Further details on the phase diagram of hard ellipsoids of revolution

Abstract

In recent work we revisited the phase diagram of hard ellipsoids of revolution (spheroids) by means of replica exchange Monte Carlo simulations. This was done by setting random initial configurations, and allows to confirm the formation of sm2 crystal structures at high densities [Phys. Rev. E 75, 020402 (2007)] for large anisotropies and stretched-fcc for small anisotropies. In this work we employed the same technique but setting the starting cells as sm2 crystal structures having the maximum known packing density [Phys. Rev. Lett. 92, 255506 (2004)]. This procedure yields a very rich behavior for quasi-spherical oblates and prolates. These systems, from low to high pressures, show the following phases: isotropic fluid, plastic solid, stretched-fcc solid, and sm2 solid. The first three transitions are first order, whereas the last one is a subtle, probably high order transition. This picture is consistent with the fact of having the sm2 structure capable of producing the maximally achievable density.

Densest Local Structures of Uniaxial Ellipsoids

“…5(b) demonstrates a surprising symmetry between ellipsoids of reciprocal aspect ratios: Both ϕ g and σ approximately coincide. This finding continues a series of unexplained correspondences between oblate and prolate ellipsoidal particles, for example, the equilibrium phase diagram [9] and packing fractions ϕ cry of the densest known crystals [7]. Figure 6 displays the frequency of Voronoi cells in our dense disordered packings with a given coordination number N and packing fraction ϕ l .…”

“…For example, pebbles and sand grains vary widely in size and shape, and the kissing and packing problems lack rigorous answers. Generalizations of the sphere-packing problem to congruent aspherical particles have been intensely studied [7][8][9][10][11], motivated both by applications in granular matter [12][13][14][15][16][17] and by advances in the synthesis of colloidal particles with prescribed shapes [18,19]. In general, aspherical shapes pack denser than spheres, and it could be shown that the sphere is a local pessimum for lattice packing [20,21].…”

Phase diagram of two-dimensional hard ellipses

“…One should note that the overall appearance obtained for the 2D phase diagram (Fig. 7) markedly resembles that of 3D systems of prolate and oblate ellipsoids, spherocylinders, and cut-spheres with variable aspect ratio (see references 32,[45][46][47] ). In particular, the isotropic-nematic transition line goes up in occupied area (volume) fraction upon decreasing the particle aspect ratio to eventually meet up with a strongly first-order and almost anisometric-independent fluid-solid transition.…”

“…It is faster to get a stationary state by decompressing packed cells than by compressing lose random configurations 32 . We first perform the necessary trial moves at the desired state points to ensure the development of a stationary state (on the order of 1 × 10 12 trial moves).…”

“…To avoid the inherent hysteresis associated to transitions as far as possible 32 , we are implementing the replica exchange Monte Carlo technique [33][34][35] . It is based on the definition of an extended ensemble whose partition function is given by Q ext = nr i=1 Q i , being Q i the partition function of ensemble i and n r the number of ensembles.…”