Abstract
Liquid crystals are anisotropic fluids with long-range directional order. They can be easily used to create topological defects, but creating a controlled topological defect is difficult and involves many tasks and complex processes. However, in our study, we were able to easily generate disclinations in the symmetry-breaking boundaries of an azo dye-doped nematic liquid crystal cell owing to photoisomerization and symmetry-breaking isotropic-nematic phase transition. The method proposed here marks the starting point for the easier control of topological defects in liquid crystals.
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1. Introduction
Liquid crystals (LCs) possess both liquid and solid properties and exhibit a variety of supramolecular structures. The nematic liquid crystal (NLC) phase, which has the greatest symmetry in known LC phases, exhibits a long-range directional order. Hence, the NLC molecules tend to align in one direction, which is the average alignment direction called director n.
Topological defects cannot be eliminated through continuous changes. They are characterized by topological charges k, and the law of conservation of topological charges controls the merging and decay of defects [1]. Topological defects are commonly produced in NLCs because director n is easily deformed for various reasons owing to the soft properties of NLCs. However, controlling the creation of the desired topological defects is difficult. Although methods, such as the dispersion of topological colloids [2–4], change of boundary conditions [5,6], and laser irradiation [7–10], have been used to create topological defects in NLCs, the process remains difficult. Consequently, this difficulty prevents NLCs from emerging as optimal materials for topological defect research.
In this study, we used rubbed bare glass substrates without alignment layers, which allowed DR1 azo dye to be adsorbed [11] onto the glass surface for photoalignment. This provided the initial alignment condition in which NLC molecules were aligned parallel to the glass substrate in the rubbing direction. Because the photoisomerization [12,13] of the DR1 azo dye caused the molecules to be aligned perpendicular to the polarization of light and generated heat [14,15], a laser tweezer was introduced to control the photoisomerization of the laser spot. When the laser spot, which had been in an isotropic state owing to the laser irradiation, became nematic after turning off the laser, the DR1 dye molecules that were adsorbed on the glass surface and aligned in a direction perpendicular to the incident polarization of the laser light caused the LC molecules to be oriented in the same direction along the DR1 molecules. Because the polarization of the irradiated laser light was parallel to the initial director ${{\mathbf n}_0}$, there was a boundary at which symmetry was broken between the outside and inside of the photoaligned domain.
Similar to the early universe, spontaneous symmetry breaking (SSB) occurs during the isotropic-nematic (I-N) phase transition of LCs [16–18] and forms a dense tangle of topological disclinations (topological line defects). However, in the absence of the symmetry-breaking boundary (SBB), disclinations cannot remain because of pair annihilation [19]. In our study, the SBB, which prevented the complete disappearance of the disclinations, was generated by photoisomerization, and the SSB I-N phase transition occurred simultaneously because of the heat generated; this enabled us to create disclinations at the SBB. In the SBB, disclinations [20] with topological charges (winding numbers) of k = +1/2 and k = -1/2 could remain, and the topological charge, which is the topological invariant, is always conserved [21].
Therefore, we were able to rapidly and simply create disclinations at the SBB by the photoisomerization of the azo dye and the occurrence of SSB in the I-N LC phase transition. The method of generating the topological charges presented in this study is significant because it can aid in basic research and future applications.
2. Experimental
In this experiment, 5CB (4′-Pentyl-4-biphenylcarbonitrile, Tc = 35°C) NLCs were doped with 0.15 wt % of Disperse Red 1 (DR1; N-Ethyl-N- (2-hydroxyethyl)-4-(4-nitrophinylazo) aniline, ${\mathrm{\lambda }_{\textrm{max}}}$ = 502 nm) dye. DR1 is a pseudo-stilbene-type azobenzene chromophore. When irradiated, a trans isomer is photoexcited to a cis isomer, which then becomes a trans isomer by absorbing the same wavelength of light or emitting heat. After consecutive trans-cis and cis-trans photoisomerization, the DR1 molecules align perpendicular to the polarization of the irradiating light. In addition, because of the generated heat, the laser spot of the NLCs can move to an isotropic state, and the isotropic domain of the LC undergoes an I-N phase transition after the laser is turned off.
To make NLC cells, the cover (Matsunami) and soda-lime slide (Marienfeld) glass substrates were rubbed with a cloth, and the two glasses were sandwiched, maintaining a gap with the mixture of UV curing epoxy and spacers (1 or 2.5 μm). The samples were then cured under UV light. The cell was filled with the 5CB and DR1 mixture using capillary force in the isotropic phase at 36°C. Except for the experiment corresponding to Fig. 3, cells with a thickness of 2.5 μm were used in all experiments. For obtaining the experimental results presented in Fig. 3, a cell with a thickness of 1 μm was used. The 5CB and DR1 were purchased from Sigma-Aldrich.
