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

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.

Figure 1

The function $W_{13}\left(\vec{k}\right)$ for a system of hard ellipsoids of aspect ratio 0.2 at the volume fraction $\phi =0.360$.

Figure 2

Ratios of the Frank elastic constants as a function of $S_4/S$ for aspect ratio 5.0. Solid line (blue) corresponds to the theoretical expression of $K_3/K_2$ given in Eq. (14) and data points ($•$) are from the simulations. Dashed line (red) corresponds to the theoretical expression of $K_1/K_2$ given in Eq. (14) and data points ($\times$) are from the simulations.

Figure 3

Ratios of the Frank elastic constants as a function of $S_4/S$ for aspect ratio 0.2. Solid line (blue) corresponds to the theoretical expression of $K_3/K_2$ given in Eq. (14) and data points ($•$) are from the simulations. Dashed line (red) corresponds to the theoretical expression of $K_1/K_2$ given in Eq. (14) and data points ($\times$) are from the simulations.

Figure 4

Frank elastic constants as a function of $S_4/S$ for $e=5.0$: $K_1$ and $K_2$ in (a) and $K_3$ in (b). Lines correspond to the expressions given in Eq. (14) and data points are from the simulations; triangles indicate the data from Tjipto-Margo et al. [19].

Figure 5

Frank elastic constants as a function of $S_4/S$ for $e=0.2$: $K_1$ and $K_2$ in (a) and $K_3$ in (b). Lines correspond to the expressions given in Eq. (14) and data points are from the simulations; triangles indicate the data from Tjipto-Margo et al. [19].

Figure 6

Snapshots of the SM2 crystal for aspect ratio 2.5. The colors indicate the two preferred orientations.

Figure 7

Volume fraction $\phi$ as a function of the reduced pressure $P^{*}$ for $e=2.5$.Two jumps indicate two phase transitions. The inset shows a zoom-in on the region of $P^{*}\in [38.00,40.00]$.

Figure 8

Bond-orientational order parameter $Q_6$ as a function of the reduced pressure $P^{*}$ for $e=2.5$. Large change of $Q_6$ near $P^{*}=52.50$. Inset shows a zoom-in on the region of $P^{*}\in [38.00,52.00]$.

Figure 9

Nematic order parameter $S$ as a function of the pressure for $e=2.5$. Strong variation of the $S$ near $P^{*}=38.60$ and noticeable decrease of $S$ near $P^{*}=52.50$. Inset shows a zoom-in on the region of $P^{*}\in [38.00,40.00]$.