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Faculty and Senior Participants: Jasna Brujic, Paul M. Chaikin, David G. Grier, David J. Pine, E. Dianne Rekow, Nadrian C. Seeman, Mike J. Shelley, Paul J. Steinhardt, Van P. Thompson, Sal Torquato, Marcus Weck, Jun Zhang, Michael D. Ward
Other: 7 Graduate Students, 5 Postdocs
Confocal Studies of Packing. Postdoctoral research associates Maxime Clusel and Eric Corwin are investigating the packing of polydisperse spheres with Brujic, using confocal microscopy measurements, numerical simulations and theoretical analysis. At a given density, particulate systems pack into a mechanically stable and amorphous jammed state. Theoretical frameworks have explored a connection between this jammed state and the glass transition, a thermodynamics of jamming, as well as geometric modeling of random packings. In their study, Clusel, Corwin and Brujic used 3D measurements of polydisperse packings of emulsion droplets to build a simple statistical model for random packing. The complexity of the global packing was distilled into a local stochastic process. From the perspective of a single particle, the packing problem is reduced to the random formation of nearest neighbors, followed by a choice of contacts among them. The two key parameters in the model, the available space around a particle and the ratio of contacts to neighbors, are directly obtained from experiments. Remarkably, this granocentric view captures the properties of the polydisperse emulsion packings, ranging from the microscopic distributions of nearest neighbors and contacts to local density fluctuations and all the way to the global packing density. Further applications to monodisperse and bidisperse systems quantitatively agree with previously measured trends in global density. This model therefore reveals a general principle of organization for random packing and lays the foundations for a theory of jammed matter. A manuscript has been accepted by Nature.
Geometry of tetrahedral and ellipsoidal random structures. Graduate Student Alex Jaoshvili, with Chaikin and Torquato, has developed the computational technology to analyze MRI and X-ray tomographic images of arbitrarily shaped objects to identify their positions and orientations. In experimental studies we have concentrated on the properties of ellipsoids and tetrahedra. The ellipsoids have been made extremely rough; hence they have high effective friction. Consequently, the number of neighboring contacts is reduced relative to low friction disordered structures. This could produce low yield, low strength ceramics. On the other hand, the tetrahedral systems, when randomly jammed, have many neighboring constraints and a high density. They are more “random” (less ordered than similar randomly arranged spheres) in terms of both orientational and translation correlation functions. A ceramic made from tetrahedral particles poured into a mold and sintered would therefore be more isotropic and homogenous as well as stronger and with higher yield that a ceramic made with spherical particles.
Diversity of Disordered Sphere Packings. Torquato and collaborator Stillinger have demonstrated that disordered sphere packings can have densities anywhere between the maximally random jammed value (0.64) and the theoretical upper limit typically associated with close-packed ordered arrangements. Elementary smooth functions (beyond contact) are employed to construct pair correlation functions that mimic jammed disordered sphere packings. A translational order metric was used to discriminate between degrees of order in the packings presented. The degree of order must increase to achieve higher packing fractions, which is consistent with previous work by Torquato.
Optimal Packings of Superballs. Superballs (whose shapes are defined by |x1|2p+|x2|2p+|x3|2p =1) provide a versatile family of convex particles (p >0.5) with both cubic- and octahedral-like shapes as well as concave particles (0 < p < 0.5) with octahedral-like shapes. We have provided analytical constructions for the densest known superball packings for all convex and concave cases. The candidate maximally dense packings are certain families of Bravais lattice packings wherein each particle has 12 contacting neighbors, which possess the global symmetries consistent with certain symmetries of a superball. The evidence indicates that packings for convex superballs (p > 0.5) are most likely the optimal ones. The maximal packing density as a function of p is nonanalytic at the sphere-point (p = 1) and increases dramatically as p moves away from unity.
Colloids with molecular contours. Despite their irregular shapes, organic molecules readily crystallize with nanometer-scale unit cells and numerous distinct packing arrangements (17 2D plane groups and 230 3D space groups) distinguished by unique groups of symmetry operations. In contrast, micron-sized colloids are spherical and crystallize in face-centered cubic (FCC) or hexagonal close-packed (HCP) lattices. Chaikin and Ward are using photolithographic methods to fabricate anisotropic polymeric micron-scale particles with congruent surfaces, particularly shapes that mimic the contours of actual molecules, to explore how shape directs packing and whether it gives correspondence to molecular crystals. For example, a key question is whether the symmetry operations that favor close packing in molecular van der Waals crystals (i.e. glide planes, screw axes, inversion centers) are applicable to larger objects. The assembly of these particles will be driven by dielectrophoretic fields supplied by an “electric bottle,” recently developed in Chaikin’s lab. In order to achieve the contours required for this project for micron-sized colloids, graduate students Brian Olmsted and Pengchang Song have designed a hard mask that will capitalize on the high resolution of the mask aligner and reveal the ultimate resolution of the complex shapes that will be fabricated. The mask contains 60 arrays with 6 shapes each at 5 different length scales ranging from 2 – 10 microns.
