Coexistence of light-induced thermocapillary and orientational effects in thin nematic films with a free surface

The effect of nonlinear light action on a thin (∼10 µm) films of the nematic liquid crystal deposited onto the absorbing substrate is experimentally investigated. The dynamics of the orientational and thermocapillary effects is directly studied. The two types of orientational processes were found out. The first one appears for several hundreds of milliseconds when the light beam irradiation is turned on or off. The second one develops much slowly and does not relax during the light beam irradiation.


Introduction
The light beam absorption in isotropic liquid causes the nonlinear response due to variation of its properties [1][2][3]. For instance, the light beam heating can change the surface profile forming a dimple, which works as a lens for transmitted light [4,5].This effect is mainly caused by the decrease in surface tension and the appearance of thermocapillary forces inducing the hydrodynamic flows [6][7][8].
Thermo-optical effects are much less investigated for the anisotropic liquids, i.e. for liquid crystals (LCs). In contrast to the ordinary liquids, LCs have partial orientational and, in some cases, translational ordering. On the macroscopic level, the average direction of the long molecular axes is defined by a unit vector, the LC director. The director field is very sensitive to various external stimuli, like electric, light and thermal fields. Thus, one can expect the interplay between the heat flux and the LC orientation when the light beam is absorbed in the medium. The most known example of thermal LC orientation is the Lehmann effect [9,10], the director rotation in chiral nematic LCs, which, in particular, can be induced by light [11]. The light beam absorption can cause thehydrodynamic flows resulting in the director reorientation in hybrid and twist aligned nematic films [12][13][14][15]. It is interesting to note that the director deformation can be a consequence of the temperature gradient only [16,17]. In this case, the temperature gradient field results in LC director deformation similarly to electric and magnetic fields. In the previous study, we described the orientational effect induced by light beam heating of nematic LCs with free surfaces [18]. The nematic film was deposited onto the indium-tin-oxide (ITO) glass substrate which provides the homeotropic anchoring and particular light absorption. An air-LC interface restricts the heat outflow and the axially symmetric heat flux reorients the LC director forming an umbilical defect. As for the isotropic liquids, the dimple formation is accompanied by the LC director deformation or appears without it.
In this study, we directly observe both the light-induced surface distortion and LC director reorientation using optical microscopy methods. In particular, we focus on the moments just after turning on and off the light beam focused onto the thin nematic films with a free surface.

Experimental
The E7 nematic liquid crystal(Synthon Chemicals) was deposited onto the ITO-coated glass substrate. The LC droplet of the size of about 2 mm and variable thickness was held on the substrate by capillary forces. Because of the wettability of ITO-coated surface by the LC, the edge of the LC droplet can be considered as a wedge film (Fig. 1a) whose surface can be modified by a focused light beam (Fig. 1b). Both LC surfaces (LC-ITO and LC-air) provide homeotropic boundary conditions and, hence, specify the uniform orientational distribution. The optical setup (Fig. 1c) consisted of solid-state continuous-wave laser (SSP-LN-532-FN-300-0.5-LED, CNI, China) with the wavelength of λ = 532 nm, home-made mechanical shutter with switching on and off times ∼ 1 ms, focusing lens, the sample with visualization scheme, and semitransparent screen. The radius of laser beam w 0 = 26 µm (at the intensity level of e −2 ) was measured by the "knife-edge" method [19]. The sample was placed vertically in the beam wais. The angle of incidence of the p-polarized light beam was 45 • . The diffracted light beam was observed on the semitransparent screen placed behind the sample. The image of the illuminated area was observed with the help of a high-speed camera equipped with the 16X optical objective with a large working distance. For background illumination, two light emitting diodes (LEDs) with luminescence at λ LED ∼ 620 nm were used separately or simultaneously. The first LED source allows one to visualize the orientational deformation when the sample is placed between crossed polarizers (polarizer P and analizer A). The light from the second LED was partially reflected by the glass plate (GP2) and then gave the reflection image. The opened and closed shutter positions and camera recording were triggered by microcontroller. The moments of the light beam switching were controlled using a photodiode (PD) by the registration of light reflected by the glass plate (GP1) placed after the shutter. The experiments were carried out at room temperature.

