Confined Assemblies of Colloidal Particles with Soft Repulsive

Article pubs.acs.org/JACS

Confined Assemblies of Colloidal Particles with Soft Repulsive Interactions Gaoxiang Wu,† Hyesung Cho,† Derek A. Wood,‡ Anthony D. Dinsmore,‡ and Shu Yang*,† †

Department of Materials Science and Engineering, University of Pennsylvania, 3231 Walnut Street, Philadelphia, Pennsylvania 19104, United States ‡ Department of Physics, University of Massachusetts Amherst, Hasbrouck Lab, 666 North Pleasant Street, Amherst, Massachusetts 01003, United States W Web-Enhanced Feature * S Supporting Information *

ABSTRACT: We investigate the microconfinement of charged silica nanoparticles dispersed in refractive index matching monomers in poly(dimethylsiloxane) (PDMS) porous membrane. Here, the silica colloidal particles interact with each other and the pore wall via electrostatic double layer forces. Different from the hard sphere systems where the assembled morphologies are prescribed by the diameter ratio between the cylindrical confinement and the nanoparticles, here we observe a much richer variety of assemblies that are highly sensitive to both bulk and local nanoparticle concentration with fixed particle size and channel size. The experimentally observed assembly morphologies are consistent with theoretical predictions from the literature, based on Yukawa potential in the low packing density regime. Also, most of the configurations found in the experiment are well described by computer simulations using pairwise additive long-range repulsive interactions, demonstrating the ability to control the system to obtain a desired structure.

■

INTRODUCTION Spherical colloidal particles with isotropic interactions pack into phases with high coordination numbers, including face centered cubic (fcc) and body centered cubic (bcc) structures, to minimize free energy. Under physical confinement, however, interfacial forces, structural frustration, and symmetry breaking can play more dominant roles in determining the organization of colloidal particles. As a model system, colloidal assemblies in cylindrical confinement have drawn considerable interests in the soft matter community. Based on the hard sphere packing model in cylindrical channels, researchers have shown both experimentally1−14 and theoretically15−23 that the colloidal particles can pack into a wide variety of programmed morphologies (e.g., zigzag, helical, zipper-like wire structures) and chirality depending on the ratio of pore diameter vs particle diameter,16,17 the competing interactions, and the boundary effects.11 The spontaneous formation of spirals or so-called phyllotaxis is common in biological systems,15 including plants (e.g., sunflower seeds and leaves and pine cones),24 DNA and protein assemblies,25 collagen fibrils,18 microfilaments of actin, and molecular microtubules.26 At nanometer scale, the structural arrangement of fullerene C60 or water molecules confined in nonpolar pores, for example, carbon nanotube (CNTs), offers significant insights into biological functions such as gating and proton flow.27 Study of packing and orientation of molecules in turn sheds light on molecular forces and molecular motions in nanoconfinement.28 Nevertheless, the short-range hard sphere models commonly used in literature failed to capture some of the more complex structures in molecular assemblies and biological systems, © XXXX American Chemical Society

where long-range repulsion or soft interactions, are more common. The ability to control the soft interactions will, in turn, allow us to explore a diverse range of phase behaviors and manipulate them using a small external perturbation. However, direct and in situ observation, and thus interpretation, of the phases of living systems at atomic and molecular levels is challenging. Therefore, assemblies of soft colloids at the (sub)micrometer scale could potentially offer an analogy to the intermolecular interactions, where the range of potential to the particle or molecule size could be rendered similar. Here, we prepare colloidal particle suspensions with longrange repulsive interaction, “soft colloids”, from charged silica nanoparticles (NPs, ∼500 nm in diameter) dispersed in photocross-linkable monomers of similar refractive index and study the colloidal packing morphologies in microchannels as a result of soft interactions with fixed dimension (diameter 1.8 μm and height 8 μm). Our system can be cross-linked to lock the assembled colloids within the micropillars for later direct imaging by techniques such as scanning electron microscopy (SEM) with nanometer resolution, which is unmatched by conventional optical microscopy techniques that are commonly used to observe colloidal suspensions. We also directly image the assemblies in the third dimension using focused ion beam (FIB) to cut the samples in different directions to reveal hidden particles in a row within specific packing shapes, which might not be observed by direct SEM imaging procedure. In bulk, due to electrostatic double layer forces, the NPs form a random Received: December 18, 2016

