Rotatable Diffraction Gratings Based on Cholesteric Liquid Crystals with Phototunable Helix Pitch

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1 Rotatable Diffraction Gratings Based on Cholesteric Liquid Crystals with Phototunable Helix Pitch Alexander Ryabchun, * Alexey Bobrovsky, Joachim Stumpe, and Valery Shibaev A novel type of rotatable diffraction volume gratings based on cholesteric liquid crystals with phototunable helix pitch is elaborated. For this purpose the cholesteric liquid crystalline mixture with high helix pitch tunability and reversible photoinduced helix handedness inversion containing azobenzenederivative of the chiral-photochromic dopant is developed. It was shown that the prepared cholesteric mixture under the hybrid (homeotropic planar) boundary conditions spontaneously forms a well-oriented striped domain texture which acts as a phase grating. Under the effect of light the changes of helix pitch take place due to the molecular photoreaction of chiralphotochromic dopant causing the variation of the period of striped domain structure and its rotation. The clockwise and counterclockwise rotation of the obtained gratings can be achieved by switching between UV and visible light, correspondingly. The maximum angle of the continuous rotation is 690, while the total rotation caused by UV light illumination reaches The creation of a variety of complex-organized structures by local light exposure of the cholesteric domain texture is demonstrated. The observed advanced photooptical effects have potentially wide and important applications from scientific and applied points of view. 1. Introduction Among the thermotropic liquid crystals (LCs) a distinctive place belongs to cholesteric liquid crystals (CLCs). Their periodic helical supramolecular structure and high sensitivity to the external fields make them very promising stimuli-responsive materials for different applications in photonics, electrooptics, display technology, creation of optical sensors, and other applications. [1 11 ] CLC materials possess a unique supramolecular helical structure predetermining their optical properties. The specific values of helix pitch are determined by the chemical structure of substances forming cholesteric mesophase. In the most cases a cholesteric phase is formed by doping the nematic matrix with Dr. A. Ryabchun, Dr. J. Stumpe [+] Fraunhofer Institute for Applied Polymer Research Geiselbergstr. 69, Potsdam-Golm, Germany ryabchunmsu@gmail.com Dr. A. Ryabchun, Dr. A. Bobrovsky, Prof. V. Shibaev Chemistry Department Moscow State University Lenin Hills 1, Moscow , Russia [+] Present Address : University Potsdam, Chemistry Department, Am Mühlberg 11, Potsdam, Germany a chiral additive (dopant) characterized by the definite helical twisting power, β ; this phenomenological parameter shows an ability of the dopant to twist the nematic structure (Equation (1) ): β = 1 P / X (1) where X is the concentration of the chiral dopant. It should be mentioned that the sign of the β is positive for a right-handed cholesteric helix and negative for the lefthanded one. Also the β value is the sum of individual contributions of each enantiomer presented in the system. This value strongly depends on the geometry of the chiral fragments and molecular interactions (steric, van der Waals, etc.) between the mixture components. These relations between chiral dopants structure and helical twisting power allowed one to create ways for phototuning of the helix pitch. [12 14 ] In many previously studied systems light exposure induces the photochemical E /Z isomerization of aromatic anisometric part of the chiral compound resulting in formation a bent-shaped Z- isomer having lower β -values as compared to the initial rodlike E-isomer (Figure 1 ). One of the most promising and important areas of CLC application is related to creation of the cholesteric diffraction gratings. [15 28 ] There are several principally different ways to produce the phase gratings in CLC. The first method is based on the exposure of the planar-oriented layers of CLC (when helix axis is perpendicular to the sample plane) to the weak electric fields. At the certain values of applied field (threshold-like behavior) and of confinement ratio d /P (where d thickness of cholesteric layer) the uniform aligned striped domains appear acting as phase grating. Up to date 1D [15,16 ] and 2D [24,25 ] types of the gratings were achieved, as well the possibility of their stabilization by polymer networks was shown. [26 ] The second method of the generation of diffraction gratings in CLCs involves the exploitation of the homeotropically aligned cholesteric layers (when helix axis is parallel to the sample plane). [27,28 ] In addition, substrates with vertical aligning layers must be rubbed unidirectionally to produce the oriented striped domains, otherwise the conventional (nonoriented) fingerprint texture would be observed. However, when using the second method, it is quite complicated to obtain gratings of a decent quality on a relatively large area. Cholesteric gratings discussed above can be tuned by electric and thermal fields along the grating vector WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 1

