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Self-Organization of Particles with Planar Surface Anchoring in a Cholesteric Liquid Crystal Niek Hijnen, Tiffany A. Wood, David Wilson, and Paul S. Clegg* School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom Received April 9, 2010. Revised Manuscript Received June 15, 2010 We present birefringence and fluorescence confocal microscopy studies of melamine particles in a liquid-crystalline host solvent. The liquid crystal has a cholesteric phase at room temperature with a helical pitch that can be modified by changing the composition. The pitch employed here is always less than the particle diameter (3 μm). We demonstrate via birefringence that the mesogens preferentially anchor flat at the melamine surface. Via studies in a sample cell with aligning surfaces we show that although the particles form chains in a nematic liquid crystal they organize in 2D plates in a cholesteric. Fluorescence confocal microscopy and particle location analysis are used to determine the radial distribution function and to evaluate the particle aggregation number as a function of pitch length. We discuss possible explanations for the self-organization.
1. Introduction Colloidal particles experience new particle-particle interactions when dispersed in a liquid-crystalline solvent.1 These effective interactions are due to each particle distorting the ordering of the anisotropic medium at the expense of elastic energy. The form of the distortion is also controlled by the strength and orientation of molecular anchoring at the particle surface. Typically, a pair of particles can minimize the elastic energy cost by adopting a preferred separation with some fixed orientation with respect to the far-field ordering direction of the medium. For the case of particles in a nematic liquid crystal, the behavior has been studied in great detail.1,2 When the mesogens exhibit homeotropic anchoring at the particle surface, a hyperbolic hedgehog defect can form and the long-range interaction has a dipolar character. In the case of planar surface anchoring (and weak homeotropic anchoring3), long-range interactions with quadrupolar character result. In addition to particle-particle interactions, there is also an attraction between a particle and a line defect (disclination) in a nematic.4 Here we explore the behavior of particles with planar anchoring in a cholesteric (twisted nematic) liquid crystal where limited observations exist until now. This is a fascinating medium in which to probe the behavior of colloidal particles because it has an intrinsic length scale, the helical pitch, which can be comparable to the size of the particles. Molecular alignment in a cholesteric liquid crystal can be described using two vectors: the director for local alignment n and the helical axis z. The director is always perpendicular to z and describes a helix with a characteristic pitch length (p). Because the molecular orientation is periodic in the z direction, its mathematical description is similar to that of a layered medium. Both orientational order and positional order can be disrupted by inclusions. The layer curvature modulus, K, is proportional to the Frank bending modulus, K3, and is independent of the pitch *Corresponding author. E-mail:
[email protected]. (1) Stark, H. Phys. Rep. 2001, 351, 387. (2) Poulin, P.; Weitz, D. A. Phys. Rev. E 1997, 57, 626. (3) Musevic, I.; Skarabot, M.; Tkalec, U.; Ravnik, M.; Zumer, S. Science 2006, 313, 954. (4) Pires, D.; Fleury, J.-B.; Galerne, Y. Phys. Rev. Lett. 2007, 98, 247801.