A

DOI: 10.1021/jacs.6b12975 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Article

Journal of the American Chemical Society

Figure 1. (a) Schematic illustrations of the assembly process and revealing of the assembled particles within the PDMS micropore array by first extracting the assembled structures and later using oxygen plasma etching to remove the outside polymer layer. (b) Magnified schematics and SEM images of the structures corresponding to the box shown in panel a. Scale bar = 2 μm. the PDMS membrane was cured at 365 nm at a dosage of 2 J/cm2 (UV light source from Newport Inc.) in a nitrogen chamber. To extract the cured suspension from the PDMS membrane, additional 20 μL of ETPTA with 3% v/w of Darocur 1173 was cast on top of the PDMS, which was then covered with a clean glass slide and cured at 365 nm at a dosage of 2 J/cm2. After peeling off the PDMS mold, we obtained the micropillar array of assembled nanoparticles embedded within the ETPTA matrix. To reveal the silica NP assembly morphology within the cylindrical confinement, the micropillars were subjected to oxygen plasma (Gatan Plasma System) at a power of 30 W for 12−20 min, giving an etching rate of ∼25 nm/min for the cross-linked ETPTA. Characterization of the Bulk Silica NP Suspensions. To observe the assembly of the silica NP suspension in bulk, the suspension was first infiltrated into a rectangular glass capillary with cross-section dimension of 0.1 mm × 2 mm. The suspension was UV cured at a dosage of 2 J/cm2, and the cured composite was taken out by breaking the glass capillary. Oxygen plasma etching of 2 min was applied to have a clear view of colloidal particle assemblies along the capillary wall. To image the cross-section, the sample was immersed in liquid nitrogen and fractured for observation in SEM. Characterization of the Assembled Particles in Micropillars. The micropillars packed with silica NPs were cut off from the substrate using a razor blade for observation under SEM (FIB Strata, voltage of 5 kV). To confirm the packing within each micropillar, we tilted the sample stage to obtain a side view. For internal structures of the packed particles, the micropillars were cut in half by FIB at a 30 kV acceleration voltage and a current of 400 pA.

hexagonal close-packed (rhcp) structure at as low as 7.5 vol % of colloids in monomers. The varied concentration of particles in the bulk does not vary packing symmetry, yet the lattice constant decreases for packing more particles. As opposed to bulk phase assembly, a rich variety of assembly morphologies is observed in microchannels when varying the particle volume fraction in monomers from 15 to 40 vol %, which are in good agreement with molecular dynamics simulation results accounting for the electrostatic interactions. Unlike the hard sphere model systems where the confined structures are determined by the diameter ratio of microchannels to colloidal particles, we find that local concentration of the colloidal particles within the cylindrical confinement plays a critical role in the evolution of the assembled structures.

■

EXPERIMENTAL SECTION

Silica NP/Trimethylolpropane Ethoxylate Triacrylate Suspensions. Monodispersed silica NP powder (500 nm in diameter according to the vendor and 495 ± 20 nm determined by SEM) was purchased from Alfa Aesar. To enhance the electrostatic repulsion between the particles, we activated the surface silanol groups, rendering the NP surface negatively charged, by hydrolyzing the particles in 0.1 M HCl aq. solution overnight, followed by centrifugation twice in water and redispersing the particles in ethanol (Thermo Fisher Scientific Inc.). The silica NPs were ready for use after evaporating ethanol in an oven at 65 °C overnight. Monomers, trimethylolpropane ethoxylate triacrylate (ETPTA, Mn ≈ 428, Sigma-Aldrich) were washed with deionized (DI) water repeatedly to remove ionic species until the conductivity became less than 1 μS/cm (measured by Oakton ECTestr 11 dual-range, pin-style pocket conductivity tester). To disperse silica particles in ETPTA, the pelletized silica powder was added into ETPTA, followed by ultrasonication until a homogeneous suspension was obtained. Then, 3% v/w of photoinitiator, Darocur 1173 (Sigma-Aldrich), was added to the suspension. The volume fraction of the suspension is defined as V , where Vsilica is the volume of the silica particles, f = V +silica V silica