A topological charge was generated in the NLC cell using a laser tweezer. The laser tweezer consisted of a linearly polarized and continuous TEM00-mode wave from a semiconductor laser (Coherent, SF 532, $\mathrm{\lambda }\; $ = 532 nm), an inverted microscope (Nikon Ti-U) equipped with a piezo stage (PI GmbH & Co. KG), and a CCD (Point Grey Research). The laser tweezer played a dual role of facilitating optical microscopy as well as providing the thermal and photoalignment effects caused by the photoisomerization of DR1 molecules. We used Olympus PLN ×20 (NA 0.4) and ×40 (NA 0.65) objective lenses for the laser tweezer and optical microscopy. The ×20 and ×40 objective lenses made laser spots with radii of 3.5 and 6 μm in dye-doped NLC cells, respectively. The ×20 objective lens was used to obtain the results depicted in Figs. 2 and 4, and a ×40 objective lens was used for acquiring the results in Figs. 1 and 3. The intensities were calculated by dividing the incident laser power by the area of the laser spot. The laser light intensity was 0.3 mW/μm2 for the experiments corresponding to Figs. 2 and 3, and 0.5 mW/μm2 for that corresponding to Fig. 4.
For optical microscopy, polarized optical microscopy (POM) and bright-field microscopy with a polarizer (BFMP) were used to determine the positions and types of topological defects. The POM image with a broadband half-wave plate $(\textrm{HWP};\; \mathrm{\lambda }$ = 400–800 nm), which is inserted after the LC cell between the crossed analyzer (A) and polarizer (P), shows the texture with colors in relation to the alignment direction of the LCs. The colors of the POM with an HWP (POMH) image provide information about the two-dimensional director field n(r). Information about the direction of molecular alignment obtained from POMH images varies depending on the cell thickness because the birefringence of the LC layer changes with its thickness. If the thickness of the cell is 2.5 μm, the green color indicates that the director is along the 2 o'clock direction, which is the direction of the fast axis h of the HWP, whereas the pink color indicates that the director is along the 10 o'clock direction, which is perpendicular to the fast axis h of the HWP. Conversely, if the cell is of 1.0 $\mathrm{\mu}\mathrm{m}$ in thickness, the green and pink colors indicate that the alignment of the director is in the 10 and 2 o’clock directions, respectively.
3. Results and discussion
We fabricated LC cells by rubbing the soda-lime-silica glass substrates, which allowed the LCs to align in a direction parallel to the glass substrate in a low anchoring energy state. Therefore, inside the LC cell, long rod-shaped DR1 molecules were aligned along the LCs in the same direction, and on the glass surface, the -OH end groups of the DR1 molecules were bound to the silanol group on the glass surface for adsorption [11]. Accordingly, the topological defects formed by the planar anchoring condition were line defects [20,22], that is, disclinations formed between two substrates with topological charges k = +1/2 or k = -1/2.
Figure 1(a) shows the I-N phase transition due to the heat generated in photoisomerization, which results in the photoalignment of the adsorbed DR1 molecules on the glass substrates. Laser light, polarized in the direction parallel to ${{\mathbf n}_0},$ incident on the LC cell, forms an isotropic domain Piso (radius riso = 10 μm) with an area larger than that of the laser spot (radius r = 3.5 μm). The area of Piso is proportional to the intensity of the laser (Fig. 1(c)). On the surface, the adsorbed DR1 molecules align perpendicular to the polarization direction of the laser light. During the I-N phase transition after the laser light is turned off, the LC molecules on the surface of the substrate are anchored by the DR1 molecules that are aligned and adsorbed on the substrates and have easy axis in the same direction along the DR1 molecules. Therefore, the director ${\mathbf n}$ in the laser spot becomes perpendicular to the initial director ${{\mathbf n}_0}$. However, LC molecules outside the laser spot are oriented again in the direction of ${{\mathbf n}_0}$ because they are not aligned by photoisomerization. Thus, the internal director (${\mathbf n}$) and the external director (${{\mathbf n}_0}$) of the laser spot become perpendicular to each other, resulting in the SBB, where the direction of director is changed. In this SBB, the multi-domains created during the SSB I-N phase transition can remain, which enables the formation of topological charges. Therefore, the laser light is turned off at time t = 0 and the tangled disclinations disappear by pair annihilations (from t = 0 to t = 44 ms). However, in the boundary where the symmetry is broken by the photoalignment, the formation of topological defects, as shown in Fig. 1(a) (the POM image at t = 69 ms and the next BFMP image), occurs in this SBB because of the symmetry-breaking I-N phase transition. Figure 1(b) shows the director field n(r) of the topological charge generated in the SBB and is drawn by overlapping the positions of the isotropic domain, laser spot, SBB, so that it aids in understanding the creation geometry of topological charges due to the I-N SSB phase transition. In Fig. 1(c), which depicts the POMH images showing ${\textrm{P}_{\textrm{iso}}}$ according to the laser intensity, the area of ${\textrm{P}_{\textrm{iso}}}$ is observed to increase in proportion to the laser intensity (Fig. S1 of Supplement 1).
