pubs.acs.org/Langmuir © 2009 American Chemical Society
Structure of Multi-Component Colloidal Lattices at Oil-Water Interfaces Huan Ma and Lenore L. Dai* Department of Chemical Engineering, Arizona State University, Tempe, Arizona 85287 Received June 11, 2009. Revised Manuscript Received August 21, 2009 We have successfully assembled two-component S-PS/AS-PS (sulfate-treated polystyrene/aldehyde sulfate-treated polystyrene) and three-component S-PS/AS-PS/C-PS (sulfate-treated polystyrene/aldehyde sulfate-treated polystyrene/ carboxylate-treated polystyrene) colloidal lattices at poly(dimethylsiloxane)-water interfaces. The colloidal particles assemble into long-range-ordered structure and oscillate around their equilibrium positions. Different types of particles distribute randomly in the lattice with no obvious phase separation. In the two-component colloidal lattices, the S-PS particles form mostly sixfold lattice sites, whereas the AS-PS particles largely form fivefold defect sites. The calculated attractive capillary force is stronger for the AS-PS particles, which likely explains their tendency to aggregate compared to the S-PS particles. In addition, we have performed total force calculation and extrapolated the surface charge densities of the particles in the oil phase.
Colloidal particles at fluid interfaces have been a topic of great interest in chemistry, physics, biology, and engineering during the past decades. This is because colloidal particles are present in various industrial processes, consumer products, biological environments, and medical treatments, and many of them involve fluid interfaces. While most studies focus on the emulsifier function of colloidal particles to stabilize an emulsion (Pickering emulsion),1-7 we are interested here in the self-assembly of multicomponent colloidal lattices at oil-water interfaces. Self-assembly of colloidal particles into 2D or 3D colloidal crystals offers an effective bottom-up approach to fabricate materials with advanced functionality and unique applications, such as photonic bandgap crystals,8-11 nanoporous membranes,12,13 chemical and biochemical sensors,14 and optical devices.15 2D colloidal crystals can also be used as masks for self-assembly of nanosphere lithography,16 colloidal stamps for embossing and replica molding,17 and lenses for projection photolithography.18 In addition, the study of two-dimensional colloidal crystals at liquid interfaces is expected to inspire other related research fields. For example, it offers an alternative experimental model in physics to investigate phase transitions with molecular and “atomic” resolution, which can be manipulated easily in comparison *Corresponding author. E-mail:
[email protected]. (1) Akartuna, I.; Studart, A. R.; Tervoort, E.; Gonzenbach, U. T.; Gauckler, L. J. Langmuir 2008, 24, 7161–7168. (2) Tsuji, S.; Kawaguchi, H. Langmuir 2008, 24, 3300–3305. (3) Melle, S.; Lask, M.; Fuller, G. G. Langmuir 2005, 21, 2158–2162. (4) Stancik, E. J.; Kouhkan, M.; Fuller, G. G. Langmuir 2004, 20, 90–94. (5) Madivala, B.; Vandebril, S.; Fransaer, J.; Vermant, J. Soft Matter 2009, 5, 1717–1727. (6) Ma, H.; Dai, L. L. J. Colloid Interface Sci. 2009, 333, 807–811. (7) Chen, T.; Colver, P. J.; Bon, S. A. F. Adv. Mater. 2007, 19, 2286–2289. (8) Xia, Y.; Gates, B.; Li, Z. Adv. Mater. 2001, 13, 409–413. (9) Joannopoulos, J. D.; Villeneuve, P. R.; Fan, S. H. Nature 1997, 386, 143–149. (10) Li, J. A.; Han, Y. C. Langmuir 2006, 22, 1885–1890. (11) Ozin, G. A.; Yang, S. M. Adv. Funct. Mater. 2001, 11, 95–104. (12) Schepelina, O.; Zharov, I. Langmuir 2007, 23, 12704–12709. (13) Schepelina, O.; Zharov, I. Langmuir 2006, 22, 10523–10527. (14) Holtz, J. H.; Asher, S. A. Nature 1997, 389, 829–832. (15) Pan, G. S.; Kesavamoorthy, R.; Asher, S. A. Phys. Rev. Lett. 1997, 78, 3860–3863. (16) Kempa, K.; Kimball, B.; Rybczynski, J.; Huang, Z. P.; Wu, P. F.; Steeves, D.; Sennett, M.; Giersig, M.; Rao, D. V. G. L. N.; Carnahan, D. L.; Wang, D. Z.; Lao, J. Y.; Li, W. Z.; Ren, Z. F. Nano Lett. 2003, 3, 13–18. (17) Choi, D. G.; Jang, S. G.; Yu, H. K.; Yang, S. M. Chem. Mater. 2004, 16, 3410–3413. (18) Wu, M. H.; Whitesides, G. M. Appl. Phys. Lett. 2001, 78, 2273–2275.
