Get 20M+ Full-Text Papers For Less Than $1.50/day. Subscribe now for You or Your Team.

Learn More →

Three-dimensional positioning and control of colloidal objects utilizing engineered liquid crystalline defect networks

Three-dimensional positioning and control of colloidal objects utilizing engineered liquid... ARTICLE Received 23 Dec 2014 | Accepted 14 Apr 2015 | Published 21 May 2015 DOI: 10.1038/ncomms8180 OPEN Three-dimensional positioning and control of colloidal objects utilizing engineered liquid crystalline defect networks 1 1 2,w 1 H. Yoshida , K. Asakura , J. Fukuda & M. Ozaki Topological defects in liquid crystals not only affect the optical and rheological properties of the host, but can also act as scaffolds in which to trap nano or micro-sized colloidal objects. The creation of complex defect shapes, however, often involves confining the liquid crystals in curved geometries or adds complex-shaped colloidal objects, which are unsuitable for device applications. Using topologically patterned substrates, here we demonstrate the controlled generation of three-dimensional defect lines with non-trivial shapes and even chirality, in a flat slab of nematic liquid crystal. By using the defect lines as templates and the electric response of the liquid crystals, colloidal superstructures are constructed, which can be reversibly reconfigured at a voltage as low as 1.3 V. Three-dimensional engineering of the defect shapes in liquid crystals is potentially useful in the fabrication of self-healing com- posites and in stabilizing artificial frustrated phases. 1 2 Division of Electrical, Electronic and Information Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan. Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba 305-8568, Japan. Present address: Research Institute for Sustainable Chemistry, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba 305-8565, Japan. Correspondence and requests for materials should be addressed to H.Y. (email: yoshida@eei.eng.osaka-u.ac.jp). NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications 1 & 2015 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 iquid crystals find applications in diverse scientific dis- shapes. Circular, spiral-like and chiral disclination networks are ciplines, ranging from optics, electronics, mechanics, biology generated in an achiral liquid crystal, pentylcyanobiphenyl (5CB), 1–5 Land cosmology . Their usefulness derives from their and three-dimensional colloidal superstructures are constructed broken rotational symmetry, which gives rise to spontaneous by using the disclination networks as templates. In addition, as alignment that can be controlled through boundary conditions at the disclinations exist in the bulk of the liquid crystal slab, interfaces or by an external field. It is well known that liquid efficient electric-field tuning is demonstrated, requiring only 1.9 V crystal displays operate by controlling the birefringence in a slab to shrink the length by B12%. The concept of defect engineering of nematic liquid crystal, which is the simplest, non-trivial we propose introduces the possibility of fabricating liquid crystal ordered phase of a liquid crystal. In a nematic liquid crystal, rod- composites with controlled structures that may be used in a like molecules are packed such that they have no positional order variety of applications. but have orientational order with the long axes of the molecules pointing along the ‘director’, defined by a unit vector, n, with head–tail symmetry (that is, n and –n are equivalent). Results The vectorial nature of the director (n¼ n) enables nematic Disclination generation by topological surface anchoring. liquid crystals to accommodate various kinds of topological Projection exposure photoalignment is employed to fabricate the defects, or singularities in the director field, n(r), also known as topologically patterned substrates. A linearly polarized light pas- disclinations . The fact that liquid crystals typically show textures sing through a bow-tie-shaped slit is imaged onto a glass substrate with characteristic length scales in the micrometre range have coated with a photoaligning layer by a combination of a tube lens rendered them particularly attractive for the testing of various and an objective lens. The sample stage and polarizer are rotatable topological theorems. Nematic liquid crystals confined in spheres and are controlled electronically so that the ratio of their rotation spontaneously form bulk and surface defects obeying predictions speeds, o /o , is equal to an integer ; the strength of the polarizer stage from the Gauss–Bonnet and Poincare´–Hopf theorems of defect, s, is then given by (1 o /o ). The combination polarizer stage 7,8 topology . In recent times, the same theorems were confirmed of s and the initial polarization direction, c, where c¼ 0 is set in an inverted system, in which colloidal particles having different parallel to the slit opening, defines the orientation pattern for a topological genera were dispersed in liquid crystals . Moreover, given slit shape. For the straight bow-tie-shaped slit used in our the disclinations were found to self-organize into knotted or first experiment, the easy axis at a given position is given by linked structures, in response to the knot in the colloidal particle n¼ (cosj, sinj, 0), where j¼ s tan (y/x)þ c, with the x–y 10,11 itself, or chirality of the surrounding liquid crystal host . plane taken to be parallel to the substrate with the origin at the Although disclinations had historically been subjects of study defect core (Supplementary Fig. 1). A cell is constructed using two of purely scientific interest, some recent studies have shown substrates containing the same pattern and the 5CB is inserted in interest in disclinations as tools to be exploited technologically. the cell via capillary forces. The resulting textures are observed by For example, optical vortices, which are light beams carrying a means of polarized optical microscopy (POM) and two-photon topological charge, are generated via light–matter interactions excitation microscopy (TPEM) . 12,13 in a liquid crystal slab with topological defects ; colloidal Figure 1 shows POM images of the samples patterned with particles doped in liquid crystals generate a network of different defect strengths. When the patterns on the two disclinations that confer the composite the properties of a substrates are aligned (Fig. 1a–d), black stripes appear between 14,15 self-healing gel ; and disclinations have been used as crossed polarizers where the director is parallel to one of the scaffolds in which to trap conductive or plasmonic particles to polarizers. The number of the dark stripes is equal to 4|s| . As the potentially realize three-dimensional micro-wires or tunable patterns on the two substrates are laterally separated, disclination 16–20 metamaterials . The potential of liquid-crystal-based lines that appear as thin dark lines are seen connecting the two composites originates from the fact that they can self-organize defect centres, with their number being equal to 2|s| (Fig. 1e–h). A into structures that are not easily attainable via conventional movie recorded during this process shows that the disclinations top–down fabrication technology . One of the challenges for appear as soon as the patterns are separated, and increases their widespread use, however, is to develop a means of in size while retaining their shape as the separation increases controlling the disclination numbers and shapes. Fabrication of (Supplementary Movie 1). The different colours observed in Fig. 1 complex-shaped structures are not only difficult and corresponds to the liquid crystal being observed at different cumbersome, but the disclinations generated by such structures temperatures and thus possessing different birefringence. Because are bound to their surfaces, rendering positional control and of the strong anchoring imposed, the patterns are stable even at 9–11,22 tuning difficult . On the other hand, although patterned- temperatures close to the clearing point. rubbing-based methods can generate disclinations running The number of disclinations emanating from an imprinted 19,20,23,24 through the bulk in a flat liquid crystal slab , studies defect is governed by s through the conservation law of reported to date have only succeeded in generating defect lines topological charge. When one considers a plane parallel to and with simple (linear or circular) shapes and the possibility of in the vicinity of the cell substrate, one can safely define the tuning the disclination shapes in three dimensions has not been strength of a disclination line penetrating it, because the substrate discussed. imposes planar alignment and, therefore, out-of-plane director In this work, we demonstrate controlled generation of a three- distortions in the vicinity of the substrates are extremely dimensional disclination network by confining a liquid crystal energetically unfavourable. The strength of a disclination line is slab between two substrates that possess topological surface þ 1/2 or  1/2, as a disclination line of higher strength splits into anchoring conditions, that is, the substrates contain a singular lines of strength þ 1/2 or  1/2, reducing the Frank elastic point or defect around which the orientational easy axis rotates by energy associated with the director distortions . In addition, only an integral multiple of p. Interestingly, the disclination line disclination lines of the same sign remain, as a pair of disclination numbers are controlled by the topological charge or strength of lines of strength þ 1/2 and  1/2 mutually annihilate to reduce the defect (the number of 2p rotations), whereas their shapes are the elastic energy . Therefore, the number of disclination lines controlled by the far-field director distribution surrounding the emanating from an imprinted defect of strength s must be 2|s|, to defect. This role sharing between defect generation and shape conserve the topological charge. Because of technical difficulties morphing is exploited to engineer disclinations into non-trivial in fabricating perfect defects of high strength , one often 2 NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 ARTICLE –45 –90 Figure 1 | Disclination generation from topological patterns created with a linear slit. POM images of liquid crystal cells with orientational patterns (s, c) ¼ (1, 0) (a), (s, c) ¼ (2, 0) (b), (s, c)¼ (3, 0) (c) and (s, c) ¼ (4, 0) (d). The lateral separation of the two substrates is 0. Arrows indicate the direction of polarizers. Scale bars, 