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Spontaneous Formation of Regular Defect Array in Water-in-Cholesteric Liquid Crystal Emulsions Makoto Yada,*,† Jun Yamamoto,† and Hiroshi Yokoyama†,‡ Yokoyama Nano-structured Liquid Crystal Project, ERATO, Japan Science and Technology Corporation, 5-9-9 Tokodai, Tsukuba, Ibaraki, 300-2635, Japan and Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan Received March 20, 2002. In Final Form: June 28, 2002 We have investigated the spontaneous formation of the regular quadrilateral defect array in cholesteric emulsions, composed of water, surfactants, and cholesteric liquid crystals. Both at the substrate surface and at the surfactant-coated droplet surface, a homeotropic anchoring is enforced to the adjacent liquid crystal. We observe nucleation of numerous point defects, in the cholesteric planar texture immediately after termination of shear to the emulsion, which leads to the formation of the regular defect array. We examined the temporal changes in density, size, and the positional correlation of point defects through the formation process of the defect array by means of two-dimensional fast Fourier transformation (2D FFT) image analysis. Two distinct stages were identified in the formation process; the early stage is the nucleation and growth process of point defects, and the late stage is the rearrangement process of point defects to the regular defect array. Water droplets destabilize the arrangement of cholesteric helix, which induces the transition from the shear-induced planar alignment to the homeotropic orientation.
Introduction In natural biological systems such as cells, brain tissues, and neural networks, spontaneously formed nanoscale complex liquid-crystalline structures are abundant and are known to play a significant physiological role. Examples of naturally occurring lyotropic liquid crystals are also readily found in our foods as well as in a variety of industrial fields. These are mixtures of oil, water, and surfactants and are called emulsions or microemulsions. Emulsions are also deeply related to industrial technologies such as soaps, cosmetics, paints, and so forth for the spontaneous formation of nanoscale structures because of their immiscibility and segregation mechanism. The recent hike of nanotechnology has led to a resurgence of interest into both scientific and technological aspects of microemulsions. The self-organization of mesoscopic superstructures such as membranes, tubes, sponges, and so forth with a characteristic nanometer-order length scale is expected to serve as a rich path for the so-called “bottomup” approach, which is supposed to complement or even replace the top-down nanofabrication technology in future. Here, we report on the self-organization behavior of the liquid-crystal emulsions, that is, the system of water droplets dispersed in a liquid-crystal host.1 A water droplet distorts the orientation of the adjacent liquid crystal and is expected, when the surface anchoring is sufficiently large, to behave topologically as a core of orientational point defect yet with a much lower energy of formation because of its nonsingularity. The induced elastic distortion extends over a long distance in liquid crystals and creates novel interactions between water droplets.2 Re* To whom correspondence should be addressed. E-mail: yada@ nanolc.jst.go.jp. † Yokoyama Nano-structured Liquid Crystal Project. Tel: +81298-47-9818. Fax: +81-298-47-9819. ‡ National Institute of Advanced Industrial Science and Technology. (1) Poulin, P.; Stark, H.; Lubensky, T. C.; Weitz, D. A. Science 1997, 275, 1770. (2) Lev, B. I.; Tomchuk P. M. Phys. Rev. E 1999, 59, 591.
cently, there are studies on nematic emulsions1-6 and microemulsions7 composed of nematic liquid crystals, water, and surfactants. In nematic emulsions, Poulin et al. observed linear chains of water droplets in a nematic liquid crystal, which is formed by the balance of dipoledipole attractive and defect-mediated repulsive interactions.1 On the other hand, “transparent nematic phase” was found in nematic microemulsions, where the nematic order exists in the microscopic length scale, but the longer range anisotropy is completely disrupted as a result of the droplet-induced distortions.7 We describe here a different type of liquid-crystal emulsion, consisting of water and cholesteric liquid crystals, namely, cholesteric emulsions. A cholesteric phase has a spontaneous long-range helical structure, although its local molecular ordering is identical to that of a nematic phase. Owing to the spontaneous helix, cholesteric liquid crystals show more complicated textures than nematics, and we expect that the effect of the distortion by the surface anchoring of water droplets induces more unique textures and rheological properties. Moreover, there is a possibility that the cholesteric helix may generate a novel interaction between water droplets.8 There are not so many studies on cholesteric emulsions.8,9 In this paper, we found the regular quadrilateral defect array formed after applying the shear in the cholesteric emulsions. Shear is applied parallel to glass plates, both owing to the alignment of liquid-crystal molecules and the fragmentation of water droplets. In previous studies, there are some reports that regular defect arrays were observed in layered pure liquid crystals, such as choles(3) Poulin, P.; Weitz, D. A. Phys. Rev. E 1998, 57, 626. (4) Lubensky, T. C.; Petty, D.; Currier, N.; Stark, H. Phys. Rev. B 1998, 57, 610. (5) Monval, O. M.; Dedieu, J. C.; Krzywicki, T. G.; Poulin, P. Eur. Phys. J. B 1999, 12, 167. (6) Lanzo, J.; Nicoletta, F. P.; Filpo, G. D.; Chidichimo, G. Liq. Cryst. 2000, 27, 1029 (7) Yamamoto, J.; Tanaka, H. Nature 2001, 409, 321. (8) Fukuda, J.; Lev, B. I.; Yokoyama, H. Phys. Rev. E 2002, 65, 031710. (9) Zapotocky, M.; Ramos, L.; Poulin, P.; Lubensky, T. C.; Weitz, D. A. Science 1999, 283, 209.
