Article pubs.acs.org/Langmuir
Crystallization of Micrometer-Sized Particles with Molecular Contours Pengcheng Song, Brian K. Olmsted, Paul Chaikin, and Michael D. Ward* Department of Physics and Center for Soft Matter Research and Department of Chemistry and Molecular Design Institute, New York University, 100 Washington Square East, New York, New York 10003-6688, United States S Supporting Information *
ABSTRACT: The crystallization of micrometer-sized particles with shapes mimicking those of tetrabenzoheptacene (TBH) and 1,2:5,6-dibenzanthracene (DBT), both flat polyacenes, in an electric field results in the formation of ordered 2D packings that mimic the plane group symmetries in their respective molecular crystal equivalents. Whereas the particles packed in low-density disordered arrangements under a gravitational gradient, dielectrophoresis (under an ac electric field) produced ordered high-density packings with readily identifiable plane group symmetry. The ordered colloidal assemblies were stable for hours, with the packing density decreasing slowly but with recognizable symmetry for up to 12 h for the TBH-shaped particles and up to 4 h for the DBT-shaped particles. This unexpected stability is attributed to jamming behavior associated with interlocking of the dogbone-shaped (TBH) and Z-block (DBT) particles, contrasting with the more rapid reduction of packing density and loss of hexagonal symmetry for disk-shaped particles upon removal of the electric field. The TBH-shaped and DBT-shaped particles assemble into the p2 plane group, which corresponds to the densest particle packing among the possible close-packed plane groups for these particle symmetries. The p2 symmetry observed for the TBH-shaped and DBT-shaped colloid crystal emulates the p2 symmetry of the (010) layers in their respective molecular crystals, which crystallize in monoclinic lattices. Notably, DBT-shaped particles also form ordered domains with pgg symmetry, replicating the plane group symmetry of the (100) layer in the orthorhombic polymorph of DBT. These observations illustrate that the 2D ordering of colloid particles can mimic the packing of molecules with similar shapes, demonstrating that packing can transcend length scales from the molecular to the colloidal.
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INTRODUCTION As illustrated by Kitaigorodsky nearly five decades ago, molecules tend to crystallize in space groups that permit maximal packing density; for molecules with low symmetry, this is aided by inversion centers and translational symmetries of glide and screw axes.1,2 Kitaigorodsky also examined the packing of arbitrarily shaped 2D objects in the 17 2D plane groups, wherein the objects were characterized by either identity symmetry (i.e., C1) or higher symmetry elements (i.e., n-fold axes and mirror planes). In 2D, dense packing is favored by the existence of glide planes and inversion centers, whereas mirror planes frustrate dense packing. Colloidal spheres typically assemble into close-packed face-centered cubic (FCC) or hexagonal close-packed (HCP) lattices in 3D, whereas in 2D the p6m plane group is favored.3−5 Directional forces in colloidal triblock Janus spheres conspire to form a Kagome lattice.6 The simple symmetry of spheres, however, precludes a more expansive exploration of packing in the 230 available space groups and 17 plane groups. The diversity of packing in molecular crystals reflects the rich variety of shapes, symmetry, and conformational isomerism characteristic of molecules, which because of their low molecular symmetry tend to crystallize in low-symmetry triclinic and monoclinic © 2013 American Chemical Society
space groups, often through glide, screw axis, and inversion symmetry operations. Although near-field microscopy methods have been used to investigate the crystallization of molecular crystals on the nanometer scale,7−11 visualization of self-assembly on the molecular level remains a challenge. Scanning tunneling microscopy, for example, enables the visualization of molecules on substrates, often in the form of 2D crystals, but examples of assembly in real-time are few.9−11 Atomic force microscopy has been used for the real-time visualization of crystal growth on the nanometer scale but does not allow for direct observations of molecular assembly.7,8 Instead, molecular assembly and the intermolecular interactions responsible are usually inferred from single-crystal structures obtained posthumously using Xray diffraction methods. Colloidal particles with shapes mimicking molecules can provide an opportunity for the direct visualization of the relationship between symmetry and packing into 2D and 3D lattices. Moreover, the crystallization of colloidal particles can be regulated with a high degree of control Received: June 19, 2013 Revised: August 3, 2013 Published: August 28, 2013 13686