100mm. (e–h) POM images of the same sample as in a–d after separating the patterns on the two substrates by 200mm. Spatial distribution of the twist angle for substrates with orientational patterns (s, c) ¼ (1, 0) (i), (s, c) ¼ (2, 0) (j), (s, c) ¼ (3, 0) (k) and (s, c) ¼ (4, 0) (l), calculated by placing the defect centres of the top and bottom substrates at (0.41X, 0.5X) and (0.59X, 0.5X), respectively, where X is the width of the figure. encounters imperfect defects in which the defect core is split into head and tail equivalence of the director allows this shift of defects of strength 1/2 (ref. 27). However, the overall topological C (x, y) C (x, y)by p. As 5CB is achiral, the elastic energy of a t b charge, and hence disclination numbers, are also conserved in this twist distortion with C (x, y) C (x, y) ¼ p/2 is equal to that for t b case, as an imperfect defect of strength s splits into 2|s| defects of C (x, y) C (x, y) ¼ –p/2). A discontinuous shift of the twist- t b strength 1/2. handedness must be accompanied by a disclination line, around It is also interesting to note that this law applies when the which the director rotates by p. Calculation of C (x, y) C (x, y) t b substrates composing a cell are patterned with differing values of for different imprinted defect strengths successfully reproduces s. Supplementary Fig. 2 shows a sample fabricated by sandwiching the disclination line shapes and positions (Fig. 1i–l). two substrates patterned with s¼ 1 and  2 defects. As The role sharing of defect generation and shape control by the predicted, 2|s| disclinations emanate from each defect; however, topological charge and far-field orientational pattern allow for as there is a mismatch in the defect strength, the number of disclination numbers and shapes to be engineered. We change the disclinations connected between the two defect centres is limited slit shape from a straight bow tie to a logarithmic spiral to the smaller value of |s|. The unconnected disclinations extend (Supplementary Fig. 3). The topological charge is still defined by outwards past the region covered by the orientational pattern, the relative speeds of the two rotating stages, but the far-field resulting in a network that is less symmetric. director now follows the pattern defined by the slit, that is, 1 2 2 1/2 The shapes of the disclination lines are determined from the j ¼ s {tan (y/x) ln ((x þ y ) )} þ c (the sign of the second far-field orientational pattern surrounding the defect core. Let term in the logarithm varies depending on the direction from C (x, y) and C (x, y) denote the azimuthal angles of the director which the sample is observed; Fig. 2a–c). Figure 2d–f shows POM t b at the top and bottom surfaces, respectively, at a given lateral images of the disclination lines created from spiral patterns with position, (x, y). When C (x, y)aC (x, y), the director is twisted s ¼ 1, 2 and 3 (c¼ 0). Similar to Fig. 1, the number of t b along the cell normal and relaxes the Frank elastic energy .If disclinations varies according to the topological charge or C (x, y) C (x, y) exceeds p/2, the handedness of the twist strength of the imprinted defect pattern. However, the resultant t b reverses, so that C (x, y) C (x, y) becomes –p/2 (note that the shape is different from the cases in which a linear slit is used and t b NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications 3 & 2015 Macmillan Publishers Limited. All rights reserved. Twist angle (°) ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 –45 –90 Figure 2 | Disclination generation from topological patterns created with a spiral slit. POM images of liquid crystal cells with disclination strengths (s, c) ¼ (1, 0) (a), (s, c) ¼ (2, 0) (b) and (s, c) ¼ (3, 0) (c), when the lateral separation of the two substrates is 0. Scale bars, 100mm. (d–f) POM images of the same sample as in a–c after separating the patterns on the two substrates by 200mm. Spatial distribution of the twist angle for substrates with spiral orientational patterns (s, c) ¼ (1, 0) (g), (s, c)¼ (2, 0) (h) and (s, c) ¼ (3, 0) (i), calculated by placing the defect centres of the top and bottom substrates at (0.4X, 0.5X) and (0.6X, 0.5X), respectively, where X is the width of the figure. is clearly affected by the far-field director profile. The obtained a twisted disclination ring to surround the particle. The shapes are again in agreement with those predicted from the disclination-decorated particles are then attracted towards the spatial distribution of the twist angle (Fig. 2g–i). surface-induced disclination via elastic interactions, minimizing the director deformation . Figure 3b shows the POM image of the colloidal superstructure constructed using substrates patterned Templated assembly of colloidal particles. The twist distri- with a spiral defect of strength 1. TPEM confirms that the particles butions mentioned above can predict only two-dimensionally are distributed three-dimensionally within the cell, with a roughly projected disclination shapes, although they are, in reality, regular spacing between two adjacent particles (Fig. 3c, see also three-dimensional, because of the cell asymmetry in the depth Supplementary Movie 2). As chain structures comprising a smaller direction. Simulation of the order parameter tensor based on the number of particles were observed with similar inter-particle Landau–de Gennes free energy confirms that the disclination spacings, we infer that the spacing between the particles is the lines do run three dimensionally within the cell, connecting the potential minimum at which the long-range attractive and short- two defect centres imprinted on each substrate (Fig. 3a, see also range repulsive forces (due to director deformation) are balanced Supplementary Fig. 4 for disclination networks generated using for particles located on a disclination line . Fourier (Fig. 3d,e) and substrates with different boundary conditions). This allows three- space-frequency (Supplementary Fig. 5) analyses of the particle dimensional composites to be constructed by using the network chain yield 4.3mm as the dominant inter-particle distance. This of disclination lines as a template. We decorate the disclination corresponds to an inter-particle distance to particle radius ratio of lines with silica microspheres of 3-mm in diameter and observe B2.9, which is slightly larger than 2.46, the value obtained for their distribution by means of POM and TPEM (a dichroic dye is particle chains formed in a uniformly aligned nematic liquid also doped in the liquid crystal to detect the particle positions crystal . The structure at equilibrium is stable and is not from the fluorescence contrast). The silica particles are coated destroyed unless the host nematic liquid crystal reaches the with DMOAP (dimethyloctadecyl[3-(trimethoxysilyl)propyl] isotropic phase, because of the large trapping potential (estimated ammonium chloride) to impose vertical alignment at the particle to be of the order of B500 k T for the 3-mm particles dispersed in surface , and so the director distortion around the particle causes 5CB; ref. 19) imposed on the particles. 4 NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved. Twist angle (°) NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 ARTICLE The shape of the disclination network can be further tuned by lengths. The two assemblies cannot be superposed regardless of adjusting the initial angles (c) on the top and bottom substrates. how they are rotated or translated, implying they are chiral. This Offsetting the initial angles of the two substrates induces wide structural controllability is another consequence of the role symmetry breaking, which results in the generation of asymmetric sharing between the defect generation and shape morphing. disclination lines connecting the defect centres. Figure 4 shows the disclination patterns fabricated by sandwiching spirally patterned substrates with (s, c)¼ (1, p/6) and (1, 0), and (s, c)¼ (1,  p/6) Electric-field tuning of disclination shapes. Finally, active and (1, 0), on the front and rear substrates, respectively. One of control of the disclination lines is demonstrated by applying an the disclination lines appears shorter than the other and the electric field. The electric field rotates the 5CB director along TPEM profile along the disclinations shows that the vertical the field and, thus, rearranges the disclination lines into an positions of the particles are inverted with respect to the path energetically more favourable state. As the particles are trapped Distance to particle radius ratio 2 468 10 Distance (µm) Fluorescence intensity Max. Min. Figure 3 | Templated three-dimensional assembly of colloidal particles. (a) Three-dimensional profile of the disclination network formed between spirally patterned substrates with (s, c) ¼ (1, 0), calculated from a Landau–de Gennes theory. The cell gap has been extended twofold for clarity. (b) POM image of the disclination network decorated with colloidal particles of 3mm in diameter. The white dashed line indicates the direction along which the cross-sectional profile was measured. Scale bar, 20mm. (c) Cross-sectional TPEM profile along the disclination shown in b. The dashed lines mark the substrate boundaries. (d,e) FFT magnitude of the TPEM intensity along the left and right particle chains shown in c. Fluorescence intensity Min. Max. Figure 4 | Chiral assembly of colloidal particles. (a,b) Colloidal particles trapped in the disclination lines generated from spiral defects of (s, c)¼ (1, p/6) and (1, 0) (a), and (s, c)¼ (1,  p/6) and (1, 0) (b), on the front and rear substrates, respectively. The white dashed lines indicate the direction along which the cross-sectional profile was measured and the solid white arrows indicate the defect centre that exists on the front substrate. Scale bars, 20mm. (c,d) TPEM profile along the disclination line, corresponding to a,b. The top and bottom of each figure corresponds to the front and rear substrates, respectively. NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications 5 & 2015 Macmillan Publishers Limited. All rights reserved. Magnitude (x10 ) ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 by the disclination lines, their positions are also reconfigured. front is attached. Based on TPEM analysis, the wall front is Figure 5a–d are POM images of the defect under the influence of located where the particles (and hence the disclination lines) are a square-wave electric field (1 kHz) applied in the cell-normal repelled from the bulk and attracted to either the top or the direction. As the voltage is increased, spiralling wall disclinations bottom substrates (Fig. 5e–h). Therefore, an electric field not only (with the appearance of a thick thread) form in the surroundings changes the particle positions two dimensionally, but also induces and connect to the disclination lines, approximately halfway three-dimensional reconfiguration. Figure 5i–k shows the tuning between the imprinted defect centres. As the elastic anisotropy of range of the disclination network evaluated by measuring the 5CB (ref. 30) causes regions with larger twists to have a larger two-dimensionally projected length of the disclination line and Frederiks transition threshold , a Frederiks transition front is the vertical position of each particle at various applied voltages, initiated in the regions with the smallest twist and creates a twist where the cell gap is normalized to 1. Below the Frederiks wall at their boundaries (Supplementary Fig. 6). As seen in transition threshold at 1.3 V, the two-dimensionally projected Fig. 5b–d, the walls change shape depending on the applied length of the disclination line remains almost unchanged (with voltage and kinks appear in the disclination lines where the wall variations smaller than 0.6%) and the particles within a single 0.0 V 1.5 V 1.7 V 1.9 V Particle #1 Particle #12 Particle #13 Particle #24 Fluorescence intensity Min. Max. 1.0 1.0 Particle #1 0.8 0.8 0.6 0.6 Particle #24 0.4 0.4 Particle #12 0.2 0.2 240 0.0 0.