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to other models such as dusty plasmas,19 magnetic bubbles,20 and electrons in helium (He-3).21 In biology, counterparts of colloidal particles also exist including the protein particles in the crystalline monomolecular cell surface layers (S-layers) of bacteria or archaea.22 Driven by potential impacts on both fundamental and applied research, very recently, colloidal lattices formed at liquid interfaces using Pickering emulsions as experimental templates have received increasing attention. Sixfold “surface crystals” were observed on the surface of either a hemispherical droplet attached on the sample cell wall23-26 or a free-floating droplet.27 Hydrophobic sulfate-treated polystyrene (S-PS) particles25,26 and poly(methyl methacrylate) (PMMA) particles23,24,27 were demonstrated to self-assemble into hexagonal colloidal lattices with interparticle spacing several times larger than the particle diameter (approximately 1 μm), respectively, whereas the 3.2-μmdiameter carboxy-coated polystyrene latex particles28 were shown to form hexagonally close-packed structure at high pH values when more surface acid groups were dissociated. Colloidal lattices on droplet surfaces open a new avenue to engineer novel structures, such as colloidosomes29 and microcapsules.30 In addition, it helps to validate the classic Thomson problem experimentally, which is to find the minimal Coulomb energy configuration of point charges on a conducting sphere.31 However, most of the 2D (19) Feng, Y.; Goree, J.; Liu, B. Phys. Rev. Lett. 2008, 100, 205007. (20) Seshadri, R.; Westervelt, R. M. Phys. Rev. Lett. 1991, 66, 2774–2777. (21) Konstantinov, D.; Kono, K. J. Low Temp. Phys. 2008, 150, 236–241. (22) Sleytr, U. B.; Sara, M.; Pum, D.; Schuster, B. Prog. Surf. Sci. 2001, 68, 231– 278. (23) Leunissen, M. E.; van Blaaderen, A.; Hollingsworth, A. D.; Sullivan, M. T.; Chaikin, P. M. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 2585–2590. (24) Leunissen, M. E.; Zwanikken, J.; van Roij, R.; Chaikin, P. M.; van Blaaderen, A. Phys. Chem. Chem. Phys. 2007, 9, 6405–6414. (25) Tarimala, S.; Wu, C.; Dai, L. L. Langmuir 2006, 22, 7458–7461. (26) Dai, L. L.; Tarimala, S.; Wu, C.; Guttula, S.; Wu, J. Scanning 2008, 30, 87– 95. (27) McGorty, R.; Fung, J.; Kaz, D.; Ahn, S.; Manoharan, V. N. In Measuring Dynamics and Interactions of Colloidal Particles with Digital Holographic Microscopy; Digital Holography and Three-Dimentional Imaging; OSA Technical Digest; Optical Society of America, 2008, DTuB1. (28) Binks, B. P.; Rodrigues, J. A. Angew. Chem., Int. Ed. 2005, 44, 441–444. (29) Cayre, O. J.; Noble, P. F.; Paunov, V. N. J. Mater. Chem. 2004, 14, 3351– 3355. (30) Bon, S. A. F.; Chen, T. Langmuir 2007, 23, 9527–9530. (31) Bausch, A. R.; Bowick, M. J.; Cacciuto, A.; Dinsmore, A. D.; Hsu, M. F.; Nelson, D. R.; Nikolaides, M. G.; Travesset, A.; Weitz, D. A. Science 2003, 299, 1716–1718.