■

RESULTS AND DISCUSSION Long-range interactions between colloidal particles can be realized through their electrostatic repulsion. Derjaguin− Landau−Verwey−Overbeek (DLVO) theory describes the contribution of electrical double layer repulsion and van der Waals (vdW) attraction to stabilize the charged particle dispersion.30 The decay of the potential in the electrical double layer is governed by the Debye screening length (k‑1), which is dependent on ionic concentration, c, and dielectric constant of the dispersion, ε. For monovalent salt such as NaCl in electrolyte,

ETPTA

estimated from the mass and density (2.04 g/cm3) of silica particles,29 and VETPTA is the volume of the monomers. Assembly of Silica NPs. Before infiltration into the porous membrane, the silica NP/ETPTA suspension was vortexed and sonicated for 15 min, respectively. The poly(dimethylsiloxane) (PDMS) microporous membrane was replicated from the silicon master with a square array of micropillars (diameter of 1.8 μm and height of 8 μm). Ten microliters of silica NP suspension was dropped on top of the PDMS membrane to infiltrate the suspension via capillary force. After 1 min, the excess suspension remaining on the PDMS membrane was removed using a razor blade. The suspension in

−1

k

⎛ 2e 2c ⎞1/2 =⎜ ⎟ ⎝ εε0kBT ⎠

(1)

where e is the charge of the electron and ε0 is the permittivity of vacuum. Therefore, to create a system with long-range electrostatic repulsion, first, vdW attraction should be B


Article


smaller than the typical value in hard sphere packing, ∼ 49 vol %.11,38 Compared to the bulk structure, packing of soft colloids within the cylindrical confinement could be influenced by multiple factors, including the interparticle electrostatic repulsion, the boundary condition at the PDMS wall of the microchannels, and the air/suspension interface. To demonstrate the effect of soft interactions between particles to the packing behaviors, here, we fixed the dimensions of the particle and cylindrical confinement as 495 ± 20 nm (NP diameter), 1.8 μm (cylindrical pore diameter), and 8 μm (cylindrical pore height), respectively. The only variable is the bulk volume fraction of silica NPs in ETPTA, f = 15−40 vol % with an increment of 5 vol % to investigate how particles are accommodated as the number of particles entrapped in the confinement varies. Since NP/EPTPA pillars are cross-linked, we can directly image them in SEM. To better view the assembly structures along the pillar height, we cut the pillars off from the substrate for examination at different tilting angles (Figure S2). It can be seen that the silica NPs are uniformly dispersed throughout the entire pillar structures, suggesting that the cross-linking rate is fast enough to avoid perturbation and, thus, allows us to capture the packing phase of NPs in ETPTA. For hard sphere packing, the particles are jammed within the confinement; additional particles cannot be fitted into the confinement because there is no space to explore unless the diameter of the cylinder is increased. In our system, the packing morphology is strongly affected by both the bulk and local concentrations of the suspension. As more and more particles are forced to pack into the cylindrical confinement with fixed diameter and length, the interparticle distance is reduced but particles remained separated due to the long-range repulsion (see Figure 2d and Figure S3). Unlike the bulk assembly symmetry, which remained as rhcp for colloidal particles with volume fraction above 7.5 vol %, packing morphology evolved as the volume fraction of the bulk colloidal suspension increases (Figures 3−5), which should be attributed to packing confinement. In particular, the packing morphology of the silica particles is extremely sensitive to the local concentration, that is, the number of particles trapped in each pillar (N). Even at the same bulk particle concentration, the coexistence of