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 Voltage (V) Voltage (V) Voltage (V) Figure 5 | Field-induced reconfiguration of disclination shapes and particle positions. (a–d) POM images of the colloid-decorated disclination network constructed using two substrates with spiral defects of (s, c) ¼ (1, 0) at various applied voltages. White dashed lines indicate the direction along which the cross-sectional profile was measured. Scale bars, 20mm. (e–h) TPEM profiles along the disclination lines in a–d.(i) Voltage dependence of two- dimensionally projected disclination length measured from the POM images. Relative vertical positions of the particles in the lower (j) and upper (k) chains in the POM images, where the cell gap is normalized to 1. Particles are numbered from 1 to 24 in the order or appearance along the profile path (see e). 6 NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved. Projected disclination length (µm) Relative vertical position Relative vertical position NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 ARTICLE chain are displaced either to the top or bottom substrates. Above avenue of investigation is the induction of artificial frustrated the threshold, the disclination network steeply shrinks, reducing phases. Experiments and theory have shown that liquid its length by B12 % at 1.9 V (Fig. 5i). The vertical displacement crystals can sustain periodic or particle-like self-organized 41,42 behaviour also changes at the threshold and strongly depends on structures in the presence of defects . The creation of the position of the particle with respect to the wall front. The wall disclination arrays with controlled numbers, lattice constants front position gradually shifts along the particle chain, and causes and symmetry may lead to the discovery of liquid crystal phases a reversal in the direction of vertical displacement; only the previously unknown. particles that have experienced a reversal in displacement direction show a steep change in position (Fig. 5j,k). For the Methods two colloidal chains studied here, the third particle within the Patterned photoalignment. Light from a high-pressure mercury lamp was filtered using a bandpass filter with centre wavelength of 436 nm and irradiated on a slit chain (particles 3 and 22) showed the largest tuning range, with mask (Supplementary Fig. 1), which was imaged onto the sample using a pair of the maximum shift reaching 41.1% of the cell thickness. lenses with f ¼ 100 mm and f¼ 18 mm. A motorized polarizer was placed between On further increasing the voltage, it is found that the walls the two lenses and the sample stage was also motorized; the rotation speeds for the undergo a ‘pincement’ transition, in which a wall separates into two stages were controlled as described in the main text using LabVIEW software. The sample was irradiated at an intensity of 0.3 mW for 60 s before being rotated two disclinations bound to each substrate confining the liquid by 3, the apex angle of the slit mask. crystal and extends outside the boundary of the alignment pattern (Supplementary Movie 3). The attraction of the particles to the top and bottom substrates observed in Fig. 5b–d is therefore Fabrication of the liquid crystal cells. For the samples shown in Figs 1 and 2, the cells were fabricated from two 1-mm-thick glass substrates, onto which a layer of considered to be a pre-transitional effect leading to the pincement an azobenzene-based photoalignment material (DIC, LIA-03) was spin coated. transition. Above the pincement transition, the disclinations show This photoalignment layer provides ‘planar’ liquid crystal alignment with the easy a complex movement, which in some cases causes the particle axis perpendicular to the polarization of the impinging light. The substrates positions to alternate within the disclination network, or be were sandwiched temporarily using bead spacers of size 9mm and patterned by photoalignment. The two substrates were offset after infiltrating the liquid crystal transported to outside the patterned region. However, the 5CB, which shows the nematic liquid crystal between 22 Cand 35 C. The transient path of the disclinations depends on the manner in observed colour is determined by the optical retardation of the sample, which is which the electric field is applied (for example, whether a voltage affected by the actual cell gap and observation temperature. The samples were increase is applied instantaneously or gradually) and, although the observed at different temperatures to illustrate the stability of the alignment as well as to emphasize the difference in the texture as follows: Fig. 1a–d, 34 C, 29 C, disclination lines retain their original shapes when the voltage is 30 C and 32 C, respectively, and Fig. 2a–c, 34 C, 33 C and 30 C, respectively. removed, the particles often do not return to their original For the samples shown in Figs 3–5, a 150-mm-thick cover slip was used as one positions (Supplementary Movie 3). In contrast, below the of the substrates for the purpose of performing TPEM. Substrates coated with a pincement transition, the tuning of both disclination shapes and 100-nm-thick layer of indium tin oxide were used for the sample shown in Fig. 5, to apply a voltage. The samples for Figs 3 and 5 were fabricated by offsetting the particle positions is fully reversible. defect patterns after a single photoalignment process, whereas the sample for Fig. 4 was fabricated by patterning the two substrates independently and sandwiching them afterwards to a lateral separation distance of 100mm. The liquid crystal was Discussion doped with silica particles (JGC Catalysts and Chemicals, Shinshikyu SW 3mm) and a dichroic dye (Exciton, DCM), both at a concentration of 1 wt%. The particles The giant electrical tunability of particle positions is a feature that were coated with DMOAP following the procedure described in ref. 28. has not been observed in other methods that allow control of particle positions in nematic liquid crystals. Patterned photo- Two-photon excitation microscopy. TPEM is a fluorescence imaging technique alignment (with non-topological patterns) and indented surfaces which uses two-photon absorption to achieve three-dimensional resolution . The have been shown to induce localized elastic potentials at which a contrast in fluorescence intensity between the dye-doped liquid crystal and the 32,33 particle can be trapped , introducing the possibility of non-fluorescent silica particles allows detection of the particle distribution within controlling the crystallographic orientation of three-dimensional the specimen. A commercial confocal laser scanning microscope (Zeiss, LSM-510) colloidal crystals . However, localized elastic potentials induced was used in conjunction with a titanium-sapphire laser (Spectra Physics, Maitai) with wavelength of 800 nm, pulse width of 150 fs and repetition rate of 82 MHz. An by surface conditions are difficult to tune using an electric field, as oil-immersion objective lens with magnification of  63 and numerical aperture of the surface condition itself, which defines the elastic potential, 1.4 was used to acquire the images. remains unchanged. The use of bulk disclinations is a viable alternative for engineering the trapping potential landscape in Simulation of the defect profile. The defect profiles were calculated by liquid crystals, as they have large trapping potentials and can minimizing the free energy of the liquid crystal cell as a functional of the change shape easily in response to director deformations. orientational order parameter of second-rank tensor (Q ). The free energy after ij Furthermore, the disclinations generated here are robust in that appropriate rescaling is expressed as F ¼ dr f þ f , where f ¼ local grad local pffiffiffi pffiffiffi 2 3 2 2 (1/2)ATrQ –(1/3)BTrQ þ (1/4)C(TrQ ) , with A ¼ 3 6 8 =3ðÞ o0 , B ¼ 3 6 their existence is topologically protected and thus self-heal even and C ¼ 4, which is the local part of the free energy density (Tr is the trace of a from large distortions. tensor), and f ¼ (1/2)L (r Q) (r Q) þ (1/2)L (r Q) (r Q) , which is grad 1 ij ij 2 j j Our approach to engineering disclinations in nematic liquid the elastic free-energy density due to the spatial inhomogeneity of Q . Here, ij crystals has a wide variety of applications, as the embedded summations over repeated indices are implied, (r Q) e r Q and ij ist s tj (r Q) r  Q , where e is the Levi–Civita antisymmetric symbol. It is note- particles are not limited to silica microspheres. For example, it j i ij ist worthy that setting L ¼ L corresponds to the so-called one-constant approxi- 1 2 would be possible to construct tunable chiral emitters or mation (K ¼ K ¼ K , where K , K and K are the splay, twist and bend 11 22 33 11 22 33 metamaterials by embedding fluorescent or metallic nanoparticles 6 elastic constants, respectively ). Here we set L ¼ 0.2 and L ¼ 0.8, corresponding to 1 2 16,35,36 in the disclinations . Such composites will not only possess K /K ¼ K /K ¼ 0.4. It is also worth noting that Q ¼ Q (n n –(1/3)d ) with 22 11 22 33 ij 0 i j ij Q ¼ 1 minimizes F. See refs 42,29 for the free energy and its rescaling. The