Light-responsive microstructures in droplets of the twist-bend nematic

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Langmuir

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Light-responsive microstructures in droplets of the twist-bend nematic phase Alexey Eremin,∗,† Hajnalka Nádasi,† Margarita Kurochkina,† Osamu Haba,‡ Koichiro Yonetake,‡ and Hideo Takezoe¶ †Otto von Guericke University, Inst. of Physics, 39016 Magdeburg, Germany ‡Department of Organic Materials Science, Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata 992-8510, Japan ¶Toyota Physical and Chemical Research Institute, 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan E-mail: [email protected]

Abstract We report on the structure and optical manipulation of the director configurations in emulsions of liquid crystalline droplets of a compound exhibiting the nematic (N) and the twist-bend nematic phases (NTB ). We demonstrate a decrease of the ratio of the bent elastic constant K33 to the splay one K11 by nearly two orders of magnitude with decreasing temperature in the N phase. The director structures in liquid crystal droplets doped with a photoswitchable surfactant without and under ultraviolet (UV) light are discussed in the light of a strong elastic anisotropy of the investigated compound. We also compare our findings with the results obtained in doped nematic droplets of a conventional 4-cyano-4’-pentylbiphenyl (5CB) liquid crystal. The dynamics of droplets in the NTB phase by UV light irradiation are also studied using polarizing and confocal microscopies.

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Introduction The broken rotational symmetry of nematic liquid crystals defines their unique mechanical and optical properties. 1,2 One of the essential features of liquid crystals (LC) is the possibility to easily control their molecular alignment by external fields. This makes liquid crystals indispensable in a broad range of applications from displays to smart optical devices and sensors. 3 The external-field-induced performance of such materials is critically influenced by the LC elasticity and the interactions between the mesogens and the confining surfaces (anchoring). Surface anchoring and the elastic anisotropy (the ratios of three elastic constants) are important for fast electro-optical response. The role of anchoring is crucial for LC in confined geometries, and it is a topic of intensive scientific research. Emulsions of nematic droplets in water are one of the interesting examples of confined LC systems, and have been extensively studied. 4–10 The director orientation inside the droplet is determined by the anisotropy of the elastic constants and by the anchoring condition at the LC/water interface. The topology of the spherical droplet necessarily requires the presence of a topological defect (point or line) inside the droplet or at its boundary, in case of the strong anchoring. For weak anchoring, the topological defects can be expelled from the droplets. Depending on the ratio of the elastic constants K33 /K11 , radial and bipolar configurations occur in droplets with orthogonal anchoring. 7,11 A bipolar configuration appears in case of the strong tangential anchoring. 7 Control of the elastic anisotropy allows to control the equilibrium director configurations and to drive structural transitions reported earlier by several groups. 4–10,12 Manipulation of the anchoring condition is another way to induce structural transitions in LC emulsions. Naturally, adsorption of surfactants can modify the anchoring and even drive orthogonal-to-tangential transformation. 8 Recently, non-uniform anchoring was used to produce Janus droplets with hybrid configurations of the director. 13 Another interesting development in the field of LC droplets is their applications as biosensors. Cholesteric droplets have photonic structures, and their optical response is sensitive to the anchoring 2


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conditions. 14 Thus, the adsorption/desorption processes of biomolecules at interfaces lead to structural transitions and optical changes. Orientational ordering transitions in thin films at the aqueous/LC interfaces can be driven by the surfactant adsorption, 8 enzymatic reactions 15 and even the adsorption of viruses. 16–18 Light-active surfactants such as azo molecules allow to control the anchoring conditions by exposing to the ultraviolet (UV) light. In our previous work, we reported light-driven switching of the director configuration in 5CB droplets doped with a small amount of azodendrimer. 19–22 Combination of UV and visible (VIS) illumination (λ > 450 nm ) allowed us to vary the anchoring strength continuously. 19 Structural transitions were also observed in the smectic A phase. 22 In the past few years, a novel type of a nematic phase has been discovered, which is distinguished by a heliconical arrangement of the director at the nanoscale. This phase is designated as the twist-bend nematic phase (NTB ). 23–28 In contrast to the cholesteric phase, the molecules in the NTB are tilted with respect to the helix axis by less than 90 degrees. Although the properties of this phase are somewhat similar to the smectics, the structure of the NTB lacks the positional order. 29 The pseudo-layer structure was established by the transmission electron microscopy 30 and the heliconical structure was experimentally established by the resonant x-ray diffraction. 23,25 The existence of this phase was originally proposed by Meyer based on the spontaneous appearance of the bend flexoelectric polarization. 31 Later Dozov proposed a model based on the elastic instability driven by the form anisotropy of the mesogens. In this model, the bend elastic constant becomes negative in the NTB phase and the stability is determined by the higher order terms in the free energy expansion. 32 The theory of the NTB phase is still in the focus of the intensive research. 26,29,33,34 Recent models of the NTB phase suggest the formation of long helical agglomerates of the mesogens. 35 It is reasonable to assume that the spatial correlations between the mesogens already develop in the nematic phase. In liquid crystals exhibiting the N and NTB phases, the high-temperature nematic phase 3


