Dynamic electric polarization of nematic liquid crystals subjected to a shear flow

The effect of coupling between the dipole moment and the orientation is explored based on a relaxation equation for the second rank alignment tensor characterizing the molecular order in liquid crystals and a corresponding equation for the electric polarization. The orientational dynamics leads to a time dependence of the electric polarization. We propose a possibility to measure these effects via the resulting magnetic fields of the magnitude $\mid \mathbf{B}\mid \approx {10}^{-9}\mathrm{T}$. Furthermore, the presence of the electric polarization modifies the orientational dynamics as demonstrated in solution phase diagrams.

Figure 1

Phase plots of the dipole vector components $d_1$ vs $d_2$ and the time evolution of $d_3$. The temperature is $\vartheta =0$; the other model parameter are ${\lambda }_k=1.0$, $\dot{\gamma }=1.9$, ${\kappa }_d=\kappa =0$, ${\vartheta }_d=0.1$, $E^{*}=0.04$, and $c=0.5$.

Figure 2

Phase plots of $a_3$ vs $a_4$ at $\vartheta =0$, ${\lambda }_k=1.0$, $\dot{\gamma }=3.3$, ${\kappa }_d=\kappa =0$, ${\vartheta }_d=0.1$, $E^{*}=0.04$, and $c=-1.0$.

Figure 3

Phase plots of the dipole vector components $d_2$ vs $d_1$ and the time evolution of $d_3$, parameters as in Fig. 2.

Figure 4

The solution phase diagram at temperature $\vartheta =0$ for the model parameters ${\kappa }_d=\kappa =0$, ${\vartheta }_d=0.1$, and $c=0.5$ for the upper plot and $c=-0.5$ for the lower. The letters are abbreviations for tumbling $\left(T\right)$, wagging $\left(W\right)$, kayaking-tumbling $\left(\mathit{KT}\right)$, kayaking-wagging $\left(\mathit{KW}\right)$, aligning $\left(A\right)$, complex $\left(C\right)$, and log rolling $\left(\mathit{LR}\right)$.