length the functions of the introduced particles but also show self- 0 pffiffiffi has been rescaled so that the rescaled unit length corresponds to 2 2x ’ 40 healing properties, as the disclination lines are topologically nanometres, where x ’ 15 nanometres is the nematic coherence length . protected. Furthermore, the self-assembly behaviour of such The two confining surfaces (parallel to the xy plane) impose Dirichlet boundary colloidal composites can be tuned by changing the shape and conditions fixing Q there, corresponding to the strong anchoring conditions in the ij 9,37 experiments. We set Q ¼ Q (n n –(1/3)d ), where Q ¼ 1 and n ¼ (cos Y(x, y), topology of the introduced particles . On the other hand, liquid ij 0 i j ij 0 sinYðx; yÞ; 0). The angle Y(x, y) is chosen so that it reproduces the experimental crystalline materials may exhibit previously unseen mechanical, surface orientation profiles described in the main text. The other boundaries magnetic, or electronic properties as a result of containing (parallel to the xz or yz plane) impose no surface energy. ‘engineered’ topological defects, as topology is known to affect The free-energy functional is minimized on a cubic lattice of dimension 38–40 such properties of a material . Finally, another important 640  640 20, with the lattice spacing equal to 1 in the rescaled unit. Offset of the NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications 7 & 2015 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 two defects is set to 100, 5 times as large as the cell thickness. We let the initial 26. Nersisyan, S. R., Tabiryan, N. V., Mawet, D. & Serabyn, E. Improving vector profile Q ¼ 0 (except at the confining surfaces) relax via a simple rotational ij vortex waveplates for high-contrast coronagraphy. Opt. Express 21, 8205–8213 relaxation equation, @Q (r)/@t¼ dF/dQ (r)þ ld , where the Lagrange ij ij ij (2013). multiplier l ensures TrQ¼ 0. In the figures, defects are defined by the regions with 27. Mawet, D. et al. Optical vectorial vortex coronagraphs using liquid crystal weaker orientational order and are identified by the isosurfaces TrQ ¼ 0.6. polymers: theory, manufacturing and laboratory demonstration. Opt. Express Although the thickness of the simulation box, D0.8mm, is much smaller than that 17, 1902–1918 (2009). of the experimental cell, the former can be further rescaled to fit the latter as long as 28. Skarabot, M. et al. Interactions of quadrupolar nematic colloids. Phys. Rev. E the director profile n and the position of the resulting disclinations are concerned. 77, 031705 (2008). It is because in the bulk of the nematic liquid crystal with uniaxial order, the elastic 29. Fukuda, J., Stark, H., Yoneya, M. & Yokoyama, H. Interaction between two energy in terms of the tensor-order parameter Q reduces to the Frank elastic ij spherical particles in a nematic liquid crystal. Phys. Rev. E 69, 041706 (2004). energy in terms of n that does not possess any characteristic lengths. Furthermore, 30. Madhusudana, N. V. & Pratibha, R. Elasticity and orientational order in rigid surface anchoring (fixed Q ) in our simulations does not introduce any ij some cyanobiphenyls: Part IV. Reanalysis of the data. Mol. Cryst. Liq. Cryst. 89, additional lengths either (anchoring extrapolation length is zero). This is the reason 249–257 (1982). why our simulations successfully reproduce the shape of the disclinations observed 31. De Lo´zar, A., Scho¨pf, W., Rehberg, I., Svensˇek, D. & Kramer, L. Transformation experimentally. from walls to disclination lines: statics and dynamics of the pincement transition. Phys. Rev. E 72, 051713 (2005). 32. Silvestre, N. M., Liu, Q., Senyuk, B., Smalyukh, I. I. & Tasinkevych, M. Towards References template-assisted assembly of nematic colloids. Phys. Rev. Lett. 112, 225501 1. Yeh, P. & Gu, C. Optics of Liquid Crystal Displays (Wiley, 2010). (2014). 2. Adam, D. et al. Fast photoconduction in the highly ordered columnar phase of 33. Martinez, A., Mireles, H. C. & Smalyukh, I. I. Large-area optoelastic a discotic liquid crystal. Nature 371, 141–143 (1994). manipulation of colloidal particles in liquid crystals using photoresponsive 3. Yu, Y., Nakano, M. & Ikeda, T. Photomechanics: directed bending of a polymer molecular surface monolayers. Proc. Natl Acad. Sci. 108, 20891–20896 (2011). film by light. Nature 425, 145 (2003). 34. Nych, A. et al. Assembly and control of 3D nematic dipolar colloidal crystals. 4. Nakata, M. et al. End-to-end stacking and liquid crystal condensation of 6 to 20 Nat. Commun. 4, 1489 (2013). base pair DNA duplexes. Science 318, 1276–1279 (2007). 35. Higashiguchi, K., Yasui, K., Ozawa, M., Odoi, K. & Kikuchi, H. Spatial 5. Bowick, M. J., Chandar, L., Schiff, E. A. & Srivastava, A. M. The cosmological distribution control of polymer nanoparticles by liquid crystal disclinations. Kibble mechanism in the laboratory: string formation in liquid crystals. Science Polym. J. 44, 632–638 (2012). 263, 943–945 (1994). 36. Plum, E., Fedotov, V. A. & Zheludev, N. I. Extrinsic electromagnetic chirality in 6. Chandrasekhar, S. Liquid Crystals (Cambridge University Press, 1992). metamaterials. J. Opt. Pure Appl. Opt. 11, 074009 (2009). 7. Volovik, G. E. & Lavrentovich, O. D. [Topological dynamics of defects: 37. Lapointe, C. P., Mason, T. G. & Smalyukh, I. I. Shape-controlled colloidal boojums in nematic drops]. Zh Eksp Teor Fiz 85, 1997–2010 (1983). interactions in nematic liquid crystals. Science 326, 1083–1086 (2009). 8. Kle´man, M. & Lavrentovich, O. D. Soft Matter Physics: An Introduction 38. Urayama, K. Network topology–mechanical properties relationships of model (Springer, 2003). elastomers. Polym. J. 40, 669–678 (2008). 9. Senyuk, B. et al. Topological colloids. Nature 493, 200–205 (2013). 39. Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic ˇ ˇ ˇ ˇ 10. Tkalec, U., Ravnik, M., Copar, S., Zumer, S. & Musevic, I. Reconfigurable knots skyrmions. Nat. Nanotechnol. 8, 899–911 (2013). and links in chiral nematic colloids. Science 333, 62–65 (2011). 40. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 11. Martinez, A. et al. Mutually tangled colloidal knots and induced defect loops in 82, 3045–3067 (2010). nematic fields. Nat. Mater. 13, 258–263 (2014). 41. Smalyukh, I. I., Lansac, Y., Clark, N. A. & Trivedi, R. P. Three-dimensional 12. Marrucci, L., Manzo, C. & Paparo, D. Optical spin-to-orbital angular structure and multistable optical switching of triple-twisted particle-like momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. excitations in anisotropic fluids. Nat. Mater. 9, 139–145 (2010). 96, 163905 (2006). 42. Fukuda, J. & Zumer, S. Quasi-two-dimensional Skyrmion lattices in a chiral 13. Slussarenko, S. et al. Tunable liquid crystal q-plates with arbitrary topological nematic liquid crystal. Nat. Commun. 2, 246 (2011). charge. Opt. Express 19, 4085–4090 (2011). 14. Zapotocky, M., Ramos, L., Poulin, P., Lubensky, T. C. & Weitz, D. A. Acknowledgements Particle-stabilized defect gel in cholesteric liquid crystals. Science 283, 209–212 This study was partly supported by the PRESTO programme from JST and the Photonics (1999). Advanced Research Center (PARC) at Osaka University. J.F. is supported by JSPS Grant- 15. Yamamoto, T. & Yoshida, M. Viscoelastic and photoresponsive properties of in-Aid (KAKENHI) for Scientific Research (C) (grant number 25400437). We thank DIC microparticle/liquid-crystal composite gels: tunable mechanical strength along Corporation for kindly providing the photoaligning material. with rapid-recovery nature and photochemical surface healing using an azobenzene dopant. Langmuir 28, 8463–8469 (2012). 16. Senyuk, B. et al. Shape-dependent oriented trapping and scaffolding of Author contributions plasmonic nanoparticles by topological defects for self-assembly of colloidal K.A. and H.Y. performed the experiments. J.F. performed theoretical calculations. All dimers in liquid crystals. Nano Lett. 12, 955–963 (2012). authors discussed the results and worked on the manuscript. H.Y. conceived and 17. Ohzono, T. & Fukuda, J. Zigzag line defects and manipulation of colloids designed the project. in a nematic liquid crystal in microwrinkle grooves. Nat. Commun. 3, 701 (2012). Additional information 18. Pires, D., Fleury, J.-B. & Galerne, Y. Colloid particles in the interaction field of a Supplementary Information accompanies this paper at http://www.nature.com/ disclination line in a nematic phase. Phys. Rev. Lett. 98, 247801 (2007). naturecommunications 19. Agha, H., Fleury, J. & Galerne, Y. Micro-wires self-assembled and 3D- connected with the help of a nematic liquid crystal. Eur. Phys. J. E Soft Matter Competing financial interests: The authors declare no competing financial interests. Biol. Phys. 35, 82 (2012). 20. Fleury, J.-B., Pires, D. & Galerne, Y. Self-connected 3D architecture of Reprints and permission information is available online at http://npg.nature.com/ microwires. Phys. Rev. Lett. 103, 267801 (2009). reprintsandpermissions/ 21. Ravnik, M., Alexander, G. P., Yeomans, J. M. & Zumer, S. Mesoscopic How to cite this article: Yoshida, H. et al. Three-dimensional positioning and control of modelling of colloids in chiral nematics. Faraday Discuss. 144, 159–169 (2010). colloidal objects utilizing engineered liquid crystalline defect networks. Nat. Commun. 22. Cavallaro, M. et al. Exploiting imperfections in the bulk to direct assembly of 6:7180 doi: 10.1038/ncomms8180 (2015). surface colloids. Proc. Natl Acad. Sci. 110, 18804–18808 (2013). 23. Zhuang, Z., Suh, S.-W., Kim, Y. J. & Patel, J. S. Defect in the circular-circularly This work is licensed under a Creative Commons Attribution 4.0 rubbed liquid crystal cell with off-center alignment. Appl. Phys. Lett. 76, 3005 International License. The images or other third party material in this (2000). 24. Murray, B. S., Pelcovits, R. A. & Rosenblatt, C. Creating arbitrary arrays of two- article are included in the article’s Creative Commons license, unless indicated otherwise dimensional topological defects. Phys. Rev. E 90, 052501 (2014). in the credit line; if the material is not included under the Creative Commons license, 25. Denk, W., Strickler, J. & Webb, W. Two-photon laser scanning fluorescence users will need to obtain permission from the license holder to reproduce the material. microscopy. Science 248, 73–76 (1990). To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ 8 NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nature Communications Springer Journals

Three-dimensional positioning and control of colloidal objects utilizing engineered liquid crystalline defect networks

Loading next page...