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colloidal lattices studied so far only comprise single species particles, whereas lattices with multiple species particles are often more attractive. Very recently, several computational studies predicted that variable lattice structures may be formed by particles with different sizes at certain particle number ratios.32-34 However, the prediction could hardly be validated experimentally due to the difficulty in controlling the particle size and number ratios.35 Here, we report the success of self-assembling multicomponent colloidal lattices formed by particles with different surface chemistry, charge, and hydrophobicity. The inclusion of foreign particle species may affect the lattice structure, as well as introduce additional functionality to the colloidal lattice. In our experiments, poly(dimethylsiloxane)-in-water Pickering emulsions containing surface-treated polystyrene particles were prepared using an ultrasonic processor, Sonics VibraCell, 500 W model. The poly(dimethylsiloxane) oil (Rohodorsil Fluid 47 V5, viscosity of 5 cSt at 25 °C) and water (HPLC grade) were purchased from Rhodia and Fisher Scientific, respectively, and used as received. The solid particles were negatively charged FluoSpheres from Molecular Probes and received as 2% dispersion in distilled water with 2 mM sodium azide. We have chosen three different types of particles: sulfate-treated polystyrene particles (S-PS; with the diameter of 1.00 ( 0.03 μm, surface charge density of 0.029 C/m2 and excitation/emission wavelengths of 580/605 nm), aldehyde-sulfate-treated polystyrene particles (AS-PS; with the diameter of 1.00 ( 0.03 μm, surface charge density of 0.088 C/m2, and excitation/emission wavelengths of 505/515 nm), and carboxylate-treated polystyrene particles (C-PS; with the diameter of 1.10 ( 0.04 μm, surface charge density of 0.325 C/m2, and excitation/emission wavelengths of 540/560 nm). Each emulsion sample contains 1 g of water, 0.1 g of oil, and 0.1 g of particle or particle mixture dispersion (S-PS/AS-PS = 1:1 or S-PS/AS-PS/C-PS = 1:1:1). Typically, a sample is prepared by adding water, particle, and oil sequentially into a sample vial and processing ultrasonically in an ice-water bath 4 times at 21% amplitude for a duration of 1 s each time. When preparing multicomponent colloidal lattices, we have also tried to first add water, one type of particles, and oil, followed by an ultrasonic processing, then add the second type of particles and process ultrasonically again. The experimental observations show that the different preparation procedures do not have significant influence on the self-assembly of colloidal lattices. The colloidal structure was imaged using a confocal laser scanning microscope Leica SP2 or SP5 under ambient conditions (with a typical temperature of 21-22 °C). The particle coordinate center positions and the fast Fourier transform (FFT) pattern were analyzed using ImageJ, and the Voronoi diagrams were constructed using MATLAB. Following the above procedures, one-, two-, and three-component colloidal lattices were successfully assembled and observed on droplets pinned onto microscope glass slides. Figure 1a,b represents confocal microscope images of the AS-PS colloidal lattice and S-PS colloidal lattice, respectively. The inset FFTs of the images show six distinct first-order peaks with multiple higherorder reflections. The pattern is similar to those observed on polystyrene-polyvinylpyridine (PS-PVP) block copolymer films with ordered microdomains and can be interpretated as an indication of the long-range-ordered structure.36,37 The colloidal (32) Stirner, T.; Sun, J. Z. Langmuir 2005, 21, 6636–6641. (33) Fornleitner, J.; Lo; Verso, F.; Kahl, G.; Likos, C. N. Soft Matter 2008, 4, 480–484. (34) Rabideau, B. D.; Bonnecaze, R. T. Langmuir 2005, 21, 10856–10861. (35) Monteux, C.; Jung, E.; Fuller, G. G. Langmuir 2007, 23, 3975–3980. (36) Park, S.; Wang, J.; Kim, B.; Xu, J.; Russell, T. P. ACS Nano 2008, 2, 766–772. (37) Segalman, R. A.; Hexemer, A.; Hayward, R. C.; Kramer, E. J. Macromolecules 2003, 36, 3272–3288.