Controllable Nanoglue. The ability of single-stranded DNA to form a variety of folded ‘secondary’ structures is frequently used in DNA nanotechnology, but has so far not been explored for the assembly of (nano)colloidal structures. Postdocs Leunissen and Dreyfus, with Chaikin and Seeman, have shown how loop and hairpin formation in the DNA coatings of micron-sized particles allow in situ control of both the inter-particle binding strength and particle association kinetics. Using different temperature and concentration protocols, interactions between the particles can be finely tuned and even inhibited, rendering them essentially inert unless they are heated or held together - like a nano contact glue. A simple quantitative model describes the underlying competition between intra- and inter-particle DNA hybridization, while our experiments demonstrate how the self-protected interactions enable the assembly of stable designer clusters, which can be re-activated later on. The availability of switchable self-protected interactions thus allows for more versatile, multi-stage assembly approaches involving nanoparticles and micro-colloids. In addition, the structures formed are indefinitely stable in the presence of other structures and particles. Conventional colloids with these attractive interactions would simply aggregate whereas this system is stable indefinitely.
Colloidal Cluster Tectonics. Weck, Pine, and Ward are developing the science of directed assembly of complex building blocks with tunable interactions implemented over a range of length scales. In particular, symmetry and molecular recognition concepts are being devised that employ polymeric and small molecule tectonics for the assembly of colloids across multiple length scales. The strategy is based on colloidal particles with "sticky patches" based on polymer tethers, containing terminal structure directing groups such as hydrogen bonding motifs or metal coordination complexes, arranged with prescribed symmetries. Using standard self-assembly procedures, the patchy particles can then be assembled into well-defined 3D networks of colloidal clusters with network symmetries that reflect propagation of the local symmetry of the sticky patches on the colloidal cluster. Staff scientist Andrew Hollingsworth, graduate students Si Kyung Yang and Yufeng Wang, and undergraduate Sonal Patel have developed protocols for the synthesis of acid-containing patchy particles. Furthermore, Yang and Patel have developed a synthetic methodology towards the synthesis of heterotelechelic polymers containing an alcohol group on one terminus (for ester formation with the acid group on the patchy particles) and a structure-directing group on the other end. The synthetic strategy is based on the combination of ring-opening metathesis polymerization with functionalized ruthenium initiators and polymer chain terminators.
Fabrication and assembly of “swimmers”. Pine and Chaikin, working with collaborator Bibette, developed a method using magnetic aggregation of asymmetric colloidal dumbbells to form micron-scale helical clusters. Such clusters offer the potential for controllable transport and separation in low Reynolds number environments using externally applied electric or magnetic fields or circularly polarized light. If such a particle could be rotated about its axis, then it should transport itself (and a payload) by corkscrewing through the fluid. Establishing the hydrodynamic properties of the aggregates is the essential first step toward the design of microfluidic devices employing these aggregates. To do this, Shelley and postdocs Keaveny have performed hydrodynamic calculations. This work has revealed that indeed such aggregates will rotate and hence swim under an applied torque. Moreover, the aggregate geometry has surprising consequences for this motion; for larger ratios of the dumbbell asymmetry, the coupling between rotations and translations changes sign as the number of doublets in the aggregate increases. Consequently, if the aggregate is too long, it will swim in the direction opposite to intuition. This feature is associated with the emergence of a more complex superhelical structure in the aggregate morphology.
Pine and Chaikin recently demonstrated that oscillating shear can cause particles that initially are randomly distributed to self-organize through a process in which collisions between particles diminish with time. A new project explores how such an irreversible/reversible transition occurs in a suspension of rods; in particular it investigates the physical processes by which oscillating shear flow might cause a suspension of rods to organize. Franceschini and Pine, working with Dr. Elisabeth Guazzelli, a visiting scientist from the University of Marseille, have discovered that suspensions of non-Brownian rods undergo irreversible/reversible transitions at much lower concentrations than do spheres. Preliminary measurements suggest that shear-induced irreversible motions are both more localized and more violent in suspensions of rods. The measurements reveal a non-trivial coupling between what appears to be random orientational movements and cooperative translational motion. The team is developing methods to quantitatively measure and characterize the rod dynamics and will be working with Shelley and collaborator Morris (CCNY, Chemical Engineering) to predict the temporal evolution and organization of the hydrodynamically interacting rods.
