Electroclinic effect in chiral smectic-$A$ liquid crystal elastomers

Chiral smectic-$A$ liquid crystal elastomers are rubbery materials composed of a lamellar arrangement of liquid crystalline mesogens. It has been shown experimentally that these materials shear when subjected to an electric field due to the electrically induced tilt of the director. Experiments have also shown that shearing a chiral smectic-$A$ elastomer gives rise to a polarization. Roughly, the shear force tilts the directors which, in turn, induce electric dipoles. This paper builds on previous works and models the electromechanical response of smectic-$A$ elastomers using free energy contributions that are associated with the lamellar structure, the relative tilt between the director and the layer normal, and the coupling between the director and the electric field. To illustrate the merit of the proposed model, two cases are considered—a deformation induced polarization and an electrically induced deformation. The predictions according to these two models qualitatively agree with experimental findings. Finally, a cylinder composed of helical smectic layers is also considered. It is shown that the electromechanical response varies as a function of the helix angle.

Figure 1

A schematic of the electromechanical response of a smectic-$A$ elastomer. The chirality vector $\mathbf{q}$ points out of the plane.

Figure 2

(a) The shear angle $\varphi$ and (b) the tilt angle $\theta$ as a function of the applied voltage $V$. The inset plots depict the predicted response subjected to high voltages. The continuous and the dashed curves correspond to the exact and the approximated predictions, respectively.

Figure 3

$\mathbf{p}·\widehat{\mathbf{X}}$ as a function of the applied voltage $V$. The inset depicts the predicted response as a result of high voltages. The continuous and the dashed curves correspond to the polarization [Eq. (12)] with $c={10}^{-4}$ and $0{\text{V}}^{-1}$, respectively.

Figure 4

(a) The shear angle $\varphi$ and (b) the tilt angle $\theta$ as a function of the normalized nominal stress $s$.

Figure 5

$\mathbf{p}·\widehat{\mathbf{X}}$ as a function of the normalized nominal stress $s$.

Figure 6

A schematic of the electromechanical response of a cylinder with helical layers.

Figure 7

(a) The twist $\delta$ and (b) the change in the enclosed volume $\frac{v_t}{V_t}$ as a function of the applied voltage for various helix angles at $p=0$.

Figure 8

(a) The twist $\delta$ and (b) the change in the enclosed volume $\frac{v_t}{V_t}$ as a function of the applied voltage for a cylinder comprising helical layers with a ${\psi }_0=45\circ$ angle for various pressures.