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through the use of electric fields, which for carefully chosen particle−solvent combinations can coerce the motion and dense packing of particles.12−15 In principle, the Kitaigorodsky guidelines are scaleindependent, suggesting common packing rules for molecular crystals and assemblies of colloids derived from particles with shapes mimicking molecules. Investigations of colloid crystallization, however, have largely been limited to simple shapes, such as spheres and assorted simple polygons. In contrast, the constituents of molecular crystals typically have complex shapes that dramatically influence packing, with most molecular crystals adopting low-symmetry space groups. Molecules that crystallize solely through dispersive interactions (e.g., molecules without structure-directing forces such as hydrogen bonding) are generally thought to pack up to the repulsive limit, not unlike particles under the influence of electric fields. Herein, we describe the use of a dielectrophoretic cell for the 2D crystallization of micrometer-sized particles with the shape of tetrabenzoheptacene (TBH) and 1,2:5,6-dibenzanthracene (DBT). The ordered ensembles of TBH- and DBT-shaped particles exhibit plane group symmetries that mimic the plane group symmetries in their respective molecular crystal equivalents. The TBH-shaped and DBT-shaped particles assemble into the p2 plane group, which corresponds to the densest particle packing among the possible close-packed plane groups for these particle symmetries. The p2 symmetry observed for the TBH-shaped and DBT-shaped colloid crystal emulates the p2 symmetry of the (010) layers in their respective molecular crystals, which crystallize in monoclinic lattices. Notably, DBT-shaped particles also from ordered domains with pgg symmetry, replicating the plane group symmetry of the (100) layer in the orthorhombic polymorph of DBT. These observations illustrate that the 2D ordering of objects that pack up to a repulsive limit can transcend length scales from the molecular to the colloidal.
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Figure 1. Lithographic fabrication of particles. (a) Spin coating of a sacrificial layer; (b) spin coating of the SU-8 photoresist; (c) exposure of the photoresist to UV light (λ = 360 nm) through a photomask with apertures corresponding to the particle shape; (d) curing and development of the photoresist; and (e) dissolution of the sacrificial layer and release of the photoresist particles. in piranha solution (3:1 H2SO4/H2O2) for 20 min, rinsed with deionized water, and dried with a stream of nitrogen (Caution! Piranha solution is strongly acidic and strongly oxidizing. It should never be lef t unattended if hot, it should not be stored in a closed container, and it should not be disposed of with organic solvents.) The wafers were then held at 120 °C for 20 min on a hot plate to remove residual water and plasma cleaned with ambient gas for 1 min to improve sacrificial layer adhesion (Harrick−Plasma PDC-001). A sacrificial layer (Microchem Omnicoat) was applied by spin coating on the cleaned silicon wafer at 3000 rpm for 30 s, producing a 50-nm-thick film. The wafer with the sacrificial layer was baked at 200 °C on a hot plate for 60 s and allowed to cool to room temperature. Photoresist (SU-8 2002, MicroChem Corp.) was then applied by spin coating on top of the sacrificial layer at 5000 rpm for 30 s, resulting in a film thickness of SU-8 of between 1.1 and 1.3 μm. The photoresist was then prebaked at 95 °C for 60 s on a hot plate and allowed to cool to room temperature, exposed to UV light (λ = 360 nm) through a particle photomask under hard/ vacuum contact, and postbaked at 95 °C for 70 s. The wafer assembly then was submerged in SU-8 developer (MicroChem) for 60 s with gentle agitation, rinsed for 10 s with developer to remove any un-crosslinked photoresist residue, and dried under nitrogen. A final hard bake was performed at 150 °C in air for 15 min to increase the hardness and solvent resistance of the photoresist as well as anneal any microscopic cracks in the photoresist. The wafer assembly then was immersed in PMGI 101 developer (101A, Microchem Corp.) for 10 min at room temperature to dissolve the sacrificial layer and release the particles from the wafer. The particles