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is also distinguished by an unusual temperature-dependent bend elastic constant, which becomes extraordinary small upon approaching the N-NTB transition (the elastic anomaly). 30,36 This elastic anomaly also exists in the N phase in compounds containing bent-shaped molecules. 37 To understand this kind of behavior, one should consider the steric interactions between the mesogens. In rod-shaped liquid crystal, usually, K33 > K11 > K22 . Approaching the smectic-A phase, it is known that K33 and K11 diverge as a pretransitional effect. Experimentally, the NTB occurs mostly in dimeric mesogens which adopt a bend structure. The main contribution to stabilizing the nematic phase comes from the van der Waals dispersion forces. Polarization and sterical anisotropy essentially contribute to those forces. Steric anisotropy of the bent-shaped molecules locally favors a bent arrangement of the mesogens. However, a pure bend cannot fill the volume without voids or topological defects. On the other hand, a combination of the bend and twist or bend and splay result in structures topologically compatible with a uniform director field. Thus, the bent shape of the mesogens favors lower K33 than in the case of rod-shaped mesogens. A substantial reduction of the bend elastic constant K33 was observed in mixtures of rod-shaped and bentshaped liquid crystals. 37 In single-component nematic phases by bent-shaped mesogens K33 is usually smaller than K11 . 36,38,39 In this paper, we report on the behavior of the nematic director in emulsions of liquid crystal droplets dispersed in an isotropic fluid and doped with a photswitchable dendrimer. We demonstrate temperature- and light-driven configurational transitions in the nematic phase and the formation of the periodic microscopic structures in the NTB phase. The results are compared with the behavior of the well-studied liquid crystal 5CB. We attribute the peculiarities of the NTB droplets to the elastic anisotropy of the new material.

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Experimental Section We used a commercially available 5CB (4-cyano-4’-pentylbiphenyl, Sigma-Aldrich, phase diagram: isotropic 35◦ C N 18◦ C crystal) and a liquid crystalline mixture M provided by Merck KGaA (phase diagram: isotropic 69◦ C N 26◦ C NTB −17◦ C glass ). The liquid crystals were doped with a small amount (0.1-0.3 wt%) of poly(propyleneimine)-based azo dendrimer 19–22,40 for most of the experiments. Liquid crystalline emulsions were prepared by dispersing the liquid crystal/dendrimer mixture in a glycerol/water 4:1 mixture, stirring and slowly annealing it from 70◦ down to room temperature. Textures were observed in commercial sandwich cells (E.H.C., Japan) with thicknesses 5 µm, 10 µm, and 25 µm and hollow rectangular capillaries manufactured in borosilicate glass (CM Scientific, 0.10 mm × 1.00 mm). Substrate surfaces were either non-treated or rubbed polyimide layers along antiparallel directions. Polarizing microscopy (POM) observations and birefringence measurements were conducted using an AxioImager D.1 microscope (Carl Zeiss GmbH, Germany). VIS light from a 100 W tungsten lamp was used to illuminate the sample in the transmission mode. Simultaneously, UV light (HBO100) was cast on the sample from the reflection port of the microscope. The light intensity in the range of 0.1 - 2.0 mW/mm2 was measured using an optical power and energy meter (1936R, Newport Corp.). Polarizing confocal laser scanning microscopy (CLSM) was conducted using a Leica TCS SP8 CLSM microscope on samples doped with 0.01 wt% of a dichroic dye (n,n’-bis(2,5-di-tert-butylphenyl)- 3,4,9,10-perylenedicarboximide (BTBP), Sigma-Aldrich) excited at λ = 488 nm. Magnetic and electric Fréedericksz transitions were studied using capacitance measurements of a liquid crystal cell by a Solatron 1260A impedance analyzer at 5 kHz. Custom-made electromagnet 0 - 650 mT was used for the magnetic measurements. To extract the elastic constants K11 and K33 , we fit the field dependence of the dielectric permittivity to a theoretical expression given in the literature. 41 K22 was determined from the measurements of the twist Fréedericksz transition.