minimized by matching the refractive indices of suspension medium and dispersed particles in visible wavelength.30,31 Second, the dielectric constant of solvent must be low.32 Thus, the concentration of electrolyte in dispersion is very low such that k−1 can reach the same order of magnitude of the particle size.33 Third, to directly image the assembled structures, it will be desirable to lock the structures in the dispersion without altering them. Here, we dispersed silica NPs in trifunctional monomers (ETPTA), which can be photo-cross-linked almost instantaneously after UV exposure to lock the assembled particle structure.34,35 Meanwhile, in visible wavelengths, ETPTA has a refractive index (n = 1.47) comparable to that of silica (n = 1.45), thus effectively reducing vdW attraction between the particles. Here, interparticle interactions are dominated by electrostatic repulsion from partially dissociated silanol groups on the particle surfaces.36,37 After repetitively washing the monomers with DI water, k−1 in our system should be ∼100 nm (see detailed calculation in Supporting Information), allowing for study of packing of “soft colloids” within the cylindrical microconfinement. The mixture was infiltrated into the PDMS porous membrane, followed by UV curing (see Figure 1a,b). To reveal the particle assembly structures inside the micropillars, the polymers near the outside surface were removed by oxygen plasma (see Figure 1a). For comparison, the morphology of silica NPs in bulk was obtained from NP/ETPTA suspension in a rectangular glass capillary (2 mm × 0.1 mm). As seen in Figure 2a−c, at 7.5 vol % loading of silica NPs, rhcp structures

Figure 2. (a, b) Top-view (a) and cross-sectional view (b) SEM images of the cross-linked colloidal suspension (7.5 vol %) in bulk, showing random hexagonal close-packing (rhcp) of silica NPs. Inset in panel a is the Fourier transform of the image, confirming hexagonal packing in the x−y plane. (c) Schematics showing the packing of the colloidal particles in the monomer suspension before UV curing. D is the interparticle distance in the close-packed plane; h is the interplane distance. (d) Relationship of D and h vs the bulk volume fraction of NPs ( f). The lines indicate the ideal relationship from rhcp. The shaded region is the amorphous phase.

were observed in bulk, where NPs were hexagonally packed in the x−y plane but randomly layered along the z direction. Despite different volume fractions up to 40 vol %, the assembly symmetry remained as rhcp in bulk. In Figure 2d, we plotted the relationship of interparticle distance (D) and interlayer spacing (h) (see definition in Figure 2c) vs volume fraction (f). The D and h predicted from rhcp structures are in good agreement with experimental measurement. The phase transition from amorphous to ordered structures occurred between 5 vol % (see Figure S1) and 7.5 vol %, significantly

Figure 3. Summary of the dominant achiral packing phases in the micropore arrays as the bulk NP concentration increases from 15 to 40 vol %. The assembled structures are formed by staggered stacking of particle layers consisting of different number of particles: top, SEM images; bottom, illustration of the morphology of two consecutive layers (represented in different colors) of particles at the outer surface of the micropillar. For phases S7 and S8, we also observed a 1D inner column of particles. C


Article


since in all the observed phases there remains significant spacing between particles. To better understand the long-range electrostatic repulsion in our system, we compared the experimental observations with the theoretical predictions by Oğuz et al.19 on helicity of charged particles assembled in a cylindrical tube with Yukawa pair-potential, a commonly used potential to describe the electrical double layer between colloids. In their studies, the assembled phases are also found to be strongly related to the packing density of the particles, where the packing phases can be predicted based on two dimensionless parameters: reduced line density, η = Na/L, and reduced inverse screening length. λ = κa, where N is the number of particles confined in a cylinder of length L, and a is the radius of the cylindrical confinement. Here, a qualitative comparison between the theoretical model and our experimental systems is made to illustrate the physical phenomenon of the packing phase evolution in the experimental system with long-range repulsive interaction. It is noted that there are two discrepancies between the theoretical model and our experimental systems. (1) In the theoretical model by Oğuz et al.,19 the particles were considered as point particles with a zero physical radius and trapped on the surface of the cylindrical confinements. However, in our experiments, the particle had a physical size, radius (r) of ∼250 nm. (2) The center of the particles is not on the surface of the cylindrical confinements but located inside of the cylinders (see Figure 1b). To address these differences, we define a in our experiments as a = R − l − r, where l is the distance between the particle surface and the channel wall. Thus, here, a represents the radius of the cylinder whose surface intersects the centers of the packed particles near the wall of the channel, and its value can be estimated directly from SEM images (see Figure S5). When the particle concentration in the dispersion increased, particles were packed closer to the wall of the microchannel. Thus, the value of a increased as the bulk concentration of the suspension increased (see Table 1). L

