Spontaneous Patterning of Confined Granular Rods

Abstract

Vertically vibrated rod-shaped granular materials confined to quasi-2D containers self organize into distinct patterns. We find, consistent with theory and simulation, a density dependent isotropicnematic transition. Along the walls, rods interact sterically to form a wetting layer. For high rod densities, complex patterns emerge as a result of competition between bulk and boundary alignment. A continuum elastic energy accounting for nematic distortion and local wall anchoring reproduces the structures seen experimentally.PACS numbers: 45.70.Qj, 61.30.Eb, 61.30.Hn From nanometer sized molecules forming liquid crystals to timber floating down a river, rod shaped materials pervade our everyday existence. Onsager first demonstrated that hard core steric interactions suffice to order rods in thermal equilibrium [1]. Above a critical concentration, orientational entropy is sacrificed for gains in translational entropy; therefore, crowding alone induces a temperature-independent isotropic-nematic (I-N) transition [2]. In this entropically driven transition, the kinetic motion of the rods serves as a mechanism for adequately sampling phase space. While thermal excitation mixes microscopic particles, macroscopic rods require an externally applied energy for randomization. For both vertical and horizontal vibrations, a density dependent nematic to smectic-like transition was previously observed for granular rods [3]. Such driven dissipative systems, however, are far from equilibrium and need not evolve to states of maximal configurational entropy. For example, prior studies utilizing macroscopic rods focused on jammed or other metastable states [3,4].Here, we report on finite-sized driven dissipative granular systems of rods in steady-state that share many properties of lyotropic liquid crystals at equilibrium. We find that short ranged hard core interactions determine the arrangement of the moving rods for all densities. A phase transition from a disordered isotropic state to a nematiclike state occurs as a function of rod density and rod aspect (length-to-diameter) ratio, L/D. By using excluded volume scaling predicted by mean field theories for liquid crystals, our data give a single normalized transition density for all rod L/D and densities tested.However, excluded volume interactions in the bulk cannot explain all rod behavior because confining boundaries also strongly influence rod ordering. For relatively low rod densities, experimental results for rod alignment and density profiles with respect to the wall strikingly resemble theoretical predictions [5], indicating that rods interact via hard core steric repulsions with the surrounding boundaries. As the rods become dense, rod ordering in the bulk nematic competes with rod ordering along the surrounding walls. This frustration creates distinct yet easily reproduced patterns. We account for observed structures by modeling the system as a liquid crystal undergoing the elastic deformations of splay and bend subject to a simple wall interaction [6,7]. Moreover, w...

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“…The interest in these studies is also motivated by the possibility that experiments on quasiamonolayers of vibrated granular rods can be related to thermally equilibrated molecular or colloidal fluids of hard anisotropic particles [22][23][24]. There is ample evidence that these monolayers do form liquidcrystalline phases and surface effects, nematic ordering, etc., may be explored in these experimental systems and compared with their thermal counterparts to look for similarities in their ordering behavior, especially considering that overlap or exclusion interactions are the key interactions in both systems.…”

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“…The best would be agitated layers of granular rods, for which nematic phases have been reported [12]. Although many features of these systems can be rationalized in terms of equilibrium hard-rod theories [19], some properties such as global circulation and swirls [11,12] are clearly very nonequilibrium. These systems as well as the living melanocyte nematic of Gruler et al [10] remain the most promising candidates for experimental tests of the rich range of results made here and in [5].…”

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“…The role of particle shape is now a topic of increasing attention. Recent experiments on vibrated rods [7][8][9][10][11] and rods in a hopper [12] have demonstrated the great variety of phenomena-swirling, vortices, pattern formation-that arise due to particle anisotropy alone.…”