2 Figure 1. a) The schematic representation of the hybrid-aligned (homeotropic planar) cholesteric layer with spontaneously modulated structure; P cholesteric helix pitch and L period of cholesteric grating. b) Chemical structures of the used chiral and chiral-photochromic dopants as well as scheme of the dopant MeAzoSorb photoisomerization. It was shown in ref. [29 ] that the grating vector direction can be switched between two orthogonal directions only. Another type of cholesteric diffraction gratings can be obtained in cells with hybrid-aligning boundary conditions. Schematic representation of cholesteric layer aligned in this way is presented in Figure 1 a. In these cells one substrate stimulates a uniform planar alignment and the other one causes a homeotropic (vertical) orientation of LC molecules. In vicinity of the later one the cholesteric layers tend to reorient vertically; however, layers rotation is hindered by planar surface anchoring at the opposite substrate. Due to the elastic forces cholesteric layers experience a sinusoidal periodic tilt to minimize their free energy and as a result planar cholesteric texture becomes spontaneously periodically distorted in a way providing appearance of unidirectionally oriented striped domains. This approach has been realized only in a few studies. [30,31 ] The authors in refs. [32 34 ] considered a similar phenomenon by realizing a regular surface relief in CLC liquid films coated on substrate. The main feature of this approach is the ability to adjust not only the period of diffractive gratings but also continuously rotate them which is extremely useful for nonmechanical beams steering devices. [16,21,28 ] In the paper [31 ] the authors have managed to achieve a continuous rotation of the cholesteric gratings at an angle of 48 by applying an electric field and 101 by thermal treatment. It is obvious that the rotation of the gratings occurs due to changes of cholesteric helix pitch. As it was shown before one of the most effective ways to control the supramolecular helix pitch in a wide range is the utilization of chiral-photochromic dopant undergoing reversible or irreversible isomerization under the action of light leading to extreme changes of helix pitch. [14,35 40 ] In the present work we demonstrate a novel type of rotatable diffraction gratings by photocontrolling the helical pitch in a wide range with the possibility of reversible switching of the handedness of the supramolecular helix. For this purpose a specially designed low-molar-mass CLC mixture consisting of the nematic LC ZLI1132 and two chiral dopants MeAzoSorb and LM36 were prepared (see Figure 1 b). Diffraction gratings with extremely high continuous rotation ability in both clockwise and counterclockwise directions were obtained using this mixture. Moreover, the possibility of creation of a complex diffraction structures by photopatterning of hybrid-aligned CLC layers was illustrated. The chiral-photochromic compound MeAzoSorb (Figure 1b) was used as dopant for the induction of a right-handed helix of cholesteric phase. [41 ] Its molecular structure consists of the isosorbide optically active core and two azobenzene side fragments providing the photoresponsive properties. The most important features of the dopant are photooptical reversibility of the E /Z isomerization process and thermal stability of the Z -isomer due to the lateral methyl substituents. The helical twisting power of the dopant MeAzoSorb calculated using Grandjean-Cano method is about 61.5 µm 1 (see Figure S2d, Supporting Information, for detailed description). In order to maximize the effect of photoinduced changes of the helix pitch and to realize a helix twist inversion the nonphotochromic chiral dopant LM36 with the ability to induce left-handed helix and significantly lower twisting power (10.3 µm 1 ) was used. 2. Results and Discussion 2.1. Photooptical Properties of CLC Mixture with Phototunable Helix Pitch The prepared CLC mixture consisting of the nematic host matrix ZLI1132 (95.5 wt%), dopant MeAzoSorb (1.5 wt%), and dopant LM36 (3 wt%) formed a right-handed helical structure. 2 wileyonlinelibrary.com 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