Figure 1(d) consists of microscopy images that show the phase transition that results from suddenly turning off the laser light after photoalignment, as shown in Fig. 1(c). The angle $\phi $ between the director ${{\mathbf n}_0}$ and the NLC molecules in the laser spot changes from 90° to 0° as it moves from the center to the periphery because of the Gaussian profile of the laser intensity. Further, $\phi $ becomes 90° more quickly regardless of the location in the laser spot for higher intensities. Thus, $\phi $ becomes 90° at the center of the laser spot, and eventually the molecules inside the spot are aligned perpendicular to ${{\mathbf n}_0}$. In addition, Fig. 1(d) shows that topological charges are generated only when the intensity of the incident laser light is high, possibly because lower intensities produce poor photoalignment but also because of the size of Piso. Topological defects cannot be created if the I-N phase transition does not occur in the SBB (2-20 mW of Fig. 1(d)). In the BFMP image in Fig. 1(d), one can clearly observe the topological charge pairs that are formed, and the corresponding topological charge values are indicated. Because the topological charge k must be preserved when the topological defects are formed, the k = +1/2 and k = -1/2 disclinations are formed in the same number. Hence, dipolar, quadrupolar, and multipolar configurations (Figs. 2(a) and (c)–(e)) are possible.
In Fig. 2(a), we present a series of microscopy images that show the generated topological charges. Figures 2(b)–(e) show the schematic director fields (i) and microscopy images (ii)–(iv) of the topological charges created in the SBB. There may not be topological charges, as shown in Fig. 2(b), but when a topological charge is formed, it is formed only in the SBB and obeys topological charge conservation.
In Fig. 3, we present microscopy images (a)–(e) to show that the topological charge pairs were created using the laser tweezer in the π-domain wall formed by the existing k = +1/2 and -1/2 charges. The corresponding schematic director field n(r) (Fig. 3(f)) is also shown. The polarization of the incident laser light (Lp) is parallel to the LC molecules in the center of the $\pi $-domain wall (Figs. 3(a) and (f)). Therefore, Fig. 3(a) shows that when the laser light is incident, an isotropic domain is formed due to the thermal effect caused by the photoisomerization of the DR1 molecules. Subsequently, as shown in Fig. 3(b), a 1/2 topological charge pair is formed by the SSB phase transition and photoisomerization by the DR1 molecules adsorbed on the substrates. After repeating this process several times, a series of topological charge pairs can be generated, as shown in Figs. 3(c)–(e). The generated topological charge pairs can be clearly observed inside the white box in Fig. 3(e). Figure 3(f) shows the director field n(r) of the newly created k = +1/2 and -1/2 topological charge pairs. The alignment direction of the $\pi $-domain walls between the newly formed topological charge pairs is perpendicular to that of the existing $\pi $-domain wall.
The distortion in an NLC is described as an elastic field corresponding to an electric field of the electrostatic force [24,25]. Therefore, the defect that creates distortion becomes a topological charge, and an elastic field is formed around it. An elastic field in the direction of the +1/2 charge to the -1/2 charge is formed between the existing k = +1/2 and k = -1/2 topological charges, in which the newly generated 1/2 topological dipoles are aligned within the elastic field. In other words, the generated topological dipoles are aligned in one direction because of the strong external elastic field (distortion by the existing π-wall), as if the electric dipoles are aligned within the strong electric field.