10.1021/la025757d CCC: $22.00 © 2002 American Chemical Society Published on Web 08/20/2002
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teric, smectic phase, and lyotropic lamella phase.10-19 In long-pitch cholesterics, Bouligand made geometrical analyses of polygonal focal conic textures generated by cooling from an isotropic phase.10 In planar cholesterics, a periodic cellular structure has been observed by the application of a magnetic and an electric field.11-15 In smectics, Rosenblatt et al. presented the formation mechanism of the parabolic focal conic structure by dilation of planar samples.16 On the contrary, the defect array in the cholesteric emulsion is spontaneously formed from the shear-induced planar alignment, neither by the external stimulation nor by the change of temperature. We will discuss the formation mechanism of the regular quadrilateral defect array from the results of the microscopic observation and two-dimensional fast Fourier transform (FFT) image analysis in the cholesteric emulsions. Experimental Section Cholesteric liquid crystals used in this study are mixtures of base nematics (Cr 11 °C N 116 °C I, from Dainippon ink & Chemicals) and a chiral dopant CB-15 (from Merck). Three types of cholesterics with different pitch (p ∼ 2.4, 1.3, and 0.33 µm) were prepared by changing chiral dopant concentration. The isotropic-cholesteric phase-transition temperatures are lowered with increase in the chiral dopant at the rate of 17 °C/10 wt % from 99 to 49 °C. These cholesteric pitches were evaluated either from the wavelength of selective reflection or by the GrandjeanCano method. Water-in-cholesteric liquid-crystal emulsions were prepared by mixing 90 wt % didodecyl dimethylammonium bromide (DDAB) aqueous solution into cholesteric liquid crystals in the isotropic phase. DDAB was used to stabilize small water droplets in cholesteric liquid crystals. The weight concentration of the DDAB aqueous solution in the emulsion, Cw, was changed between 0.5 and 2 wt %. The isotropic-cholesteric phase-transition temperature became at most 2 °C lower than that of the corresponding pure cholesteric liquid crystals. When the liquid crystal is in the isotropic phase, this system is equivalent to conventional water-in-oil microemulsions. The diameter of inverse micelles thus formed can be estimated to be ∼4 nm from the concentration ratio of DDAB and water. When temperature goes down to the cholesteric phase, water droplets appear by macroscopic phase separation. (We confirmed directly the appearance of micron-size water droplets in parallel plate cells with a homogeneous anchoring condition.) The anchoring at the droplet surface is likely to be homeotropic because of the adsorption of surfactant molecules. Textures of the cholesteric emulsions were observed under a polarizing microscope at 30 °C. Samples were sandwiched between a pair of glass plates with homeotropic anchoring, and the thickness was controlled from 10 to 100 µm. Although the 10 µm cell gap was adjusted by using silica particles in the usual manner, 40-100 µm thick samples were prepared under a stresscontrolled rheometer (SR-5000, from Rheometric Scientific) equipped with a layer thickness control mechanism. The rheometer was improved to allow in-situ optical monitoring by CCD camera. The cholesteric emulsion sample was subjected to a fairly strong shear of 500-1000 s-1 on a hot stage. Two-dimensional (2D) FFT image analysis was performed to observe textures by using the software of Image-Pro Plus ver.4 (from Media Cybernetics). In case of the direct application of 2D (10) Bouligand, Y. J. Phys. 1972, 33, 715. (11) Helfrich, W. J. Chem. Phys. 1971, 55, 839. (12) Rondelez, F.; Arnould, H. C. R. Acad. Sci. 1971, B273, 549. (13) Gerritsma, C.; Zanten, P. V. Phys. Lett. 1971, A37, 47. (14) Scheffer, T. J. Phys. Rev. Lett. 1972, 28, 593. (15) Rondelez, F.; Hulin, J. P. Solid State Commun. 1972, 10, 1009. (16) Rosenblatt, C. S.; Pindak, R.; Clark, N. A.; Meyer, R. B. J. Phys. 1977, 38, 1105. (17) Meeten, G. H.; Narvard, P. J. Polym. Sci., Polym. Phys. Ed. 1988, 26, 413. (18) Asher, S. A.; Pershan, P. S. J. Phys. 1979, 40, 161. (19) Benton, W. J.; Toor, E. W.; Miller, C. A.; Fort, T., Jr. J. Phys. 1979, 40, 107.