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Figure 1. Confocal microscope images of one-component colloidal lattices (a,b) and two-component colloidal lattices (c,d) at droplet surfaces. The insets show the FFT of the associated confocal microscope images. The AS-PS particles are represented in green, and the S-PS particles are represented in blue.
particles within the lattice oscillate around their equilibrium positions, as the result of constrained motion due to thermal fluctuation and underlying lattice constraint. The oscillation is in a similar way as those discussed in detail previously.25 On some of the droplet surfaces, particle aggregates were also observed coexisting with the lattice structure (see Supporting Information, Figure S1). Figure 1c,d shows representative confocal microscope images of the S-PS/AS-PS two-component colloidal lattices. The colloidal particles assemble into colloidal lattices with the particle spacing larger than the particle diameter. The FFTs show a diffuse ring. A similar pattern was observed on the PS-PVP block copolymer film with less ordered microdomains and was interpretated as an indication of the presence of a large fraction of defects.37 From both visual inspection and FFT analysis, the two-component colloidal lattice is less ordered than the onecomponent colloidal lattice. It is also interesting to note that the lattice distribution of different types of particles is random; no distinct phase separation of different types is observed. Although the two-component system contains an equal amount of the S-PS and AS-PS particles in the bulk phase, some lattices are dominated by the S-PS particles (Figure 1c) and some lattices are composed of a nearly equal number of the S-PS and AS-PS particles (Figure 1d). Lattices dominated by the AS-PS particles were hardly observed. Instead, we observed aggregates mostly formed by the AS-PS particles (see Supporting Information, Figure S1). A possible hypothesis is that the capillary attraction among the AS-PS particles is stronger than that among the S-PS particles, due to the lower hydrophobicity of the AS-PS particles. As reported by the manufacturer of the particles, the AS-PS particles are the S-PS particles modified with additional surface aldehyde groups. The aldehyde groups are more hydrophilic, and thus, the modification would make the AS-PS particle surfaces less hydrophobic than S-PS particle surfaces. The contact angles of the S-PS particles and AS-PS particles estimated from confocal microscope images are roughly 117° and 100°, DOI: 10.1021/la9021036
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Figure 3. Histograms of particle spacing in one- and two-component colloidal lattices, respectively.
respectively. The calculation of the capillary force will be presented later. To further characterize the structure of these colloidal lattices, we have constructed Voronoi diagrams and analyzed the defect number, concentration, and configuration. A Voronoi diagram is a mathematical tool to assist visualizing the topology of a lattice, which divides the space into polygons with shared sides having equal distances to the two adjacent particle center locations.37,38 Here, it can be constructed from the particle centers in snapshots of confocal microscope images. The number of polygon sides reflects the coordination number of a particle, which is the number of nearest neighbors.37-39 In an ideal triangular lattice, all particles have a coordination number of 6. Fourfold, fivefold, and sevenfold coordinated sites observed in our experiments are defined as defects, similar to previous defect analyses on simulated or experimentally observed one-component colloidal lattices.31,39,40 Figure 2a,b represents the Voronoi diagrams of the one-component colloidal lattices (Figure 1a,b). The distorted hexagonal cells indicate low local hexagonal symmetry of the lattice, and in fact, perfect hexagonal symmetry can hardly be observed due to the continuous oscillation of these particles. Figure 2c shows the Voronoi diagrams of a two-component colloidal lattice (Figure 1c) with color-coded defect sites. The defect concentration can be calculated from the counts of the defect sites and sixfold lattice sites in the Voronoi diagram of each droplet. Incomplete cells near the edges (gray color in Figure 2a-c) were not taken into account. In any of the systems, although the data are scattered, the defect