multiple packing structures was often observed (see Figure S4). We did not investigate NP concentration above 40 vol % since the suspension is too viscous for capillary infiltration into the microchannels, possibly due to particle jamming and significant shear thickening effects at high volume fraction.39 In Figure 3, we show the examples of packing structures formed by stacking layered particles in a consecutive manner. The schematics illustrate the NP assembly in each layer. As the bulk concentration is increased, the increased number of particles is accommodated by increasing either the number of layers or the number of particles per layer along the cylinder’s axis. For example, S2 and S4 phases both have staggered layers of two particles per layer, while more particles are accommodated in S4 (20 vol %) vs S2 (15 vol %) with the increased number of layers. Similar trends were observed for phases S6 (30 vol %) vs S3 (20 vol %) and S8 (40 vol %) vs S7 (30 vol %). As more particles are entrapped in the microporous channels, the number of particles per layer packed around the wall increased from one in phase S1 to five for S7 and S8. The particles prefer to pack around the wall due to the electrostatic repulsion from each other. However, as the packing density increases, particles also reside at the center of the cylinder. As shown in Figure 4, in the case of S7 phase (30 vol %), we

Figure 4. FIB cut SEM images of the colloidal assembly showing the internal structures of the packing phase S7 at 30 vol %. A 1D column of NPs packed in the center is indicated by the dashed rectangles.

observed that besides packing of 5 per layer, an additional particle takes the center position of the pillar, leading to the formation of a one-dimensional (1D) column of silica NPs and a zigzag structure wrapping around the surface of the cylindrical confinement. In addition to achiral structures shown in Figure 3, we also observed a variety of helices (both right and left handed) from colloidal packing in cylinders. While double and triple helices have been reported in the literature from hard sphere models,16,18 here, we observed 3, 4, and 5 stranded helices of particles packed in each pillar (Figure 5), reminding us of the diverse nature of the assemblies by “soft colloids”. Clearly, the strong electrostatic repulsion between silica particles is the main driving force to the particle assemblies

Table 1. Comparison of Experimentally Observed Phases with Theoretical Prediction by Oğuz et al.19 vol % 15 20 a

observed phase

aa (nm)

N/L (μm−1)

Λ

η

predicted phase from ref 19

S1 S2 S3 S4

∼300 ∼350 ∼380 ∼400

∼2 ∼3.7 ∼5.2 ∼5

3 3.5 3.8 4

0.6 1.3 2.0 2.0

N2 N4 N6 N4

Measured from SEM images.

is 8 μm, and N is determined from the number of particles per layer and the total number of layers of particles entrapped in the pillar. Here, since the channel length is significantly larger than the particle size (i.e., L/r = 16) and the Debye screened length (i.e., Lκ = 80), it is plausible that the pores are long enough such that the boundaries should have minimum effects on the packing structures within the microchannels. Accordingly, we calculated these parameters (see Table 1) and compared them with those predicted by Oğuz et al.19 Despite the aforementioned discrepancy between theory and experiments, we found a substantial coincidence between the experimentally observed phases and the predicted ones, S1, S2, S3, and S4. In simulation, the particles are packed in the N2 phase with the zigzag stacking of one particle per layer at the lowest packing density. As the density of particles increases, the

Figure 5. SEM images of different helical structures from NP assemblies in the micropore arrays with multiple helical strands of particles labeled with different colored dots connected by dashed lines. D


