Direct Visualization of Spatiotemporal Structure of Self-Assembled

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Direct Visualization of Spatiotemporal Structure of Self-Assembled Colloidal Particles in Electrohydrodynamic Flow of a Nematic Liquid Crystal Yuji Sasaki,*,† Hikaru Hoshikawa,† Takafumi Seto,† Fumiaki Kobayashi,† V. S. R. Jampani,*,‡ Stephan Herminghaus,‡ Christian Bahr,‡ and Hiroshi Orihara† †

Division of Applied Physics, Faculty of Engineering, Hokkaido University, North 13 West 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan ‡ Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany S Supporting Information *

ABSTRACT: Characterization of spatiotemporal dynamics is of vital importance to soft matter systems far from equilibrium. Using a confocal laser scanning microscopy, we directly reveal three-dimensional motion of surface-modified particles in the electrohydrodynamic convection of a nematic liquid crystal. Particularly, visualizing a caterpillar-like motion of a selfassembled colloidal chain demonstrates the mechanism of the persistent transport enabled by the elastic, electric, and hydrodynamic contributions. We also precisely show how the particles’ trajectory is spatially modified by simply changing the surface boundary condition.

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INTRODUCTION Systems where surface-treated inclusions are immersed in a unidirectionally ordered anisotropic fluid, i.e., nematic liquid crystals (NLCs), have attracted enormous scientific interest in the past decade or so. In NLCs, the average molecular orientation is usually characterized by the unit vector n, called the director. The director distortion around the particles due to the so-called anchoring effect is accompanied by topological defects, which shows unique physical properties different from the isotropic counterparts. It is well-known that a hyperbolic point defect induced around the spherical particle with homeotropic anchoring forms an elastically dipolar structure that gives rise to the anisotropic interaction between particles,1−3 also leading to unconventional self-assembled structures from one to three dimensions (3D).4−6 In addition to the static properties, colloidal dynamics is quite unique in anisotropic fluids. Even simple Brownian diffusion shows anisotropic properties,7 and local deformable structure plays an essential role in 3D.8,9 Particularly, recent progress on particle transportation in NLC matrix using ac electric fields shed a new light on dynamic properties of nematic colloids.10−13 In NLC, the transport of dipolar colloids is initiated by an unbalancing induced ionic charge due to the asymmetric director field around the particle.10,11 This concept of liquid crystal enabled electrophoresis (LCEEP) is applicable to a swarming motion of colloids by photoactivated surface14 and a caterpillar-like motion enabling directed cargo transport.15 Recently, there is an increasing demand for controlled motion of small particles in fluid systems, while these are © 2015 American Chemical Society

nonequilibrium states that require further fundamental scientific progress. The spatial and temporal characterization is of special importance for 3D motion, which is ubiquitous in various fields of active matter systems such as collective phenomena in biological systems,16 squirmers,17 and directed self-assembly.18−20 In liquid crystal media, more complex effects including surface anchoring at the interfaces, hydrodynamic flow, elastic contribution at local structure, and external fields could be considered. This is closely related to hydrodynamics of liquid crystals under microfluidic environments.21,22 In this article, we explore the spatiotemporal dynamics of surface-modified particles subjected to a weak hydrodynamic flow of an anisotropic fluid. We focus on our recent finding of a unique caterpillar-like motion of self-assembled particles15 enabled by the electrohydrodynamic convection (EHC). Although, in the earlier work, the stereoscopic approach was tested only for the single particle, the data lack the information on the particles’ absolute location in the cell. To unveil the whole mechanism precisely, a confocal microscopy observation was employed. This is a powerful technique that has shown, for example, the levitation of colloids in NLCs, colloidal locations, interactions in chiral nematic medium, structural relaxation of colloidal clusters near the colloidal glass transition, and so on.23−27 However, experiments especially with regard to the Received: February 4, 2015 Revised: March 9, 2015 Published: March 16, 2015 3815

DOI: 10.1021/acs.langmuir.5b00450 Langmuir 2015, 31, 3815−3819

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Langmuir dynamic behavior in anisotropic fluids have been quite limited so far. Here, we show that three-dimensional direct observation plays a decisive role for the particle dynamics in anisotropic fluids. We successfully characterize the relationship between the flexible colloidal structure and the local interactions creating persistent controlled dynamics.

