Director reorientation in a nematic liquid crystal with a photosensitive layer

We use a molecular-motor model previously proposed for a nematic cell with an azo-dye monolayer to calculate the director orientation when light is normally impinged on the cell. We consider an initial planar configuration for which one of the surrounding plates, which we call the reference plate, is submitted to a hard-anchoring boundary condition. The other confining plate has a coating monolayer of azo-dye molecules such that the change of the orientation of azo-dye isomers, due to light, causes changes in the nematic director. The boundary conditions on both plates along with the optical field determine the director configuration in the bulk. The existence of periodic solutions for the density of isomers in trans and cis states, corresponding to weak optical fields, has been discussed in the literature. Using a similar approach, we find an approximate expression for the density of isomers, written in terms of the director angle, which allows us to close the equation for the director configuration on the boundary having a photosensitive plate. We decouple the director's angle and the isomer densities by assuming extremely different temporal time scales between them. We show for a given sample that switching times inversely depend on the trans-cis transition rate of photoexcitation whereas relaxation times do not depend on it. On the other hand, switching and relaxation times linearly depend on effective surface viscosity values. Our model allows us to estimate surface viscosity values.

Figure 1

Director orientation when the nematic cell is illuminated with horizontally polarized light (polarization in the direction of the initial planar configuration) for different transition rates of photoexcitation. Light is switched off after 200 s. The initial condition is a planar nematic cell with ${\theta }_0=0^{{}^{\circ }}$. The following parameters were used: ${\psi }_2=0$, ${\nu }_{10}=0$, ${\nu }_{20}=1$, ${\mu }_c=0$, $\gamma =0.08$ Pa s (5CB), ${\gamma }_e=564$ nm, $\sigma =kT/U_{01}=2$, $U_{02}=0$, $L={10}^{-5}$ m, $K={10}^{-11}$ N, and ${\mu }_1=8\times {10}^3$ ${\text{m}}^2/{\text{V}}^2\text{s}$.

Figure 2

Director orientation when the nematic cell is illuminated with horizontally polarized light for certain trans-cis transition rates of photoexcitation. The initial conditions are those of a planar cell. There are two possible director orientations, one clockwise and the other counterclockwise. The parameter values are the same as in Fig. 1.

Figure 3

Director orientation when the nematic cell is illuminated with vertically polarized light for two different trans-cis transition rates for light intensity. The initial condition is a twisted nematic cell of $\pi /2$. There are two possible director orientations under photoexcitation: clockwise, which increases the twist at around $\pi$, and counterclockwise, which evolves to the initial planar configuration. Light is switched off after 200 s.

Figure 4

Director orientations when the nematic cell is illuminated with horizontally and vertically polarized light for two different trans-cis transition rates for the light intensity. The initial condition is a planar cell for horizontally polarized light (HPL) and a twist cell at $\pi /2$ for vertically polarized light (VPL).

Figure 5

Switching time $t_s$ vs trans-cis transition rates for light intensity $\mu$. They are inversely proportional. Horizontally polarized illuminating light with initial planar configuration is considered. The squares correspond to numerical calculations obtained by using this model while the solid line is a fitted curve, for the same parameter values as in Fig. 1.

Figure 6

Director direction $\theta$ vs time for different values of effective surface viscosity (rate between surface viscosity and bulk viscosity) ${\gamma }_e$ and the same parameters as in Fig. 1, with $\mu ={\mu }_1$ and horizontally polarized light. The light is switched off after 200 s.

Figure 7

Switching time $t_s$ vs effective surface viscosity ${\gamma }_e$. The squares correspond to numerical calculations obtained by using this model while the solid line curve is a fitted line, for the same parameters as in Fig. 1, with $\mu ={\mu }_1$ and horizontally polarized light.

Figure 8

Relaxation time $t_r$ vs ${\gamma }_e$. The relaxation time is the required time to reorient the cell from the maximum twist to 10% of ${\theta }_m,$ after turning off the light. The squares correspond to numerical calculations and the solid line is a fitted line, for the same parameters as in Fig. 1, with $\mu ={\mu }_1$ and horizontally polarized light.

Figure 9

Director orientation in the nematic cell versus the normal distance and time. The light is switched off after 200 s.

Figure 10

Torque exerted on the nematic for the azo-dye molecules when the horizontal polarized light normally impinges on the nematic cell, for the same parameters as in Fig. 1, with $\mu ={\mu }_1$.