Article

Journal of the American Chemical Society packing phase shifts to the staggered stacking of two particles per layer (referred as N4), then to three particles per layer (i.e., N6). It is worth noting that simulation also predicts a re-entrant phase transition from N6 to N4 at an increased packing density, leading to a decreased number of particles per layer but increased layers. This is consistent with the observed transition from S3 to S4 in our experiments. Thus, we believe the model at least qualitatively captured the physical phenomenon of the packing phase evolution in the experimental system with longrange repulsive interactions. On the other hand, we did not observe the low-density helical phases that consist of one or two helical strands predicted by Oguz et al., even though over a hundred particle assemblies per bulk concentration were sampled. Instead, we found helical phases only at a density higher than that studied by Oguz et al., consisting of 3, 4, or 5 helical strands (H1, H2, and H3 phases). Interestingly, instead of forming the helical phases predicted by Oğuz et al. with a packing density between S3 and S4, we observed coexistence of S3 and S4 phases within a single micropore. Thus, the experimental system can be more complex than theoretical prediction. Oğuz et al. did not predict the phases at a higher packing density as shown in our experiments. To further confirm the role of long-range repulsion to the assembly behaviors in our system, we performed a molecular dynamics (MD) simulation similar to that by Oğuz et al. but at higher packing densities using parameters directly obtained from the experiments. For the electrostatic repulsion between silica NPs, Yukawa potential was used with Debye screening length of 100 nm, where particles interacted with each other and the side walls of the channel via Yukawa potential and were annealed at a temperature between 20kBT/ε and 0.002kBT/ε with ε as a parameter defined as the interaction strength between particles (Movie S1). The charge density ratio between the particles and the PDMS sidewall was set to be 200. This number was finetuned based on image analysis of 1.1-μm particles packed within the channels (diameter 1.8 μm, height 8 μm), where the packing structures are much simpler to analyze (see Figure S6). For the top and bottom of the channel, the hard-wall interaction was assumed. By placing different numbers of colloidal particles into the cylindrical pore until reaching the steady state, we found the same packing phases as those observed experimentally, where the packing morphology was extremely sensitive to the local concentration of the particles (Figure 6). Meanwhile, almost all of the phases observed experimentally can be reproduced in simulation with a relatively simple Yukawa pair interaction potential. The detailed comparison is summarized in Table 2. Here, additional particles were found to be accommodated by forming denser zigzag layered structures wrapping around the wall while filling the internal space of the 1D channel. There are two minor discrepancies: (1) the number of particles within the cylinder in simulation was slightly smaller than that observed experimentally at the same phase, and (2) simulation was not able to generate the S6 phase observed in experiments. This difference could be attributed to the boundary conditions on top and bottom of the cylindrical confinement imposed in simulation being different from the real system. In experiments, the top was exposed to air and the bottom was PDMS. Furthermore, the electrical double layer force in simulations was modeled as a simple pair-interaction potential between two particles and an approximation was considered to describe the interaction between a particle and the wall. Thus, it ignored

Figure 6. Simulated phases of the assembled colloids in micropore arrays consistent with experiments. The phases observed from experiments (shown with symbols on top of the figure) are matched with simulated packing morphology, including S4, H1, H2, S7, S8, and H3. The number of particles used in simulation is labeled beneath the images.

Table 2. Summary of the Experimentally Observed Structures in Colloidal Assemblies in Micropillar Arrays versus Those Predicted by Theory vol % phase 15 20 25

30

40

S1 S2 S3 S4 H1 H2 S5 S6 S7 S8 H3

morphology zigzag layer of 2 spheres layer of 3 spheres layer of 2 spheres 3-stranded helix 4-stranded helix layer of 4 spheres layer of 3 spheres layer of 5 spheres (1D column) layer of 5 spheres (1D column) 5-stranded helix (1D column)

predicted by literature19

predicted by us

Y Y Y Y

chirality

Y

achiral achiral achiral achiral chiral chiral achiral achiral achiral

Y

achiral

Y

chiral

Y Y Y

multibody interactions that became significant at a high packing density or when the particle size was comparable to the confinement size. Previously, Bowen and Sharif40 have shown that within the cylindrical confinement, long-range electrostatic repulsion can be altered significantly and even become attractive with the multibody interactions. Despite the structural diversity observed in experiments and the use of simple long-range Yukawa potential in simulation, the agreement between experiments and theory unequivocally confirm the role of long-range repulsive interactions within cylindrical confinement.