concentration does not show a significant dependence on the droplet size, which ranges from 20 to 40 μm [Supporting Information, Figure S2(a)]. So, the curvature effect is not a major factor in defect concentration variation. However, the defect concentration does vaguely show an increase with the AS-PS concentration in the two-component lattice [see Supporting Information, Figure S2(b)]. To further elucidate the effect of different particle species on the lattice structure, we present a bar chart of the counts of different polygons for the S-PS and AS-PS centered particles respectively, with 116 total counts, for the two-component system. As shown in Figure 2d, the S-PS particles form mostly sixfold lattice sites, with some sevenfold or fivefold defects, whereas the AS-PS form largely fivefold defects. This indicates that the inclusion of the AS-PS particles might be a major cause of defects in a two-component lattice due to different surface hydrophobicity and charge density. The idea of introducing foreign particle species of selected concentrations into a colloidal lattice may inspire novel and effective methods to fabricate twodimensional colloidal lattices at large interparticle separations with controllable defects, much more efficiently than manipulating one particle at a time using optical tweezers.41 The defects of controlled type, density, and location in a crystal can introduce additional functionality to the structure. For example, twodimensional defects in a three-dimensional photonic crystal can lead to a tunable pass band in the optical spectrum.42 It also appears that the two-component colloidal lattices have a wider particle spacing distribution than the one-component lattices. The histograms of interparticle distance of over 200 counts in 8-12 droplets for each system (S-PS, AS-PS, or S-PS/ AS-PS, respectively) are shown in Figure 3. The histograms of one-component systems show similar peak width, while the histogram of the two-component system shows a significantly broader peak. When we focus on the two-component system and sort the interparticle distance by particle types, we find that, on the same droplet, the interparticle distance between two adjacent S-PS particles (as-s) is always larger than that between an AS-PS particle and an S-PS particle(aAS-S), and the distance between two adjacent AS-PS particles (aAS-AS) is always the smallest. Interestingly, the ratio aS-S/aAS-AS is calculated to be 1.52 ( 0.06. We tentatively attribute the underlying physical origin of the defect structure and variation in interparticle spacing observed in two-component colloidal lattices to the differences in particle hydrophobicities and surface charge densities. To further elucidate their effects on the particle interactions in a colloidal lattice,
(38) Aurenhammer, F. Comput. Surveys 1991, 23, 345–405. (39) Libal, A.; Reichhardt, C.; Reichhardt, C. J. O. Phys. Rev. E 2007, 75, 011403. (40) Lin, B.; Chen, L. J. Chem. Phys. 2007, 126, 034706.
(41) Hoogenboom, J. P.; Vossen, D. L. J.; Faivre-Moskalenko, C.; Dogterom, M.; van Blaaderen, A. Appl. Phys. Lett. 2002, 80, 4828–4830. (42) Dechezelles, J.; Masse, P.; Cloutet, E.; Cramail, H.; Ravaine, S. Colloids Surf., A 2009, 343, 8–11.
Figure 2. (a,b) The Voronoi diagrams of Figure 1a,b. The diagram size is 16 μm 16 μm. (c) The Voronoi diagram of Figure 1c. The diagram size is 22 μm 22 μm. In a-c, the light green, white, and light blue fills represent fivefold, sixfold, and sevenfold sites, respectively; the gray fills represent incomplete cells at the edge of the lattice. (d) The bar chart of the counts of four-to-seven-sided polygons for S-PS and AS-PS centered particles in the two-component colloidal lattice generated from Voronoi diagrams of twelve different droplets.
