Annotation of the results obtained in 2020
Liquid crystal (LC) cells with tangential-conical boundary conditions were fabricated and studied. LC cells consisted of two glass substrates with transparent ITO electrodes on the inner sides and a cholesteric layer between them. To form the tangential-conical boundary conditions, one of the cell substrates was coated with a poly(vinyl alcohol) (PVA) film, and another one was coated with a poly(isobutyl methacrylate) (PiBMA) film. The ratio of LC layer thickness d to cholesteric pitch p was in the range from 0.6 to 1.12. The cholesteric cells were investigated by polarizing microscopy. Each sample had three rectangular electrodes with different orientations of their borders relative to the rubbing direction of PVA film. It was shown that the direction of the forming periodic structure depends both on the value of applied voltage and the angle between rubbing direction and electrode border where the growth of lines occurs. The dependences of the orientation of periodic structure on the value of applied voltage and the orientation of electrode border were obtained for the samples under study. The voltage range for the growth of lines increases when the ratio d/p grows and weakly depends on the sample thickness d. The period of the forming structure Λ does not depend on its orientation relative to the rubbing direction. Besides, the ratio Λ/p increases when sample thickness d increases. The dependences of the intensity of diffraction maxima on applied voltage were measured for the sample with d=5.0 μm and d/p=0.60. It is shown that the intensity of the first-order maximum decreases, while the intensity of other maxima increases when the value of applied voltage grows. Such behavior is typical for a periodic structure formed at different voltages. An electrically induced periodic structure is formed in a narrow voltage range during the relaxation process. This structure is characterized by the azimuthal change of the director angle in the range of about 90° on the substrate with conical anchoring. The orientation of the periodic structure coincides with the direction of growth of linear defects from the borders of the electrodes parallel to the rubbing direction. The splay deformation of periodic structure occurs for applied voltage 0.7≤U≤1.2 V in the sample with d=4.8 μm and d/p=1.12. The deformation angle of defect lines increases when voltage grows and reaches 80° at U=1.2 V. The period of structure deformation is equal to 13 μm and weakly depends on the value of electric field. The maximum of the peak-to-peak value of splay deformations observed at U=1.2 V is equal to the period of undeformed structure Λ. The deformed structure is sensitive to voltage changes and disappears at U <0.7 V and U> 1.2 V. The deformation of the defect lines does not occur after the subsequent voltage application in the range 0.7≤U≤1.2 V. Both substrates were coated with a PiBMA film in the cells with conical boundary conditions. LN-396 doped with cholesterylacetate was used as CLC. Two different constructions of the cell were used in the work. Both substrates contained a transparent ITO electrode on the inner sides in the cells where the electric field was applied perpendicular to the LC layer. In the case of applying a field in the plane of LC layer, a pair of ITO electrodes were on one substrate, while there were no electrodes on the second substrate. The formed orientational structures and their response to the applied electric field were investigated. The applied electric field perpendicular to the LC layer causes a constriction of loops and straightening of the linear defects which can result, finally, in the disappearance of defects. In cells with the equal thickness of the LC layer, it was found that the field strength at which the linear defects begin to move, as well as the field required for the annihilation of the ring defect and a pair of boojums, depends linearly on d/p. The relaxation process of structure depends on the d/p value. The initial state of the defect system is not restored for certain values of d/p parameter. The formation of a metastable configuration of the director close to periodic is possible in the relaxation process. The director configuration of this metastable structure was presented for linear approximation of the dependences of polar and azimuthal director angles. Under electric field applied in the plane of the substrates, the linear and point defects in combination with the possibility of easy azimuthal director reorientation promote the formation of regions with large deformation of the director field (“domain walls”). The position of the linear defect does not change at low electric field. Further increase in voltage causes the bend of defect line and growth of the defect area parallel to the field. A closed “domain wall” appears simultaneously with this process. The thickness of the “domain wall” decreases when the value of electric field grows. Further increase in voltage leads to a reverse reduction of the linear defect length and its straightening. If the “domain walls” approach each other, they intersect with subsequent separation. This process leads to straightening and orientation of “domain walls” along the field and appearance of a pair of boojums with topological charges m = + 1 and m = -1, localized within the "domain walls". A closed “domain wall” containing both defects appears when an electric field is applied to a ring defect with a pair of boojums. As in the case of a linear defect, there is an interval of voltages where a closed linear defect increases along the electric field. The reverse process of defect constriction occurs in a high electric field. In this case, the boojums are displaced along the “domain wall” in the direction of the linear defect. When the electric field is turned off, the new size of the ring defect is retained.