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whereas the layer compression modulus, B, is related to the Frank twisting modulus, K2, and varies with the pitch as B ≈ 1/p2.5-7 Models of defects and inclusions in lamellar phases typically use the penetration length, λ = (K/B)1/2 ≈ p, as the distance over which order is reestablished.7,8 Previous research9-19 has often focused on the changes in the rheological properties of cholesteric liquid crystals induced by dispersed particles. Zapotocky et al. found that silica particles pinned the oily streak defect structure in place.10,12 This led to growth in the storage modulus compared to the annealed bulk material. Yada et al. studied the flow properties of water-incholesteric liquid-crystal emulsions stabilized by surfactant.13,14 On cessation of shear, spherical regions of cholesteric order formed around the water droplets to fill space. Under steady flow, a hexagonal array of spheres was observed.15 The water droplets appeared to take the place of a defect at the center of the cholesteric sphere. Other experimental studies have explored the possibilities for self-assembly (e.g., templating via the fingerprint texture) and the symbiotic relationship between components.9,16,17 The changes in both reflectivity and switching properties have recently been probed.18,19 (5) de Gennes, P. G.; Prost, J. The Physics of Liquid Crystals, 2nd ed; Oxford University Press: Oxford, U.K., 1993. (6) Lubensky, T. C. Phys. Rev. A 1972, 6, 452. (7) Smalyukh, I. I.; Lavrentovich, O. D. Phys. Rev. E 2002, 66, 051703. (8) Sens, P.; Turner, M. S.; Pincus, P. Phys. Rev. E 1997, 55, 4394. (9) Hauser, A.; Kresse, H.; Glushchenko, A.; Yaroshchuk, O. Liq. Cryst. 1999, 26, 1603. (10) Zapotocky, M.; Ramos, L.; Poulin, P.; Lubensky, T. C.; Weitz, D. A. Science 1999, 283, 209. (11) Fukuda, J.; Lev, B. I.; Yokoyama, H. Phys. Rev. E 2002, 65, 031710. (12) Ramos, L.; Zapotocky, M.; Lubensky, T. C.; Weitz, D. A. Phys. Rev. E 2002, 66, 031711. (13) Yada, M.; Yamamoto, J.; Yokoyama, H. Langmuir 2002, 18, 7436. (14) Yada, M.; Yamamoto, J.; Yokoyama, H. Langmuir 2003, 19, 3650. (15) Yada, M.; Fukuda, J.; Yamamoto, J.; Yokoyama, H. Rheol. Acta 2003, 42, 578. (16) Loudet, J. C.; Barois, P.; Auroy, P.; Keller, P.; Richard, H.; Poulin, P. Langmuir 2004, 20, 11336. (17) Mitov, M.; Bourgerette, C.; de Guerville, F. J. Phys.: Condens. Matter 2004, 16, S1981. (18) Payne, J. C.; Thomas, E. L. Adv. Funct. Mater. 2007, 17, 2717. (19) Kurochkin, O.; Buchnev, O.; Iljin, A.; Park, S. K.; Kwon, S. B.; Grabar, O.; Reznikov, Y. J. Opt. A: Pure Appl. Opt. 2009, 11, 024003.
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There have been two very recent developments: first, computer simulations of particles in a cholesteric have employed the periodic defect array of the blue phase as the host.20 The disclination lines are found to attract particles independent of the surface anchoring conditions. The existence of a new periodic composite is predicted. Second, sputtering has been used to introduce gold nanoparticles into liquid-crystalline environments.21,22 This approach apparently results in particles that have surface-adsorbed mesogens from the moment they are formed. Initial studies of these nanoparticles in a cholesteric blue phase show the transition temperature being suppressed but the range for which this phase is stabilized being extended. Imaging of the particles in situ will be required for a complete interpretation of these experiments.21 Here, by contrast, we make use of large particles (dc = 3 μm) in order to show the differences in self-organization in a cholesteric medium compared to that in a nematic. In our system, the particles are always visible and the pattern of ordering of the mesogens around the particles is often visible. Although very small particles might be expected to couple only to the orientational order, these larger particles will disrupt the helical ordering more profoundly. We show how the characteristic features change as a function of the cholesteric pitch. In section 2, we describe the materials and techniques employed. We present our microscopy results and the analysis of particle distributions in section 3. We collate this information and suggest explanations in section 4. Finally, in section 5, we summarize our findings and point to new opportunities.