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which primarily determines interparticle spacing, we present a force evaluation. Since the surface charge density at the particle-oil interface (σpo) is unknown, we calculate the total force (Ftotal) as a function of σpo, taking into account the Coulombic repulsion (FCoulombic) through the oil phase due to the residual charge at the particle-oil interface and the image charge in the water,43 the capillary attraction (Fcapillary) due to undulations of the three-phase contact line,44-47 and other forces (Fother) which are negligible. Ftotal ¼ FCoulombic þ Fcapillary þ Fother
ð1Þ
The Coulombic repulsion can be calculated as45
FCoulombic
9 8 > > > > > 2> = < ðApo σpo Þ 1 L ¼ 2=2 > L2 16πR2 εε0 > > > ð2 þ cos θÞ2 2 > > þ L ; : 4
ð2Þ
where Apo = 2πR2(1 - cos θ) is the area of the particle-oil interface, L = a/(2R) is the dimensionless distance between particle centers, R is the particle radius, θ is the contact angle measured through the water phase, ε is the dielectric constant of oil, and ε0 is the permittivity of vacuum. The experimental system fulfills the assumptions of eq 2: the particle size is much larger than the Debye length and the contact angle is not very small. The Debye length k-1 is 22.3 nm for 0.18 mM sodium azide in water, calculated from k=e(ΣiZi2ni/εwεokT)1/2,45,48 where Zi and ni are the charge and bulk concentration of species i, e is the elementary charge, εw is the dielectric constant of water (εw =79.6 at 294.65 K), k is the Boltzmann constant, and T is the temperature. Measured average values of L of 4.1 μm for S-PS and of 2.6 μm for AS-PS in Figure 1c are used in our calculation and a FCoulombic vs σpo plot is shown in Figure 4a. We carefully selected σpo = 3.8 10-5 C/m2 for S-PS as the lower limit, corresponding to the minimum reported value for the degree of dissociation at particle-oil interfaces (Rpo) of sulfate polystyrene particles (3.3 10-4),49 and σpo = σpw = 0.029 C/m2 for S-PS as the upper limit, which equals the surface charge density at the particle-water interface (σpw). In Figure 4a, FCoulombic increases with σpo and the value ranges from 10-13 to 10-6 N. The capillary force can be calculated as45 Fcapillary ¼ -
3πγow δ2 sin4 θ 2RL5
among the AS-PS particles than the S-PS particles at same distances since the contact angle of the AS-PS particles is closer to 90°. This offers a possible explanation for why the AS-PS particles have a stronger tendency to aggregate than the S-PS particles. The calculated Fcapillary values at L equals 4.1 μm for S-PS and 2.6 μm for AS-PS are listed in Table 1 and are used to calculate Ftotal. Fother refers to other interaction forces in which their magnitudes are negligible, thus ignored in our calculation of the total force; most of them are listed in Table 1. First, dipolar pair interaction has been proposed to be long-range and plays an important role in some colloidal lattices.50,51 The dipolar repulsive force due to dipoles at the particle-oil interface can be calculated using the following expression46
ð3Þ
where γow is the interfacial tension of the oil-water interface, which is measured to be 44.6 mN/m using a Kr€ uss K100 tensiometer, and δ is the amplitude of the three-phase contact line undulations, which is approximately 50 nm for S-PS and ASPS particles.44 Note that, at constant L, Fcapillary reaches maximum at θ = 90°; thus, the attractive Fcapillary is always stronger (43) Horozov, T. S.; Aveyard, R.; Clint, J. H.; Binks, B. P. Langmuir 2003, 19, 2822–2829. (44) Stamou, D.; Duschl, C.; Johannsmann, D. Phys. Rev. E 2000, 62, 5263– 5272. (45) Horozov, T. S.; Aveyard, R.; Binks, B. P.; Clint, J. H. Langmuir 2005, 21, 7405–7412. (46) Horozov, T. S.; Binks, B. P. Colloids Surf., A 2005, 267, 64–73. (47) Kralchevsky, P. A.; Denkov, N. D.; Danov, K. D. Langmuir 2001, 17, 7694– 7705. (48) Kohonen, M. M.; Karaman, M. E.; Pashley, R. M. Langmuir 2000, 16, 5749–5753. (49) Aveyard, R.; Binks, B. P.; Clint, J. H.; Fletcher, P. D. I.; Horozov, T. S.; Neumann, B.; Paunov, V. N.; Annesley, J.; Botchway, S. W.; Nees, D.; Parker, A. W.; Ward, A. D.; Burgess, A. N. Phys. Rev. Lett. 2002, 88, 246102.
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Figure 4. (a) Coulombic force as a function of the surface charge density at the particle-oil interface. (b) Total force as a function of the surface charge density at the particle-oil interface. The solid lines represent forces between the S-PS particles, and the dashed lines represent the AS-PS particles. The dotted line illustrates the calculation of σpo for AS-PS from the σpo value of S-PS (see text for details).