were carefully harvested with a rubber policeman and centrifuged at 3000 rpm for 30 min, after which the developer supernatant was removed. The particles were rinsed three times with an aqueous solution containing 1% w/w F108 surfactant (BASF, Corp.). Particle Stabilization. The surfaces of the particles were functionalized with poly(ethylene oxide) (PEO) to stabilize them against aggregation by mechanically interlocking chains of PEO with the surface of the SU-8 particles.26,27 The particles were first transferred to a 5 mL volume of aqueous solution containing 1.0% w/w BASF 108 and a pluronic PEO-PPO-PEO triblock copolymer with a 44-mer region of poly(propylene oxide) (PPO) bridging 141mer regions of PEO. Toluene was added to this solution to a final polymer concentration of 0.1% w/w, which caused swelling of the particles such that the PPO block penetrated the surface and became entangled in the SU-8 particles. The amount of toluene in the solution must be carefully regulated because excess toluene can cause phase separation that prevents the interaction of the BASF 108 triblock copolymer with the particles. After 24 h, this solution was held at 98 °C for 30 min to evaporate the toluene, which resulted in the deswelling of the particles and the locking of the PPO block in the SU-
EXPERIMENTAL SECTION
Particle Fabrication. Molecular contour images of tetrabenzoheptacene (TBH) and 1,2:5,6-dibenzanthracene (DBT) were generated using crystal structure visualization program Mercury (available by download from the Cambridge Crystallographic Data Centre) and exported to AutoCAD (by Autodesk) to create a chromium-on-glass photomask comprising an array of this shape. Brownian motion of the particles required sizes of less than 10 μm, and the resolution of the e-beam method used for photomask fabrication was 0.7 μm (Image Technology, Palo Alto, CA). These characteristics precluded mask features that mimicked the shape of the respective molecules precisely. Whereas the images on the mask displayed sharp corners, the particles exhibited rounded corners because of resolution limits of the lithography process. The particles were fabricated from the SU-8 negative photoresist (Microchem Corporation, Newton, MA, USA) in a cleanroom environment using a Karl Suss MJB3 full-field UV photolithography station (Figure 1). Approximately 18.5 million TBH-shaped particles and 25 million DBT-shaped particles were fabricated per 3-in.-diameter wafer. Polished silicon wafers, used as substrates, were cleaned by immersion 13687
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8 matrix. This procedure creates SU-8 surfaces decorated with PEO chains that prevent particle aggregation through steric stabilization. The use of PEO is preferable to ionic surfactants because it avoids the introduction of ionic charge that would otherwise increase the conductivity of the particle dispersions, which can prevent the use of high electric fields necessary to drive particle assembly. Two-Dimensional Crystallization of Particles. Crystallization of the particles was achieved in a dielectrophoretic cell (Figure S1) fabricated by depositing gold (70 nm thickness) and chromium (5 nm thickness) by thermal evaporation (BAL-TEC MED 020) on a circular quartz coverslip (no. 2, 30 mm diameter, Corning Incorporated, Corning, NY, USA). The electrode pattern on the coverslip consisted of two semicircles separated by a gap (variable 1 to 2 mm) created by placing an aluminum strip over the coverslip during metal evaporation. Copper wires (0.5 mm diameter) were attached to the electrodes with silver paint (SPI Paint). The crystallization container was fabricated by attaching a quartz tube (6 mm long, 20 mm diameter, 1 mm wall thickness) to the electrode-patterned circular coverslip using a UVcurable, thiolene-based adhesive (NOA68, Norland Products). After the particle suspension was added to the container, a second circular coverslip (no. 1, 22 mm diameter) was attached to the top edge of the tube to seal the cell and prevent the evaporation of solution. The container was then filled with a particle suspension (0.5% by volume in water) containing 1% w/w F108. The volume of the particle suspension was adjusted over the range of 0.1−0.5 mL, depending on the number of particles required to achieve a desired initial areal density, which typically ranged from 10 to 50%. The density of SU-8 (1.19 g/cm3) ensured that the particles settled to the bottom of the cell. A function generator (4007DDS, BK Precision) was connected to the input side of a voltage amplifier (5×, 10×, and 20×). The two electric leads of the