Dynamics of a sheared twist-bend nematic liquid crystal

We study the flow behavior of a twist-bend nematic (${\mathrm{N}}_{\mathrm{TB}}$) liquid crystal. It shows three dynamic regimes in certain temperature and shear-rate range. In region I, $\sigma \sim \sqrt{\dot{\gamma }}$, in region II, the stress shows a near plateau, characterized by a power law $\sigma \sim {\dot{\gamma }}^{\alpha }$, where $\alpha \sim 0.1–0.4$ and in region III, $\sigma \sim \dot{\gamma }$. With increasing shear rate, $\sigma$ changes continuously from region I to II, whereas it changes discontinuously with a hysteresis from region II to III. In the near plateau (region II), we observe dynamic stress fluctuations, exhibiting regular, periodic, and quasiperiodic oscillations under the application of a steady shear. The observed spatiotemporal dynamics are close to those predicted theoretically in sheared nematogenic fluids.

Figure 1

(a) Schematic view of heliconical orientation of the molecules in the ${\mathrm{N}}_{\mathrm{TB}}$ phase. Separation between the two dotted planes represents pitch $p$, equivalent to the pseudolayer thickness. (b) Chemical structure of the compound CB9CB. (c) Polarizing optical microscope textures in the ${\mathrm{N}}_{\mathrm{TB}}$ phase in a homeotropic (left) and in a homogeneous (right) cells.

Figure 2

(a) Flow curves at different temperatures in the ${\mathrm{N}}_{\mathrm{TB}}$ phase of CB9CB LC. Solid lines show best fits to $\sigma \sim {\dot{\gamma }}^{\alpha }$. (b) Temperature variation of the onset shear rate ${\dot{\gamma }}_L$ (red circles) and the terminal shear rate ${\dot{\gamma }}_U$ (black squares) of the near plateau. Dotted curve is a guide to the eye. Inset shows the hysteresis of the transition at $T=85$ ${}^{\circ }\mathrm{C}$. The difference between the two shear rates in heating and cooling at the transition is $\mathrm{\Delta }\dot{\gamma }={\dot{\gamma }}_U-{\dot{\gamma }}_L=8 {\mathrm{s}}^{-\text{1}}$.

Figure 3

(a) Variation of $\sigma$ with $\dot{\gamma }$ in region I at different temperatures in the ${\mathrm{N}}_{\mathrm{TB}}$ phase. Solid lines are best fits to $\sigma \sim C_1\left(T\right)\sqrt{\dot{\gamma }}$. (b) Temperature variation of slope $C_1\left(T\right)$. Solid red curve is a least square fit to $C_1\left(T\right)\sim {(T_c-T)}^{0.53\pm 0.01}$ with $T_c={103}^{\circ }\mathrm{C}$. Both temperatures, $T_c$ and nematic to ${\mathrm{N}}_{\mathrm{TB}}$ transition ($T_{\text{N-NTB}}$), are marked by vertical arrows. Inset shows a log-log plot.

Figure 4

(a) Temperature variation of $\alpha$ in the near plateau. Solid red line is a best fit to the data. (b) Temperature variation of the stress jump $\mathrm{\Delta }\sigma$ in the ${\mathrm{N}}_{\mathrm{TB}}$ phase. Dashed curve is drawn as a guide to the eye.

Figure 5

(a) Variation of stress $\sigma$ with $\dot{\gamma }$ in region III at different temperatures in the ${\mathrm{N}}_{\mathrm{TB}}$ phase. Solid lines are best fits to $\sigma \sim C_3\left(T\right)\dot{\gamma }$. (b) Temperature variation of $C_3\left(T\right)$. Dashed curve is drawn as a guide to the eye.

Figure 6

Schematic diagram showing (a) multipseudolamellar cylinders in region I and (b) parallel pseudolayers in region III.

Figure 7

(a) Stress dynamics in the near-plateau regime at $T=85{}^{\circ }\mathrm{C}$. The stress oscillation time series at different shear rates. Shear rates $\dot{\gamma }=10,12,15 {\mathrm{s}}^{-\text{1}}$ lie within the stress plateau. $\dot{\gamma }=5$ and 18 ${\mathrm{s}}^{-\text{1}}$ lies just below and above the stress plateau, respectively [see Fig. 2]. (b) Corresponding Fourier power spectrum. A few harmonics of the fundamental frequency $\omega$ ($=2\pi f$) are labeled. The fundamental frequencies $\omega$ for the shear rates 10,12,15 ${\mathrm{s}}^{-\text{1}}$ are 0.17, 0.21, and 0.27 rad/s, respectively. Shearing frequencies calculated using $\mathrm{\Omega }=\dot{\gamma }tan\left(\alpha \right)$ are also shown in blue within brackets next to the shear rates.

Figure 8

(a) Stress dynamics in the near-plateau regime at $T=95{}^{\circ }\mathrm{C}$. The stress oscillation time series at different shear rates. $\dot{\gamma }=27,30,35 {\mathrm{s}}^{-\text{1}}$ lies within the stress near plateau. $\dot{\gamma }=10$ and 50 ${\mathrm{s}}^{-\text{1}}$ lies below and above the stress plateau, respectively [see Fig. 2]. (b) Corresponding Fourier power spectrum. A few harmonics of the fundamental frequency $\omega$ ($=2\pi f$) are labeled. The fundamental frequencies $\omega$ for the shear rates 27,30,35 ${\mathrm{s}}^{-\text{1}}$ are 0.47, 0.53, and 0.61 rad/s, respectively. Shearing frequencies calculated using $\mathrm{\Omega }=\dot{\gamma }tan\left(\alpha \right)$ are shown within brackets next to the shear rates.

Figure 9

Shear-rate dependent shear-stress in linear scale from $\dot{\gamma }=1{\text{s}}^{-\text{1}}$ to 85 ${\mathrm{s}}^{-\text{1}}$ at different temperatures in the ${\mathrm{N}}_{\mathrm{TB}}$ phase.

Figure 10

Synthetic root of the compound CB9CB.