2. Materials and Methods The liquid crystals were mixtures of nematic MDA-00-1444 (ne = 1.684, no = 1.507) and chiral dopant MDA-00-1445 (ne = 1.67, no = 1.5) both from Merck; the proportions were used to control the pitch length at room temperature. The spacing between defect lines in a wedge cell was used to verify the pitch.5 For a small number of experiments requiring only nematic order, 40 -pentyl-4-biphenylcarbonitrile (5CB) was used (Sigma-Aldrich). The particles (3 μm diameter) were fluorescein isothiocyanate (FITC)-labeled melamine with carboxylate-modified surfaces (Fluka). Prior to use, they were dried under vacuum at 40 C overnight. Samples for birefringence studies had a particle volume fraction of 0.1 vol % and were prepared by alternating mixing using a magnetic stirring bar and sonicating (15 min.). This was repeated four to six times until the sample appeared to be homogeneous. Samples with particle concentrations of 10 vol % were used for fluorescence confocal microscopy. Cholesteric samples containing a high volume fraction of particles do not flow, making handling challenging. To carry out fluorescence confocal microscopy studies on these samples, they were prepared and characterized in the same container. This was a sample vial with the base removed and replaced with a cover slide (attached using UV curing adhesive). Here the sample could be stirred using a magnetic stirring bar for days prior to examination. Typically, confocal microscopy was carried out after a pause of g72 h. For the sedimentation studies, samples of 10, 20, and 40% volume fraction of melamine particles in a cholesteric (p = 0.4 μm) were prepared. These were then transferred to cuvettes (Starna) with an optical path length of 1 mm; a centrifuge was used to move the sample to the bottom of the cuvette. For confocal imaging, with both types of sample cell, a Biorad Radiance 2100 scan head mounted on a Nikon TE300 microscope was employed. The dyed melamine particles were excited using an Ar (20) Ravnik, M.; Alexander, G. P.; Yeomans, J. M.; Zumer, S. Faraday Discuss. 2010, 144, 159. (21) Yoshida, H.; Tanaka, Y.; Kawamoto, K.; Kubo, H.; Tsuda, T.; Fujii, A.; Kuwabata, S.; Kikuchi, H.; Ozaki, M. Appl. Phys. Express 2009, 2, 121501. (22) Yoshida, H.; Kawamoto, K.; Kubo, H.; Tsuda, T.; Fujii, A.; Kuwabata, S.; Ozaki, M. Adv. Mater. 2010, 22, 622.
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ion 488 nm laser line in conjunction with an HQ500LP emission filter to block scattered light. Despite the helical birefringent medium, the intensity profile of the particles in the confocal images had a Gaussian profile and no ghost images were observed. For the birefringence studies, the alignment of the mesogens at the cell surfaces was induced using poly(vinyl alcohol) (PVA, 98% hydrolyzed, Mw = 13 000-23 000, Sigma-Aldrich). In particular, wedge cells with surface alignment were used so that we could determine the influence of sample thickness parallel to the helical axis. These were constructed from cover slides that were washed in 2.5 M NaOH (solvent 60 vol % ethanol in water) overnight. The cover slides were rinsed 5-10 times with water. While still wet, they were mounted on the spin coater (Cammax Pricema) and covered with a layer of a 0.3 wt % PVA solution (solvent 60 vol % ethanol in water). After ∼2 min, they were spun at 3000 rpm for 60 s and then dried in an oven at 120 C for 30 min. One of the slides was glued onto a microscopy base slide (Scientifc Glass Laboratories Ltd.) using UV glue (Norland). This was gently rubbed five times using a velvet cloth in the direction parallel to the long side of the base slide. The other coated cover slide was rubbed in the same way and placed on top with a Mylar spacer (∼50 μm thick) at one end to create a small angle (∼0.14) between the two rubbed surfaces. Finally, the two sides perpendicular to the rubbing direction were fixed using UV glue. We used a Nikon Eclipse E800 microscope to view the sample between crossed polarizers, usually g48 h after the wedged cell was filled. Images were recorded with a color QImaging Micropublisher 3.3 camera. IDL routines (by Eric Weeks and others23) were used to identify the particle coordinates from the confocal image stacks and to calculate a radial distribution function from them. Two-dimensional analysis in the XY plane was carried out so that we could separate interactions in the plane of the director from interactions in the plane of the helical axis. All radial distribution functions were calculated for r = 0.1-10 μm with Δr = 0.02 μm. Data from all of the image stacks were averaged to obtain the final radial distribution of a sample. The nearest neighbors for each particle were identified as those particles closer than the minimum between the first and second peaks of the radial distribution function. From this, we could calculate the average number of particles in each aggregate and hence quantify the size of aggregates. The percentage of particles that was found in aggregates containing more than 10 particles was also evaluated as a measure of the degree of aggregation in the system.