dielectrophoretic cell were connected to the output side of the amplifier with a 1 μF capacitor installed on one of the leads to eliminate residual parasitic dc current in the circuit. The ac electric field used here was applied at frequencies of between 10 kHz and 1 MHz, with field strengths of 75−300 V/cm. These field strengths proved sufficient to mobilize the particles under positive dielectrophoresis, given the high dielectric contrast between SU-8 (ε = 2.8) and water (ε = 78.4).11,16−19 Image Analysis. Size polydispersity was determined by image analysis of optical micrographs of the particles prior to their release from the wafer, in which the areal size distribution was determined by measuring the area of each particle by ImageJ (NIH; http://rsbweb. nih.gov/ij/) in a representative sample size (typically more than 1000 particles per set). The polydispersity was determined by fitting the area histogram to a Gaussian and then calculating the ratio of the full width at half-maximum (fwhm) to the average size (equivalent to the size at the maximum of the Gaussian fit). The total number of particles and center of mass of each particle were determined from an optical micrograph by using a customized plugin based on the code from Particle Analyzer in ImageJ. Packing fractions were calculated from the total area of particles divided by the total area of the image. The lattice parameters of ordered particle packings were determined from the fast Fourier transform (FFT) using the centers of mass as lattice points. The pair correlation function g(r), which describes the probability of finding a particle at a distance r from a reference particle m, was calculated from the centers of mass according to eq 1, where r is the center-to-center distance between two particles, ρp is the total particle density of the structure, and Nm(r, dr) is the number of particles located in an annular ring at r with a width dr.
g (r ) =
1 M
M
∑ m=1
Nm(r , dr ) ρp 2πr dr
Article
RESULTS AND DISCUSSION Particles with molecular contours can be fabricated using either top-down or bottom-up methodologies. Bottom-up methods include photochemical synthesis,20 thermal decomposition,21 and colloidal polymerization.22 These methods are suitable for fabricating particles with submicrometer dimensions, a length scale at which Brownian motion plays a substantial role in particle motion, but they have been limited to particles with simple shapes (i.e., spheres, cubes, and tetragonal).23 Topdown methods such as lithography can be used to create particles with more complex shapes, with contour features limited only by the resolution of the lithography process. Ebeam lithography can produce particles with feature sizes of tens of nanometers, whereas micrometer-sized particles can be fabricated readily using conventional photolithography methods;24 for example, UV photolithography has been used to fabricate micrometer-sized particles from the SU-8 negative photoresist.25 The particles used herein were fabricated by conventional lithography to mimic the shapes of tetrabenzoheptacene (TBH) and 1,2:5,6-dibenzanthracene (DBT), which were obtained from the single-crystal structures of these compounds (Figure 2). The lithography process produced as many as 30
Figure 2. (A) Molecular structures of TBH and DBT. Photomasks were created with a shape that traced the contour of the molecule but with sharp corners (blue); the actual particle shape exhibited more rounded corners due to resolution limits (red). (B) p2 packing of the (010) layer in a single crystal of TBH (Cambridge Structural Database REFCODE: TBZHCE). (C) p2 packing of the (010) layer in a single crystal of the monoclinic form of DBT (REFCODE: DBNTHR10). The layer contains DBT molecules having the same chirality (in 2D). (D) pgg packing of the (100) layer in a single crystal of the orthorhombic form of DBT (REFCODE: DBNTHR01). This layer contains equal numbers of DBT molecules of opposite chirality (in 2D).
million micrometer-sized particles in a single batch. These particles are stabilized against aggregation (in the absence of an electric field) by decorating their surfaces with PEO-PEG-PEO chains that provide steric stabilization.26−28 Unlike particles treated with ionic surfactants, these suspensions were stable for several weeks even in high-ionic-strength solutions such as 1 M KCl. Moreover, stabilization with this neutral surfactant avoids the introduction of ionic charge that would otherwise increase the conductivity of the particle dispersions, which can prevent the use of high electric fields necessary to drive particle assembly.
