Generation of Multiple Circular Walls on a Thin Film of Nematic Liquid Crystal by Laser Scanning
aa r X i v : . [ c ond - m a t . s o f t ] M a r Generation of multiple circular walls on a thinfilm of nematic liquid crystal by laserscanning
M. Kojima, J. Yamamoto, K. Sadakane, K. Yoshikawa ∗ a Department of Physics, Graduate School of Science, Kyoto University &Spatio-temporal Project, ICORP, JST, Kyoto 606-8502, Japan
Received 11 February 2008; in final form 2 Marc 2008h
Abstract
We found that multiple circular walls (MCW) can be generated on a thin filmof a nematic liquid crystal through a spiral scanning of a focused IR laser. Theratios between the radii of adjacent rings of MCW were almost constant. Theseconstant ratios can be explained theoretically by minimization of the Frank elas-tic free energy of nematic medium. The director field on a MCW exhibits chiralsymmetry-breaking although the elastic free energies of both chiral MCWs are de-generated, i.e., the director on a MCW can rotate clockwise or counterclockwisealong the radial direction.
Liquid crystal (LC) phases bring about a rich variety of textures as visualizedby polarizing microscopy [1]. This polymorphism in the texture results fromthe inhomogeneity in molecular alignment due to defects in the LC [2]. Overthe past few decades, much attention has been paid to colloidal dispersionsin nematic LC because of their peculiar properties, such as a topological de-fect around a particle and long-range interaction among the particles [3,4,5].This long-range interaction also results from inhomogeneity in the molecularalignment. The averaged molecular alignment is expressed as the director [2].It has been found that a strong laser beam induces a distortion in the director ∗ Corresponding author.
Email address: [email protected] (K. Yoshikawa).
Preprint submitted to Chemical Physics Letters 6 November 2018 eld of nematic LC [6]. Especially, a linearly polarized laser can orient thedirector in the illuminated region in the direction of laser polarization [7,8].It has been reported that defects in LC can be modified by use of laser ma-nipulation [9,10]. Recently, Mˇusevic et al. combined the property of a defectaround a colloidal particle suspended in nematic LC with distortion in thenematic LC induced by a laser beam. They found that a particle with a lowerrefractive index than that of the surrounding nematic medium can be pickedup with optical tweezers [11], although such a particle cannot be trapped inisotropic media. ˇSkarabot et al. showed theoretically that such extraordinarytrapping is achieved through the interaction between the laser-induced distor-tion in the director field and a topological defect near the particle [12]. Thus,the interaction between a defect in LC and a laser beam produces variousunique phenomena. Here, we tried to generate a new pattern in a nematic LCby using the interaction between a defect and a laser beam.
The nematic material 5CB (Tokyo Chemical Industry co., Japan) was putinto a microtube. Pure water was dispersed in the microtube. The nematiccontaining water droplets was vortexed. The microtube was then centrifugedfor a short period to eliminate large water droplets. The nematic containingmicron-sized droplets was placed between glass slides with a thickness a few µ m. The thickness was estimated by dividing the volume of nematic by thecontact area on the glass surface. The nematic was sheared to easily give aSchlieren texture, and the glass slides were baked at 500 ◦ C for an hour beforeuse.Observations were performed through a polarizing microscope (converted IX70,Olympus, Japan) equipped with a ×
100 oil immersion objective lens (UP-lan Apo IR, N.A. 1.35, W.D. 0.1 mm, Olympus, Japan). A linearly polarizedNd:YAG laser with a focus of ∼ Results
