Defects in vertically vibrated monolayers of cylinders

Abstract

We analyse liquid-crystalline ordering in vertically vibrated monolayers of cylinders confined in a circular cavity. Short cylinders form tetratic arrangements with C 4 symmetry. This symmetry, which is incompatible with the geometry of the cavity, is restored by the presence of four point defects with total topological charge +4. Equilibrium Monte Carlo simulations predict the same structure. A new method to measure the elastic properties of the tetratic medium is developed which exploits the clear similarities between the vibrated dissipative system and the thermal equilibrium system. Our observations open up a new avenue to investigate the formation of defects in response to boundary conditions, an issue which is very difficult to realise in colloidal or molecular systems.

Domain walls in vertically vibrated monolayers of cylinders confined in annuli

“…This system was studied previously [23,24,27], and is here reanalyzed as a reference case (note that the experiment was slightly redesigned with respect to that of Refs. [24,27]; in particular, the cavity is slightly bigger). In this section, we also define some other quantities that will be used in the other cases.…”

“…In Ref. [27], we argued that this can be explained using arguments from equilibrium elastic theory: Defects interact repulsively, via a logarithmic interaction which is mediated by the stiffness coefficient K of the intervening, tetratic phase. The value of K can be estimated from defect fluctuations and, when conveniently scaled, is of the same order as in two-dimensional liquid crystals.…”

“…In Ref. [27], it proved useful to characterize the motion of the defects in terms of distribution functions. We also adopt this approach here and define f 1 (r), the radial function, which gives the spatial distribution of the defects with respect to their distance r from the center of the cavity.…”

“…More recently, it has been shown that metallic rods of small aspect ratio may form global tetratic (i.e., fluid monolayers with fourfold orientational order) patterns inside circular cavities [20], along with the presence of what seem to be four point-defected regions, symmetrically located at the corners of a square inscribed in the circle [24,27]. The interpretation of these regions in terms of point topological charges that restore the broken fourfold symmetry of the tetratic director when confined to a circular cavity is appealing.…”

“…This analogy has been exploited in Ref. [27] to extract an elastic constant that mediates the interaction between defects. The value of this constant turns out to be of the same order of magnitude as typical two-dimensional elastic constants of liquid crystals [27].…”