(1)
Packing fractions of hypothetical close-packed plane groups (i.e., plane groups that permit six nearest neighbors) were calculated using AutoCAD, beginning with an array of particles with a particular plane group symmetry but with an expanded lattice in which the particles were not densely packed. The initial lattice was then compressed until the edges of each particle contacted six neighbors. 13688
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Figure 3. Size distribution of the photomask and corresponding (A) TBH-shaped particles and (B) DBT-shaped particles, as measured by ImageJ (National Institutes of Health) using the particle analyzer plug-in module. The TBH-shaped particle data represent a population of 1500 apertures and particles. The DBT-shaped particle data represent a population of 1000 apertures and particles.
suspension as a lubricant to reduce the higher frictional forces between the particles and the glass surface of the cell. TBH-Shaped Particles. In the absence of self-aggregation, external forces such as gravity or centripetal forces are required to provoke assembly.31,32 Alternatively, dielectrophoretic forces can be used to drive the assembly of colloidal particles.12,13 The structure and symmetry of particle packings can be regulated by tuning the strength and frequency of the ac electric field, adjusting the dielectric contrast between the particle and the solvent, and altering the particle size and geometry.33−35 Under an electric field of 75−300 V/cm at 10 kHz, the TBH-shaped particles aligned with their major axes parallel to the electric field, restricting their rotational freedom. The dielectric constant of the particles (ε = 2.8) was lower than that of the aqueous medium (ε = 78.4), coercing the particles to migrate toward the center of the dielectrophoretic cell. The TBHshaped particles initially assembled as 1D chains as a result of electric polarization along the major axes (Figure 4A).5,19 The chains move laterally as collective units that suggest electric polarization along directions not parallel to major axes until they encounter other chains to form small rafts (Figure 4B) with structures that are likely stabilized by electrostatic interactions between polarized particles. During a period of approximately 1 h, the particles assemble into larger arrays lacking long-range order but containing locally ordered domains (Figure 4C). Although adventitious counterions and surface-bound PEO chains may suppress the polarization somewhat, the observation of chaining and long-range packing in response to the electric field indicates only a minor influence of these factors. After approximately 10 h, the domains exhibit long-range order over approximately 200 μm (Figure 4D), interrupted by only occasional defects corresponding to misoriented or broken particles. The time scale of formation of these ordered domains is large compared to that reported for rounded particles such as ellipsoids.35b The TBH-shaped particles are flat, however, which requires that they slide in order to assemble rather than roll, which would be expected to reduce their mobility compared to that of rounded particles. Moreover, the irregular shapes of the TBH and DBT particles require that approaching chains sample the translational space to achieve the densely packed structures. Both factors would slow the assembly of the ordered domains. These large domains pack with plane group symmetry p2 and lattice parameters of a = 5.4 μm, b = 10.3 μm, and β = 104.4°,
Whereas the constituents of molecular crystals are rigorously identical, particles prepared by lithography are naturally polydisperse, which can introduce defects and, in extreme cases, frustrate crystallization and long-range order. Size and shape polydispersity was determined by image analysis of optical micrographs of the particles prior to their release from the wafer, in which the areal size distribution was determined by measuring the area of each particle in a representative sample size (typically more than 1000 particles per set). Image analyses reveal that the lithography process produces particles that are approximately 30% larger than expected from the sizes of the photomask apertures (Figure 3). The polydispersity can be determined by fitting the area histogram to a Gaussian and then calculating the ratio of the fwhm to the average size (equivalent to the size at the maximum of the Gaussian fit). The average aperture size and fwhm of the photomask are 35.9 and 1.0 μm2, respectively, whereas the average size and fwhm of the particles are 46.6 and 2.0 μm2, respectively. These values correspond to polydispersities of 2.6 and 4.2% for the photomask apertures and particles, respectively. Fringing and diffraction effects during the lithography process as well as the diffusion of cross-linked material within the SU-8 matrix account for the larger size of the particles. Moreover, the corners of the particles are somewhat rounded as a