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Results and discussion Behavior in bulk As mentioned above, the director configuration in liquid crystal droplets is affected by an elastic anisotropy. Hence, before showing present droplet data, we describe the temperature dependence of elastic constants of the compound M. We adopted the Fréedericksz transitions under magnetic fields, which was detected by capacitance changes. Let us first show the dielectric properties of the compound M. The measurement was made using a rubbed polyimide-treated glass cell, in which the nematic director adopts a planar (tangential) alignment. Fig. 1 shows dielectric spectra (frequency dependence of real and imaginary parts of a dielectric permittivity) at T = 42◦ C. The spectra show a dielectric relaxation mode at about 1 MHz, which can be attributed to the reorientation of the transversal dipole moments of the mesogens. Measurements of the Fréedericksz transitions were performed at a frequency of 5 kHz, which is lower than the dielectric relaxation frequency. Based on the magnetic field dependence of the dielectric permittivity, the threshold of the permittivity change gives a splay elastic constant K11 , and a bend elastic constant K33 is obtained by the best fit of the data to the torque balance equation. 42 For instance, as will be shown in Fig. 2a , a steep slope in the dependence of the Fréedericksz curve indicates a high ratio of K11 /K33 . Figure 2a shows an example of the Fréedericksz transitions, where a magnetic field was applied perpendicular to the planar cell, at T = 42◦ . As clearly shown in Fig. 2a, a distinctive feature of compound M is the sign inversion of the field-dependence of ε(B). The dielectric permittivity increases with field for temperatures above 38◦ C suggesting that εk > ε⊥ and decreases below 38◦ C indicating that εk < ε⊥ in this temperature range. The temperature dependence of the dielectric anisotropy εa (T ) is shown in Fig. 2b. It exhibits a nearly sigmoidal dependence with the sign inversion at about 38◦ C. Indeed, the threshold voltage of the electric Fréedericksz transition diverges at this temperature and no transition occurs 6


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frequency, f (Hz) Figure 1: Dielectric spectra in the nematic phase of compound M taken at T = 42◦ C. in the same geometry used in Fig. 1 below 38◦ C. We found a large elastic anisotropy of the nematic phase where the bend elastic constant K33 is considerably smaller than the splay (K11 ) and the twist constants (K22 ) (K11 = 10 pN, K22 = 7.9 pN, K33 = 0.5 pN at T = 42◦ C). This is another important feature of this compound; the large elastic anomaly typical for bent-shaped liquid crystals, particularly in liquid crystals exhibiting the NTB phase. The bend elastic constant K33 is significantly smaller than the splay elastic constant K11 (Fig. 3a). Fig. 3b shows the temperature dependence of the ratio K33 /K11 . The ratio decreases exponentially by nearly two orders of magnitude across the temperature range of the N phase. At the same time, the twist elastic constant K22 is somewhat smaller than the splay constant K11 . The ratio remains K11 /K22 > 1 in the temperature range of the nematic phase as in the conventional nematic phase. No effect on the elastic constants of the liquid crystal was found in the range of concentrations used in our studies. To test the effect of the photoisomerization on the elastic constants and the order param7