3. Results and Analysis 3.1. Colloids with Planar Surface Anchoring. To demonstrate that the mesogens adopt planar alignment at the surface of these melamine particles, we begin with the well-known case of a nematic host solvent. Figure 1 shows birefringence images of melamine dispersed in 5CB; the nematic director is aligned parallel to the bottom edge of the images. Several features are immediately obvious. First, the birefringence pattern around the particles is made up of dark lines parallel and perpendicular to the director on a white background. This is consistent with planar anchoring with the point defects (boojums) at the poles where the director meets the particle surface. Second, pairs of particles tend to touch (N.B. green circles in Figure 1a), with contact points at 30 with respect to the director. Third, large collections of particles form chains (Figure 1a,b). The kinks in the chains ensure that contact points are typically at 30 with respect to the director orientation. All of these observations point toward planar anchoring of mesogens at the particle surface.2,24 (23) Besseling, R.; Isa, L.; Weeks, E. R.; Poon, W. C. K. Adv. Colloid Interface Sci. 2009, 146, 1. (24) Smalyukh, I. I.; Lavrentovich, O. D.; Kuzmin, A. N.; Kachynski, A. V.; Prasad, P. N. Phys. Rev. Lett. 2005, 95, 157801.
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Figure 1. High-magnification birefringence images (100 objective) of melamine particles (3 μm diameter) in a nematic liquid crystal demonstrating planar anchoring. (a) A single particle and small clusters. (b) Chains of particles.
Figure 2. High-magnification birefringence images of melamine particles (d = 3 μm) in a cholesteric liquid crystal. (a) Images (p = 1.5 μm)
taken at a sample thickness of ∼5 μm in the top row and images taken at a sample thickness of ∼10 μm in the bottom row. The bottom-row images are of the same three particles but with a different choice of focal plane. Inset are the two particles with green outlines added showing that they are touching. (b) Images (p = 0.4 μm) taken at a sample thickness of ∼5 μm and at higher magnification in the top row and images taken at a sample thickness of ∼15 μm in the bottom row.
Now that the surface alignment is established, we take a look at particles in a cholesteric environment. Figure 2a shows the birefringence patterns for melamine particles in a cholesteric (p=1.5 μm). The axis of the helix, in the absence of particles, is perpendicular to the plane of the image; a well-aligned cholesteric is colored corresponding to the wavelengths not reflected out of the transmitted light. The particles appear to be surrounded by concentric bright and dark rings, albeit with some modulation around the circumference. Bright and dark rings are familiar from the cholesteric fingerprint texture, which is observed when this phase is viewed perpendicular to the helical axis. Hence we assume that the helical axis is propagating away from the surface of the particles; the separation between dark rings appears to be less than half of the pitch length (0.4-0.6 μm) possibly because the helical axis does not lie within the plane of the image. “Onion” arrangements created in surfactant phases have some similarities.25 In Figure 2a, the pitch of the cholesteric is a substantial fraction of the size of the particle (p = 1.5 μm). Here particles can be found that do not have associated disclination lines. In the lower left frame of Figure 2a, the green circles show that pairs of particles can touch. Figure 2b corresponds to p = 0.4 μm; for this (25) Diat, O.; Roux, D. J. Phys. II 1993, 3, 9.
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pitch, the particles are rarely observed in isolation and every cluster is associated with one or more disclination line. The birefringence pattern has similarities to that of water-in-cholesteric emulsions.13,14 (Any texture due to individual layers is unresolvable.) Figure 3 shows single particles and pairs of particles interacting with disclination lines in a cholesteric sample (p = 1.5 μm). Away from the particles, the defect line is dark at its edges and has a bright strip running down the center. The bright strip is consistent with having the director in the plane of the image, and the dark edges could be defects. Such an arrangement could be a τ-1/2τþ1/2 disclination separating two domains with a difference of one complete helical turn between them. As shown, the disclination line (which is half a pitch wide) connects with what appears to be a layer of cholesteric order at the surface of the particle. The enveloped particle can occupy a region of the disclination line. Similar configurations have been considered in computer simulations by Ravnik et al.;20 these modeled a small particle in a liquid crystal with infinite pitch and hence do not involve surface layers of cholesteric order. 3.2. Chains in a Nematic and Plates in a Cholesteric. The wedge-shaped sample cells provide an environment where the liquid-crystal far-field order is well-defined. This geometry can be Langmuir 2010, 26(16), 13502–13510
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used to compare the organization of the particles in a nematic and a cholesteric at least qualitatively. Variations in the distribution of particles with the thickness of the sample are also readily apparent. Figure 4 shows low concentrations (0.1 vol %) of melamine particles in a cholesteric liquid crystal. The top (bottom) row corresponds to a pitch of 1.5 μm (0.4 μm) where the helical axis is perpendicular to the plane of the Figure. In all cases for the shorter pitch and for most cases for the longer pitch, the particles are found at the junction of disclination lines. (See also ref 10.) It is evident that both the thickness of the disclination lines and the size of the clusters are larger for the shorter-pitch sample. Thinner disclination lines, associated with the wedge geometry, can be seen in the background for both samples.