 
/lp/springer-journals/three-dimensional-positioning-and-control-of-colloidal-objects-AHM0c2Jex5

References (86)

Publisher
Springer Journals
Copyright
Copyright © 2015 by The Author(s)
Subject
Science, Humanities and Social Sciences, multidisciplinary; Science, Humanities and Social Sciences, multidisciplinary; Science, multidisciplinary
eISSN
2041-1723
DOI
10.1038/ncomms8180
Publisher site
See Article on Publisher Site

Abstract

ARTICLE Received 23 Dec 2014 | Accepted 14 Apr 2015 | Published 21 May 2015 DOI: 10.1038/ncomms8180 OPEN Three-dimensional positioning and control of colloidal objects utilizing engineered liquid crystalline defect networks 1 1 2,w 1 H. Yoshida , K. Asakura , J. Fukuda & M. Ozaki Topological defects in liquid crystals not only affect the optical and rheological properties of the host, but can also act as scaffolds in which to trap nano or micro-sized colloidal objects. The creation of complex defect shapes, however, often involves confining the liquid crystals in curved geometries or adds complex-shaped colloidal objects, which are unsuitable for device applications. Using topologically patterned substrates, here we demonstrate the controlled generation of three-dimensional defect lines with non-trivial shapes and even chirality, in a flat slab of nematic liquid crystal. By using the defect lines as templates and the electric response of the liquid crystals, colloidal superstructures are constructed, which can be reversibly reconfigured at a voltage as low as 1.3 V. Three-dimensional engineering of the defect shapes in liquid crystals is potentially useful in the fabrication of self-healing com- posites and in stabilizing artificial frustrated phases. 1 2 Division of Electrical, Electronic and Information Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan. Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba 305-8568, Japan. Present address: Research Institute for Sustainable Chemistry, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba 305-8565, Japan. Correspondence and requests for materials should be addressed to H.Y. (email: yoshida@eei.eng.osaka-u.ac.jp). NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications 1 & 2015 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 iquid crystals find applications in diverse scientific dis- shapes. Circular, spiral-like and chiral disclination networks are ciplines, ranging from optics, electronics, mechanics, biology generated in an achiral liquid crystal, pentylcyanobiphenyl (5CB), 1–5 Land cosmology . Their usefulness derives from their and three-dimensional colloidal superstructures are constructed broken rotational symmetry, which gives rise to spontaneous by using the disclination networks as templates. In addition, as alignment that can be controlled through boundary conditions at the disclinations exist in the bulk of the liquid crystal slab, interfaces or by an external field. It is well known that liquid efficient electric-field tuning is demonstrated, requiring only 1.9 V crystal displays operate by controlling the birefringence in a slab to shrink the length by B12%. The concept of defect engineering of nematic liquid crystal, which is the simplest, non-trivial we propose introduces the possibility of fabricating liquid crystal ordered phase of a liquid crystal. In a nematic liquid crystal, rod- composites with controlled structures that may be used in a like molecules are packed such that they have no positional order variety of applications. but have orientational order with the long axes of the molecules pointing along the ‘director’, defined by a unit vector, n, with head–tail symmetry (that is, n and –n are equivalent). Results The vectorial nature of the director (n¼ n) enables nematic Disclination generation by topological surface anchoring. liquid crystals to accommodate various kinds of topological Projection exposure photoalignment is employed to fabricate the defects, or singularities in the director field, n(r), also known as topologically patterned substrates. A linearly polarized light pas- disclinations . The fact that liquid crystals typically show textures sing through a bow-tie-shaped slit is imaged onto a glass substrate with characteristic length scales in the micrometre range have coated with a photoaligning layer by a combination of a tube lens rendered them particularly attractive for the testing of various and an objective lens. The sample stage and polarizer are rotatable topological theorems. Nematic liquid crystals confined in spheres and are controlled electronically so that the ratio of their rotation spontaneously form bulk and surface defects obeying predictions speeds, o /o , is equal to an integer ; the strength of the polarizer stage from the Gauss–Bonnet and Poincare´–Hopf theorems of defect, s, is then given by (1 o /o ). The combination polarizer stage 7,8 topology . In recent times, the same theorems were confirmed of s and the initial polarization direction, c, where c¼ 0 is set in an inverted system, in which colloidal particles having different parallel to the slit opening, defines the orientation pattern for a topological genera were dispersed in liquid crystals . Moreover, given slit shape. For the straight bow-tie-shaped slit used in our the disclinations were found to self-organize into knotted or first experiment, the easy axis at a given position is given by linked structures, in response to the knot in the colloidal particle n¼ (cosj, sinj, 0), where j¼ s tan (y/x)þ c, with the x–y 10,11 itself, or chirality of the surrounding liquid crystal host . plane taken to be parallel to the substrate with the origin at the Although disclinations had historically been subjects of study defect core (Supplementary Fig. 1). A cell is constructed using two of purely scientific interest, some recent studies have shown substrates containing the same pattern and the 5CB is inserted in interest in disclinations as tools to be exploited technologically. the cell via capillary forces. The resulting textures are observed by For example, optical vortices, which are light beams carrying a means of polarized optical microscopy (POM) and two-photon topological charge, are generated via light–matter interactions excitation microscopy (TPEM) . 12,13 in a liquid crystal slab with topological defects ; colloidal Figure 1 shows POM images of the samples patterned with particles doped in liquid crystals generate a network of different defect strengths. When the patterns on the two disclinations that confer the composite the properties of a substrates are aligned (Fig. 1a–d), black stripes appear between 14,15 self-healing gel ; and disclinations have been used as crossed polarizers where the director is parallel to one of the scaffolds in which to trap conductive or plasmonic particles to polarizers. The number of the dark stripes is equal to 4|s| . As the potentially realize three-dimensional micro-wires or tunable patterns on the two substrates are laterally separated, disclination 16–20 metamaterials . The potential of liquid-crystal-based lines that appear as thin dark lines are seen connecting the two composites originates from the fact that they can self-organize defect centres, with their number being equal to 2|s| (Fig. 1e–h). A into structures that are not easily attainable via conventional movie recorded during this process shows that the disclinations top–down fabrication technology . One of the challenges for appear as soon as the patterns are separated, and increases their widespread use, however, is to develop a means of in size while retaining their shape as the separation increases controlling the disclination numbers and shapes. Fabrication of (Supplementary Movie 1). The different colours observed in Fig. 1 complex-shaped structures are not only difficult and corresponds to the liquid crystal being observed at different cumbersome, but the disclinations generated by such structures temperatures and thus possessing different birefringence. Because are bound to their surfaces, rendering positional control and of the strong anchoring imposed, the patterns are stable even at 9–11,22 tuning difficult . On the other hand, although patterned- temperatures close to the clearing point. rubbing-based methods can generate disclinations running The number of disclinations emanating from an imprinted 19,20,23,24 through the bulk in a flat liquid crystal slab , studies defect is governed by s through the conservation law of reported to date have only succeeded in generating defect lines topological charge. When one considers a plane parallel to and with simple (linear or circular) shapes and the possibility of in the vicinity of the cell substrate, one can safely define the tuning the disclination shapes in three dimensions has not been strength of a disclination line penetrating it, because the substrate discussed. imposes planar alignment and, therefore, out-of-plane director In this work, we demonstrate controlled generation of a three- distortions in the vicinity of the substrates are extremely dimensional disclination network by confining a liquid crystal energetically unfavourable. The strength of a disclination line is slab between two substrates that possess topological surface þ 1/2 or  1/2, as a disclination line of higher strength splits into anchoring conditions, that is, the substrates contain a singular lines of strength þ 1/2 or  1/2, reducing the Frank elastic point or defect around which the orientational easy axis rotates by energy associated with the director distortions . In addition, only an integral multiple of p. Interestingly, the disclination line disclination lines of the same sign remain, as a pair of disclination numbers are controlled by the topological charge or strength of lines of strength þ 1/2 and  1/2 mutually annihilate to reduce the defect (the number of 2p rotations), whereas their shapes are the elastic energy . Therefore, the number of disclination lines controlled by the far-field director distribution surrounding the emanating from an imprinted defect of strength s must be 2|s|, to defect. This role sharing between defect generation and shape conserve the topological charge. Because of technical difficulties morphing is exploited to engineer disclinations into non-trivial in fabricating perfect defects of high strength , one often 2 NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 ARTICLE –45 –90 Figure 1 | Disclination generation from topological patterns created with a linear slit. POM images of liquid crystal cells with orientational patterns (s, c) ¼ (1, 0) (a), (s, c) ¼ (2, 0) (b), (s, c)¼ (3, 0) (c) and (s, c) ¼ (4, 0) (d). The lateral separation