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(UApo/340, Olympus). The actuator is operated at 0.5 or 1 Hz triangular wave. One confocal image is constructed using one-half of triangle wave, and the viewing volume is 173 μm × 43 μm × 86 μm. The position determined by the fluorescence intensity is within a resolution of ∼2 μm.

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RESULTS AND DISCUSSION Single Particles with Radial Anchoring. First, the data for a single elastic dipole are shown in Figure 2. The boundaries

EXPERIMENTAL SECTION

We used the NLC compound MBBA ((4-methoxybenzylidene)-4butylaniline, Aldrich; see Figure 1A) which possesses a negative

Figure 1. Schematic illustrations of cross-sectional director profile for (A) planar alignment V0 < Vth and for (B) counter-rotating EHC rolls, V0 ⩾ Vth. The solid curves show the deflected light path by lens effect in the EHC. dielectric anisotropy of Δϵ = −0.65. Fluorescent silica particles (Micromod) with a mean diameter 2R = 3.0 μm are treated with N,Ndimethyl-N-octadecyl-3-aminopropyltrimethoxysilyl chloride (DMOAP) to induce perpendicular anchoring or N-methyl-3aminopropyltrimethoxysilane (MAP) for planar anchoring of the nematic director on the particle surface. The nematic colloidal solution was prepared by adding a small amount of surface-treated particles into the NLC. The NLC is filled in sample cells consisting of indium tin oxide (ITO)-coated glass plates spin-coated with a thin layer of polyimide and unidirectionally rubbed for providing a uniform orientation of n along the rubbing direction (planar anchoring) (Figure 1A). To construct a proper confocal image, the particles motion should be sluggish enough for the frequency of the piezo actuator. Practically, the speed of EHC flow decreases as the increase of the cell thickness, while the image quality of the thicker cell suffers from the effect of the birefringence of NLC. To satisfy both conditions, we decided to use the cell thickness of d ∼ 60 μm. The cell thickness is maintained using glass beads as spacer and is confirmed by standard interferometry. The ac voltage V = V0 cos(2πf t) is applied between the glass plates through the ITO contacts so that the electric field is parallel to the zdirection. The frequency is 50 Hz. The experiments are carried out at room temperature. When V0 exceeds a threshold value of Vth 0 ∼ 8 V, the effects of a positive conductivity anisotropy and a negative dielectric anisotropy induce the EHC as shown in Figure 1B. At the rotational center of EHC, n orients by an angle θ0 to the rubbing direction. The periodic director structure can be approximated as nz(x,z) = θ0 sin(πx/L) cos(πz/d), where L is the width of the stripe pattern. Because of the optical anisotropy Δn = ne − no where ne = 1.75 and no = 1.54 for MBBA, the refractive index of LC molecules is given as n = neno(no2 cos2 θ + ne2 sin2 θ)−1/2 to the polarized light parallel to the rubbing direction. Thus, the lens effect makes a optically modulated structure under polarizing microscope (Figure 1B). The regular pattern of parallel stripes due to the stationary EHC rolls is often referred to as Williams domains.28−31 A confocal laser scanning microscope (CLSM) observation is made to visualize the location of the particles in the EHC. We use a Nipkow disk-type confocal scanning unit (CSU22, Yokogawa) based on an inverted microscope (IX71, Olympus). Images are taken by a highspeed digital camera (C11440, Hamamatsu). Cross-sectional images are constructed by using a piezoelectric actuator (P-721.10, PI) equipped with a 40×/NA = 1.15 water immersion objective lens

Figure 2. Director field around spherical particle with homeotropic anchoring (A) and planar anchoring (B). (C) shows the velocity dependence on the electric-field strength. Motion of a single dipolar particle in MBBA (D−F). Figures correspond to the LCEEP effects (D), motion under a small EHC (E), and under a well-formed EHC (F). The dashed lines for (F) are guides to the eye for showing the boundary of the rolls added from the polarizing microscope observations. (G) is a typical motion of a boojum colloid which circulates at the outermost of a roll. (G) A boojum colloid circulating near the rotational center. The applied voltages used are 7.5 V for (D), 7.8 V for (E), 8.1 V for (F), and 8.4 V for (G, H). Scale bar: 20 μm. The height of the graph corresponds to the cell thickness.