Crystallization under nanoscale confinement. In an inter-MRSEC collaboration, Ward and collaborator Marc Hillmyer at the University of Minnesota, with co-advised graduate student Ben Hamilton, demonstrated that nanocrystals of glycine can be grown in aligned nanometer-scale cylindrical pores of nanoporous poly(styrene)-poly(dimethyl acrylamide) monoliths by evaporation of imbibed aqueous solutions. Moreover, these crystals adopt preferred orientations with their fast-growth axes aligned parallel with the pore direction. X-ray diffraction analysis revealed the exclusive formation of the metastable beta-polymorph, with crystal size comparable with the 22 nm pore diameter, in contrast to the formation of alpha-glycine in the absence of nanoscale confinement. When grown from aqueous solutions alone, the nanocrystals were oriented with their [010] and [0-10] axes, the native fast growth directions of the (+) and (-) enantiomorphs of beta-glycine, respectively, aligned parallel with the pore direction. In contrast, crystallization in the presence of racemic mixtures of chiral auxiliaries known to inhibit growth along the [010] and [0-10] directions of the enantiomorphs produced beta-glycine nanocrystals with their [001] axes nearly parallel to the pore direction. Enantiopure auxiliaries that inhibit crystallization along the native fast growth direction of only one of the enantiomorphs allow the other enantiomorph to grow with the [010] axis parallel to the cylinder. Collectively, these results demonstrate that crystal growth occurs such that the fast-growing direction, which can be altered by adding chiral auxiliaries, is parallel to the pore direction. This behavior can be attributed to a competition between differently aligned crystals due to critical size effects, the minimization of the surface energy of specific crystal planes, and a more effective reduction of the excess free energy associated with supersaturated conditions when the crystal grows with its fast-growth axis unimpeded by pore walls. The formation of a noncentrosymmetric crystalline phase because of nanoconfinement, in this case beta-glycine, also may suggest a role for this phenomenon in the genesis or amplification of biological homochirality in clay or mineral matrices. This article was featured on the cover of the Journal of the American Chemical Society (February 25, 2009) and is the subject of a podcast interview on the JACS site.
Microscopic Topography of Heterocrystal Interfaces. With collaborators Wais Hosseini and Sylvie Ferlay of the University of Strasbourg, Ward and graduate student Brian Olmstead used real-time in situ atomic force microscopy (AFM) to examine the (010) and (001) planes of isomorphous [1,4-bis(amidinium)benzene]2 M(CN)6.8H2O (M = Fe, Ru) crystals, known to exhibit growth of one of the metallate compounds on the other to produce “core-shroud” heterocrystals. These studies revealed high-fidelity epitaxial growth during heterocrystal formation or growth on roughened surfaces, depending on the crystal face and crystallization conditions. The roughened crystal surfaces that define the interface between heteroepitaxial layers under typical growth conditions are consistent with the interface structure observed by electron dispersive spectrometry, which indicated intermixing of the two materials throughout a 0.7 µm-thick interfacial region, but could not distinguish between various possible mechanisms for the intermixing. These observations suggest that the roughness of the growth interface can be regulated using specific growth protocols that minimize the intermixing of the two compounds.
Natural Quasicrystals. Quasicrystals are solids whose atomic arrangements have symmetries forbidden for periodic crystals, such as five-fold symmetry. The concept was introduced twenty-five years ago and more than 100 different quasicrystalline solids have been discovered since. Until now, however, the only known examples were synthesized in the laboratory under controlled conditions. Steinhardt has now reported the first case of a naturally occurring icosahedral quasicrystal that incorporates six distinct five-fold symmetry axes and is nearly perfect structurally (Figure 9). The mineral, an alloy of aluminum, copper and iron, occurs as micron-sized grains associated with crystalline khatyrkite and cupalite in samples obtained from the Koryak mountains in Russia. A nearly structurally perfect natural quasicrystal, formed under geologic conditions, has several implications for geology and condensed-matter physics. Clearly, the definition of a mineral, previously through to include only periodic crystals, incommensurate structures and amorphous phases, must henceforth be extended to include quasicrystals. This occurrence raises an interesting challenge to explain how quasicrystals form naturally, a question that may reveal new physical processes in the Earth. Finally, the study of natural quasicrystals may provide insights about the formation and stability of quasicrystals at temperatures and pressures not studied previously under laboratory conditions, while providing an avenue for using nature to discover new quasicrystals with compositions not yet synthesized. A manuscript by Steinhardt was published in Science.
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