Elastic properties of the nematic phase in hard ellipsoids of short aspect ratio

Abstract

We present a Monte Carlo simulation study of suspensions of hard ellipsoids of revolution. Based on the spatial fluctuations of the orientational order, we have computed the Frank elastic constants for prolate and oblate ellipsoids and compared them to the affine transformation model. The affine transformation model predicts the right order of magnitude of the twist and bend constant but not of the splay constant. In addition, we report the observation of a stable nematic phase at an aspect ratio as low as 2.5.

Scratching a 50-year itch with elongated rods

“…. observed in very recent simulation results for the elastic constants for short aspect ratio (0.2) oblate hard ellipsoids, compared to prolate ones of aspect ratio 5 [29]. Finally, we again check that the first and third elastic constant are indistinguishable in the weak ordering limit S 1: to lowest order…”

“…στ (r) = 0 (29) to ensure that O(r) has no tensorial components of order L 2 . This equation, which implicitly depends on the previously determined H (0) (r), can be used to obtain the second-order contribution to the effective field H (2) (r).…”

“…Since the denominator of Eq. 26 is a scalar, it is sufficient to require − H (2) αβ (r)M αβστ (r) + 1 24 M [1,1] στ (r) − 2M [2] στ (r) = 0 (29) to ensure that O(r) has no tensorial components of order L 2 . This equation, which implicitly depends on the previously determined H (0) (r), can be used to obtain the second-order contribution to the effective field H (2) (r).…”

“…Note that erf( √ U )/ √ U remains real even for negative values of U . We then turn to the second-order equation (29). We again note all terms are second rank tensors, which by symmetry necessarily must also be expressible on the basis n(r) ⊗ n(r) and 1, as both O(r) and H (0) (r) are expressed in this basis.…”

Preparation and Tracking of Oblate Core–Shell Polymethyl-Methacrylate Ellipsoids

“…Firstly, simulations and theory predict complex phase diagrams for suspensions of prolate and oblate ellipsoidal particles, with the appearance of isotropic and nematic fluids, plastic solids, stretched fcc-crystals, and SM2 structures. [1][2][3][4][5][6] Secondly, ellipsoidal particles have been shown to have very high random packing densities [7][8] and to exhibit jamming properties different from spherical particles 9 . Finally, many biological particles with near ellipsoidal shape, such as red blood cells and thrombocytes, but also drug carriers, exhibit shape-dependent physical properties.…”