of the two substrates is 0. Arrows indicate the direction of polarizers. Scale bars, 100mm. (e–h) POM images of the same sample as in a–d after separating the patterns on the two substrates by 200mm. Spatial distribution of the twist angle for substrates with orientational patterns (s, c) ¼ (1, 0) (i), (s, c) ¼ (2, 0) (j), (s, c) ¼ (3, 0) (k) and (s, c) ¼ (4, 0) (l), calculated by placing the defect centres of the top and bottom substrates at (0.41X, 0.5X) and (0.59X, 0.5X), respectively, where X is the width of the figure. encounters imperfect defects in which the defect core is split into head and tail equivalence of the director allows this shift of defects of strength 1/2 (ref. 27). However, the overall topological C (x, y) C (x, y)by p. As 5CB is achiral, the elastic energy of a t b charge, and hence disclination numbers, are also conserved in this twist distortion with C (x, y) C (x, y) ¼ p/2 is equal to that for t b case, as an imperfect defect of strength s splits into 2|s| defects of C (x, y) C (x, y) ¼ –p/2). A discontinuous shift of the twist- t b strength 1/2. handedness must be accompanied by a disclination line, around It is also interesting to note that this law applies when the which the director rotates by p. Calculation of C (x, y) C (x, y) t b substrates composing a cell are patterned with differing values of for different imprinted defect strengths successfully reproduces s. Supplementary Fig. 2 shows a sample fabricated by sandwiching the disclination line shapes and positions (Fig. 1i–l). two substrates patterned with s¼ 1 and  2 defects. As The role sharing of defect generation and shape control by the predicted, 2|s| disclinations emanate from each defect; however, topological charge and far-field orientational pattern allow for as there is a mismatch in the defect strength, the number of disclination numbers and shapes to be engineered. We change the disclinations connected between the two defect centres is limited slit shape from a straight bow tie to a logarithmic spiral to the smaller value of |s|. The unconnected disclinations extend (Supplementary Fig. 3). The topological charge is still defined by outwards past the region covered by the orientational pattern, the relative speeds of the two rotating stages, but the far-field resulting in a network that is less symmetric. director now follows the pattern defined by the slit, that is, 1 2 2 1/2 The shapes of the disclination lines are determined from the j ¼ s {tan (y/x) ln ((x þ y ) )} þ c (the sign of the second far-field orientational pattern surrounding the defect core. Let term in the logarithm varies depending on the direction from C (x, y) and C (x, y) denote the azimuthal angles of the director which the sample is observed; Fig. 2a–c). Figure 2d–f shows POM t b at the top and bottom surfaces, respectively, at a given lateral images of the disclination lines created from spiral patterns with position, (x, y). When C (x, y)aC (x, y), the director is twisted s ¼ 1, 2 and 3 (c¼ 0). Similar to Fig. 1, the number of t b along the cell normal and relaxes the Frank elastic energy .If disclinations varies according to the topological charge or C (x, y) C (x, y) exceeds p/2, the handedness of the twist strength of the imprinted defect pattern. However, the resultant t b reverses, so that C (x, y) C (x, y) becomes –p/2 (note that the shape is different from the cases in which a linear slit is used and t b NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications 3 & 2015 Macmillan Publishers Limited. All rights reserved. Twist angle (°) ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 –45 –90 Figure 2 | Disclination generation from topological patterns created with a spiral slit. POM images of liquid crystal cells with disclination strengths (s, c) ¼ (1, 0) (a), (s, c) ¼ (2, 0) (b) and (s, c) ¼ (3, 0) (c), when the lateral separation of the two substrates is 0. Scale bars, 100mm. (d–f) POM images of the same sample as in a–c after separating the patterns on the two substrates by 200mm. Spatial distribution of the twist angle for substrates with spiral orientational patterns (s, c) ¼ (1, 0) (g), (s, c)¼ (2, 0) (h) and (s, c) ¼ (3, 0) (i), calculated by placing the defect centres of the top and bottom substrates at (0.4X, 0.5X) and (0.6X, 0.5X), respectively, where X is the width of the figure. is clearly affected by the far-field director profile. The obtained a twisted disclination ring to surround the particle. The shapes are again in agreement with those predicted from the disclination-decorated particles are then attracted towards the spatial distribution of the twist angle (Fig. 2g–i). surface-induced disclination via elastic interactions, minimizing the director deformation . Figure 3b shows the POM image of the colloidal superstructure constructed using substrates patterned Templated assembly of colloidal particles. The twist distri- with a spiral defect of strength 1. TPEM confirms that the particles butions mentioned above can predict only two-dimensionally are distributed three-dimensionally within the cell, with a roughly projected disclination shapes, although they are, in reality, regular spacing between two adjacent particles (Fig. 3c, see also three-dimensional, because of the cell asymmetry in the depth Supplementary Movie 2). As chain structures comprising a smaller direction. Simulation of the order parameter tensor based on the number of particles were observed with similar inter-particle Landau–de Gennes free energy confirms that the disclination spacings, we infer that the spacing between the particles is the lines do run three dimensionally within the cell, connecting the potential minimum at which the long-range attractive and short- two defect centres imprinted on each substrate (Fig. 3a, see also range repulsive forces (due to director deformation) are balanced Supplementary Fig. 4 for disclination networks generated using for particles located on a disclination line . Fourier (Fig. 3d,e) and substrates with different boundary conditions). This allows three- space-frequency (Supplementary Fig. 5) analyses of the particle dimensional composites to be constructed by using the network chain yield 4.3mm as the dominant inter-particle distance. This of disclination lines as a template. We decorate the disclination corresponds to an inter-particle distance to particle radius ratio of lines with silica microspheres of 3-mm in diameter and observe B2.9, which is slightly larger than 2.46, the value obtained for their distribution by means of POM and TPEM (a dichroic dye is particle chains formed in a uniformly aligned nematic liquid also doped in the liquid crystal to detect the particle positions crystal . The structure at equilibrium is stable and is not from the fluorescence contrast). The silica particles are coated destroyed unless the host nematic liquid crystal reaches the with DMOAP (dimethyloctadecyl[3-(trimethoxysilyl)propyl] isotropic phase, because of the large trapping potential (estimated ammonium chloride) to impose vertical alignment at the particle to be of the order of B500 k T for the 3-mm particles dispersed in surface , and so the director distortion around the particle causes 5CB; ref. 19) imposed on the particles. 4 NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved. Twist angle (°) NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 ARTICLE The shape of the disclination network can be further tuned by lengths. The two assemblies cannot be superposed regardless of adjusting the initial angles (c) on the top and bottom substrates. how they are rotated or translated, implying they are chiral. This Offsetting the initial angles of the two substrates induces wide structural controllability is another consequence of the role symmetry breaking, which results in the generation of asymmetric sharing between the defect generation and shape morphing. disclination lines connecting the defect centres. Figure 4 shows the disclination patterns fabricated by sandwiching spirally patterned substrates with (s, c)¼ (1, p/6) and (1, 0), and (s, c)¼ (1,  p/6) Electric-field tuning of disclination shapes. Finally, active and (1, 0), on the front and rear substrates, respectively. One of control of the disclination lines is demonstrated by applying an the disclination lines appears shorter than the other and the electric field. The electric field rotates the 5CB director along TPEM profile along the disclinations shows that the vertical the field and, thus, rearranges the disclination lines into an positions of the particles are inverted with respect to the path energetically more favourable state. As the particles are trapped Distance to particle radius ratio 2 468 10 Distance (µm) Fluorescence intensity Max. Min. Figure 3 | Templated three-dimensional assembly of colloidal particles. (a) Three-dimensional profile of the disclination network formed between spirally patterned substrates with (s, c) ¼ (1, 0), calculated from a Landau–de Gennes theory. The cell gap has been extended twofold for clarity. (b) POM image of the disclination network decorated with colloidal particles of 3mm in diameter. The white dashed line indicates the direction along which the cross-sectional profile was measured. Scale bar, 20mm. (c) Cross-sectional TPEM profile along the disclination shown in b. The dashed lines mark the substrate boundaries. (d,e) FFT magnitude of the TPEM intensity along the left and right particle chains shown in c. Fluorescence intensity Min. Max. Figure 4 | Chiral assembly of colloidal particles. (a,b) Colloidal particles trapped in the disclination lines generated from spiral defects of (s, c)¼ (1, p/6) and (1, 0) (a), and (s, c)¼ (1,  p/6) and (1, 0) (b), on the front and rear substrates, respectively. The white dashed lines indicate the direction along which the cross-sectional profile was measured and the solid white arrows indicate the defect centre that exists on the front substrate. Scale bars, 20mm. (c,d) TPEM profile along the disclination line, corresponding to a,b. The top and bottom of each figure corresponds to the front and rear substrates, respectively. NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications 5 & 2015 Macmillan Publishers Limited. All rights reserved. Magnitude (x10 ) ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 by the disclination lines, their positions are also reconfigured. front is attached. Based on TPEM analysis, the wall front is Figure 5a–d are POM images of the defect under the influence of located where the particles (and hence the disclination lines) are a square-wave electric field (1 kHz) applied in the cell-normal repelled from the bulk and attracted to either the top or the direction. As the voltage is increased, spiralling wall disclinations bottom substrates (Fig. 5e–h). Therefore, an electric field not only (with the appearance of a thick thread) form in the surroundings changes the particle positions two dimensionally, but also induces and connect to the disclination lines, approximately halfway three-dimensional reconfiguration. Figure 5i–k shows the tuning between the imprinted defect centres. As the elastic anisotropy of range of the disclination network evaluated by measuring the 5CB (ref. 30) causes regions with larger twists to have a larger two-dimensionally projected length of the disclination line and Frederiks transition threshold , a Frederiks transition front is the vertical position of each particle at various applied voltages, initiated in the regions with the smallest twist and creates a twist where the cell gap is normalized to 1. Below the Frederiks wall at their boundaries (Supplementary Fig. 6). As seen in transition threshold at 1.3 V, the two-dimensionally projected Fig. 5b–d, the walls change shape depending on the applied length of the disclination line remains almost unchanged (with voltage and kinks appear in the disclination lines where the wall variations smaller than 0.6%) and the particles within a single 0.0 V 1.5 V 1.7 V 1.9 V Particle #1 Particle #12 Particle #13 Particle #24 Fluorescence intensity Min. Max. 1.0 1.0 Particle #1 0.8 0.8 0.6 0.6 Particle #24 0.4 0.4 Particle #12 0.2 0.2 240 0.0 0.