result of resolution limits. Polyacenes, which crystallize through noncovalent interactions, are typically planar. The crystal structures of these compounds often reveal layered motifs that suggest a preference for certain plane groups.29,30 The TBH-shaped particles mimic the shape and planarity of the TBH molecule, characterized by a “dogbone” shape with “knobs” and “hollows” invoked by Kitaigorodsky as important for the packing of molecular crystals, permitting an examination of the role of particle symmetry in packing. The crystal structure of TBH reveals (010) layers with p2 plane group symmetry (Figure 2B). The DBT-shaped particles have a Z-block shape (following the tetris nomenclature). DBT exhibits two polymorphs, a monoclinic form that contains (010) layers with p2 plane group symmetry and an orthorhombic form that contains (100) layers with pgg symmetry (Figure 2C,D). Unlike spherical and ellipsoidal particles, the TBH-shaped particles used in this work cannot roll across a surface when subjected to electric fields. Instead, they must slide, which can limit motion. A small amount of BASF F108 (1% w/w) was added to the colloid 13689
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and (010) layer in the molecular crystal have identical plane group symmetry, which is consistent with rigid objects attaining the densest packing up to a repulsive limit. The pair correlation function g(r), which describes the probability of finding a particle at a distance r from a reference particle, can be used to illustrate further the degree of order in particle arrays (Figure 6). The pair correlation function reveals
Figure 4. Stepwise assembly of TBH-shaped particles in the dielectrophoretic cell at an electric field strength of 75 V/cm. (A) Particles initially form 1D chains as a result of electric polarization, (B) followed by assembly of the chains along their edges with two knobs protruding into hollows of adjacent particles. (C) The chain assemblies then pack into a partially ordered 2D motif, (D) eventually forming an ordered packing with p2 symmetry in which one knob protrudes into each hollow of an adjacent particle. Scale bar = 10 μm.
Figure 6. Pair correlation functions g(r) calculated from the centers of mass of TBH-shaped particles in the ordered p2 and disordered assemblies. The peaks correspond to the most probable distances between particles: (1) 5.4, (2) 10.3, (3) 12.9, (4) 16.8, (5) 20.7, and (6) 31.8 μm.
as determined by FFT analysis of the centroids of each particle (Figure 5A,B). The packing arrangement of the particles in this
more clearly the high degree of order in the p2 packing. In contrast, particle assembly under a gravitational force, achieved by tilting the cell at an angle of 10° from the horizontal plane, produced disordered packing of interlocking particles at the lower edge of the cell (Figure 5C,D). The 2D packing density was 81%. The FFTs of the disordered particle packings scalar lengths are 5.5 and 10.4 μm, which correspond to the nearestneighbor separations of particles along their long and short axes. The disorder is evident from the lack of structure in the pair correlation function. The TBH-shaped particles pack in the p2 plane group, which possesses only 2-fold rotation axes. One may expect the crystallization of the TBH-shaped particles, which have two unique mirror planes, into a plane group with mirror or glide planes (Figure 7). After eliminating plane groups with three-, four-, and six-fold axes, possible candidates include pm, pg, cm, pmm, pmg, pgg, and cmm. Among these, cmm, pgg, and pmg are the closest-packed, that is, plane groups that permit six nearest neighbors surrounding each particle. The small rafts in Figure 4B appear to signal the onset of packing into the cmm plane group. These rafts, however, gradually reorder into the p2 motif. Notably, the packing fractions calculated for TBHshaped particles increase in the order pmg (0.73) < pgg (0.78) < cmm (0.82) < p2 (0.87). The packing fraction for p2 is also larger than the experimentally observed packing fraction of 0.81 observed for the disordered assemblies (Figure 5C). The observation of p2 symmetry, the most densely packed plane group, reveals the influence of effective packing pressure exerted by the electric field, which serves to maximize the packing fraction of the array by converting small rafts with cmm-like symmetry to arrays with p2 symmetry. The stability of 2D ordered particles upon the removal of the electric field was examined by measuring the packing fractions and FFT peak widths with time. The close-packed p2 assembly expands 3% after 1 h and 8% after 2 h (Figure 8), with the
Figure 5. Images of packed TBH-shaped particles acquired by optical microscopy. (A,B) Ordered particle packing in an electric field (75 V/ cm) and its corresponding Fourier transform. (C,D) Disordered particle packing formed by a gravitational gradient and its corresponding Fourier transform. Scale bar = 20 μm.