of the NLC and glass substrates, i.e., z = 0, d are confirmed by using firmly glued particles. Since the density of silica particles (ρp ∼ 1.8 g/cm3) is larger than that of NLC (ρLC ∼ 1 g/cm3), the net force of the buoyancy and gravity is 4πR3(ρLC − ρp)g/3 ∼ −0.1 pN, where the gravitational constant g ∼ 9.8 m/s2. However, the particles with radial anchoring, which accompanies a topological point defect (Figure 2A), do not perfectly settle down at the bottom substrate.11,23 This is because the particle at z = h feels an elastic repulsion ∼3A2πK(R/h)4 from the bottom substrate associated with the director distortion that lifts up the position in the z-direction.1,11,23 In our case, the height h balanced is around 10 μm without electric fields. Assuming the elastic constant K around 5 pN for MBBA, the numerical factor A depending on the anchoring around the particles amounts to ∼2.0, which is a reasonable value compared to other experiments. For small voltage V0 below a threshold value Vth 0 ∼ 8 V, the texture of the cell remains the same uniform planar alignment as observed at zero electric field (Figure 2D). The LCEEP effect moves the elastic dipole to the opposite direction of the 3816

DOI: 10.1021/acs.langmuir.5b00450 Langmuir 2015, 31, 3815−3819

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arising from the inhomogeneous director field in the EHC roll have a significant effect. Single Particles with Tangential Anchoring. When the colloidal surface anchors liquid crystal molecules in the tangential direction, two point defects, so-called boojums, appear on the particle surface (Figure 2B).38 In contrast to the homeotropic anchoring, the director distortion around the particle is now symmetric and the LCEEP effect is not present; i.e., there is no driving force for a directed motion. Accordingly, the particle circulates mainly within an EHC roll. The radius of circulation depends on the initial location of the particles. The circulating particles provide also information on the flow of the LC molecules and the flow velocity in the EHC rolls. The speed of particles near the outermost of rolls is slow, whereas it is weakly dependent on the location inside the roll. As shown in Figure 2G, the confocal measurements reveal that the particles can move around the outermost of the EHC roll in contrast to the dipole particles, indicating the weak elastic repulsion owing to the different boundary condition. The rotational period is very long because the flow speed is zero at z = 0, d. Figure 2G takes 54 s for a circulation, while the rotational period tends to become faster as the rotational center is approached. We find, for instance, that the period is around 16 s near the rotational center as shown in Figure 2H, although smaller particles must be used for quantitative discussion. Hopping to neighboring rolls can be observed from time to time since the process is allowed only for the particle positioned near outermost of EHC rolls. Dynamics of a Self-Assembled Colloidal Chain. After having revealed the motion of single particles, we mention the results for elastically connected dipolar particles, which show more intriguing colloidal dynamics. We prepare a chain made of 35 elastic dipoles by an optical manipulation technique often used for nematic colloids.5 For the sake of convenience, first we describe the results in well-formed EHC. In order to link the structure of the colloidal chain to convective rolls, the observation is made under polarizing microscope by adjusting the electric field strength sufficiently. After obtaining a stable caterpillar motion together with Williams domains, the measurement is quickly switched to the confocal mode without changing the electric filed strength to maintain the same motion. The snapshots of confocal image is shown in the left panel of Figure 3 (see also Supporting Information Movie 1). The mean x-directional speed is 0.95 μm/s. Thus, the displacement of the positions by a single scan is smaller than 1 μm. The shape deformation of the colloidal chain is nearly identical with respect to the glide plane, z = d/2 (for instance, see Figure 3A for t = 0 s and t = 24 s), also indicating little optical deflection due to small θ0. In contrast to the trajectory of a single particle, the moving chain does not form perfect squares but rather retains a curved shape, probably in order to maintain the self-assembled structure. We find that the chain locates in close proximity to the substrates, which demonstrates the repulsion ∝ h−4 from the substrate is essentially important for the persistent motion. Using the image taken by polarizing microscopy as shown in Figure 3B, it is possible to map the colloidal chain structure in the director profile of EHC. Figure 3B well corresponds to the snapshots at t = 32 s. We can easily find the boundary of the rolls as illustrated, from which, importantly, it is demonstrated that the chain passes closer to the center of the roll than the boundary. Thus, there is a phase shift between the boundaries of rolls and the trajectory. Surprisingly, the maximum angle to

