Effect of microtextured substrates on the molecular orientation of a nematic liquid-crystal sample

The in-plane orientation of a nematic liquid-crystal sample, confined by two periodic microtextured substrates, is theoretically analyzed by means of the Frank-Oseen continuum elastic theory and a suitable surface term. In addition, an easy optical method to produce such textures using photopolymeric films is presented. It is shown that, in the limit of large pattern period, the orientation depends only on the ratio of the splay and bend elastic constants $K_1∕K_3$ and on the easy axis direction of the individual stripes. In the particular case for which $K_1=K_3$, the stability depends only on the easy axis direction for a general pattern period.

Figure 1

Schematic representation of the pattern periodic microtextured substrate used in this work.

Figure 2

(a) Microtexture of period $L=15\mu \mathrm{m}$ inscribed on a photopolymer film with $\alpha \approx +60°$ and $-60°$; (b) experimental setup. The periodicity of the interference pattern is given by $\mathrm{L}=\lambda ∕2\sin \theta$.

Figure 3

Possible director configurations: state I, with ${\varphi }_0=0$; state II, with ${\varphi }_0=\pi ∕2$.

Figure 4

An example of the profile $\varphi \left(x\right)$ calculated from Eq. (6), for the two values of ${\varphi }_0$ at the border of the domain, ${\varphi }_0=\pi ∕2$ and ${\varphi }_0=0$.

Figure 5

The critical angle ${\alpha }_C$ as a function of the ratio of the splay and bend elastic constants $K_1$ and $K_3$ calculated from Eq. (8). The critical region is indicated by the solid line.

Figure 6

The energy per unit area $F∕\left(4ld\right)$ as a function of the angle at the domain boundaries ${\varphi }_0$ for $\alpha =30°$, 45°, and 60°.