Modeling a photoinduced planar-to-homeotropic anchoring transition triggered by surface azobenzene units in a nematic liquid crystal

The performance of light-controlled liquid crystal anchoring surfaces depends on the nature of the photosensitive moieties and on the concentration of spacer units. Here, we study the kinetics of photosensitive liquid crystal cells that incorporate an azobenzene-based self-assembled monolayer. We characterize the photoinduced homeotropic-to-planar transition and the subsequent reverse relaxation in terms of the underlying isomerization of the photosensitive layer. We show that the response time can be precisely adjusted by tuning the lateral packing of azobenzene units by means of inert spacer molecules. Using simple kinetic assumptions and a well-known model for the energetics of liquid crystal anchoring we are able to capture the details of the optical microscopy experimental observations. Our analysis provides fitted values for all the relevant material parameters, including the zenithal and the azimuthal anchoring strength.

Figure 1

Examples of transmittance curves as a function of time, with crossed polarizers oriented at ${45}^{\circ }$ of the magnetic field, for three different concentrations of ES [$C_{\text{ES}}$=0.218 (a), 0.817 (b), and 0.847 (c)], and four temperatures ($\delta T=T-T_{\text{NI}}=-0.3,-2,-5$, and $-10{}^{\circ }\mathrm{C}$). The sample thickness is $d=20.68\mu \mathrm{m}$ (a), 21.63 $\mu \mathrm{m}$ (b), and 21.87 $\mu \mathrm{m}$ (c). All the curves were measured in the saturation regime after a long UV exposure time $t_{\text{UV}}$ ranging between 120 and 300 s, except the dashed line in (b) for which $t_{\text{UV}}=22$ s.

Figure 2

Effective birefringence (symbols) measured at four different temperatures on the plateau of the transmittance curves as a function of the ES concentration. The horizontal solid lines give the values of the birefringence measured with a tilting compensator in a conventional planar sample (rubbed polyimide).

Figure 3

Plateau duration ($t{p}_1$) as a function of the UV exposure time. $d=21.63 \mu \mathrm{m}, C_{\text{ES}}=0.817,$ and $\delta T=-0.3{}^{\circ }\mathrm{C}$.

Figure 4

Plateau duration $t{p}_1$ (blue solid circles) and time $t{p}_2$ (red empty circles) at which the anchoring is again homeotropic as a function of the ES concentration at different temperatures: (a) $\delta T=-0.3{}^{\circ }\mathrm{C}$; (b) $\delta T=-2{}^{\circ }\mathrm{C}$; (c) $\delta T=-5{}^{\circ }\mathrm{C}$; (d) $\delta T=-10{}^{\circ }\mathrm{C}$. These two times diverge for a concentration close to 0.84. In these graphs each point represents an average over two to five measurements realized with different samples. The solid lines are the theoretical curves calculated by taking the values of the model parameters given in the text.

Figure 5

Transmittance curves measured with a fresh sample (solid lines) and with the same sample stored two months at room temperature (dashed lines). Except for the plateau duration, the curves are essentially the same. $d=21.69\mu \mathrm{m}$ and $C_{\text{ES}}=0.69$.

Figure 6

Theoretical transmittance curves calculated from the model for the samples of Fig. 1 by taking $\tau =1387$ s and the values of the parameters $\alpha$ and $\beta$ given in the text.

Figure 7

Theoretical plateau duration as a function of the UV illumination time. The curve has been calculated for the same sample as in Fig. 3 and in the same experimental conditions.

Figure 8

Time evolution of the theoretical anchoring potential when $x=0.817$ [as in Figs. 1 and 4] and $\delta T=-5{}^{\circ }\mathrm{C}$. Graph (a) shows the global evolution of the potential. The curves 1 to 6 have been calculated at time $t=0$ s, 1000 s, 2000 s, 3500 s, 6000 s, and $\infty$, respectively. Graph (b) shows the potential during the transition from planar to homeotropic. Curves 1 to 6 have been calculated at time $t=3150$ s, 3350 s, 3550 s, 3750 s, 4050 s, and 4450 s, respectively. In this example, $t{p}_1\approx 3200$ s and $t{p}_2\approx 4300$ s.