point defect with a constant levitating height. The velocity increases nonlinearly with v ∝ E02, where E0 = V0/d (Figure 2C).10,11,32 Near the threshold of EHC, the velocity amounts to ∼0.28 μm/s. The force acting on the particle from the LCEEP can be estimated as F = 6πηRv ∼ 0.79 pN. Here the viscosity η ∼ 0.05 Pa·s. Although the occurrence of the small EHC cannot be seen under polarizing microscope, interestingly the trajectory in the z-direction starts to undulate below the middle height of the cell, z ≲ d/2 (Figure 2E). In this region, particles are subject to two-directional flow along and against the transport due to the counter-rotating rolls. It is reasonable to assume that the flow speed, u, of EHC corresponds to the particle speed from which the LCEEP contribution is subtracted. At this stage, the LCEEP effect (v ∼ 0.3 μm/s) is still more dominant than that of EHC (u ∼ 0.1 μm/s) as shown in Figure 2C. The force acting on the particle by the convective flow is comparable to the gravitational effect ∼0.1 pN. The convective flow of EHC is sufficient for lifting the particles up or down. On the other hand, by taking a closer look at the trajectory in Figure 2E, it is seen that the particle speed is not constant, implying a small effect of EHC in the x-direction compared to the LCEEP contribution. It must be mentioned that the intensity of fluorescent light from the particle decreases as they are closer to the upper substrate for V ⩾ Vth 0 . This would be qualitatively assigned to the increased molecular fluctuations in EHC rolls. Further increase of the electric field leads to the sufficiently formed hydrodynamic convection, leading to visible Williams domains under microscope observation. At this stage, the particle undulation starts to apparently cross the midplane of the cell. Figure 2F shows a confocal image where the roll boundaries are marked with dashed lines from the polarizing microscope observation. It is seen that the particle position deviates from the hydrodynamic stream line near the boundaries when it goes up or down. The trajectory is almost a square shape which is symmetric along the z-direction. We notice that the lens effect has little influence on the apparent position of the particle. Namely, as shown in Figure 1B, the maximal displacement Δx of deflected light at z = d attains only a small value, which also indicates a small tilt angle θ0 in the center of a convection roll through the relation of Δx/d = 2θ0n̂/(1 + n̂)π, where n̂ = 1 − (ne/no)2. The distortion angle θ0 can be estimated by the polarizing microscopy image of EHC.33,34 For small values of θ0, the light intensity variation is ΔI/I ∼ 4θ0nd̂/(1 + n̂)λ, where λ is the wavelength of the rolls. The calculated value from our system shows ΔI/I ∼ 0.36, giving rise to θ0 ∼ 0.1 rad. This is consistent with our assumption, and the resulting displacement is of the order of 1 μm. Considering the resolution of the confocal images, the observed displacement does not give critical influence for the trajectory. Simultaneously, a small value of θ0 easily eliminates the following possibilities: Regarding the elastic force induced by the director gradient, the deformed length ξ of the director field is characterized as the reciprocal of the director gradient, i.e., ξ−1 ∼ ∂ni/∂xj (i, j = x, z) ∼ θ0/d. On this view, the free energy density is Fe ∼ (K/2)(∂ni/∂xj)(∂ni/∂xj) ∼ Kθ02/2d2. When the deformed space is replaced by the particle volume, ∼R3, the elastic force for the particle is given as ∼−Kθ02R3/2d ≪ 1 pN,11,35 which is negligible in the present case. Moreover, for MBBA, the dielectric anisotropy (Δϵ ∼ −0.65) is around 10−20 times smaller than in common cyanobiphenyl compounds such as 5CB and E7 (Δϵ ∼ 10). Thus, it seems that neither the elastic forces nor the dielectric forces36,37 3817

