed for the specific channel width of 3/2 of disk diameter in which the disk arrangement at close packing resembles zigzag ordering characteristic of a vertically oriented two-dimensional (2D) triangular lattice. In such a quasi-1D system, which is intermediate between 1D and 2D arrays of hard disks, the transverse excitations obey very specific dispersion law typical of the usual optical transverse modes. This is in a sharp contrast both to the 1D case, where transverse excitations are not possible, and to the 2D case, where the regular shear waves with a propagation gap were observed. Other peculiarities of the dispersion of collective excitations as well as some results of disk structuring and thermodynamics of the quasi-1D hard disk system are presented and discussed for a range of hard disk densities typical for fluid and distorted crystal states.

Highlights

Hard spheres and hard disks are widely accepted as the first choice approximation to model a variety of soft condensed matter objects [1]
FL and FT are the force per unit cross-section exerted along the channel length L, and the force on a segment of the horizontal wall of length L/(Nσ ) = 1/l, respectively. These forces are both of entropic origin and rather sensitive to be evaluated from computer simulations. These forces can be found from the analytical canonical partition function of a quasi-1D hard disk system reported in [10]
As for the same low linear density l 0.8, the transverse force is lower for a wider channel, the frequency of disk bouncing between the horizontal walls has to be lower for wider channels as well

Summary

Introduction

Hard spheres and hard disks are widely accepted as the first choice approximation to model a variety of soft condensed matter objects [1]. The interest has been revived in the properties of hard sphere fluid confined to a narrow channel of the width that does not exceed two hard core diameters. In such system, commonly referred to as quasi-one dimensional (quasi-1D) system [2], the hard-core particles cannot pass the nearest neighbors and their motion is restricted by the neighbors. Of a par√ticular interest is the so-called single-file quasi-1D system with the width that does not exceed (1 + 3/2) of disk diameter [3] as a disk cannot touch more than one neighbor from each side This is a substantial simplification that allows one to make a contact with the exact Tonks solution for the purely 1D hard rod system [4]. The practical interest stems from the possibility to use such a simple model to capture properties of more complex systems, e.g., to explain diffusion in zeolite and carbon channels [16,17,18], microfluidic devices [19], in the technology of bio-integrated nanodevices [3] etc. by treating the finite length axis of the quasi-1D system as the pore width

Objectives

Results

Conclusion