3 Table 1. The helix pitch values and the handedness signs of CLC mixture under UV (365 nm) and visible (436 nm) light illumination (both to the related photostationary state). PSS - photostationary state. Handedness of cholesteric helix Cholesteric helix pitch [µm] Before irradiation Right handed 2.2 PSS-UV Left handed 2.8 PSS-Vis Right handed 5 Composition of the mixture was optimized in order to obtain diffraction grating with appropriate grating period and to realize helix inversion [40b ] upon UV irradiation and to realize the confinement ratio d /P less than 3 (for the cell thickness 4.8 µm). We have experimentally demonstrated that the high thickness (or d /P ratio) does not allow one to obtain cholesteric grating with sufficient quality. These investigations were made on the wedge-like cell with hybrid (homeotropic planar) alignment filled with studied CLC mixture and presented in Figure S3 (Supporting Information). During the experiment the wedge-like cell filled with the prepared CLC mixture was exposed by UV light (365 nm) up to the photostationary state followed by visible light (436 nm) illumination to the related photostationary state. The helix pitch of the CLC mixture during the irradiation was measured using the Grandjean-Cano method (see the Supporting Information for detailed description). Kinetic curves of helix pitch evolution during UV and visible light irradiation are presented in Figure S2 (Supporting Information). The values of helix pitch together with the handedness signs for both photostationary states are gathered in Table 1. It is clearly seen that the irradiation with UV and visible light leads to the inversion of helix sign. This effect takes place due to of the presence of two chiral dopants with opposite sings of helix twisting. When β values of dopants compensate each other the totally unwound cholesteric (or compensated nematic) state is formed. Domination of one of them dictates the sign of induced helix as far as the general twisting power of the system is additive value. The flexible control of twisting power of MeAzoSorb dopant enables realize reversible switching of the handedness of cholesteric helix. It is noteworthy that a full recovery of the initial helix pitch under visible light action has not been achieved. This fact is well explained by the presence of a small concentration of the Z -isomer of MeAzoSorb in the photostationary state upon visible light exposure. It should be stressed that the complete recovery of the helix pitch is achieved slowly by thermal Z /E isomerization of MeAzoSorb at the room temperature (it occurs during several days). [41 ] the cell with UV light induces the rotation of the striped domain structure in whole sample size. The possible mechanism of cholesteric stripes rotation was proposed by Nose et al. [30 ] It consists of the pair defects creation after the stripe breakage upon helix pitch increase. Then defects move in opposite directions until then they combine with other defects with opposite sign and disappear as the result. Finally, the new formed distorted line is gradually relaxed to straight line. The defect moving process proceeds in the small area with domain boundary is about dozens of micrometers and large uniform rotation takes place after the relaxation of deformed boundaries. Usually rotation of diffraction grating is achieved within a few seconds. In order to visualize the simultaneous observation of the cholesteric grating parameters (such as direction and period) a probe beam with the wavelength 660 nm locating outside the absorbance peak of the azobenzene chromophore of chiral-photochromic dopant MeAzoSorb was used. It is known that the efficiency of diffraction on phase cholesteric gratings depends on the direction of polarization of linearly polarized light and the most effective diffraction occurs for the light with perpendicular polarization with respect to the grating vector. [19 ] In order to avoid this effect during the grating rotation we used a circularly polarized probe beam. The photos set of the evolution of probe beam diffraction pattern in the course of UV exposure are collected in Figure 3. These photos present only the first part of the process up to the compensated (or achiral) nematic state, where no light diffraction was observed (80 s of irradiation, Figure 3 ). This state is characterized by fully unwounded cholesteric pitch ( P ). Subsequent the UV irradiation leads to a switching of the chirality and to the appearance of a phase grating again (Media file is available online). As it is followed from Figures 2 and 3 the photoinduced untwisting of right-handed cholesteric helix rotates the grating clockwise. The convergence of the diffracted beams indicates the increase of the grating period. The observed effects are associated with untwisting of the cholesteric helix upon UV irradiation by the E /Z isomerization of the chiral-photochromic dopant MeAzoSorb. It is noteworthy that the irradiation with visible light induces back Z /E isomerization and the rotation of the diffraction pattern in back direction (see below for the kinetics details) Kinetic Features of Photoinduced Rotation of the Diffraction Gratings Figure 4 a represents the kinetic curves of grating rotation angle α (the angle between the grating vector and the rubbing 2.2. Formation of the Rotatable Diffraction Grating in Hybrid-Aligned Layer of CLC Mixture In the cell with hybrid (homeotropic planar) alignment (Figure 1 a) filled with the CLC mixture a well-oriented striped domain texture is spontaneously formed. Polarized optical microscopy (POM) images of the textures are depicted in Figure 2. Irradiation of Figure 2. POM images of the striped domain texture of the hybrid (homeotropic planar) aligned layer of CLC mixture under UV light exposure. Dashed arrows show the grating direction WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 3

