Clustering in vibrated monolayers of granular rods

Abstract

We investigate the ordering properties of vertically-vibrated monolayers of granular cylinders in a circular container at high packing fraction. In line with previous works by other groups, we identify liquid-crystalline ordering behaviour similar to that of two-dimensional hard rectangular particles subject to thermal equilibrium fluctuations. However, due to dissipation, there is a much stronger tendency for particles to cluster into parallel arrangements in the granular system. These clusters behave as a polydisperse mixture of long life-time `superparticles', and some aspects of the system behaviour can be understood by applying mean-field theories for equilibrium hard rectangles, based on two-body correlations, to these `superparticles'. Many other features of the granular system are different: (i) For small particle length-to-breadth ratio $\kappa$, we identify tetratic ordering at moderate packing fractions and smectic fluctuations at higher packing fractions, with no sharp transition between the two states. Both types of ordering can be explained in terms of clustering. (ii) For large $\kappa$, strong clustering precludes the stabilisation of a uniaxial nematic state, and the system exhibits a mixture of randomly-oriented clusters which, as packing fraction is increased, develops into states with smectic fluctuations, again through a diffuse transition. (iii) Vorticity excitations of the velocity field compete with smectic ordering, causing dynamic fluctuations and the absence of steady states at high densities; the tetratic state, by contrast, is very stiff against vorticity, and long-standing steady states, spatially and orientationally homogeneous except for four symmetrical defects located close to the wall, can be observed.

13 pages, 15 figures

References in corpus (4)

• Crystallization of a quasi-two-dimensional granular fluid
• Hard-body models of bulk liquid crystals
• Orientational ordering in hard rectangles: The role of three-body correlations
• Enhanced stability of tetratic phase due to clustering

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• Reducing segregation in vibrated binary-sized granular mixtures by excessive small particle introduction
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• Phases and correlations in active nematic granular systems
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• Monte Carlo simulation of entropy-driven pattern formation in two-dimensional system of rectangular particles
• Diffusion and velocity correlations of the phase transitions in a system of macroscopic rolling spheres
• Failure of standard density functional theory to describe the phase behavior of a fluid of hard right isosceles triangles
• Topology of orientational defects in confined smectic liquid crystals
• Impact of packing fraction on diffusion-driven pattern formation in a two-dimensional system of rod-like particles