Anisotropy-independent packing of confined hard ellipses

Orientational ordering and correlation in quasi-one-dimensional hard-body fluids due to close-packing degeneracy

We study the orientational ordering properties of some quasi-one-dimensional hard-body fluids, where the anisotropic particles are confined to a straight line, while they are free to rotate in a plane. We examine a class of models where the close-packing structure is degenerate, i.e., the highest possible density can be realized with different orientational ordering. We find that the close-packing degeneracy always gives rise to a diverging orientational correlation, which can be a marker of phase transition, glass formation, and jamming. In the case of isotropic or partially ordered phases at the close-packing density, the diverging orientational correlation indicates a tendency for being a strongly ordered nematic phase. However, the orientational divergence in the perfect nematic phase shows that the particles must rotate in concert to go from one closely packed structure to another.

Ordering properties of anisotropic hard bodies in one-dimensional channels

The phase behavior and structural properties of hard anisotropic particles (prisms and dumbbells) are examined in one-dimensional channels using the Parsons-Lee (PL) theory, and the transfer-matrix and neighbor-distribution methods. The particles are allowed to move freely along the channel, while their orientations are constrained such that one particle can occupy only two or three different lengths along the channel. In this confinement setting, hard prisms behave as an additive mixture, while hard dumbbells behave as a non-additive one. We prove that all methods provide exact results for the phase properties of hard prisms, while only the neighbor-distribution and transfer-matrix methods are exact for hard dumbbells. This shows that non-additive effects are incorrectly included into the PL theory, which is a successful theory of the isotropic-nematic phase transition of rod-like particles in higher dimensions. In the one-dimensional channel, the orientational ordering develops continuously with increasing density, i.e., the system is isotropic only at zero density, while it becomes perfectly ordered at the close-packing density. We show that there is no orientational correlation in the hard prism system, while the hard dumbbells are orientationally correlated with diverging correlation length at close packing. On the other hand, positional correlations are present for all the systems, the associated correlation length diverging at close packing.

Dense packings of geodesic hard ellipses on a sphere

Packing problems are abundant in nature and have been researched thoroughly both experimentally and in numerical models. In particular, packings of anisotropic, elliptical particles often emerge in models of liquid crystals, colloids, and granular and jammed matter. While most theoretical studies on anisotropic particles have thus far dealt with packings in Euclidean geometry, there are many experimental systems where anisotropically-shaped particles are confined to a curved surface, such as Pickering emulsions stabilized by ellipsoidal particles or protein adsorbates on lipid vesicles. Here, we study random close packing configurations in a two-dimensional model of spherical geodesic ellipses. We focus on the interplay between finite-size effects and curvature that is most prominent at smaller system sizes. We demonstrate that on a spherical surface, monodisperse ellipse packings are inherently disordered, with a non-monotonic dependence of both their packing fraction and the mean contact number on the ellipse aspect ratio, as has also been observed in packings of ellipsoids in both 2D and 3D flat space. We also point out some fundamental differences with previous Euclidean studies and discuss the effects of curvature on our results. Importantly, we show that the underlying spherical surface introduces frustration and results in disordered packing configurations even in systems of monodispersed particles, in contrast to the 2D Euclidean case of ellipse packing. This demonstrates that closed curved surfaces can be effective at introducing disorder in a system and could facilitate the study of monodispersed random packings.

Densest packings from size segregation of particles in geometric confinement

A correlation between density maximization and size segregation for packings of polydisperse particles in geometric confinement has been discovered, through the derivation of a general solution for the densest-packed zigzag arrangements of polydisperse particles. This solution is a size-graded structure in which the larger a particle the closer it is located to either end of the system, such that the smaller particles in the interior are encapsulated by the larger ones away from it. Any pair of different-sized adjacent particles is a grain-boundary-like configuration that reduces the overall packing efficiency of the system, and this solution corresponds to a minimization of excess-volume contributions from grain-boundary-like configurations of different-sized particles as a result of the clustering of equal- or like-sized particles. Our findings provide new insights into how structural order of polydisperse particles emerges in confined settings.

Anomalous phase behavior of quasi-one-dimensional attractive hard rods

We study a two-state model of attractive hard rods using the transfer matrix method, where the centers of the particles are confined to a straight line, but the orientations of the rods can be parallel or perpendicular to the confining line. The rods are modeled as hard rectangles with length L and width D and decorated with attractive sites at both ends of the rectangles. We find that the particles align parallel to the line and form long chains at low densities, while they turn out of the line and form a Tonks gas at high densities. With increasing the stickiness between the rods, the structural change between parallel and perpendicular states becomes stronger and the pressure vs density curve becomes almost a horizontal line at the transition pressure. We show that such a behavior is reminiscent of the first-order phase transition. This manifests in the validity of the lever rule of the phase transitions for very sticky cases.

Confinement effects on the random sequential adsorption packings of elongated particles in a slit

The behavior of a system of two-dimensional elongated particles (discorectangles) packed in a slit between the two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption model with continuous positional and orientational degrees of freedom. The aspect ratio (length-to-width ratio, ɛ=l/d) of the particles was varied within the range ɛ∈[1;32] while the distance between the walls was varied within the range h/d∈[1;80]. The properties of deposits in jammed state [the coverage, the order parameter, and the long-range (percolation) connectivity between particles] were studied numerically. The values of ɛ and h significantly affected the structure of the packings and the percolation connectivity. Particularly, the observed nontrivial dependencies of the jamming coverage φ(ɛ) or φ(h) were explained by the interplay of the different geometrical factors related to confinement, particle orientation degrees of freedom and excluded volume effects.