■

CONCLUSIONS In summary, we investigated the microconfinement of charged silica nanoparticles dispersed in refractive index matching monomers in PDMS porous membranes. Here, the silica colloidal particles interact with each other and the pore wall via electrostatic double layer forces. Different from the hard sphere systems where the assembled morphologies are prescribed by the diameter ratio between the cylindrical confinement and the nanoparticles, here we observe a much richer variety of assemblies that are highly sensitive to both bulk and local nanoparticle concentrations with a fixed particle size and channel size. The experimentally observed assembly morphologies are consistent with theoretical predictions, based on E


Article


(7) Moon, J. H.; Yi, G.-R.; Yang, S.-M. J. Colloid Interface Sci. 2005, 287, 173. (8) Vanapalli, S. A.; Iacovella, C. R.; Sung, K. E.; Mukhija, D.; Millunchick, J. M.; Burns, M. A.; Glotzer, S. C.; Solomon, M. J. Langmuir 2008, 24, 3661. (9) Irvine, W. T. M.; Vitelli, V.; Chaikin, P. M. Nature 2010, 468, 947. (10) Zerrouki, D.; Baudry, J.; Pine, D.; Chaikin, P.; Bibette, J. Nature 2008, 455, 380. (11) Lohr, M. A.; Alsayed, A. M.; Chen, B. G.; Zhang, Z.; Kamien, R. D.; Yodh, A. G. Phys. Rev. E 2010, 81, 040401. (12) Pinedo Rivera, T.; Lecarme, O.; Hartmann, J.; Rossitto, E.; Berton, K.; Peyrade, D. J. Vac. Sci. Technol. B 2008, 26, 2513. (13) Ren, B.; Ruditskiy, A.; Song, J. H.; Kretzschmar, I. Langmuir 2012, 28, 1149. (14) Cong, V. T.; Ganbold, E.-O.; Saha, J. K.; Jang, J.; Min, J.; Choo, J.; Kim, S.; Song, N. W.; Son, S. J.; Lee, S. B.; Joo, S.-W. J. Am. Chem. Soc. 2014, 136, 3833. (15) Erickson, R. O. Science 1973, 181, 705. (16) Pickett, G. T.; Gross, M.; Okuyama, H. Phys. Rev. Lett. 2000, 85, 3652. (17) Mughal, A.; Chan, H. K.; Weaire, D. Phys. Rev. Lett. 2011, 106, 115704. (18) Charvolin, J.; Sadoc, J.-F. Biophys. Rev. Lett. 2011, 6, 13. (19) Oğuz, E. C.; Messina, R.; Löwen, H. EPL 2011, 94, 28005. (20) Wood, D. A.; Santangelo, C. D.; Dinsmore, A. D. Soft Matter 2013, 9, 10016. (21) Kohlstedt, K. L.; Solis, F. J.; Vernizzi, G.; de la Cruz, M. O. Phys. Rev. Lett. 2007, 99, 030602. (22) Kohlstedt, K. L.; Vernizzi, G.; Olvera de la Cruz, M. Phys. Rev. E 2009, 80, 051503. (23) Solis, F. J.; Vernizzi, G.; Olvera de la Cruz, M. Soft Matter 2011, 7, 1456. (24) Douady, S.; Couder, Y. Phys. Rev. Lett. 1992, 68, 2098. (25) Tymczenko, M.; Marsal, L. F.; Trifonov, T.; Rodriguez, I.; Ramiro-Manzano, F.; Pallares, J.; Rodriguez, A.; Alcubilla, R.; Meseguer, F. Adv. Mater. 2008, 20, 2315. (26) Jiang, L.; de Folter, J. W. J.; Huang, J.; Philipse, A. P.; Kegel, W. K.; Petukhov, A. V. Angew. Chem., Int. Ed. 2013, 52, 3364. (27) Rasaiah, J. C.; Garde, S.; Hummer, G. Annu. Rev. Phys. Chem. 2008, 59, 713. (28) Khlobystov, A. N.; Britz, D. A.; Briggs, G. A. D. Acc. Chem. Res. 2005, 38, 901. (29) Bogush, G. H.; Tracy, M. A.; Zukoski, C. F., IV J. Non-Cryst. Solids 1988, 104, 95. (30) Israelachvili, J. N. Intermolecular and Surface Forces, 3rd ed.; Academic Press, 2011. (31) Hsu, M. F.; Dufresne, E. R.; Weitz, D. A. Langmuir 2005, 21, 4881. (32) Royall, C. P.; Leunissen, M. E.; Blaaderen, A. v. J. Phys.: Condens. Matter 2003, 15, S3581. (33) Leunissen, M. E.; Christova, C. G.; Hynninen, A.-P.; Royall, C. P.; Campbell, A. I.; Imhof, A.; Dijkstra, M.; van Roij, R.; van Blaaderen, A. Nature 2005, 437, 235. (34) Wan, Q.; Sheffield, J.; McCool, J.; Baran, G. Dent. Mater. 2008, 24, 1694. (35) Wu, Y. L.; Derks, D.; van Blaaderen, A.; Imhof, A. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 10564. (36) Kim, S.-H.; Jeon, S.-J.; Yi, G.-R.; Heo, C.-J.; Choi, J. H.; Yang, S.M. Adv. Mater. 2008, 20, 1649. (37) Yang, H.; Jiang, P. Langmuir 2010, 26, 13173. (38) Pusey, P. N.; van Megen, W. Nature 1986, 320, 340. (39) Mueller, S.; Llewellin, E. W.; Mader, H. M. Proc. R. Soc. London, Ser. A 2010, 466, 1201. (40) Bowen, W. R.; Sharif, A. O. Nature 1998, 393, 663. (41) Jin, W.; Fukushima, T.; Niki, M.; Kosaka, A.; Ishii, N.; Aida, T. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 10801.