Figure 1. Cross-polarizing microscope images of the cholesteric emulsion (CW ) 2.0 wt %, p ) 0.33 µm). (a) t ) 5 s after stopping the shear, (b) t ) 10 s, (c) t ) 1 min, (d) t ) 25 min. The sample thickness is 10 µm. Scale bar: 30 µm. FFT to polarizing microscope images, the information of the anisotropy is included in FFT spectrum. To avoid the influence of the birefringent contrast, we first generated a mesh, whose segment was so drawn as to connect nearest-neighbor point defects. These connecting lines carry all necessary information about the periodicity and the orientation of the defect array.
Results and Discussions In general, pure cholesteric liquid crystals show a planar texture, that is, the Grandjean texture20 under a sufficiently large shear. This is because liquid-crystal molecules tend to realign along the flow to minimize the viscous dissipation. The Grandjean texture induced by the shear remains stable in a homogeneous cell. Even in homeotropically aligning cells, the Grandjean texture is known to persist as long as the cholesteric pitch is much smaller than the sample thickness or the temperature is far away from the cholesteric-to-isotropic transition. On the contrary, the shear-induced Grandjean texture in cholesteric emulsions cannot be stable in a homeotropic cell for any pitch length and at any temperature. We found that a regular defect array grows spontaneously in the shear-induced planar texture after removing the shear flow field. The series of micrographs in Figure 1 shows the formation process of the defect array in a cholesteric emulsion comprised of water droplets (Cw ) 2 wt %) and the cholesteric (p ) 0.33 µm). The sample thickness is fixed at 10 µm. Before applying the shear, a usual focal conic texture was observed when cooled from the isotropic phase. The strong shear to the focal conics induced a transition to the planar texture. Immediately after stopping the shear, numerous point defects are created in the planar texture as shown in Figure 1a. The size of the single defect grows, while undergoing rapid coalescence with neighboring defects, and the point defects tend to assume a regular arrangement as shown in Figure 1b and c. After these defects fill up all space, the period of point defects is extended slowly, and the regular defect array is constructed, as shown in Figure 1d. This defect array is preserved for more than one day. All different pitch cholesteric samples (p: 0.33-2.4 µm) can form the defect array in temperature range from each isotropiccholesteric phase-transition temperature to room temperature (25˚C). On the other hand, the defect array can never be formed in samples sandwiched between homo(20) Demus, D.; Richter, L. Textures of Liquid Crystals; Verlag Chemie: Weinheim, Germany, 1978.
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Figure 3. Time evolution of the density and the size of point defects after stopping the shear (a and b, respectively). Here, the size means the average radius of isolated point defects or the average distance between point defects in the defect array.
Figure 2. Arranged concentric fingerprint texture in the defect array (CW ) 2.0 wt %, p) 2.4 µm). The sample thickness is 10 µm. Scale bar: 10 µm. (a) Upper glass surface, (b) lower glass surface. (c) Spatial distribution of the cholesteric helix (described by Bouligand10).