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dielecric anisotropy, εa

dielectric perimittivity, ε `

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Figure 2: Magnetic Fréedericksz transition in the nematic phase: a)magnetic-field dependence of ε(T ) for selected temperatures exhibit sign inversion at about 38◦ C. b) Temperature dependence of the dielectric anisotropy εa (T ) extracted from the measurements of the magnetic Fréedericksz transition in a). eter in the bulk, we performed the measurements of the birefringence ∆n and the Fréederiksz threshold under UV/VIS conditions planar aligned rubbed polyimide cells in compounds 5 CB and M. In the polyimide-treated cells, the dendrimer does not trigger the anchoring transition under UV. No significant change in ∆n was found under UV exposure. The planar texture however, became smoother und UV. The photoisomerization did not affect the Fréederiksz threshold in the range of intensities used in the experiments. The phase behavior does not significantly change when the photoswitchable dendrimer is added either. On a bare glass substrate, the NTB phase exhibits a striped optical texture under a polarizing microscope (Fig. 4). Spontaneous undulation of the director produces the variation of the optical transmission between crossed polarizers. The stripes of the 6 - 7 µm width consist of topological defect lines separated by a distorted director field. The defect lines remain dark when the sample is rotated between crossed polarizers. This indicates that the lines represent discontinuity of the director field. Those lines are reminiscent to the Meyer domains 43 observed in the meniscus of freely suspended LC films in the SmC phase. 44,45 There is a secondary, faint pattern of stripes developing perpendicular to the 8


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defect lines with a typical periodicity of 3 - 4 microns.

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Figure 3: (a) Temperature dependence of elastic constants K11 , K22 and K33 . (b) Temperature dependence of the elastic constant ratio, K33 /K11 . Under UV light, the striped pattern smoothens, and the defect lines become expelled to the glass substrate. The smoothening occurs slowly on the time scale of 5 - 10 minutes and is accompanied by a slight increase of the birefringence. On exposure to VIS light (2 mW/mm2 ), the texture slowly recovers, and the birefringence decreases again. During these exposures, the distance between the defect lines remains nearly constant, but the director distortion between them smoothens.

secondary lines primary lines

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Figure 4: (a) Polarizing microscopy images of the NTB phase on a glass substrate: (a) without UV and (b) under 0.8 mW/mm2 UV illumination. 9


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Nematic droplets The size of the droplets dispersed in a glycerol/water mixture varies from 5 to 50 µm. Figures 5 and 6 shows nematic droplets of compound M and 5CB, respectively, in polarized

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Figure 5: Polarizing microscopy images of the nematic droplets of compound M ( T = 42◦ C). Microscope images (with a waveplate) at the initial state before UV irradiation (a) and at a transition state by UV irradiation (b), where the expulsion of the defect to the boundary occurs. Corresponding director fields are also shown. (c) and (d) are bright-field and POM+waveplate images of a droplet under VIS light after UV irradiation. The director configuration is given in (e). (f)-(h) correspond to the UV-induced bipolar state: bright-field microscopy (f), POM under crossed polarizers (g) and a scheme of the director configuration (h). light. Both droplets look identical in the samples annealed from the isotropic phase: The droplets feature a topological hedgehog defect in the center and the radial configuration of the director field both in the compound M and 5CB. But this feature is only in virgin droplets before UV irradiation in the compound M (Fig. 5a). Under the exposure to the UV, the azo-dendrimer molecules adsorbed at the LC/water interface, undergo a photoisomerization 10


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resulting in a tangential anchoring condition of the nematic director n. 19,20,46,47 This process is accompanied by an expulsion of the central hedgehog defect to the boundary (Fig. 5b) of the droplet. Under VIS light an axial state with a disclination loop is preferred. Prolonged UV exposure induces the transition from the axial state (Fig. 5c-e) to the bipolar state with a pair of defects of the strength 1/2 situated at the opposite poles of the droplet (Fig. 5f-h). After the termination of UV light and the subsequent exposure to the VIS light, relaxation

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Figure 6: Polarizing microscopy images of the nematic droplets of 5CB (T = 25◦ C). Micrographs (a) and (b) correspond to the initial state without UV illumination in bright field and polarizing microscopy (with a waveplate), respectively. (d) and (e) were made under UV illumination. Corresponding configurations of the director field are given in (c) and (f), respectively. The scale bar corresponds to 35 µm. of the director occurs differently in these two compounds. The 5CB droplets relax to a state with a single hedgehog point defect either at the boundary or, occasionally, at the center. Droplets of compound M adopt a configuration with a single disclination loop at the boundary (Fig. 5e). The difference between the two configurations can be attributed to the excess of the bend deformation in droplets of compound M. Large elastic anisotropy and low values of the bend elastic constant K33 favor the configuration with the disclination loop over the hedgehog configuration dominated by the splay deformation. 11


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A

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Figure 7: Liquid crystal lens formed at the glass substrate. (a) The image under VIS light condition shows effectively radial alignemt of the projection of the slow optical axis. (b) Spiral texture observed under UV light. The schemes below show the director field distribution in the vertical cross-section for (a) and the horizontal projection for (b). The scale bar is 10 µm.