Figure 9

Normalized absorbance of a $C_{\text{ES}}=0.69$ sample at $\delta T=-5{}^{\circ }\mathrm{C}$ after 120 s irradiation with UV light. The feature pointed to by an arrow corresponds to the planar-to-homeotropic transition. The solid line corresponds to a fit to first order kinetics.

Figure 10

Comparison between the values of the relaxation time, $\tau$, obtained from absorbance measurements ($◯$) and from the fit to the transmittance data ($\square$). The sample has $C_{\text{ES}}=0.69$. The solid line is a guide for the eye.

Figure 11

Ising walls and disinclination lines (indicated by the arrows) observed immediately after the UV illumination. $d=21.69\mu \mathrm{m}$ and $C_{\text{ES}}=0.69$ and $\delta T=-0.3{}^{\circ }\mathrm{C}$.

Figure 12

Typical intensity profiles measured at different $\delta T$ between crossed polarizers along a line perpendicular to the wall and perpendicular to the magnetic field (line ab in Fig. 11). Sample thickness $d=21.69\mu \mathrm{m}$ and $C_{\text{ES}}=0.69$.

Figure 13

(a) Coordinate system for a $\pi$-wall in a magnetic field; (b) Representation on the unit sphere $S_2$ of the director field across a Bloch wall (blue trajectories) and an Ising wall (red trajectories). For each type of walls, there are two possible trajectories (drawn in solid and dashed lines, respectively) depending on the sense of rotation of the director.

Figure 14

Transmittance curves in a mixed sample. (a) Experimental curves measured in a sample of thickness $d=21.5\mu \mathrm{m}$ and $C_{\text{ES}}$ = 0.356. (b) Corresponding theoretical curves calculated for different values of $l_a$ (given on the graph) by taken the values of the parameters $\alpha , \beta$, and $\tau$ given in Sec. 3c, and the values of the birefringence given in Fig. 2.

Figure 15

Order of magnitude of the anchoring energy $W_a$ (a) and of the characteristic time $\tau$ (b) as a function of temperature.

Figure 16

Definition of the coordinate system and angles $\alpha$ and $\varphi \left(z\right)$ used in Sec. 5a.

Figure 17

(a) Transmittance between crossed polarizer and analyzer as a function of the rotation angle of the magnetic field for $d=49.96\mu \mathrm{m}$ and $\delta T=-2.1{}^{\circ }\mathrm{C}$. The solid line is the theoretical curve that corresponds to ${\overline{l}}_a=46\mu \mathrm{m}$. In this example $r={\alpha }_1/{\alpha }_2=1.105$; (b) Computed values of the $r$-ratio as a function of ${\overline{l}}_a$. From the previous experimental value $r=1.105$ we deduced ${\overline{l}}_a=46\mu \mathrm{m}$. $d=49.96\mu \mathrm{m}$ and $\delta T=-2.1{}^{\circ }\mathrm{C}$.

Figure 18

(a) Azimuthal extrapolation length as a function of temperature. The points on the right of the vertical dashed line have been obtained with the rotating-field method. The points on the left have been measured with the static method. (b) Azimuthal anchoring energy as a function of temperature. The solid lines are guides for the eye.

Figure 19

Transmittance as a function of the rotation angle of the magnetic field at $\delta T=-5{}^{\circ }\mathrm{C}$. The crosses are the experimental points. The solid line has been calculated by taking ${\overline{l}}_a=3.7\mu \mathrm{m}$. The dashed and dotted lines correspond to ${\overline{l}}_a=2.7$ and $4.7\mu \mathrm{m}$, respectively.

Figure 20

Birefringence as a function of temperature at $\lambda =633\mathrm{nm}$.

Figure 21

Twist constant as a function of temperature.

Figure 22

Magnetic coherence length as a function of temperature.