Figure 1 shows the responses of a brush distributed from a wedge disclinationfor horizontally and vertically polarized laser beams. The disclination waspinned to the glass substrate by chance. The strength of the disclination was-1/2, as judged from the response in the texture for a simultaneous rotationof the polarizer and analyzer of the polarizing microscopy while maintainingcrossed nicols. When the brush was illuminated by a horizontally polarizedlaser beam (Fig. 1 (a)), the texture showed a minute change (Fig. 1 (b)). Onthe other hand, with a vertically polarized laser beam, the illuminated brushwas repelled from the beam spot and the texture was completely changed fromFig. 1 (c) to Fig. 1 (d). The responses of the neighboring brush connected to anidentical disclination core for polarized beams were inverted: the neighboringbrush was only repelled from the horizontally polarized laser beam. When thelaser was shut off, the conformation of the brush returned back to the textureseen before the laser irradiation. The distances between the repelled brush andlaser spot were distributed broadly. We confirmed experimentally that brusheswhich grew from disclination cores ( ± ±
1) are repelled from either ahorizontally or vertically polarized beam spot. The responses of a disclinationcore to a linearly polarized laser beam have been reported by Hotta et al. [10].Figure 2 shows the emergence of a single-ring pattern. The real time movie ofthe process is available from the internet [13]. The single-ring pattern centeredon the beam spot was generated by a laser scanning along the trajectorydepicted schematically in Fig. 2 (A). We have chosen the velocity of the laserscan so as to grasp the brush in a steady manner. Actually, the spot was movedstep-by-step, where typical one step is ∼ µ m, and during the step-motionthe speed was chosen ∼ µ m/s. The present disclination core is identicalto that in Fig. 1. Figure 2 (B) (a)-(f) show snapshots at each point on thescanning trajectory in Fig. 2 (A). The beam spot passed through withoutchanging the conformation of the brush (Fig. 2 (a)), whereas the neighboringbrush was repelled from the beam spot(Fig. 2 (b)). When the spot was furtherbroken into the brush, the plucked part of the brush spontaneously closedand a dark ring centered on the beam spot was formed(Fig. 2 (c)-(d)). Thedark ring kept up with the motion of the laser spot with deformation from acomplete circle. When the beam spot came to rest, the dark ring relaxed intoa symmetrical circular form (Fig. 2 (e)). The laser spot coated with the darkring repelled the brush (Fig. 2 (f)), which was not repelled in the case of a barelaser spot (Fig. 2 (a)). We have succeeded in generating this pattern only from ± µ m/s. In addition, thegenerated ring patterns broke down when the velocity of the laser spot wasabove 100 µ m/s. The sizes of the dark rings have a broad distribution.3 ig. 1. (color online). Responses of a brush on a thin film of liquid crystal for polar-ized laser beams. (a), (c) A wedge disclination with a strength of -1/2, just beforelaser irradiation. (b) A horizontally polarized laser beam illuminates the brush. (d)A vertically polarized laser illuminates the same region as in (b). The brush is onlyrepelled from the vertically polarized laser spot. In both cases, the textures recov-ered almost reversibly when the laser irradiation was shut off. Figures (a’)-(d’) areschematic illustrations of the director fields of (a)-(d) respectively. The red circles inthe primed figures represent the position of the beam spot. The double-headed ar-row represents the direction of the polarizer and analyzer in polarizing microscopy. Figure 3 shows the appearance of a triple-ring pattern when the laser spotfollows a trajectory ∼ a + 1/2 disclination core. The real time movie of theprocess is available from the internet [14]. The spot was moved step-by-step,where the typical one step is ∼ µ m, and during the step-motion the speedwas chosen below 30 µ m/s. The scanning process corresponds to three iter-ations of the pattern used to generate a single-ring pattern. The number ofrings increased when the beam spot passed across the brushes (Fig. 3 (B) (a)-(d)). The patterns typically measure dozens of micrometers, which is morethan 10-fold larger than the size of the beam spot. When the laser irradia-tion is shut off, the patterns shrink toward the center. The extinction time ofthe pattern is on the order of a second, which is much longer than that of asingle-ring pattern. In Fig. 4 is shown the example of a quadruple-ring, whichwas generated with a similar procedure.In a generating process of the multiple-ring pattern, a new ring is formedoutside of the existing multiple-ring pattern. When the new ring is created, theinner rings shrink in size. The radii of dark rings have a broad size distribution.The extinction time of a multiple-ring pattern due to shutting-off of the laseris extended with an increase in the number of rings.4 ig. 2. (color online). Generation of a single-ring wall by laser scanning. (A)Schematic representation of the trajectory of laser scanning around a disclination.