final stage differs somewhat from the structures of the chain rafts formed in the early stage, illustrating that optimized packing directs the structure of the larger assembly. The p2 symmetry of the colloid crystal is also observed in the (010) layer of the single-crystal form of TBH, which crystallizes in the P21/n space group, with a = 24.613 Å, b = 3.860 Å, c = 25.895 Å, and β = 95.85°. The arrangement of the colloid particles differs somewhat from that in the molecular crystal, which may reflect the presence of interlayer interactions in the 3D molecular crystal as well as slightly different contours introduced by hydrogen atoms. Nonetheless, the colloid crystal 13690
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electric field (Figures 9 and S2). The stability of the p2 crystals of TBH-shaped particles can be attributed to jamming behavior associated with interlocking of the dumbbell shapes.
Figure 9. Dependence of packing fraction and FFT peak width on time for TBH-shaped and disk-shaped particles after removal of the electric field.
Figure 7. Calculated close-packed structures for TBH-shaped particles: (A) pmg plane group (packing fraction = 0.73), (B) pgg plane group (packing fraction = 0.78), (C) cmm plane group (packing fraction = 0.82), and (D) p2 plane group (packing fraction = 0.87). The packing fraction calculated for the p2 plane group is identical to that observed experimentally (Figure 5A).
DBT-Shaped Particles. As for TBH-shaped particles, dielectrophoresis coerces the formation of the dense packing of DBT (Figure 10). These particles are chiral in 2D, with
Figure 8. Optical microscopy images of TBH-shaped particles after removal of the electric field at 0, 1, and 2 h. The fast Fourier transforms to the right of each image reveal the slow expansion of the ordered assembly over time. Scale bar = 10 μm.
Figure 10. (A) DBT-shaped particles in the anti-Z orientation packing in the p2 plane group formed in a electric field (150 V/cm) and (B) its corresponding Fourier transform. (C) DBT-shaped particles packing in the pgg plane group. (D) The p2 packings exhibit more long-range order than the pgg packings, which typically form small domains. Scale bar = 5 μm.
retention of p2 symmetry throughout. The expansion is more rapid near the edge of the 2D crystals, and the edges are more disordered, which can be attributed to unrestricted Brownian motion of the particles. This is not unlike the melting behavior of organic crystals in which the surface is presumed to melt more easily than the interior.36 A visual inspection of successive frames reveals that an assembly initially expands perpendicular to the chains until the particles are less interlocked, after which the particles in the chain are free to rotate and the assembly expands in all directions. After 12 h, the p2 symmetry is still evident from optical microscopy although it is not evident in the FFT, which exhibits only well-defined isotropic rings corresponding to average particle−particle distances of 5.4 and 10.3 μm. In contrast, the hexagonal p6m order of disk-shaped particles (diameter = 9 μm) decayed much more rapidly, becoming completely disordered within 2 h after removal of the
opposite hands denoted here as “Z” and “anti-Z”. The predominant packing motif exhibits plane group symmetry p2 with lattice parameters of a = 6.4 μm, b = 6.0 μm, and β = 103.8° (Figure 10A,B). These values are similar to those for the (010) layer of one of the crystalline DBT polymorphs (polymorph 1), which crystallizes in the monoclinic P21 space group with a = 6.590 Å, b = 7.840 Å, c = 14.170 Å, and β = 103.50° (CSD REFCODE: DBNTHR10).37 The packing fraction of the p2 particle assembly was 87%, in close agreement with the value calculated (89%) for the dense packing of DBT-shaped particles in the p2 plane group (Figure 10C,D). The p2 plane group was the densest among the three possible plane groups that permit six nearest neighbors surrounding each particle. As for the TBH-shaped particles, 13691
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the p2 colloid crystal of DBT-shaped particles was more stable than the hexagonal assemblies of disk-shaped particles, although the p2 symmetry was recognizable for only up to 4 h rather than 12 h. Notably, the DBT-shaped particles also formed regions with rectangular pgg plane group symmetry (Figure 10C), although this was clearly a minority phase. The minor contribution of the pgg structure is consistent with its lower packing density (82%, calculated) compared to that of the p2 phase. The best estimates of the lattice constants for the pgg domains are a = 10.0 μm and b = 8.2 μm, with a packing density of 80%. The pgg packing motif is identical to the (100) layer of the other crystalline DBT polymorph (polymorph 2), which crystallizes in the