Figure 3. High-magnification birefringence images of melamine particles (d = 3 μm) in a cholesteric liquid crystal with p = 1.5 μm. Images taken (a, c) at a sample thickness of ∼5 μm and (b) at a sample thickness of ∼15 μm.
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In Figure 5, we show the clusters of particles and the birefringence of the liquid crystal at high magnification. The particles are arranged in flat plates (which was verified by viewing the same cluster from both above and below) and are often in close contact.
Figure 5. High-magnification images of clustered melamine particles (d = 3 μm) in a cholesteric liquid crystal, with sample thicknesses of approximately 15 μm. (a) A sample with p = 1.5 μm and (b) a sample with p = 0.4 μm. For the longer-pitch sample (a), one or two “cholesteric planes” between particles are frequently evident.
Figure 4. Microscopy images at 10 magnification of 0.1 vol % melamine particles in a cholesteric liquid crystal in a wedged cell using crossed polarizers. The helical axis is perpendicular to the plane of the image (well away from particles). Sample thicknesses are approximately (a, c) 5 μm and (b, d) 25 μm. The top row (a, b) shows samples with p = 1.5 μm, and the bottom row (c, d) is for p = 0.4 μm. Langmuir 2010, 26(16), 13502–13510
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Figure 6. Confocal images at high magnification of melamine particles (10 vol. %) in the nematic (top row) and the cholesteric (bottom row) with p = 0.4 μm.
The flat clusters are surrounded by broad defect lines associated with the axis of the helix turning from being parallel to the cluster to being perpendicular to the cluster. Consistent with a helical axis in the plane of the image, the spacing of the lines within the broad defect is roughly half a pitch length. Because of the large pitch, more key details are evident in Figure 5a. Here many pairs of particles can be seen that are separated by one or two lines of fingerprint texture. This suggests that layers of cholesteric aligned on one particle surface can be shared by two particles. This is not general; some particles touch while others are separated by layers of liquid crystal. Away from the particles, the cholesteric remains well-aligned. These same features could be present in Figure 5b but are unresolvable because of the shorter pitch. In principle, the confinement of particles within plates could be unrelated to particle-particle interactions and could be due to the influence of the external walls of the cell. We test this idea both by using wedge-shaped cells (where a switch to 3D aggregation for thicker parts of the cells was not observed) and by using different cells that are many millimeters thick (and do not have PVA treated/rubbed surfaces). The thicker cells cannot be used for birefringence studies, and instead we employ confocal microscopy (Figures 6, 7, and 9). Figure 6 shows the behavior of melamine particles (10 vol %) in nematic and cholesteric samples in great detail. Here the nematic is MDA-00-1444 and the cholesteric has a pitch of p = 0.4 μm. These are fluorescence confocal images taken using a 100 objective lens. The difference in the behavior of the particles in a nematic and cholesteric host is unambiguous. The top row of images shows particles in a nematic host where it is clear that the particles are forming short chains. There are occasional junctions between the chains. The bottom row of images shows particles in a cholesteric host where the particles appear to be arranged in small flat plates parallel to the base of the sample holder. We will discuss later the possible cause of this difference. In both rows of Figure 6, there is variability in the particleparticle separation. This will be analyzed in greater detail via the radial distribution function (section 3.3). 3.3. Changes in Behavior with the Cholesteric Pitch. We have begun by demonstrating that particles with planar alignment form chains in a nematic liquid crystal and flat plates in a cholesteric liquid crystal. The data presented so far concerns cholesterics where the pitch is fixed. Next we wish to look at samples 13506 DOI: 10.1021/la101420c