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 Voltage (V) Voltage (V) Voltage (V) Figure 5 | Field-induced reconfiguration of disclination shapes and particle positions. (a–d) POM images of the colloid-decorated disclination network constructed using two substrates with spiral defects of (s, c) ¼ (1, 0) at various applied voltages. White dashed lines indicate the direction along which the cross-sectional profile was measured. Scale bars, 20mm. (e–h) TPEM profiles along the disclination lines in a–d.(i) Voltage dependence of two- dimensionally projected disclination length measured from the POM images. Relative vertical positions of the particles in the lower (j) and upper (k) chains in the POM images, where the cell gap is normalized to 1. Particles are numbered from 1 to 24 in the order or appearance along the profile path (see e). 6 NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved. Projected disclination length (µm) Relative vertical position Relative vertical position NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 ARTICLE chain are displaced either to the top or bottom substrates. Above avenue of investigation is the induction of artificial frustrated the threshold, the disclination network steeply shrinks, reducing phases. Experiments and theory have shown that liquid its length by B12 % at 1.9 V (Fig. 5i). The vertical displacement crystals can sustain periodic or particle-like self-organized 41,42 behaviour also changes at the threshold and strongly depends on structures in the presence of defects . The creation of the position of the particle with respect to the wall front. The wall disclination arrays with controlled numbers, lattice constants front position gradually shifts along the particle chain, and causes and symmetry may lead to the discovery of liquid crystal phases a reversal in the direction of vertical displacement; only the previously unknown. particles that have experienced a reversal in displacement direction show a steep change in position (Fig. 5j,k). For the Methods two colloidal chains studied here, the third particle within the Patterned photoalignment. Light from a high-pressure mercury lamp was filtered using a bandpass filter with centre wavelength of 436 nm and irradiated on a slit chain (particles 3 and 22) showed the largest tuning range, with mask (Supplementary Fig. 1), which was imaged onto the sample using a pair of the maximum shift reaching 41.1% of the cell thickness. lenses with f ¼ 100 mm and f¼ 18 mm. A motorized polarizer was placed between On further increasing the voltage, it is found that the walls the two lenses and the sample stage was also motorized; the rotation speeds for the undergo a ‘pincement’ transition, in which a wall separates into two stages were controlled as described in the main text using LabVIEW software. The sample was irradiated at an intensity of 0.3 mW for 60 s before being rotated two disclinations bound to each substrate confining the liquid by 3, the apex angle of the slit mask. crystal and extends outside the boundary of the alignment pattern (Supplementary Movie 3). The attraction of the particles to the top and bottom substrates observed in Fig. 5b–d is therefore Fabrication of the liquid crystal cells. For the samples shown in Figs 1 and 2, the cells were fabricated from two 1-mm-thick glass substrates, onto which a layer of considered to be a pre-transitional effect leading to the pincement an azobenzene-based photoalignment material (DIC, LIA-03) was spin coated. transition. Above the pincement transition, the disclinations show This photoalignment layer provides ‘planar’ liquid crystal alignment with the easy a complex movement, which in some cases causes the particle axis perpendicular to the polarization of the impinging light. The substrates positions to alternate within the disclination network, or be were sandwiched temporarily using bead spacers of size 9mm and patterned by photoalignment. The two substrates were offset after infiltrating the liquid crystal transported to outside the patterned region. However, the 5CB, which shows the nematic liquid crystal between 22 Cand 35 C. The transient path of the disclinations depends on the manner in observed colour is determined by the optical retardation of the sample, which is which the electric field is applied (for example, whether a voltage affected by the actual cell gap and observation temperature. The samples were increase is applied instantaneously or gradually) and, although the observed at different temperatures to illustrate the stability of the alignment as well as to emphasize the difference in the texture as follows: Fig. 1a–d, 34 C, 29 C, disclination lines retain their original shapes when the voltage is 30 C and 32 C, respectively, and Fig. 2a–c, 34 C, 33 C and 30 C, respectively. removed, the particles often do not return to their original For the samples shown in Figs 3–5, a 150-mm-thick cover slip was used as one positions (Supplementary Movie 3). In contrast, below the of the substrates for the purpose of performing TPEM. Substrates coated with a pincement transition, the tuning of both disclination shapes and 100-nm-thick layer of indium tin oxide were used for the sample shown in Fig. 5, to apply a voltage. The samples for Figs 3 and 5 were fabricated by offsetting the particle positions is fully reversible. defect patterns after a single photoalignment process, whereas the sample for Fig. 4 was fabricated by patterning the two substrates independently and sandwiching them afterwards to a lateral separation distance of 100mm. The liquid crystal was Discussion doped with silica particles (JGC Catalysts and Chemicals, Shinshikyu SW 3mm) and a dichroic dye (Exciton, DCM), both at a concentration of 1 wt%. The particles The giant electrical tunability of particle positions is a feature that were coated with DMOAP following the procedure described in ref. 28. has not been observed in other methods that allow control of particle positions in nematic liquid crystals. Patterned photo- Two-photon excitation microscopy. TPEM is a fluorescence imaging technique alignment (with non-topological patterns) and indented surfaces which uses two-photon absorption to achieve three-dimensional resolution . The have been shown to induce localized elastic potentials at which a contrast in fluorescence intensity between the dye-doped liquid crystal and the 32,33 particle can be trapped , introducing the possibility of non-fluorescent silica particles allows detection of the particle distribution within controlling the crystallographic orientation of three-dimensional the specimen. A commercial confocal laser scanning microscope (Zeiss, LSM-510) colloidal crystals . However, localized elastic potentials induced was used in conjunction with a titanium-sapphire laser (Spectra Physics, Maitai) with wavelength of 800 nm, pulse width of 150 fs and repetition rate of 82 MHz. An by surface conditions are difficult to tune using an electric field, as oil-immersion objective lens with magnification of  63 and numerical aperture of the surface condition itself, which defines the elastic potential, 1.4 was used to acquire the images. remains unchanged. The use of bulk disclinations is a viable alternative for engineering the trapping potential landscape in Simulation of the defect profile. The defect profiles were calculated by liquid crystals, as they have large trapping potentials and can minimizing the free energy of the liquid crystal cell as a functional of the change shape easily in response to director deformations. orientational order parameter of second-rank tensor (Q ). The free energy after ij Furthermore, the disclinations generated here are robust in that appropriate rescaling is expressed as F ¼ dr f þ f , where f ¼ local grad local pffiffiffi pffiffiffi 2 3 2 2 (1/2)ATrQ –(1/3)BTrQ þ (1/4)C(TrQ ) , with A ¼ 3 6 8 =3ðÞ o0 , B ¼ 3 6 their existence is topologically protected and thus self-heal even and C ¼ 4, which is the local part of the free energy density (Tr is the trace of a from large distortions. tensor), and f ¼ (1/2)L (r Q) (r Q) þ (1/2)L (r Q) (r Q) , which is grad 1 ij ij 2 j j Our approach to engineering disclinations in nematic liquid the elastic free-energy density due to the spatial inhomogeneity of Q . Here, ij crystals has a wide variety of applications, as the embedded summations over repeated indices are implied, (r Q) e r Q and ij ist s tj (r Q) r  Q , where e is the Levi–Civita antisymmetric symbol. It is note- particles are not limited to silica microspheres. For example, it j i ij ist worthy that setting L ¼ L corresponds to the so-called one-constant approxi- 1 2 would be possible to construct tunable chiral emitters or mation (K ¼ K ¼ K , where K , K and K are the splay, twist and bend 11 22 33 11 22 33 metamaterials by embedding fluorescent or metallic nanoparticles 6 elastic constants, respectively ). Here we set L ¼ 0.2 and L ¼ 0.8, corresponding to 1 2 16,35,36 in the disclinations . Such composites will not only possess K /K ¼ K /K ¼ 0.4. It is also worth noting that Q ¼ Q (n n –(1/3)d ) with 22 11 22 33 ij 0 i j ij Q ¼ 1 minimizes F. See refs 42,29 for the