Reorientation dynamics of nematics encapsulated in microscopic volumes in a strong electric field

We theoretically describe a new regime of reorientation of the director field $\mathbf{\hat n}$ and velocity $\mathbf{v}$ of a nematic liquid crystal (LC) encapsulated in a rectangular cell under the action of strong electric field $\mathbf{E}$ directed at angle $\alpha(\sim\pi/2)$ to the horizontal surfaces bounding the LC cell. The numerical calculations in the framework of nonlinear generalization of the classical Eriksen–Leslie theory showed that at certain relations between the torques and momenta affecting the unit LC volume and $E\gg E_{\operatorname{th}}$, transition periodic structures can arise during reorientation of $\mathbf{\hat n}$, if the corresponding distortion mode has the fastest response and, thus, suppresses all the rest of the modes, including uniform ones. The position of sites of these periodic structures is affected by the value of field $E$, angle $\alpha$, and the character of anchoring of LC molecules to the bounding surfaces. The calculations performed for the nematic formed by 4-n-penthyl-4’-cyanobiphenyl showed that several vortexes can form in an LC cell under the action of reorientation of the nematic field; the boundaries of these vortexes are determined by the positions of periodic structure sites.