Figure 4 shows the result of topological charges that are formed at the SBB by photoalignment with the polarization parallel to the boundary direction. The linearly polarized laser light (Lp) in parallel with ${{\mathbf n}_0}$ is slowly moved to form a domain that is vertically aligned with ${{\mathbf n}_0}$. Figure 4(a) shows the director field n(r) created in this manner. To create a topological charge, the polarization direction of the laser light incident on the symmetry-breaking domain boundary was Lp ($\theta$ = 50°), which was parallel to the molecular alignment direction of the domain boundary. As shown in Fig. 4(a), the photoalignment (within 100 s) in the isotopic state was performed by the linearly polarized laser light (Lp) located in the SBB. If the laser is turned off after the photoalignment, the phase transition occurs followed by the creation of topological charges. This is shown in the schematic director field n(r) in Fig. 4(b), and the experimental results are presented in Figs. 4(c)–(f). Figures 4(c) and (d) are POM images depicting the experimental results that correspond to Fig. 4(b). In Figs. 4(c) and (d), we observe that the isotropic domain with planar anchoring is induced by strong laser light, and at the boundary of the isotropic domain, a pair of antipodal surface topological defects called boojums [26] are formed in the direction of the director in a nematic. The position of a pair of boojums varies when the laser light is located inside and outside the photoaligned domain. Inside the photoaligned domain (Fig. 4(c)), a pair of boojums is induced on the top and bottom of the isotropic domain, whereas outside the photoaligned domain (Fig. 4(d)), it is induced on the left and right of the isotropic domain. Hence, the initial orientation ${{\mathbf n}_0}$ and the orientation ${\mathbf n}$ inside the domain are perpendicular to each other, and it is confirmed that the intended photoaligned domain is formed. In addition, topological dipoles are formed at the edge of the domain. Figure 4(e) is a POMH image showing the experimental results that correspond to Fig. 4(b), and the orientation direction information of LC molecules related to the color of the domain is reflected in Fig. 4(b). Figure 4(f) is a BFMP image showing the charge values of the topological defects formed by photoalignment and I-N phase transition. In other words, the topological charge was formed because the orientation direction was partially changed in the symmetry-breaking region by the photoalignment.
In summary, we were able to easily create 1/2 topological charges in NLCs using a laser tweezer. DR1 azo dye-doped 5CB nematic LCs were used, and an LC cell was fabricated using soda-lime-silica glass substrate to utilize the photoalignment effect of DR1 adsorption on the substrate. Using unidirectionally rubbed glass substrates, LCs were oriented in the rubbing direction parallel to the substrate, and DR1 molecules aligned parallel to the LCs were adsorbed on the glass substrates. When the laser light that was polarized in the direction parallel to ${{\mathbf n}_0}$ was incident on the LC cell, DR1 molecules absorbed the laser light, and then photoisomerization occurred. An isotropic domain was formed in the laser spot owing to heat generation, and the DR1 molecules adsorbed on the substrates were simultaneously aligned perpendicular to the polarization of the laser light. Thereafter, when the phase transition occurred after the laser was turned off, the DR1 molecules that were adsorbed on the surface and aligned perpendicular to the polarization direction anchored the LC molecules in the same direction. Consequently, they possessed easy axes perpendicular to the laser polarization when the nematic phase was formed. Therefore, when the I-N phase transition occurred after irradiation for a certain period, the director of the LC changed in the easy axis direction, and this photoalignment was more effective at higher intensities of the irradiating laser. Meanwhile, the boundary of the photoaligned domain, the symmetry-breaking region, can be formed of multiple domains by symmetry breaking that occurs during the phase transition, allowing 1/2 disclinations to remain. Furthermore, topological charges can be created by the partial photoalignment of the symmetry-breaking region. The topological charge must be preserved such that equal numbers of k = +1/2 and k = -1/2 topological charges are created.
4. Conclusions
For decades, topological defects in LCs have been considered disadvantageous. However, their formation goes beyond academic research and has become a very important and interesting research topic in diverse areas. Despite many efforts to create desirable topological defects, it is difficult to control the director field to achieve the same. However, we were able to generate 1/2 topological charges owing to the SSB phase transitions and photoisomerization in NLCs doped with azo dyes. The elastic field created by the topological charge in the NLCs corresponds to the electric field created by the electric charge.
In addition, because the mechanism of charge creation and formation of an elastic field are associated with a wide range of disciplines, from the SSB phase transitions in the early universe to quantum chromodynamics (QCD) strings, research on topological charges is of great importance. Therefore, our proposed methods can further expand the understanding of topological charges and can possibly be extended to nematic colloids [27], where various types of feedback can be observed by controlling the defects induced by light and colloidal defects.
Funding
National Research Foundation of Korea (2021R1A6A1A10044154).
Acknowledgments
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2021R1A6A1A10044154).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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