geneous anchoring glass plates; here, water droplets readily coalesce after stopping the shear, eventually leaving only oily streaks in the planar texture. For the long-pitch cholesteric (p ) 2.4 µm), the spatial distribution of cholesteric helix in the defect array is visually observable. As shown in Figure 2, the defect array is accompanied by a regular arrangement of concentric fingerprint patterns, which fills the entire volume between upper and lower glass surfaces. This result clearly shows that the defect array has a regular three-dimensional lattice of the cholesteric helix and point defects, presumably stabilized by the interplay between uniform helical order and homeotropic anchoring glass surfaces. This arrangement of the cholesteric helix closely resembles the cholesteric polygonal texture described by Bouligand10 in early 1970s. The polygonal texture, however, was formed in certain neat cholesterics and could appear only at a temperature close to the cholesteric-isotropic transition
point. In the absence of water droplets, the defect array can never be spontaneously generated well inside the cholesteric phase from the shear-induced planar-aligned samples. Water droplets, therefore, clearly play a decisive role in the formation dynamics of the defect array. Figure 3 shows the time dependence of the density and the size of point defects after stopping the shear for different concentration of DDAB aqueous solution in the emulsions, Cw. (The cholesteric pitch and the sample thickness are fixed at 0.33 and 10 µm, respectively.) Here, the size of point defects is defined as their average radius of isolated defects (in Figure 1a) or the average distance between point defects in the defect array (in Figure 1c and d). In Cw: 1.5-2.0 wt %, we found two distinct stages in the formation process of the defect array. The early stage is 0 < t < 10 s after stopping the shear, and the late stage is t > 10 s. In the early stage, the density and the size of point defects steeply increase as shown in Figure 3a and b, and the defects fill up all the available space by the time around t ) 10 s. No clear differences were found in the growth rates of the density and the size of point defects as a function of water droplet concentration in the early stage. In the late stage (t > 10 s), on the other hand, the density gradually decreases with time, whereas the size increases. In this stage, the defect size and the defect density are no longer independent as in the early stage because the point defects are already virtually close-
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Figure 5. Integrated scattering intensity profiles of Figure 4. (a) Radial direction, as a function of wavenumber k. An arrow at each time points to the first peak. (b) Azimuthal direction.
Figure 4. 2D FFT patterns corresponding to the positional correlation of point defects in Figure 1a-d.
packed. From Figure 3, the equilibrium period of the defect array is independent of the concentration of water droplets, although the growth rate is accelerated with increase in water droplet concentration. When the water content is kept fairly low, that is, Cw: 0.5-1.0 wt %, the number of water droplets cannot be large enough to yield the complete defect array. At 1.0 wt %, the defect array can now form, but its period seems to reach saturation at a smaller length compared to that in higher water droplet concentration. As shown in Figure 3a, emulsions with higher water content (1.5-2.0 wt %) even show a slow decrease in defect density for t > 10 s. This observation strongly indicates that there exists an optimal defect density to which the system relaxes, provided sufficient amount of water is available. In lower concentration of the DDAB solution (Cw ) 0.5 wt %), only isolated point defects randomly appear from the planar texture. Although the density at t ) 30 min reaches a value comparable to the maximum value attained with a higher water content, the defect array cannot be generated because the defect size is not sufficiently large to fill up the entire volume. To extract more quantitative information about the positional correlation among point defects, we carried out a 2D Fourier transform analysis of the micrographs in Figure 1. As mentioned in a previous section, a mesh connecting the defect centers was first generated, and the 2D FFT was applied. Figure 4a-d shows the time evolution of the 2D FFT patterns for the 2.0 wt % DDAB aqueous solution. Figure 5a and b are the radial and angular distribution functions obtained by integrating the scattering intensity over the radial and azimuthal direction, which provide us with the information on the periodicity and the orientational correlation of the defect array, respectively. Figure 4a shows the FFT pattern at t ) 5 s after terminating the shear. Only a highly diffuse scattering showed up during the early stage (t < 10 s), indicating the absence of any periodicity and orientational order among point defects. In the late stage (t > 10 s), however, a clear scattering peak appeared as a ring shown in Figure 4b-d, corresponding to the evolution of finite periodicity among point defects. As shown in Figure 5a, the first- and second-order peaks became appreciable only
