Dynamical behavior of the director field for splay-bend deformations in nematic liquid crystals

The exact dynamical evolution of the director field for splay-bend deformations, in nematic liquid crystal samples limited by inhomogeneous surfaces, is determined in the one-constant approximation. The initial conditions and boundary-value problem concerning the situation of strong anchoring at the surfaces of a sample of slab shape of thickness $d$ is analytically solved in the presence of a time dependent external electric field, and taking into account the viscous torque. The results are used to analytically obtain the time dependence of the phase shift between the two components of a linearly polarized beam impinging perpendicularly on the sample. The analysis can be relevant to investigate the phase retardation of a nematic cell submitted to an external voltage which is lower than or in the order of the Féedericksz threshold to induce deformations in the sample.

Figure 1

(a) Profile of the tilt angle $\theta (0,\zeta ,t)$ versus $\zeta$ for different amplitudes of the step-like applied field. Solid line for $t=0$ and the other lines for $t=1.5$. (b) $⟨{\theta }^2⟩$ versus dimensionless time $t$ for different strengths of the step-like applied field.

Figure 2

Time dependence of the exact profile of the tilt angle in the center of the sample $\theta (0,0,t)$ for different strengths of the applied field. In (a) the field has the form ${\alpha }^2\left(t\right)={\alpha }_0^{2}t$ and in (b) $\alpha \left(t\right)$ has the step-like profile of (12).

Figure 3

(a) Profile of the tilt angle $\theta (1,\zeta ,t)$ for three different values of the dimensionless time $t$. (b) $⟨{\theta }^2⟩$ versus $t$ for different strengths of the constant applied field. The curves were depicted for $\lambda ∕d=\pi$.