Results and Discussion
The interference of light reflected by the LC-substrate and LC-air interfaces results in the formation of bright and dark lines (Fig. 2a-2d).Note that these interference patterns are similar to those observed for isotropic liquids [4,5]. The LC thickness varies between bright and dark lines by the value of δh = λ LED /4n o , where n o = 1.52 is the refractive index of an ordinary light wave. Thus, the surface profile can be reconstructed by the positions of brightness extrema along the x axis ( Fig. 2e) with an accuracy of δh ∼ 0.1 µm. Typical LC film profiles before and during the laser irradiation are shown in Fig. 2f. The variation of LC film thickness |δh| with time ( Fig. 2g) is measured by alternating brightness in the area of the light beam axis. The obtained data clearly show that the light beam irradiation results in the gradual variation of surface profile. The initial region in temporal dependence can be approximated by the exponential curve |δh| = |δh max |(1 − exp(−t/τ )) with the characteristic time τ ∼ 3 ms, where |δh max | is the maximum thickness change. Thus, despite of the relatively slow process of thermocapillary effect [18], the initial development is at least one order of magnitude faster.
At the LC thickness of about h ∼ 10 µm and light beam power P = 80 mW, the light-induced director deformation is visualized by the bright areas in crossed polarizers (Fig. 3). Initially, only small bright regions due to the surface inhomogeneity are visible (Fig. 3a). During the light beam exposure, the bright cross appears, then becomes more intense and finally vanishes ( Fig. 3b-3f). This bright cross corresponds to the axially symmetric orientational deformation (Fig.1b). Surprisingly, the bright cross is temporary observed after turning off the light beam ( Fig. 3g-3l). The described effect is non-local; the size of the director deformation is several times larger than the diameter of the light beam. The appearance of the bright cross in the visualization scheme is accompanied by broadening the light beam passed through the sample.
A more complex process occurs at higher light beam power (Fig. 4). The large bright cross developes and starts to relax during several tens of milliseconds after turning on the light beam (Figs. 4a-4e). Then the smaller bright cross manifests itself (Figs. 4f). It becomes more intense for several seconds (Figs. 4f-4h) and does not change during the further light irradiation. The size of this cross pattern, which corresponds to the axially symmetric director deformation, is comparable to the beam diameter 2w 0 . After turning the light beam off, this deformation relaxes and, as in the previous case, the large bright cross pattern is temporary formed (Figs. 4i-4n).
Note that the described effects do not depend on the light beam polarization and only slightly depend on the angle of incidence. The orientational deformation is symmetrical with respect to the axis which is normal to the plane of substrate in spite of the oblique incidence of the light beam.
Thus, we have two types of thermo-optical orientation in the LC film. The first one is nonsteady-state and depends on the rate of the film thickness variation (Fig. 5). The increase in the light beam power leads to the more rapid variation of the film thickness as well as the  growth of its absolute saturation value. We suppose, that this director deformation is due to the director alignment along the hydrodynamic flows [20]. This effect is caused by the anisotropy of translational viscosity coefficients and can be easily observed, for example, when the LC is filled into the glass cell under the action of capillary forces. The lack of positional anchoring on the free surface facilitate the hydrodynamical flow formation [21]. A slight distortion of the cross texture (see, for example, Fig. 5d) in the direction of the thickness increase can be caused by higher values of the velocity near the surface (Fig. 1b). Switching the light beam off results in the reverse flow and the director is locally oriented along it.
The second type requires sufficient light beam intensities, develops much slowly and remains  Figure 4. Polarizing microscopy images of the irradiated region (formed by the transmitted light) at different moments during and after the light beam exposure. The light beam power is P = 120 mW, the exposure time is t exp = 4000 ms, the LC film thickness on the light beam axis is h = 9.1 µm. Figure 5. The time dependences of thickness variation |δh| during and after the light beam irradiation. The light beam power is P = 80 (1) and 120 mW (2), the exposure time is t exp = 4000 ms. The inset illustrates the initial stage of thickness variation. the same (Fig.4h) when the LC film thickness variation reaches the plateau (see curve 2 in Fig.5). This can be caused either by the temperature gradient [16,17] or by the circular flow convection observed in LCs and polymers [22,23].
Both types of director deformation require further theoretical study as well as computer simulations to determine the physical origin of the orientational processes more precisely. The situation can be more complex because of the interference of a number of effects, which cause the director reorientation [10].

Conclusion
To summarize, the thermo-optical orientational processes are studied experimentally for thin nematic films with free surfaces. The light absorption by the ITO layer causes both thermocapillary and orientational effects. The non-steady-state orientational deformation is observed during several hundreds of milliseconds after turning on or off the light beam. The rapid variation of the film thickness in the irradiated area indicates the development of hydrodynamic flows near the LC surface which can be responsible for this deformation. At sufficient light beam intensities, the stable LC orientation is formed. The latter one can be caused by both hydrodynamic flows and thermo-orientational effect. In each case the orientation is axially