Fdipole-oil ¼
3pn 2 64πεε0 R4 L4
ð4Þ
where pn - πpσR2 sin2 θ is the dipole moment of the part of particle in contact with oil, p is the average dipole moment of one polar group, and σ is the surface dipole density. The average dipole moment of one polar group is estimated to be on the order of 10-30 C 3 m. The surface dipole density approximately equals the number of dissociable groups on the particle surface, which can be estimated by dividing the surface charge density at a complete dissociation by the elementary charge. The σ value is 0.72 nm-2 for S-PS and 2.20 nm-2 for AS-PS. The calculated Fdipole-oil is 10-18 to 10-16 N for the S-PS particles and 10-16 to 10-14 N for the AS-PS particles, thus contributing very little to the total force. A different type of dipolar repulsion (Fdipole-water) may have originated from the dipole perpendicular to the oil-water (50) Pieranski, P. Phys. Rev. Lett. 1980, 45, 569–572. (51) Hurd, A. J. J. Phys. A 1985, 18, 1055–1060.
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Table 1. Possible Interactions between Two S-PS Particles Separated at 4.1 μm and Two AS-PS Particles Separated at 2.6 μm at the Water-Poly(dimethylsiloxane) Interface
FCoulombic/N Fcapillary/N Fdipole-oil/N Fdipole-water/N Fcapillary-gravity/N Fvan der Waals/N
S-PS
AS-PS
(see Figure 4a) -5.9 10-13 10-18 to 10-16 1.4 10-16 -2.9 10-25 -(10-18 to 10-19)
(see Figure 4a) -8.7 10-12 10-16 to 10-14 9.6 10-15 -3.6 10-25 -(10-18 to 10-19)
interface due to the asymmetric distribution of the free ions at the particle surface and can be calculated by45,51 F dipole-water ¼
3π2 ε sin2 θσ p 2 w 8ε0 εw 2 R2 k4 L4
ð5Þ
where σpw is the surface charge density at the particle-water interface. The calculated value of Fdipole-water is approximately 1/1000 of Fcapillary, and thus can be neglected. Dipoles may also originate from the surface-dissociated groups and the cloud of counterions near the particle-water interface.54 However, the dipolar electrostatic interaction of this origin has been shown to be negligibly small for hydrophobic particles54 and is not taken into account in the presented total force calculation. In addition, the capillary attraction may also have different origins. Other than the capillary force we have included in the calculation, which is due to undulations of the three-phase contact line, the capillary force may also be induced by the deformation liquid interfaces by the electrostatic field around the charged colloidal particle or the weight of a colloidal particle. The part induced by the electrostatic field has been shown to be short-ranged and significant only at interparticle spacing smaller than twice the particle diameter.45,52 The gravity induced capillary force25,53 (Fcapillary-gravity) has a value on the order of 10-25 N, which can be neglected. Finally, the van der Waals force (FvanderWaals) between micrometer-sized particles25 and the hydrophobic interaction54 have also been shown to be negligibly small at large particle spacing and are not taken into account in the presented total force calculation. Figure 4b is a plot of Ftotal vs σpo for the S-PS and AS-PS particles, respectively. Stamou and co-workers stated that “hexagonal order is very rare unless one restricts the area available to the system, bringing the particles so close together that the repulsive term dominates.”44 Here, we assume that Ftotal between any pair of particles equals a colloidal lattice at equilibrium. As shown in Figure 4b, Ftotal is mostly repulsive (positive values), and at equal Ftotal, σpo for S-PS is always larger than σpo for AS-PS except at very low σpo where Fother cannot be neglected. In the inset of Figure 4b, we graphically illustrate the calculation of σpo for the AS-PS particles. With the estimated Rpo value of 0.01 for the S-PS particles,55 the Rpo is calculated correspondingly to be 1195 μC/m2. Thus, Ftotal can be determined, and the corresponding σpo for the AS-PS particles, which is constrained by the same Ftotal, can be obtained. Using the six pairs of interparticle distance values obtained experimentally, the average σpo for AS-PS is determined to be 635 ( 42 μC/m2, which is much smaller than the σpo for S-PS. The larger σpo values of the S-PS particles are (52) Danov, K. D.; Kralchevsky, P. A. J. Colloid Interface Sci. 2006, 298, 213– 231. (53) Chan, D. Y. C.; Henry, J. D.; White, L. R. J. Colloid Interface Sci. 1981, 79, 410–418. (54) Martinez-Lopez, E.; Cabrerizo-Vilchez, M. A.; Hidalgo-Alvarez, R. J. Colloid Interface Sci. 2000, 232, 303–310. (55) Aveyard, R.; Clint, J. H.; Nees, D.; Paunov, V. N. Langmuir 2000, 16, 1969– 1979.