after 10 s. The first-order peak then grew sharper, while undergoing a downward shift with time. Furthermore, the second- and third-order peaks became more clearly visible. Finally at t ) 25 min, the scattering rings were split into four brushlike anisotropic scattering patterns as shown in Figure 4d. The azimuthal angle dependence of the scattering intensity also shows four separate peaks, as shown in the lower part of Figure 5b. These results indicate the fourfold rotational symmetry of the defect array is consistent with the microscope image in Figure 1d. From the above results, we noticed two steps in the formation process of the defect array. The first step is the nucleation and growth of point defects from the shearinduced planar texture, and the second step is the rearrangement of the defects into the regular array after filling up all space of point defects. In the initial stage (0 < t < 10 s), there could in principle be two possible routes to the generation of point defects, that is, nucleation growth and spinodal decomposition.21,22 A characteristic feature of a spinodal decomposition is that the wavenumber of the instability appears from the early stage. In our case, point defects are generated without any positional correlation as already confirmed in Figure 4a. We have actually seen in Figure 1a that the size of point defects has a broad distribution in the early stage, showing that the point defects were not simultaneously generated. This behavior is only consistent with the nucleation and growth mechanism. Initially, the strong shear makes liquid-crystal molecules aligned parallel to the glass plates and makes water droplets fragmented and dispersed homogeneously at the same time. After removing the shear, the shear-induced planar alignment begins to be distorted to restore homeotropic orientation induced by the anchoring effect on the glass plates. Since liquid-crystalline molecules must rearrange cooperatively in macroscopic length scales to transform the planar to the homeotropic orientation, the shear-induced planar alignment never changes to the homeotropic in pure cholesterics without water droplets. Water droplets can strongly distort the orientation of the director owing to the homeotropic anchoring at the interface. Therefore, the shear-induced planar texture of cholesteric emulsions includes many defect cores and hence has a higher free energy than the presheared pure cholesteric phase. Distortions of liquid-crystalline order around water droplets may reduce the height of energy barrier for the creation of critical nuclei. On the contrary, when water droplets are not abundant, the nucleation of (21) Bates, F. S.; Wiltzius, P. J. Chem. Phys. 1989, 91, 3258. (22) Tanaka, H. Phys. Rev. E 1995, 51, 1313.
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Figure 6. Dependence of the period of the defect array on the sample thickness and the cholesteric pitch (a and b, respectively). (a) The cholesteric pitch is fixed at 1.3 µm, (b) the sample thickness, 10 µm.
point defects cannot readily occur, effectively stabilizing the initial planar structure. As the defects tend to fill all the available space through the second stage (t > 10 s), the distribution of point defects becomes largely periodic. This indicates the existence of a repulsive interaction between point defects. When two point defects mutually approach, the elastic energy increases owing to the distortion of the liquid-crystalline order induced by the mismatch of the cholesteric helix. This elastic interaction between point defects can be sufficiently large to drive the periodicity of the defect array. When the water concentration is sufficiently high (Cw: 1.5-2.0 wt %, see Figure 3b) so that excess number of water droplets are always available, the period of the defect array no longer depends on the water concentration. Figure 6, on the other hand, shows the variation of the period of the defect array as a function of the sample thickness and the cholesteric pitch. The period is uniformly affected by these parameters, which suggests that the final period is automatically adjusted in such a way as to minimize the distortion energy of the cholesteric helix in the defect array. As shown in Figure 6, the period is proportional to the square root of the thickness and the pitch. This behavior agrees with the known property of periodic textures
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induced by a magnetic or electric field, applied parallel to the helical axis of the cholesteric planar texture.11-15 Finally, one may ask where the water actually exists in the defect array. Although no definitive answer can be given at present because of our inability to observe it directly, the frequent coalescence of point defects with water-rich oily streaks in homogeneous texture suggests that the water should be closely associated with point defects. It seems also likely by energetic reasons that the water should accumulate at the point defect to make the core region less singular and reduce the orientational elastic strain at the core. Further study aimed to confirm this conjecture is now underway using the confocal fluorescent microscopy, and the results will be reported elsewhere. Conclusions We found that the regular defect array is formed spontaneously after stopping the shear in the cholesteric emulsions for the first time. There are two steps in the formation process of the defect array. The first step is the nucleation and the growth of point defects from the planar texture. The distortion of the liquid-crystalline order around water droplets plays a role to reduce the barrier energy to make critical nuclei of point defects. It is the most important point that the preshear fragmentizes and disperses water droplets in the planar texture. On the contrary, the second step is the construction of the regular defect array. When all space is filled up by defects, the regularity in the period of point defects appears owing to the interaction between neighboring defects, which is introduced by elastic spatial distortion of the cholesteric helix. After that, the period of the defect array is adjusted to minimize the deformational energy of cholesteric liquid crystals. The cholesteric liquid-crystalline order is frustrated by the surface-anchoring effect of water droplets and the frustration leads to the defect array; however, the final defect array seems to be stabilized by the existence of water droplets at the core region of point defects. LA025757D
