Computer simulation study of a mesogenic lattice model based on long-range dispersion interactions

In contrast to thermotropic biaxial nematic phases, for which some long sought for experimental realizations have been obtained, no experimental realizations are yet known for their tetrahedratic and cubatic counterparts, involving orientational orders of ranks 3 and 4, respectively, also studied theoretically over the last few decades. In previous studies, cubatic order has been found for hard-core or continuous models consisting of particles possessing cubic or nearly cubic tetragonal or orthorhombic symmetries; in a few cases, hard-core models involving uniaxial ($D_{\infty h}$-symmetric) particles have been claimed to produce cubatic order as well. Here we address by Monte Carlo simulation a lattice model consisting of uniaxial particles coupled by long-range dispersion interactions of the London-De Boer-Heller type; the model was found to produce no second-rank nematic but only fourth-rank cubatic order, in contrast to the nematic behavior long known for its counterpart with interactions truncated at nearest-neighbor separation.

Figure 1

Simulation results for the potential energy, obtained with different sample sizes. Meaning of symbols: circles: $l=10$; squares: $l=12$; triangles: $l=16$; diamonds: $l=20$, crosses: $l=24$. Here and in the following figures, with the exception of simulation results for $C^{*}$, the statistical errors mostly fall within symbol sizes. Here as well as for Figs. 2, 5, and 6, panel a covers the whole investigated temperature range, and panel b presents the transition region in greater detail.

Figure 2

Simulation results for the configurational specific heat $C^{*}$, obtained with different sample sizes; same meaning of symbols as in Fig. 1. The associated statistical errors, not shown, range between 1% and 5%.

Figure 3

Simulation results for the orientational order parameter ${\overline{\tau }}_2$, obtained with different sample sizes; same meaning of symbols as in Fig. 1.

Figure 4

Simulation results for the orientational order parameter $\overline{q^{\prime }}$, obtained with different sample sizes; same meaning of symbols as in Fig. 1.

Figure 5

Simulation results for the orientational order parameter ${\overline{\tau }}_4$ obtained with different sample sizes; same meaning of symbols as in Fig. 1.

Figure 6

Simulation results for the susceptibility ${\chi }_4$, obtained with different sample sizes; same meaning of symbols as in Fig. 1.

Figure 7

Comparison between different definitions of the fourth-rank order parameter, based on simulation results obtained for the largest investigated sample size $l=24$. Meaning of symbols: circles ${\overline{\zeta }}^{\prime }$; squares: ${\overline{\zeta }}_{\max }$; triangles: ${\overline{\tau }}_4$.

Figure 8

Histograms of the single-particle potential energy $u$, obtained for $l=24$ and different temperatures in the transition region. Meaning of symbols for panel (a): black continuous line: $T^{*}=2.2075$; red dashed line: $T^{*}=2.210$; blue dashed-dotted line: $T^{*}=2.211$. Meaning of symbols for panel (b): black continuous line: $T^{*}=2.212$; red dashed line: $T^{*}=2.213$; blue dashed-dotted line: $T^{*}=2.214$. Meaning of symbols for panel (c): black continuous line: $T^{*}=2.215$; red dashed line: $T^{*}=2.216$; blue dashed-dotted line: $T^{*}=2.217$.

Figure 9

Histograms of the fourth-rank order parameter ${\tau }_4$, obtained for $l=24$ and different temperatures in the transition region. Meaning of symbols for panel (a): black continuous line: $T^{*}=2.2075$; red dashed line: $T^{*}=2.210$; blue dashed-dotted line: $T^{*}=2.211$. Meaning of symbols for panel (b): black continuous line: $T^{*}=2.212$; red dashed line: $T^{*}=2.213$; blue dashed-dotted line: $T^{*}=2.214$. Meaning of symbols for panel (c): black continuous line: $T^{*}=2.215$; red dashed line: $T^{*}=2.216$; blue dashed-dotted line: $T^{*}=2.217$.