Two-state model for nematic liquid crystals made of bent-core molecules

Nematic ($N$) liquid crystals made of bent-core molecules exhibit unusual physical properties such as an intermediate phase between the $N$ and isotropic ($I$) phases, a very weak $NI$ transition as inferred from magnetic birefringence measurements in a low field, which is apparently incompatible with a large shift in the $NI$ transition temperature ($T_{ni}$) measured under a high field. Using our conformational studies on the aromatic cores, we propose that only conformers which are more straightened than those in the ground state (GS) form clusters with a few layers, which persist even in the isotropic phase, as inferred from x-ray and rheological experiments. We present a Landau–de Gennes theory of the medium, including an orientational coupling between the clusters and the GS molecules, which accounts for all the unusual properties. The intermediate phase to isotropic transition is predicted to exhibit critical behavior at a very low magnetic field of $<1\mathrm{kG}$.

Figure 1

Two conformations of the aromatic core of chlororesorcinol BC molecule. With ten carbon-atom chains replacing the methyl groups at both ends, the compound exhibits $N$ phase, which has been extensively studied. Most of the conformations as in (a) have relatively large moments of inertia $I_{min}$ about the long axes, with $15\%$ in excited-state conformations as in (b), with lower $I_{min}$.

Figure 2

(a) Temperature variations of the order parameters. $S_c$ (top), $S_m$ (middle), and $S_g$ (bottom) show jumps at the nematic to coupling induced paranematic phase transition at $T_{npn}\simeq 354.45\mathrm{K}$ and also at the very weak paranematic to isotropic transition at $T_{pni}\simeq 354.93\mathrm{K}$. Temperature variations of the specific heat $C_v$ around (b) $T_{npn}$ and (c) $T_{pni}$. Note the large difference in the $C_v$ scales between (b) and (c).

Figure 3

Variations of the field induced order parameters with $E_h$. From top to bottom, $S_c, S_m$, and $S_g$. (a) At $T=355.4\mathrm{K}, \sim 1\mathrm{K}$ above $T_{npn}, S_c$ saturates at higher values of $E_h$ inducing similar variations in $S_g$ and $S_m$. (b) $T=366.4\mathrm{K}$ is $\sim 12\mathrm{K}$ above $T_{npn}$, and the smaller values of the order parameters exhibit linear variations.

Figure 4

(a) Effective inverse Cotton-Mouton coefficient $\mathrm{CMC}=E_h\left(1-x+Jx\right)/S_m$ as a function of temperature for $E_h=25\mathrm{ergs}/\mathrm{c}{\mathrm{m}}^3$. (b) Temperature variations of $S_m$ for different magnetic fields. The lowest curve is for $E_h=0$, with an increment in $E_h$ of $1.35\times {10}^3\mathrm{ergs}/\mathrm{c}{\mathrm{m}}^3$ (or about $120{\mathrm{T}}^2$) between successive higher curves. The highest, $E_h=12.15\times {10}^3\mathrm{ergs}/\mathrm{c}{\mathrm{m}}^3$, is close to the critical value, with $T_{\mathrm{crit}}\approx 355.62\mathrm{K}$.

Figure 5

Temperature variations near $T_{pni}$ of the average orientational order parameter at different magnetic fields. The lowest curve is for $E_h=0$, with an increment of $0.011\mathrm{ergs}/\mathrm{c}{\mathrm{m}}^3$ in $E_h$ between successive curves. The critical field corresponds to $E_h=0.055\mathrm{ergs}/\mathrm{c}{\mathrm{m}}^3$, and the critical temperature $\simeq 354.938\mathrm{K}$.