where the cholesteric pitch is systematically increased until it begins to approach the particle size. Figure 7 is an overview of the behavior of melamine particles (10 vol %) in a liquid-crystalline host as a function of pitch length and depth into the sample. Images were taken using fluorescence confocal microscopy. At the top is the shortest pitch (p = 0.4 μm), and at the bottom is a nematic (infinite pitch); to the left are images at the surface and to the right are images deep inside the sample (20 μm). As already discussed in some detail, in the nematic sample the particles are organized into chains whereas in all of the cholesteric samples, independent of pitch, the particles are organized into flat plates. Although this is a common feature of the cholesteric samples, there is a systematic, qualitative change with the pitch. We observe that the average number of particles in an aggregate (aggregation number) for the short pitch (top row) is much larger than the number for the long pitch (penultimate row). The aggregation number for the longest pitch is only a little larger than that for the nematic (bottom row). Using automatic particle location techniques,23 we have evaluated the distribution of cluster sizes (Figure 8). We present both the average size of the plate (aggregate number) and the proportion of clusters involving more than 10 particles. Both show essentially the same trend as a function of the pitch length. Clusters become significantly larger at the point where the pitch becomes significantly smaller than the particle size. To further support our claim that the particles in a cholesteric are organized in plates, we have resliced the confocal image stacks26 such that the distribution in the z direction is shown (Figure 9). The two columns are different locations in each stack; the rows show the different pitch lengths (as in Figure 7), where the shortest pitch is at the top and the nematic is at the bottom. It is clear from this image that the particles in the top projections are organized into small plates. In progressing from the short pitch to the longer pitch lengths, the plates of particles appear to become less flat. Equivalent resliced data for a nematic liquid crystal at the bottom of the Figure shows that the chains of particles are clustered in the z direction. For quantitative analysis, we use the radial distribution funcP tion: g(r) = Rβ δ(r - |rR-rβ|)/(4πr2δrΦ). Here rR and rβ are the (26) Rasband, W. S. National Institutes of Health: Bethesda, MD, 1997-2006; http://rsb.info.nih.gov/ij/.
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Figure 7. Overview images of melamine (d = 3 μm) particles dispersed in liquid crystals with different pitch lengths at a concentration of
10 vol %. Each row shows three images of one image stack recorded between 0 and 20 μm into the sample. (From left to right, the depth into the sample increases.) From top to bottom, the rows show images from samples with cholesteric pitch lengths of 0.40, 0.80, and 1.50 μm, and the nematic (MDA-00-1444).
positions of particles within the same plate, and Φ is the volume fraction of the sample. The particle locations have been extracted from confocal images for use in this analysis. They were separated into groups that showed the same z coordinate (to within a particle radius), and these were identified as belonging to the same plate for calculating g(r). In turn, the radial distribution functions have been used to determine the mean and standard deviation of the particle-particle separation. Figure 10 shows the radial distribution function. The principal peak for the p = 0.4 μm (27) The principal peak of the radial distribution function for the nematic sample is larger than might be expected; this is the least-viscous sample, and because of sedimentation, the effective volume fraction observed in the plane being imaged is higher than the nominal volume fraction used for normalization.