(B) Snapshots at the points labeled in (A). (a) The laser beam illuminates theregion near the brush, where the director of the LC is parallel to the laser polar-ization. (b) The laser beam repels the brush, where the director is perpendicularto the laser polarization. (c) The beam spot bulldozes out part of the brush. (d)The plucked brush is closed spontaneously and a ring pattern emerges. (e) The ringis a complete circle while the beam spot is at rest. (f) The laser spot covered bya circular wall repels the brush, although the director on the brush is parallel tothe laser polarization. When the laser beam is shut off, the ring pattern disappearsimmediately. The white arrow in (B)(a) represents the position of the beam spot inthe observation area.The position is common in (a)-(f). Other symbols are identicalto those in Fig. 1 Let us discuss the mechanism of the change in the conformation of the brushin Figs. 1 and 2. Since the nematic had a planar configuration, we considerthe system to be two-dimensional. The interaction between the local directorand the laser beam can be interpreted in terms of the change in the dielectricfree energy ∆ F E , which can be written as [8]∆ F E = Z d r ( − ∆ ǫ π | n ( r ) · E ( r ) | ) (1)5 ig. 3. (color online). Formation of triple circular walls induced by laser scanningalong the trajectory illustrated in (A) around a +1/2 wedge disclination. The cor-responding snapshots at each labeled point are given in (B). (a) Single, (b) doubleand (c) triple rings appear around the beam spot. (d) Time-averaged texture of thetriple circular walls over 6 s. (d’) Averaged radial intensity profile of (d) with errorbars. When the laser irradiation is shut off, the rings disappear within a few s. Thesymbols are the same as in the previous figures.Fig. 4. (color online). Quadruple walls generated from a plural number of disclina-tions through a laser scanning. where ∆ ǫ = ǫ k − ǫ ⊥ is the anisotropy in the dielectric constants betweenparallel ǫ k and perpendicular ǫ ⊥ to the director. The symbols n ( r ) and E ( r )represent the director and oscillating electric field, respectively, of the incidentlaser beam at position r . Since the nematic phase of 5CB has a positive value in∆ ǫ ( ; ǫ , where ǫ is the dielectric constant of vacuum [15] ), the directorin the illuminated region prefers to be oriented along the direction of laserpolarization.In our experiments, the optical torque for the director is strong enough tocompletely orient the illuminated director along the direction of laser polar-ization, because the beam spot appeared as black circles for both vertically6nd horizontally polarized laser beams. As a consequence, the illuminateddirector behaves as a boundary condition for the director field. When the illu-minated director and polarization of the incident laser beam are parallel, thetexture remains constant, because the illuminated director is already suitedfor the laser-induced boundary condition. When the director and laser polar-ization are perpendicular, the illuminated director is forced to rotate along thedirection of polarization of the incident laser. As a result, the director fieldand texture change so as to satisfy the laser-induced boundary condition. Wenoted that the distances between the repelled brush and the laser spot arenot constant in the experiments. This suggests that the interaction betweenthe repelled brush and the laser spot is affected by the laser polarization anddirector distortion due to other disclination cores, distributed in the outsidearea of the photographs.Figure 3 (d’) shows the intensity profile of Fig. 3 (d). The radii r i , which havemaximal values in the intensity profile, are approximately