 

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Annotation of the results obtained in 2018
The liquid crystal (LC) cells with tangential-conical anchoring have been studied. LC cells are consisting of the two glass substrates with transparent ITO electrodes on the inner sides and nematic or cholesteric LC layer between them. To create a tangential-conical boundary conditions in the cells, the one substrate was covered with polyvinyl alcohol (PVA) film and another substrate was covered with poly(isobutyl methacrylate) (PibMa) film. The cholesteric LC cells with the ratio of LC layer thickness to the cholestric pitch d/p in the range from 0.14 to 2.92 have been considered. The formed orientation LC structures within nematic and cholesteric cells with d/p varied from 0.14 to 2.92 have been studied by the methods of polarizing microscopy and numerical calculation. The domain structures with a various tilt angle of director are formed within the nematic cells with d/p = 0.14. The uniform mono-domain twisted structure is formed at d/p = 0.28. The structure with defect lines creating the elongated loops is formed at d/p = 0.44. The periodic structure with the period equaled approximately 2p is formed within the cells of 6.5 µm thickness at d/p = 0.60. It has been found that the LC layer thickness (the helix pitch of cholesteric) is the additional parameter assigning the forming structure. A topology of director field distribution on the substrate with conical anchoring has been studied by the method of rotating analyzer. The formed orientation structures have been considered under electric field. It has been shown that an electric field changes the azimuthal twist angle of director on the substrate with conical anchoring within the cholesteric cell with tangential-conical boundary conditions. An application of electric field to the orientation structures with defect lines results in a change of their length both in the positive and negative direction subject to the magnitude of applied voltage. The dependence of velocity of changing line length on applied voltage has been measured for the sample with d/p = 0.44. It has been shown for the periodical structures (d/p ≥ 0.44) the magnitude of applied voltage influences both a velocity and a growth direction of the defect lines. So, the length of lines increases (growth of lines) within the cells of 6.3 µm LC layer thickness and d/p = 0.60 in the voltage range from 0 to 1.3 V. In this range, the angle between the rubbing direction of PVA and the direction of lines growth varies from 80 to 0 degrees. The orientation of defect lines remains after switching-off filed caused their growth. A change of light polarization transmitted through the LC cell with defect-less twisted cholesteric structure conditioned by the director reorientation under electric field has been simulated and measured. The parameters of light diffracted on the phase diffraction grating being a periodic structure formed at tangential-conical boundary conditions with d/p ≥ 0.64 (d = 6.7 мкм) have been studied. The observable diffraction pattern is symmetric relative to the zero maximum. It has been shown that the maximums of the first order are linearly polarized. A light polarization of the first eights of maximums has been measured. The periodic structure was formed by means of increasing of defect lines length under 1.05 V voltage. In this case the diffraction grating is oriented at another angle relatively the rubbing direction in comparison with the original grating. The dependence intensity of diffraction maximums on the applied voltage has been measured for such grating.

 

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Annotation of the results obtained in 2019
CLC cells of two types have been studied for the reporting period: the cells with tangential-conical boundary conditions and the cells with the conical surface anchoring at both substrates. To study CLC cells with tangential-conical boundary conditions, a number of samples with different thickness of cholesteric layer d and ratio d/p > 0.44 (p – cholesteric pitch) has been prepared. The formed orientational structures and their response to the applied electric field have been investigated. It has been shown the defects as a loop or line arise within the cells depending on the thickness of LC layer. A director orientation has been identified by means of the rotating analyzer method. It has been demonstrated, near the defects the areas with under-twisted and over-twisted cholesteric are formed in comparison with the equilibrium twisting of LC far from the defect. An applied electric field causes a transformation of defects in two different ways. In the first case, a constriction of the loop or a reduction of defects length until their total disappearing are observed. In the second case, a transformation of the defect line is accompanied by the appearance of a new type of defect. The director orientation near of this defect has been determined. It should be noted that the second way of defects transformation in the LC cells was observed for the first time. For certain ratios of d/p the periodic structure of linear defects containing U-shaped defects disrupting a periodicity is realized in LC cells. A formation mechanism of U-shaped defects has been studied. Based on these data an approach to the formation of homogeneous periodic structures has been proposed using different electrodes areas in the LC cell. The polarizing parameters (polarization azimuth and ellipticity angle) of radiation transmitted through the cholesteric layer have been also determined for the prepared CLC cells with tangential-conical boundary conditions. The polarizing parameters of transmitted radiation and their dependence on the applied voltage have been simulated. The obtained results are in good agreement with the experimental data. It has been demonstrated that a cholesteric with tangential-conical boundary conditions can be used to the fabrication of achromatic electro-controllable rotator of linear light polarization. To study CLC cells with conical anchoring at both substrates, the wedge-shaped sample with a variable ratio of d/p from 0.33 to 1.0 has been prepared. The formed orientational structures have been investigated. The main proper peculiarities of structures have been determined and systematized and their response to the applied electric field has been studied. The defect lines presenting the areas where the conical boundary conditions change to the tangential ones at both substrates are observed in the sample. The defect lines can rotate through 180° and near the turn, the boojums of +1 strength can form. If the defect line shapes a loop then the boojums with +1 and -1 strength are formed inside and outside the loop, respectively. The applied electric field causes a constriction of loops and straightening of the linear defects which can result, finally, in the disappearance of defects. After switching-off field, the defect lines are restored for ratio d/p > 0.9. At that, the additional disturbances of the director field arise in the twisted structure.

 

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