4 Figure 3. The evolution of the diffraction pattern of cholesteric grating upon UV light irradiation. P pitch of cholesteric helix. direction of the aligning polyimide layer) and its period upon UV light exposure. This process can be divided into three stages. The first stage is the untwisting (Δ β < 0) of right-handed helical structure which is characterized by the exponential growth of grating rotation angle (clockwise) as well as the grating period. The absence of diffraction takes place at the second stage which corresponds to the totally untwisted cholesteric helix or compensated nematic phase. During the third stage the diffraction grating reappears but now the cholesteric helix has the opposite sign (i.e., lefthanded helix). The irradiation results in twisting (Δ β > 0) of the cholesteric helix and consequently brings to an increase of the grating rotation angle (also clockwise). The grating period decreases during the cholesteric helix twisting. A set of processes changing the grating angle and its period for the first and third stages are clearly demonstrated in polar diagrams (Figure 4, below the graphs). The monoexponential character of the angular dependence can be attributed to the first order kinetics of the photoisomerization of the azobenzene dopant MeAzoSorb. It should be emphasized that the continuous Figure 4. Kinetic curves of stripe direction angle (solid squares) and gratings period (open squares) upon UV light exposure a) and the following visible light illumination b). Polar diagrams of angular dependences of the grating periods are presented below each fi gure, correspondingly. Dashed lines are the fi rst-order kinetics approximations; solid lines on polar diagrams correspond to the rational function approximation as discussed in the text. Arrows on the polar diagrams indicate the rotation direction of the diffraction pattern. 4 wileyonlinelibrary.com 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

5 rotation of the diffraction grating is considerably larger ( 692 or almost two full turns of grating) for the material proposed in the current paper in comparison with the maximum values of the rotation angle (101 ) which have been reported previously. [31 ] At the same time the total rotation of the grating by UV light irradiation is as large as It should be pointed out that the given values are determined by a number of parameters such as confinement ratio ( d /p ), elastic constants of LC, and anchoring energies. Subsequent visible light exposure initiates Z /E back photoisomerization of the dopant MeAzoSorb and, as consequence, the entire sequence of the processes described above is repeated in reverse order (Figure 4 b). As in the case of UV light exposure, it is also possible to identify three stages. At the first stage the untwisting (Δ β < 0) of the left-handed helical structure occurred that is characterized by the rotation of the diffraction grating counterclockwise. The second stage corresponds as previously to the compensated nematic state and the absence of grating. At the third stage the change in the sign of chirality and twisting (Δ β > 0) of the right-handed cholesteric helix is observed. The grating rotation is counterclockwise. It is clearly seen in Figure 4 b that the rotation angle reaches only about 90 and the values of the grating period do not return to their initial values. The reason for this was discussed above. Thus, a continuously rotation of the diffraction volume grating can occur in both directions for each handedness of cholesteric helix. Summarized data of grating rotation direction for right- and left-handed cholesteric helical structures are presented in Table 2. It is noteworthy that these results are consistent with the previously reported data concerning to thermoand electro-controllable hybrid-aligned cholesteric gratings [30,31 ] and the photoinduced surface relief pattern rotations. [32,33 ] Careful examination of the kinetic curves revealed the complicated character of the grating period changes upon irradiation, while the monotonic growth of rotation angle occurred. The observed dependences as consequences of the irradiation with UV and visible light are presented in Figure 4 a,b (open squares), respectively. It is possible to distinguish the flat areas where the period does not change significantly upon the exposure and the areas of the rapid period growth (or jump-like behavior). Previously, so called vertically aligned LC layer model instead of conventional middle-lc layer model [19 ] was