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2) by a gradual increase of the electric field from zero. Under no electric field, we see that the whole colloidal chain levitates by ∼10 μm from the bottom substrate. The levitating height is irrespective of the number of particles within the resolution of our measurements. The chain does not show considerable motion below the threshold value; i.e., the LCEEP is less effective for longer chains. Here the speed is ∼0.1 μm/s, which crudely amounts to around one-third of the maximum speed of a single particle below Vth 0 . This is because the role of the asymmetric director distortion at both ends of the chain becomes small relative to the entire size. Using the above findings obtained for well-formed EHC, the expected positions of center of rolls are illustrated in Figure 3C. We can see that first some part of chain is lifted up by the emergence of the convective flow. The force must be larger than the gravitational effect. The decreased LCEEP effect is still comparable to the Stokes drag force from the EHC. On the other hand, the flow pointing to the negative z-direction at the boundary of counterrotating rolls does not bend the colloidal chain that does not reach the bottom substrate because the elastic repulsion between the colloid and substrates hinders the chain to move down more than certain extent as with single elastic dipoles. Thus, the serpentine structure is formed at around z = d/2. During the development to the well-formed William domains, in this case, the tail part of the chain starts to move upward and creates the undulation (t = 100 s to t = 120 s of Figure 3C). As the field strength approaches the threshold, the caterpillar structure of colloidal chain is formed, and its transportation of the chain subject to the hydrodynamic flow starts. Eventually, at sufficiently high field strength the speed of the colloidal caterpillar increases dramatically where the hydrodynamic effect is transmitted to the whole structure continuously from counter-rotating roll to roll. We can also obtain the information on the deflection of light path.

Figure 3. Cross-sectional view of the motion of a colloidal caterpillar by CLSM. Left panel (A) corresponds to the motion in a welldeveloped EHC. A snapshot of polarizing microscopy (B) corresponds to the image for t = 32 s of (A). Right panel (C) shows a transient process of a colloidal chain as the applied field is increased. Dashed lines are guide to eyes for the drift of the rolls. For both panels, solid ovals and circles denote the EHC rolls predicted by the measurements.

the x-direction is 80° (see Figure 3A for t = 16 s). Since the individual particles of the chain align their dipolar axis along the local director (which is along the x-axis ± θ0), the elastic pair interaction between two particles would be very weak or even repulsive.39 One possibility to retain an attractive interaction between two neighboring particles in the chain would be a transformation of the hedgehog point defect to a −1/2 disclination ring.38 Indeed, the regions where the chain moves up (or down) are jammed with particles, which could modify the point defect into a moderate shape. However, to confirm this assumption, more precise data including the director profile near the particle would be needed. We notice that the deformation of the colloidal chain is due to the hydrodynamic force from upstream (or downstream) lines near the boundary of rolls. Moreover, the light intensity of the fluorescent particle gives information on the deflected light passing through the EHC. As a typical example, we confine our attention to Figure 3A at t = 32 s where the light path is schematically drawn besides two counter-rotating rolls. The chain near the left side of the counterclockwise roll has very weak intensity, while the intensity becomes stronger in the middle of two rolls, i.e., the EHC boundary. Even though the value of θ0 is small, the collected light has a significant effect as a whole as we observe the Williams domains from polarizing microscope. Thus, it is possible not only to study the hydrodynamic effects but also to confirm optical information by tracking the particles. On the basis of the above information, we further study the forming process of the undulating caterpillar structure of the colloidal chain (Figure 3C and Supporting Information Movie

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SUMMARY In summary, we have investigated the three-dimensional spatiotemporal behavior of colloidal particles and colloidal chains in electrohydrodynamic convections rolls of a nematic liquid crystal. Direct tracking of particles by confocal laser scanning microscopy revealed the importance of the hydrodynamic flow, the ac electrophoresis (LCEEP) effect, and the elastic forces. Namely, the flow of EHC dominantly determines the shape of the self-assembled particles in motion, whereas the particles are not allowed to touch the substrates due to the repelling elastic interaction that sharply increases in the close vicinity of them. The LCEEP contribution plays a role for putting the particles on the persistent trajectory, which is visualized by the confocal observation. In this work, we used only MBBA and a fixed particle size. The detailed experiments by changing liquid crystals and the size of particles would be interesting. More importantly, we believe that our results and approach could be applicable to various dynamical colloidal systems under the microfluidic environments consisting of anisotropic fluids.

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ASSOCIATED CONTENT

S Supporting Information *

Movies S1 and S2 (20× speed) for a self-assembled colloidal chain obtained from a confocal laser scanning microscopy. This material is available free of charge via the Internet at http:// pubs.acs.org. 3818

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (Y.S.). *E-mail [email protected] (V.S.R.J.). Present Address

V.S.R.J.: RIKEN Center for Emergent Matter Science (CEMS), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partly supported by a Grant-in-Aid for Scientific Research on Innovative Areas ”Fluctuation & Structure” (No. 25103006) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

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DOI: 10.1021/acs.langmuir.5b00450 Langmuir 2015, 31, 3815−3819