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sample is noticeably shorter and wider than those of the other two presented. This might suggest that the longer pitch and nematic27 samples have a better-formed local organization of particles. Figure 11 show the particle-particle separation and the full width at half-maximum height of the principal peak of the radial distribution function. Both quantities are shown as a function of 1/p2 (proportional to the layer compression modulus, B, of the cholesteric liquid crystal). The nematic (p = ¥) and cholesteric results are shown on the same graph. The particle-particle separation (Figure 11) grows as the pitch becomes shorter and saturates for the three shortest pitches. The width of the principal peak of the radial distribution function (Figure 11) also grows with 1/p2. In this case, the growth is slow for the nematic and DOI: 10.1021/la101420c
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long-pitch samples, with a more marked change for the shortpitch samples. In section 4, we will attempt to correlate these observations with the detailed of images of the clusters presented in Figure 5. 3.4. Aging and Sedimentation. The same region of a sample (melamine d = 3 μm, 0.1 vol %) has been viewed repeatedly over 1 week (Figure 12). It is observed that the initial arrangement of disclination lines changes slowly with time. Defects appear to be annealing a little within the first few days following sample preparation. Annealing occurs via some disclination lines disappearing altogether and others straightening out. In some places, it appears that the clusters of particles are moving closer together. Changes become unobservable after a week. To determine whether, over a long period of time, the particles would be ejected from the cholesteric host altogether we prepared samples and left them for 18 months. The samples had volume fractions of 10, 20, and 40% with p = 0.4 μm. No sedimentation is observed over the duration of the experiment. By contrast, melamine particles in a nematic host (10 vol %) sedimented within a day.
anchoring of the mesogens. Consistent with our schematic, it is possible that cholesteric layers envelope the particles; however, other defect structures are also possible. For example, the modulation observed in the concentric rings around the particles (Figure 2a) might be due to a twist originating from a defect pattern at or close to the surface; any such arrangement is difficult to resolve with optical microscopy. Because of the tangential anchoring of the mesogens at the particle surface, the helical axis, z, is homeotropically aligned at the particle surface. As shown throughout our results, a population of these particles aggregate in the form of a 2D plate. Computer simulations28 have been used to show that 2D plates will also form when particles, with surfaces favoring homeotropic anchoring, are dispersed in a nematic liquid crystal. In the nematic case, plate formation occurs perpendicular to the far-field
4. Discussion In this section, we will offer a qualitative explanation of the observed particle-plate formation and make a comparison with simulations in a related system. Furthermore, our experiments have isolated a series of trends as a function of the cholesteric pitch length (average particle-particle separation, spread of particle-particle separation, aggregation number, and plate flatness). We will try to determine how these trends relate to the underlying properties of the cholesteric host. Concentric layers of cholesteric order are observed around the particles (Figure 2a), as depicted in a simplified form in Figure 13a. This is a consequence of the particle surface favoring tangential
Figure 8. Variation in aggregation behavior with pitch obtained from the analysis of confocal images of particles in planes. Circles and left axis: average size of particle aggregates in a nematic liquid crystal and cholesteric liquid crystals of different pitch lengths. Squares and right axis: percentage of particles in aggregates containing more than 10 particles.
Figure 10. Radial distribution functions of the melamine (d = 3 μm) particles in a nematic liquid crystal and cholesteric liquid crystals of different pitch lengths obtained from the analysis of confocal images of particles in planes.
Figure 11. Graph showing the particle-particle separation from the peak position in the radial distribution function (squares, left axis) and the variation of the width of the peak (diamonds, right axis) both versus 1/p2. The values were derived from the radial distribution function shown in Figure 10.
Figure 9. Side projection of melamine particles (d = 3 μm) in a cholesteric liquid crystal created from the image stacks presented in Figure 7. From top to bottom, the rows show projections from samples with cholesteric pitch lengths of 0.40, 0.80, and 1.50 μm and the nematic (MDA-00-1444). The two columns are from different locations in each sample.
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Figure 12. Birefringence images at approximately the same position taken on days 1 and 3. The network of disclination lines is slowly rearranging. This cholesteric sample (p = 0.4 μm) contains 0.1 vol % melamine particles.
Figure 13. Cartoons showing the proposed organization of the cholesteric liquid crystal around the particles. (a) Top view of the onionlike arrangement. (b) Helical order between two particles viewed from the side; λ-1/2 lines may form in the gap. (c) Plane of particles in contact as viewed from the side.
orientation of the nematic director as a consequence of the defect loops shared between particles; the structure is dynamically arrested. A defect loop surrounding an isolated particle is called a Saturn ring, and the pattern of distortion of the nematic host has quadrupolar symmetry. We would like to consider whether the plate formation in our cholesteric samples might have a similar cause. A quadrupolar distortion will form as the helical axis, z, turns from homeotropic anchoring at the particle surface to farfield ordering perpendicular to the plane of the image. This is equivalent to the behavior of the director, n, in the nematic case. Here the similarity seems to end. The Saturn ring defect loop has a topological charge of 1/2. This means that rotating by 180 around this line will leave the system unchanged. For the nematic director, which is a headless vector, this is true. The helical axis is an axial vector; a rotation of 180 about a perpendicular axis results in a change of handedness. This means that the cholesteric cannot support Saturn ring defects. Although our system and the simulations of the nematic are similar, they are not identical. The quadrupolar distortion may still drive the plate formation, but it will not be mediated by defect lines of this type. (28) Araki, T.; Tanaka, H. Phys. Rev. Lett. 2006, 97, 127801.