r = 0.5 µ m, r =1.8 µ m and r = 6.0 µ m, where the subscript indicates i = 1, 2, 3. In the sameway, the radii r ′ i , which take minimal values, are approximately r ′ = 1.0 µ m, r ′ = 3.4 µ m and r ′ = 11.0 µ m. Thus, the ratios r i /r ′ i are found to be ∼ n on a multiple-ring pattern depends only on the distance r from the center of the beam spot. Therefore, the director field on a multiple-ring pattern is expressed as n = ( n x , n y , n z ) = (cos ψ ( r ) , sin ψ ( r ) , ψ is the azimuthal angle of the director. With one constant approximation ofthe elastic constants [2], the elastic free energy F ela can be written as F ela = Z K ( ∂ α n β ∂ α n β )d r . (2)where K is the elastic constant of nematic medium. We consider the boundaryconditions of a multiple-ring pattern as follows. Since the director on the beamspot is adjusted to the direction of laser polarization in the experiments, weadopt ψ ( r c ) = ψ c as an inner boundary condition, where r c corresponds to theradius of the beam spot (2 r c ≃ wavelength λ , ∼ µ m) and ψ c is the azimuthangle of the direction of laser polarization. The parameter r b is introduced asa cut-off length at which the director recovers the orientation angle ψ b in thebulk, where r b is several tens of µ m. If we minimize the elastic free energy, ψ ( r ) is given as ψ ( r ) = ( ψ b − ψ c ) log( r/r c )log( r b /r c ) + ψ c (3)7 ig. 5. (color online). Existence of a chiral pair in MCW. The intensity of bothMCWs are based on Eq. (3). The director fields (blue lines) are calculated from Eq.(3). (a) Clockwise MCW ( ψ b =-1.75 π ). (b) Counterclockwise MCW ( ψ b =1.75 π ). Theparameters r b /r c =32.0, ψ c =0 are the same in the two cases. In the experiments,chirality is determined by the trajectory of scanning. Eq. (3) is independent of the elastic constant K . Eq. (3) indicates constantratios between r i and r ′ i in the intensity profile. The difference ψ ( r i ) − ψ ( r ′ i )may be π/ − π/
4. Thus, we havelog( r i /r ′ i ) = log( r b /r c )( ψ ( r i ) − ψ ( r ′ i )) / ( ψ b − ψ c ) (4)where the right-hand term is a constant. In the results shown in Figs.2 and3, the properties of a ring pattern, such as the size and extinction time, maydepend on r b and ψ b originated in other disclinations. To control the size ofthe pattern, it is essential to control the distortion in the director field farfrom the laser spot.Eq. (3) gives the director field on the pattern. The director on the patternrotates along the radial direction. In the texture of a multiple-ring pattern,the director on a dark ring is perpendicular to that of the adjacent rings. Thus,a multiple-ring pattern is found as multiple circular walls (MCW) [2].Figure 5 shows the existence of a chiral pair in MCWs calculated from Eq.(3). There are clockwise (Fig. 5 (a)) and counterclockwise (Fig. 5 (b)) MCWs,where the intensity profiles of Fig. 5 (a) and (b) are identical. In addition,the elastic energies of MCW in Fig. 5 (a) and (b) are also degenerated. Inthe experiments, we observed the chirality of MCWs by using the analyzerrotation technique [16]. This chirality in MCWs is controlled by choosing theproper trajectory of laser scanning.There have been several reports of target patterns with many rings in a thinfilm of SmC LC [16,17,18,19,20]. If we compare our results to those reports,the C-director of the SmC phase plays the role of the director of the nematic.Especially, an expression similar to Eq. (3) was previously obtained for theazimuth angle of C-director [17]. 8 Conclusion
We have reported a novel method for generating MCWs, which are a stabledirector field in nematic LC, through the use of proper laser scanning. We haveshown that the chirality of MCWs can be controlled by choosing a suitabletrajectory of laser scanning.
Acknowledgements
This work was supported by Technology of Japan and by a Sasakawa ScientificResearch Grant (No. 19-643) from The Japan Science Society, Grant-in-aidfor young researchers from Kyoto University Venture Business Laboratory(KU-VBL) and a Grant-in-Aid for Scientific Research on Priority Areas (No.17076007) from the Ministry of Education, Culture, Sports and Science.
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