Yukawa potential in the low packing density regime. Most of the configurations found in experiments are well described by computer simulations using pairwise additive long-range repulsive interactions. The study presented here offers new insights into directing the colloidal assemblies in a cylindrical confinement, which in turn will allow us to create much richer and more complex phases not seen in hard sphere systems. We note that in our system the range of potential to the particle diameter is roughly 1/5, within the range of intermolecular interaction. Therefore, our studies could potentially provide model systems to study the classical problems such as crystallization and melting, supramolecular assemblies in organic and biological systems,41 and exploration of chirality and large surface area for applications, including organic solar cells,42 anisotropic electrical conduction,41 proton conduction and its biological functions,27 temperature responsive alignment and controlled release,26 sensing,5 catalysis, and optoelectronics.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.6b12975. Estimation of the Debye screening length in NP/EPTPA suspensions, additional SEM images of the assembled structures, and additional MD simulation results (PDF) W Web-Enhanced Feature *

A video of molecular dynamics of particles within the channel via Yukawa potential and cooled with simulated annealing is available in the online version.

■

AUTHOR INFORMATION

Corresponding Author

*[email protected] ORCID

Gaoxiang Wu: 0000-0002-1158-9792 Shu Yang: 0000-0001-8834-3320 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work is supported by the National Science Foundation (NSF) Materials Science and Engineering Center (MRSEC) Grants to the University of Pennsylvania, DMR-1120901 (S.Y.), and to Brandeis University on Bioinspired Soft Materials, DMR-1420382 (subcontracted to University of Massachusetts for D.A.W. and A.D.D.).

■

REFERENCES

(1) Yin, Y.; Lu, Y.; Gates, B.; Xia, Y. J. Am. Chem. Soc. 2001, 123, 8718. (2) Li, F.; He, J.; Zhou, W. L.; Wiley, J. B. J. Am. Chem. Soc. 2003, 125, 16166. (3) Li, F.; Badel, X.; Linnros, J.; Wiley, J. B. J. Am. Chem. Soc. 2005, 127, 3268. (4) Kumacheva, E.; Garstecki, P.; Wu, H.; Whitesides, G. M. Phys. Rev. Lett. 2003, 91, 128301. (5) Wu, Y.; Cheng, G.; Katsov, K.; Sides, S. W.; Wang, J.; Tang, J.; Fredrickson, G. H.; Moskovits, M.; Stucky, G. D. Nat. Mater. 2004, 3, 816. (6) Moon, J. H.; Kim, S.; Yi, G.-R.; Lee, Y.-H.; Yang, S.-M. Langmuir 2004, 20, 2033. F


Article

Journal of the American Chemical Society (42) Hill, J. P.; Jin, W.; Kosaka, A.; Fukushima, T.; Ichihara, H.; Shimomura, T.; Ito, K.; Hashizume, T.; Ishii, N.; Aida, T. Science 2004, 304, 1481.

G


Confined Assemblies of Colloidal Particles with Soft Repulsive

Recommend Documents