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As the pitch is changed, the elastic properties of the cholesteric change with it, altering the optimum arrangement of the particles. The layer compression modulus has a prefactor proportional to 1/p2 (i.e., distortions of the bulk order are more energetically expensive at shorter pitch). Organizing the liquid crystal at the top and bottom of the particles does not by itself induce an elastic energy penalty because the planar anchoring condition is consistent with the farfield orientation of the helical axis (Figure 13b,c). By contrast, planar alignment cannot always be achieved around the particle equator (and this might result in a distortion with quadrupolar symmetry). We observe that the system minimizes the elastic energy penalty by forming flat plates of particles in the plane perpendicular to the helical axis. By clustering together in plates, the distorted liquid crystal around the equator can be shared by several particles and therefore minimized (Figure 13c). The final configuration of the liquid crystal surrounding a particle is a compromise between satisfying the preferred surface anchoring and minimizing distortion to the bulk order. The aggregation number (Figure 8) and flatness (Figure 9) show that the formation of large, flat plates of particles becomes increasingly common at shorter pitch. This supports the idea that perturbations of the cholesteric order become less likely as the layer compression modulus increases. When particles are close but not touching, fingerprint texture is sometimes observed between them (Figure 5a). This situation is pictured in Figure 13b, with the helical axis running between the two particles, giving the fingerprint texture when viewed from the top. As shown in our data, the number of pitch lengths between particles is not constant within the same sample or within the same plate. This means that the particle-particle separations may tend to be quantized in units of half a pitch length, which might have a significant influence on how the radial distribution function, g(r), varies as the pitch changes (Figure 11). When the pitch is small, the formation of cholesteric layers between particles will result in a broadening of the principal peak of g(r) and a shift in its position. For very large pitch (i.e., when p is the particle radius), the same phenomena will increase the particle-particle separation to the extent that the separation of this pair will fall outside the principal peak. Hence, it will not result in peak broadening or a shift in the average separation. If one or several helical turns of cholesteric order are forming between particles, then this could explain why the principal peak is narrow and the separation is small for long pitch lengths in Figure 3.
5. Summary Our experiments have probed the behavior of particles in the cholesteric phase of a liquid crystal. The particle surfaces promote DOI: 10.1021/la101420c
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Article
planar alignment of the mesogens. High-magnification birefringence patterns of isolated particles suggest that, at least for some pitch lengths, cholesteric layers wrap around the particles. Our results also show that collections of particles form 2D plates in the cholesteric phase; this is qualitatively different from the chains formed in the nematic phase. As the pitch of the cholesteric helix is increased (via changes in composition), the size of the plates decreases, as does the particle-particle separation. We suggest that the former may be a consequence of the decrease in the layer compression modulus whereas the latter appears to be due to the wrapping of particles in cholesteric layers. We have presented results for particles in a cholesteric liquid crystal at fixed temperature, where the pitch length was set by
13510 DOI: 10.1021/la101420c
Hijnen et al.
choosing the sample composition. These studies point the way toward novel effects in samples where the pitch is a strong function of temperature. Here we would expect disclination lines to appear suddenly (rather than be annealed away), together with steadily growing plates of particles upon cooling to shorter pitch. Acknowledgment. We are grateful to the EPSRC (EP/ E030173/1), the Nanomaterials: Chemistry and Physics program of Utrecht University, and the Erasmus program of the European Commission for financial support. We thank M. Cates, J. Lintuvuori, D. Marenduzzo, and A. Pawsey for helpful discussions.
Langmuir 2010, 26(16), 13502–13510