orthorhombic Pcab space group with a = 8.263 Å, b = 11.466 Å, and c = 15.238 Å (CSD REFCODE: DBNTHR01).38 The 2-fold rotational center on the DBT-particle remained in the p2 global packing symmetry. As for the TBH-shaped particle assemblies, the arrangements of the colloid particles differ somewhat from those of the molecules in the molecular crystals, but the plane group symmetries are replicated. The p2 particle assembly and the (010) layer of crystalline monoclinic DBT contain particles and molecules of a single chirality (in 2D), respectively. Prior to application of the electric field, the number of particles in the anti-Z orientation slightly exceeds the number of particles in the Z orientation, in roughly a 54:46 ratio. This bias toward the anti-Z orientation is attributed to the lithographic process, which relied on a mask that projected the anti-Z image to the top surface. The development process afforded particles that were dissymmetric across their thickness, with sharp corners at the bottom of the particles (in contact with the silicon wafer) but rounded corners at the top. The preference for the anti-Z orientation in the electric cell reflected a slight preference for the side with the rounded corners facing upward. Interestingly, the chains and the final p2 particle domains were enriched in the anti-Z orientation compared to the initial ratio, with more than 60% of the particles in the anti-Z orientation. This suggests that assembly is accompanied by an amplification of the slight initial excess of the anti-Z orientation. During assembly, Z-oriented particles were observed to “flip” out of the plane during their incorporation into chains of particles with the anti-Z orientation (Figure S3). A pgg particle assembly requires an equal number particles of opposite chirality (in 2D), like the (100) layer of orthorhombic crystalline DBT (Figure 2). Unlike the p2 packings, the pgg particle assemblies are highly disordered with only local regions resembling the pgg-like packing. This may be attributed to the less dense packing of the pgg plane group and the requirement for precise ordering of both Z and anti-Z orientations.
Figure 11. Calculated close-packed structures for DBT-shaped particles in (A) the pgg plane group (packing fraction = 0.82), (B) the pg plane group (packing fraction = 0.88), and (C) the p2 plane group (packing fraction = 0.89).
nearest neighbors is not unlike layer packings in molecular crystals, wherein the centers of molecules often define lattices approaching hexagonal closest packing or face-centered cubic packing even though the molecules have complex shapes.39 Organic molecules that crystallize solely through dispersive interactions (e.g., molecules without structure-directing forces such as hydrogen bonding) are generally thought to pack up to the repulsive limit, which is mimicked here by the TBH- and DBT-shaped particles under the influence of an electric field. This correspondence is evident from the p2 symmetry observed for the TBH-shaped particle assemblies and the (010) layer motif in single crystals of tetrabenzoheptacene (Figure 2) and is corroborated by the observation of two packing arrangements, p2 and pgg, in DBT-shaped particles that mimic the (010) and (100) layer packings in single crystals of the monoclinic and orthorhombic polymorphs of DBT. Collectively, these observations illustrate that 2D packing can transcend length scales from the molecular to the colloidal.
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SUMMARY Colloidal assemblies of spheres and polygons often exhibit 2D symmetries that reflect the point group symmetry of the individual particles; that is, rotation axes and mirrors in the particle are preserved in the global 2D packing. Only the 2-fold symmetry is preserved in the packing of TBH-shaped particles, which have 2mm symmetry. DBT-shaped particles have 2-fold symmetry but lack mirror symmetry, packing predominantly in the p2 plane group but with small domains exhibiting pgg symmetry. Notably, the objects in these plane groups have a coordination number of six; that is, each object is surrounded by six contacting nearest neighbors. The tendency of the particles to pack in plane groups in which each molecule has six
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ASSOCIATED CONTENT
S Supporting Information *
Additional optical microscopy images of circular and Z-shaped particles. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. 13692
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ACKNOWLEDGMENTS This work was supported primarily by the MRSEC Program of the National Science Foundation under award number DMR0820341. We thank Dr. Eric Furst and Mr. Mark Panczyk (University of Delaware) for helpful discussions.
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