11214 DOI: 10.1021/la9021036
Figure 5. A representative confocal microscope image of a threecomponent colloidal lattice (bulk concentration of S-PS/AS-PS/CPS at 1:1:1). FFT is shown as the inset. The scale bar represents 20 μm. Blue, green, and red represent the S-PS, AS-PS, and C-PS particles, respectively.
consistent with Horozov and co-workers’ result that more hydrophobic silica particles have larger σpo than less hydrophobic silica particles.45 A possible explanation given by the authors is the surface charge of particle-oil interfaces by donor-acceptor interactions, which involves an electron transfer.45,56 Both Horozov’s and our experimental results indicate that σpo strongly depends on the hydrophobicity or the contact angle θ. Other parameters which might also influence σpo include the particle size and liquid-phase compositions. More experiments are needed for a better understanding of the origin and dominating factors of σpo. The force evaluation on the two-component colloidal lattices shed more light on the interaction among colloidal particles at the oil-water interfaces, which is important in assembling lattices of desirable structures and spacing. Finally, following similar procedures but employing a third species C-PS, three-component S-PS/AS-PS/C-PS colloidal lattices can be self-assembled, as shown in Figure 5. Similar to the two-component colloidal lattices, the particles assemble into colloidal lattices with interparticle distance larger than the particle diameter and oscillate around their equilibrium positions. No distinct phase separation of different particle types was observed. Particle aggregates were also observed on some particle surfaces. Surprisingly, the FFT of the confocal microscope image (Figure 5 inset) shows azimuthally smeared peaks, which indicates that the three-component lattice is less ordered than the one-component lattice but more ordered than the two-component lattice. More quantitative investigation is in progress to explain this observation. In summary, the one-, two-, and three-component colloidal lattices were successfully assembled at poly(dimethylsiloxane)water interfaces. The colloidal particles assemble into long-rangeordered structure and oscillate around their equilibrium positions. Different types of particles distribute randomly in the lattice with no obvious phase separation or pattern. In the two-component colloidal lattices, the S-PS particles form mostly sixfold lattice sites, whereas the AS-PS particles largely form fivefold defect sites. The calculated attractive capillary force is stronger for the AS-PS particles, which likely explains their tendency to aggregate compared to the S-PS particles. In addition, we have performed total force calculation and extrapolated the surface charge densities of the particles in the oil phase. Acknowledgment. We are grateful to the W. M. Keck Bioimaging Laboratory in the School of Life Sciences at the (56) Lyklema, J. Adv. Colloid Interface Sci. 1968, 2, 67.
Langmuir 2009, 25(19), 11210–11215
Ma and Dai
Arizona State University for instrumental usage. The MATLAB program for Voronoi diagram was developed within the Department of Scientific Computing at the Florida State University. We also thank Professor Bryan D. Vogt for helpful discussions on the lattice order analysis. This work is supported by the National Science Foundation (CBET0922277).
Langmuir 2009, 25(19), 11210–11215
Letter
Supporting Information Available: Representative confocal microscope images of particle aggregates coexisting with lattice structure on droplet surfaces observed in the oneand two-component systems as well as the dependence of defect concentration on droplet size and AS-PS particle concentration. This material is available free of charge via the Internet at http://pubs.acs.org.
DOI: 10.1021/la9021036
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