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Some droplets attach to the surface and form lenses. Under VIS-light condition they appear dark between crossed polarizers. This indicates that the director field is aligned preferably along the observation axis i.e. perpendicular to the glass substrate at the bottom and perpendicular to the droplet surface at the top. Under UV irradiation, the birefringence drastically increases and the dark cross texture transforms into a spiral (Fig. 7). Lefthaded as well as right-handed spirals appear, indicating that the twisting sense is selected arbitrarily. Upon ceasing UV and re-exposing the droplets to VIS light, the spiral relaxes to the low-birefringent state with a straight Maltesian cross. This situation has been observed in lenses formed by bent-core liquid crystals and described in Ref. 48 The spiral configuration is attributed to the degenerated planar configuration at the surface of the droplet and the tendency of the azo-linkage to align along the light beam direction to minimize absorption. 48

Behaviour of droplets in the NTB phase The transition into the NTB phase of compound M is visible only in freely suspended droplets with a significantly large radius R > 20 µm. In the NTB phase, near the transition to the nematic, a regular striped texture with a period of 1.5 - 2 µm develops on the surface of the droplet (Fig. 8). Exposure to UV light (I ≈ 0.5 mW/mm2 ) disturbs the director configuration and completely destroys the stripe pattern (Fig. 8). Occurrence of director fluctuations suggests an induced transition to the nematic phase at the boundary of the droplet. At lower temperatures (2◦ below N-NTB transition), the response to the UV is significantly slowed down. No UV-induced melting could be observed. Some droplets eventually adhere to the glass substrate of the capillary or the cell, as observed by CLSM (Fig. 9). By wetting the glass substrate, the droplets form hemispherical cups or lenses (Fig. 9c). The pattern of stripes is particularly well seen at a flat LC/glass interface (Fig. 9b). On cooling, the stripes grow and fold until they fill the interface completely (Fig. 10). In some droplets the lines fold forming a structure similar to that with a topological 13


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Figure 8: Time series of POM images of an NTB droplet of compound M (T = 25◦ C) exposed to the UV light. The size of the droplet is 30 µm and the period of the stripes is 1.7 µm.

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Figure 9: CLSM images of an NTB lens attached to the substrate (T = 23◦ C): (a) in transmission between crossed polarizers. (b) Confocal image of a section close to the substrate. The arrows indicate neighboring stripes of director distortion. (c) Confocal image of the droplet vertical cross-section.

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(a)

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Figure 10: POM images of a NTB droplet at T = 23◦ C without UV (a) and under UV illumination (b). UV intensity is 0.8 mW/mm2 . The dotted line shows a selected director deformation stripe. The dashed line indicates the discontinuity line separating the folded stripes. defect s = 1/2 as shown in Fig. 10a) by dashed lines. A distinct radial discontinuity line marks the contact between the folded stripes in some droplets. In other droplets, the stripes remain disordered. Since the birefringence of the stripe pattern varies only slightly on UV irradiation, we can assume only a minor distortion of the director field. The stripes are also visible in the bright-field microscopy where the contrast is achieved due to the focusing lens effect of the pattern (due to a variation of the effective refractive index). When the pattern is exposed to the UV, the stripe pattern reversibly smoothens, but it does not disappear. Since the characteristic length scale ξ = K/W of the director deformation is given by the ratio of the elastic constant K and the anchoring strength W , strong temperature dependence of the elastic anisotropy is favorable for studying the coupling between the elasticity of the director and the director configuration in the restricted geometry. From that standpoint, compounds exhibiting the N-NTB transition become advantageous systems for their strong elastic anomaly. The primary difference between the nematic phases of 5CB and compound M is the elastic anisotropy. The bend elastic constant of the compound M is significantly smaller than the twist and the splay elastic constants unlike in 5CB. Such elastic anisotropy favors bend 15