proposed by Lin. [31 ] According to this model a stripe domain is formed in the direct vicinity to the substrate with homeotropic (vertical) boundary conditions (see also Figure 1 a) that was supported by scanning electron microscopy (SEM) measurements of a polymer-stabilized structure. In this case, the azimuthal angle Table 2. Summarized data of grating rotation direction for right- and left-handed cholesteric helical structures. of LC director orientation ( φ or α in our case) near the substrate with homeotropic aligning conditions dictates the orientation of diffraction grating and is given by Equation ( 2) : [42,31 ] ϕ = 2 π( d/ P) It should be emphasized that the LC director near the substrates with homeotropic alignment can freely rotate allowing the grating vector to slew continuously in the cell plane. To our knowledge there is no model describing the relationship of the helix pitch and a period of undulations of cholesteric layer under hybrid (homeotropic planar) boundary conditions. Therefore, for the experimental data approximation we have proposed that the cholesteric grating period ( L ) is proportional to the square root of the helical pitch (as for the ideal planar-aligned cholesteric layers, see the Supporting Information), namely L ( P d) 1/2. [19,22 ] This approach provided good agreement with the experimental data (solid red lines on polar diagrams in Figure 4, see also Figure S4, Supporting Information), but only qualitatively, and did not explain the jump-like behavior. It is interesting to note that the minima in all first derivative graphs (Figure S4) coincide exactly with the rubbing direction of one of the substrate. In other words, the period of the diffraction gratings practically does not change when it is codirectional with the rubbing direction and changes dramatically when it is perpendicular. The similar jump-like behavior of the grating period in the nonhybrid homogeneous planaroriented cholesteric layers under the influence of an electric field was thoroughly studied by Gvozdovskyy. [43 ] It was shown that the surface anchoring energy plays the main role for the jumps of the period of field-induced cholesteric grating. For high values of the anchoring energy the jumps of the period are observed, whereas in the case of sufficiently small energy only monotonic period growth was found. These peculiarities qualitatively explain the observed angular dependences of the gratings period in our experiments. Thus, we can conclude that, firstly, the grating rotation angle monotonically changes in the wide range under irradiation since there are no preferable azimuthal directions of LC director near the vertical-aligning substrate and cholesteric helix can freely adjust its pitch to satisfy the condition of the surface. Secondly, the grating period evolution during exposure possesses jumpwise behavior due to the strong anchoring at the opposite substrate with unidirectional planar-aligning layer. Proposed CLC material and method can find practical applications in nonmechanical beam steering devices giving a new strong impact on the possibility for highperformance steering not only in one dimension (along the grating direction) [21 ] but also in 2D. (2) Handedness of cholesteric helix Δ β a) Grating rotation direction Right handed <0 Clockwise >0 Counterclockwise Left handed <0 Counterclockwise >0 Clockwise a) Positive values of Δ β correspond to the twisting of cholesteric helix, negative to the untwisting Photopattering of Hybrid-Aligned CLC Layers Wide possibilities of manipulation of optical properties are opened owing to the use of hybrid-aligned layers of CLC with phototunable helix pitch for the creation of complex, photopatterned volume gratings. For example, the local irradiation of the striped domain cholesteric texture with focused beam having a 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 5

6 Figure 5. POM images of cholesteric grating resulted from localized irradiation of the right-handed helical structure a,c) with UV light (365 nm, dose 10 and 100 µj, correspondingly) and the left-handed helical structure b) with visible light ( nm, dose 50 µj). POM image of the striped-patterned cholesteric grating which was produced by illumination of the sample through the striped mask (amplitude diffraction grating with the period of 90 µm) with UV light d). All POM microphotographs were made in cross polarizers. Scale bars are equal to 100 µm. Gaussian light intensity distribution leads to appearing of spiral textures observed between crossed polarizers ( Figure 5a,b). Untwisting of the right-handed (Figure 5 a) and left-handed (Figure 5 b) cholesteric helices under the action of UV and visible light, respectively, results in the formation of differently directed spiral textures. The higher exposure dose causes a local switching of the helix handedness and one can see the coexistence of the right- and left-handed cholesteric domain textures (Figure 5 c). Another notable type of texture was obtained when the hybrid-oriented cholesteric layer was illuminated by UV light through a mask (Figure 5 d). We have used the amplitude diffraction grating with a period of 90 µm as a mask. Figure 5 d shows the alternating areas of striped domains with approximately perpendicular orientation of stripes of cholesteric grating. Thus, proposed approach and developed materials open space for all kinds of art to create different unusual and complex textures on the basis of cholesteric diffraction gratings. Moreover, our experimental results open new directions of the further developments of precisely controllable diffraction elements and devices. 