Electric-field-induced flow-aligning state in a nematic liquid crystal

The response of shear stress to a weak ac electric field as a probe is measured in a nematic liquid crystal under shear flow and dc electric fields. Two states with different responses are clearly observed when the dc electric field is changed at a constant shear rate: the flow aligning and non–flow aligning states. The director lies in the shear plane in the flow aligning state and out of the plane in the non–flow aligning state. Through application of dc electric field, the non–flow aligning state can be changed to the flow aligning state. In the transition from the flow aligning state to the non–flow aligning state, it is found that the response increases and the relaxation time becomes longer. Here, the experimental results in the flow aligning state are discussed on the basis of the Ericksen-Leslie theory.

Figure 1

(a) Experimental setup. The sample is sheared by using a parallel-plate rheometer under dc and ac electric fields. (b) The flow is applied in the $x$ direction, the velocity gradient is in the $z$ direction, and the electric field is applied in the $z$ direction.

Figure 2

The dc electric-field dependence of the flow alignment angle ${\theta }_0$ in the FAS at shear rates of 10 and $40{\mathrm{s}}^{-1}$ numerically obtained for 8CB from Eq. (5).

Figure 3

(a) Dependence of $|\Delta {\sigma }_{1,1}|$ on $\Delta E$ at $E_0=100\mathrm{V}\mathrm{m}{\mathrm{m}}^{-1}$ and (b) $|\Delta {\sigma }_{2,2}|$ on $\Delta E^2$ at $E_0=0\mathrm{V}\mathrm{m}{\mathrm{m}}^{-1}$ at a shear rate of $10{\mathrm{s}}^{-1}$ at a frequency of $\omega =0.63\mathrm{rad}{\mathrm{s}}^{-1}$. Linear relationships are obtained at low electric fields.

Figure 4

Frequency dispersions of the first-order harmonic response $\Delta {\sigma }_{1,1}\left(\omega \right)$ at a shear rate of $10{\mathrm{s}}^{-1}$ for several dc electric fields. The dispersions are clearly distinguishable between NFAS (a,b) and FAS (c–f). Solid lines for the FAS are calculated on the basis of the Ericksen-Leslie theory.

Figure 5

$E_0$ dependence of the peak or dip frequency of the imaginary part, ${\omega }_{\mathrm{peak}}$, where dots are experimental results, a solid line is obtained from calculated frequency dispersion curves using Eq. (11), and a dashed line is $1/\tau$ calculated from Eq. (9).

Figure 6

$E_0$ dependencies of the first-order response at very low frequency ($0.63\mathrm{rad}{\mathrm{s}}^{-1}$ for the experiment and exactly zero for the theory), $\mathrm{Re}\left[\Delta {\sigma }_{1,1}(\omega \to 0)\right]$, for shear rates of 10 and $40{\mathrm{s}}^{-1}$.

Figure 7

Frequency dispersions of the second-order harmonic response $\Delta {\sigma }_{2,2}\left(\omega \right)$ at a shear rate of $10{\mathrm{s}}^{-1}$ for several dc electric fields. The dispersions are clearly distinguishable between the NFAS (a,b) and the FAS (c–f). Solid lines in the FAS are calculated on the basis of the Ericksen-Leslie theory.

Figure 8

$E_0$ dependencies of the second-order response at a very low frequency ($0.3\mathrm{rad}{\mathrm{s}}^{-1}$ for the experiment and exactly zero for the theory), $\mathrm{Re}\left[\Delta {\sigma }_{2,2}(\omega \to 0)\right]$, for shear rates of 10 and $40{\mathrm{s}}^{-1}$.

Figure 9

$E_0$ dependencies of ${\sigma }_0$ at shear rates of 10 and $40{\mathrm{s}}^{-1}$. It is difficult to distinguish the FAS and NFAS based on ${\sigma }_0$.