free energy and its rescaling. The length the functions of the introduced particles but also show self- 0 pffiffiffi has been rescaled so that the rescaled unit length corresponds to 2 2x ’ 40 healing properties, as the disclination lines are topologically nanometres, where x ’ 15 nanometres is the nematic coherence length . protected. Furthermore, the self-assembly behaviour of such The two confining surfaces (parallel to the xy plane) impose Dirichlet boundary colloidal composites can be tuned by changing the shape and conditions fixing Q there, corresponding to the strong anchoring conditions in the ij 9,37 experiments. We set Q ¼ Q (n n –(1/3)d ), where Q ¼ 1 and n ¼ (cos Y(x, y), topology of the introduced particles . On the other hand, liquid ij 0 i j ij 0 sinYðx; yÞ; 0). The angle Y(x, y) is chosen so that it reproduces the experimental crystalline materials may exhibit previously unseen mechanical, surface orientation profiles described in the main text. The other boundaries magnetic, or electronic properties as a result of containing (parallel to the xz or yz plane) impose no surface energy. ‘engineered’ topological defects, as topology is known to affect The free-energy functional is minimized on a cubic lattice of dimension 38–40 such properties of a material . Finally, another important 640  640 20, with the lattice spacing equal to 1 in the rescaled unit. Offset of the NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications 7 & 2015 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8180 two defects is set to 100, 5 times as large as the cell thickness. We let the initial 26. Nersisyan, S. R., Tabiryan, N. V., Mawet, D. & Serabyn, E. Improving vector profile Q ¼ 0 (except at the confining surfaces) relax via a simple rotational ij vortex waveplates for high-contrast coronagraphy. Opt. Express 21, 8205–8213 relaxation equation, @Q (r)/@t¼ dF/dQ (r)þ ld , where the Lagrange ij ij ij (2013). multiplier l ensures TrQ¼ 0. In the figures, defects are defined by the regions with 27. Mawet, D. et al. Optical vectorial vortex coronagraphs using liquid crystal weaker orientational order and are identified by the isosurfaces TrQ ¼ 0.6. polymers: theory, manufacturing and laboratory demonstration. Opt. Express Although the thickness of the simulation box, D0.8mm, is much smaller than that 17, 1902–1918 (2009). of the experimental cell, the former can be further rescaled to fit the latter as long as 28. Skarabot, M. et al. Interactions of quadrupolar nematic colloids. Phys. Rev. E the director profile n and the position of the resulting disclinations are concerned. 77, 031705 (2008). It is because in the bulk of the nematic liquid crystal with uniaxial order, the elastic 29. Fukuda, J., Stark, H., Yoneya, M. & Yokoyama, H. Interaction between two energy in terms of the tensor-order parameter Q reduces to the Frank elastic ij spherical particles in a nematic liquid crystal. Phys. Rev. E 69, 041706 (2004). energy in terms of n that does not possess any characteristic lengths. Furthermore, 30. Madhusudana, N. V. & Pratibha, R. Elasticity and orientational order in rigid surface anchoring (fixed Q ) in our simulations does not introduce any ij some cyanobiphenyls: Part IV. Reanalysis of the data. Mol. Cryst. Liq. Cryst. 89, additional lengths either (anchoring extrapolation length is zero). This is the reason 249–257 (1982). why our simulations successfully reproduce the shape of the disclinations observed 31. De Lo´zar, A., Scho¨pf, W., Rehberg, I., Svensˇek, D. & Kramer, L. Transformation experimentally. from walls to disclination lines: statics and dynamics of the pincement transition. Phys. Rev. E 72, 051713 (2005). 32. Silvestre, N. M., Liu, Q., Senyuk, B., Smalyukh, I. I. & Tasinkevych, M. Towards References template-assisted assembly of nematic colloids. Phys. Rev. Lett. 112, 225501 1. Yeh, P. & Gu, C. Optics of Liquid Crystal Displays (Wiley, 2010). (2014). 2. Adam, D. et al. Fast photoconduction in the highly ordered columnar phase of 33. Martinez, A., Mireles, H. C. & Smalyukh, I. I. Large-area optoelastic a discotic liquid crystal. Nature 371, 141–143 (1994). manipulation of colloidal particles in liquid crystals using photoresponsive 3. Yu, Y., Nakano, M. & Ikeda, T. Photomechanics: directed bending of a polymer molecular surface monolayers. Proc. Natl Acad. Sci. 108, 20891–20896 (2011). film by light. Nature 425, 145 (2003). 34. Nych, A. et al. Assembly and control of 3D nematic dipolar colloidal crystals. 4. Nakata, M. et al. End-to-end stacking and liquid crystal condensation of 6 to 20 Nat. Commun. 4, 1489 (2013). base pair DNA duplexes. Science 318, 1276–1279 (2007). 35. Higashiguchi, K., Yasui, K., Ozawa, M., Odoi, K. & Kikuchi, H. Spatial 5. Bowick, M. J., Chandar, L., Schiff, E. A. & Srivastava, A. M. The cosmological distribution control of polymer nanoparticles by liquid crystal disclinations. Kibble mechanism in the laboratory: string formation in liquid crystals. Science Polym. J. 44, 632–638 (2012). 263, 943–945 (1994). 36. Plum, E., Fedotov, V. A. & Zheludev, N. I. Extrinsic electromagnetic chirality in 6. Chandrasekhar, S. Liquid Crystals (Cambridge University Press, 1992). metamaterials. J. Opt. Pure Appl. Opt. 11, 074009 (2009). 7. Volovik, G. E. & Lavrentovich, O. D. [Topological dynamics of defects: 37. Lapointe, C. P., Mason, T. G. & Smalyukh, I. I. Shape-controlled colloidal boojums in nematic drops]. Zh Eksp Teor Fiz 85, 1997–2010 (1983). interactions in nematic liquid crystals. Science 326, 1083–1086 (2009). 8. Kle´man, M. & Lavrentovich, O. D. Soft Matter Physics: An Introduction 38. Urayama, K. Network topology–mechanical properties relationships of model (Springer, 2003). elastomers. Polym. J. 40, 669–678 (2008). 9. Senyuk, B. et al. Topological colloids. Nature 493, 200–205 (2013). 39. Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic ˇ ˇ ˇ ˇ 10. Tkalec, U., Ravnik, M., Copar, S., Zumer, S. & Musevic, I. Reconfigurable knots skyrmions. Nat. Nanotechnol. 8, 899–911 (2013). and links in chiral nematic colloids. Science 333, 62–65 (2011). 40. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 11. Martinez, A. et al. Mutually tangled colloidal knots and induced defect loops in 82, 3045–3067 (2010). nematic fields. Nat. Mater. 13, 258–263 (2014). 41. Smalyukh, I. I., Lansac, Y., Clark, N. A. & Trivedi, R. P. Three-dimensional 12. Marrucci, L., Manzo, C. & Paparo, D. Optical spin-to-orbital angular structure and multistable optical switching of triple-twisted particle-like momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. excitations in anisotropic fluids. Nat. Mater. 9, 139–145 (2010). 96, 163905 (2006). 42. Fukuda, J. & Zumer, S. Quasi-two-dimensional Skyrmion lattices in a chiral 13. Slussarenko, S. et al. Tunable liquid crystal q-plates with arbitrary topological nematic liquid crystal. Nat. Commun. 2, 246 (2011). charge. Opt. Express 19, 4085–4090 (2011). 14. Zapotocky, M., Ramos, L., Poulin, P., Lubensky, T. C. & Weitz, D. A. Acknowledgements Particle-stabilized defect gel in cholesteric liquid crystals. Science 283, 209–212 This study was partly supported by the PRESTO programme from JST and the Photonics (1999). Advanced Research Center (PARC) at Osaka University. J.F. is supported by JSPS Grant- 15. Yamamoto, T. & Yoshida, M. Viscoelastic and photoresponsive properties of in-Aid (KAKENHI) for Scientific Research (C) (grant number 25400437). We thank DIC microparticle/liquid-crystal composite gels: tunable mechanical strength along Corporation for kindly providing the photoaligning material. with rapid-recovery nature and photochemical surface healing using an azobenzene dopant. Langmuir 28, 8463–8469 (2012). 16. Senyuk, B. et al. Shape-dependent oriented trapping and scaffolding of Author contributions plasmonic nanoparticles by topological defects for self-assembly of colloidal K.A. and H.Y. performed the experiments. J.F. performed theoretical calculations. All dimers in liquid crystals. Nano Lett. 12, 955–963 (2012). authors discussed the results and worked on the manuscript. H.Y. conceived and 17. Ohzono, T. & Fukuda, J. Zigzag line defects and manipulation of colloids designed the project. in a nematic liquid crystal in microwrinkle grooves. Nat. Commun. 3, 701 (2012). Additional information 18. Pires, D., Fleury, J.-B. & Galerne, Y. Colloid particles in the interaction field of a Supplementary Information accompanies this paper at http://www.nature.com/ disclination line in a nematic phase. Phys. Rev. Lett. 98, 247801 (2007). naturecommunications 19. Agha, H., Fleury, J. & Galerne, Y. Micro-wires self-assembled and 3D- connected with the help of a nematic liquid crystal. Eur. Phys. J. E Soft Matter Competing financial interests: The authors declare no competing financial interests. Biol. Phys. 35, 82 (2012). 20. Fleury, J.-B., Pires, D. & Galerne, Y. Self-connected 3D architecture of Reprints and permission information is available online at http://npg.nature.com/ microwires. Phys. Rev. Lett. 103, 267801 (2009). reprintsandpermissions/ 21. Ravnik, M., Alexander, G. P., Yeomans, J. M. & Zumer, S. Mesoscopic How to cite this article: Yoshida, H. et al. Three-dimensional positioning and control of modelling of colloids in chiral nematics. Faraday Discuss. 144, 159–169 (2010). colloidal objects utilizing engineered liquid crystalline defect networks. Nat. Commun. 22. Cavallaro, M. et al. Exploiting imperfections in the bulk to direct assembly of 6:7180 doi: 10.1038/ncomms8180 (2015). surface colloids. Proc. Natl Acad. Sci. 110, 18804–18808 (2013). 23. Zhuang, Z., Suh, S.-W., Kim, Y. J. & Patel, J. S. Defect in the circular-circularly This work is licensed under a Creative Commons Attribution 4.0 rubbed liquid crystal cell with off-center alignment. Appl. Phys. Lett. 76, 3005 International License. The images or other third party material in this (2000). 24. Murray, B. S., Pelcovits, R. A. & Rosenblatt, C. Creating arbitrary arrays of two- article are included in the article’s Creative Commons license, unless indicated otherwise dimensional topological defects. Phys. Rev. E 90, 052501 (2014). in the credit line; if the material is not included under the Creative Commons license, 25. Denk, W., Strickler, J. & Webb, W. Two-photon laser scanning fluorescence users will need to obtain permission from the license holder to reproduce the material. microscopy. Science 248, 73–76 (1990). To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ 8 NATURE COMMUNICATIONS | 6:7180 | DOI: 10.1038/ncomms8180 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved.

Journal

Nature CommunicationsSpringer Journals

Published: May 21, 2015

There are no references for this article.