3. Conclusions Photo-optically rotatable phase gratings based on hybrid-alignment of CLCs with photocontrollable helix pitch were produced for the first time. Due to the specially prepared CLC mixture containing nonphotochromic and azobenzene-based chiral compounds it was possible to realize fully reversible photoswitching of helix handedness. It was shown that the irradiation with UV light of both right- and left-handed cholesteric structures rotates the diffraction volume gratings clockwise. On the other hand, visible light irradiation induces the counterclockwise rotation of cholesteric gratings. The grating rotation is caused by the changes of helix pitch resulted from the photoinduced molecular isomerization of chiral-photochromic dopant. The maximum angles of continuous gratings rotation reached values as high as 692. Nonmonotonic behavior of gratings periods during exposure was revealed. New method of creation of complex-organized diffraction structures based on local illumination of hybridaligned cholesteric layers was demonstrated. The developed CLC material and described procedure of gratings fabrication can be used in nonmechanical beam steering devices and for other applications in optoelectronics, photonics, and spectroscopy. 4. Experimental Section Materials : Low-molar-mass LC ZLI1132 produced by Merck (mixture of cyanophenyl-cyclohexanes derivatives; isotropization temperature 71 C) was exploited as a nematic host matrix. Dopants LM36 and MeAzoSorb were used for the induction of cholesteric mesophase in the ZLI1132 host. Dopant MeAzoSorb was synthesized as we described previously. [41 ] Dopant LM36 was obtained according to the synthetic path described in ref. [ 44 ]. The cholesteric mixture was prepared by dissolving ZLI1132, MeAzoSorb, and LM36 in proper ratio in chloroform. Then the solvent was slowly evaporated and the residue was dried in vacuum at 50 C for several hours. Sample Preparation : Sandwich-like cells with hybrid (planar and homeotropic) alignment fi lled with cholesteric mixture were composed. One of the cell substrate was coated with planar-aligning polyimide (Sunever, grade 7992, Nissan Chem.) and following was unidirectional rubbed. The other substrate was treated by homeotropic-alignment polyimide (Sunever, grade 1211, Nissan Chem.). Teflon 4.8 µm spacers were used in order to control thickness of the cells. The obtained cells were fi lled with CLC mixtures using capillary forces at room temperature. Light Source : The samples were irradiated at room temperature with the collimated light of a high-pressure mercury lamp (HBO lamp, 100 W, Osram equipped with interference fi lters at 365 nm, I 0.56 mw cm 2 and at 436 nm, I 1.94 mw cm 2 ). The intensity of light was measured by a LaserMate-Q (Coherent) intensity meter. Measurements : For monitoring of the grating rotation processes and determination of the gratings period a laser diode was exploited ( λ = 660 nm, 3.5 mw). The probe laser beam was circularly polarized 6 wileyonlinelibrary.com 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

7 by using the polarizer and an achromatic quarter-wave plate. The laser wavelength was chosen as 660 nm to prevent photoinduced back Z /E isomerization of MeAzoSorb dopant (absorbance spectrum is presented in Figure S1, Supporting Information). In order to obtain images of the diffraction patterns digital photocamera (Canon) was used. For the gratings parameters determination, obtained photomaterials were processed by special software (AxioVision 4.8, Carl Zeiss ). The gratings period was calculated from diffraction angles data. Calculated values fully corresponded to ones measured by polarized optical microscopy (Polarizing microscope AxioPlan 2, Carl Zeiss ). Supporting Information Supporting Information is available from the Wiley Online Library or from the author. 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Ryabchun, M. Cigl, V. Hamplová, M. Kašpar, F. Hampl, V. Shibaev, J. Matter. Chem. C 2014, 2, [42] We have used absolute values of the angle, since it depends on rotation direction. [43] I. Gvozdovskyy, Liq. Cryst. 2014, 41, [44] A. Bobrovsky, N. Boiko, V. Shibaev, Polym. Sci. A 1997, 39, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 7

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