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deformation over the splay one in compound M. Although the initial director configurations in 5CB and M droplets are radial, the configurations recovered after UV exposure are substantially different. The equatorial axial configuration (Fig. 5e) is dominated by the bend deformation of the director, and it was observed in systems with sufficiently weak surface anchoring. 11 Repeated exposure to intense electric and magnetic fields results in the equatorial axial configuration. 49 Alternatively, the axial configuration appears in cholesteric droplets in the transition from the positive to the negative twist state. 50,51 It is also an intermediate state between the bipolar and radial configurations. 7 Let us turn to discuss the droplets in the NTB phase, where characteristic striped patterns are observed. Director field instability in planar cells results in a pattern of stripes with a period determined by the cell thickness. 52 Those stripes are attributed to the HelfrichHerault instability of pseudo-layers formed by the helical structure. 53 In the case of droplets, the modulation appears to be restricted to the boundary of the droplet. The folding of the stripes leads to a discontinuity line connecting the two poles of the droplet. The striped pattern is reminiscent of the fingerprint pattern observed in the cholesteric shells with modulated anchoring. 13 Indeed, in the NTB phase, the structural transformation of the director is strongly hindered by the rigidity of the nano-heliconical structure. At the same time, the modulation tendency of the director can be supported by selective adsorption/desorption of the azo-dendrimer at the region of tangential and tilted configurations. This spatially modulates the anchoring strength providing the feedback in the pattern formation. Additionally, the dilative strain on the stripes results in a distortion of the fingerprint-like texture. UV exposure only weakly affects the microstructures in the NTB phase. Only close to the NTB -N transition temperature, the structure can be reversibly erased. This can be attributed to a light-driven decrease of the order parameter due to the photo-isomerisation of the dendrimer or by absorption-induced heating to the nematic state. Another important effect which contributes to the structural transformation of the director field is the elasticity and order parameter in the bulk affected be the photoisomerization 16


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process. One example is the dynamical disorganising effect of push-pull-azobenzene-dye reported in 54 for the BMAB/5CB. To test the effect of the bulk, we performed the measurements of the birefringence and the Fréederiksz threshold under UV/VIS conditions. Birefringence is directly related to the orientational order parameter and the Fréederiksz threshold is determined by the elastic constant. In agreement with our previous studies in 5CB, 19 we found no effect of the dendrimer on the the bulk elasticity of liquid crystals. The measurements of the Fréederiksz threshold under UV/VIS conditions in the LC/dendrimer mixtures did not show any significant change of the elastic constants within 1 % accuracy. It is important to mention that the molar fraction used in our experiments is nearly two orders of magnitude smaller than reported in Ref. 54 The inversion of the temperature dependence of the dielectric anisotropy εa (T ) in compound M can be attributed to the dielectric behavior of the constituents in the mixture. Many mixtures are known to exhibit a complex dependence of the dielectric permittivity. This is often related to the interactions between the components such as hydrogen bonding or polar correlations as well as conformational changes. 55–57 However, the sign inversion of εa occurs rarely. 55 The investigation to identify the real cause of the dielectric anisotropy inversion and to find other compounds showing the same phenomenon is a future important problem.

Conclusions In summary, we investigated photo-induced transformations in the nematic and twist bend nematic droplets of compound M with an azo-dendrimer surfactant. Extremely small bend elastic constants K33 compared with K11 appears to stabilize the axial director configuration with a disclination loop. In the NTB phase, the droplet surface exhibits a modulated structure which is related to the anchoring condition on the surface.

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Acknowledgement The authors thank Dr. Melanie Klasen-Memmer and Dr. Matthias Bremer from Merck KGaA for providing us with the liquid crystal mixture. This research was supported by Deutsche Forschungsgemeinschaft, project ER 467/8-2 and the DFG Major Research Instrumentation Programme 329479947. We are also immensely grateful to Prof. Ralf Stannarius for fruitful discussions and his expertise.

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Light-responsive microstructures in droplets of the twist-bend nematic

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