Publications and Patents

2009

A 'Granocentric View of Random Packing of Jammed Emulsions
NYU MRSEC Investigators - Jasna Brujic, Eric Corwin, Maxime Clusel
07.30.09

Text Box: Schematic representation of polymerase-catalyzed generation of DNA scaffolds with pendant monomers from nucleoside-monomer substrates (B = nucleotide; two monomers here depicted as blue and green pendant groups). The knot structure, enforced by the oligonucleotide sequence, contains a sequence-specific ordering of the monomers along the scaffold. Polymerization of the monomers attached to the knotted scaffold by a second enzyme, followed by cleavage from the scaffold, produce a copolymer with a knot topology and a sequence encoded by the oligonucleotide sequence. How many sweets fit into a jar? This question depends on the shape and sizes of the sweets, the size of the jar, and how the jar is filled. Surprisingly, this ancient question remains unanswered because of the complex geometry of the packing of the sweets. Moreover, as any contestant knows, guessing the number of sweets in the jar is difficult because the sweets, a.k.a. particles, located at the center of the jar are hidden from view and can't be counted. Imagine if you could see inside!

To answer the question of how particles pack in general, researchers at New York University made a transparent, fluorescent packing of oil droplets in water, which allowed them to record 3D images and examine the local geometry of each member of the pack. What does a packing look like from the point of view of a grain within, i.e. a "granocentric" view? They found that packing strongly depends on the size distribution, that is, larger particles pack with more neighbors than the small ones and vice versa. Nevertheless, the average number of contacts per particle always stays the same to preserve mechanical stability. These experimental clues led to a model that describes the geometry, connectivity, and density of the sphere packings. This means that starting from a set of particles of known sizes, the density of packing can be determined, making it possible to guess the number of sweets in the jar!

Packing problems are important in technological settings as well, ranging from oil extraction through porous rocks to grain storage in silos to the compaction of pharmaceutical powders into tablets. The ability to predict the packing of polydisperse particles (meaning a range of sizes in a single system) has significant impact on these and related technologies.

A 'granocentric' view of random packing of jammed emulsions - M. Clusel, E. Corwin, A. Seimans, J. Brujic; Nature, 2009, 406, 611-615

Professor Jasna Brujic's Nature Article is also covered by the National Science Foundation, Scientific American, Time Online (UK), The New York Post, Spektrum Direkt (In German - login required), Science Daily, Taragana, news.SmasHits.com, Futurity.org, and Abril.com (In Spanish)


Dense packings of the Platonic and Archimedean solids
MRSEC Investigators - Salvatore Torquato, Yang Jiao
08.13.09

Text Box: Schematic representation of polymerase-catalyzed generation of DNA scaffolds with pendant monomers from nucleoside-monomer substrates (B = nucleotide; two monomers here depicted as blue and green pendant groups). The knot structure, enforced by the oligonucleotide sequence, contains a sequence-specific ordering of the monomers along the scaffold. Polymerization of the monomers attached to the knotted scaffold by a second enzyme, followed by cleavage from the scaffold, produce a copolymer with a knot topology and a sequence encoded by the oligonucleotide sequence. How can you pack as many grains as possible into a large container? This ancient question is of great practical importance and depends on the details of the shape of the grains, and how the container is filled. It is a notoriously difficult question to answer even for simple shapes (like spheres), not to mention more complex shapes.

To answer the question of how densely particles with complex shape can pack, researchers at Princeton University developed and carried out computer simulations of the four non-tiling Platonic solids – regular polyhedra known since the ancient Greeks – the tetrahedron, icosahedron, dodecahedron and octahedron. From the simulations, they found the densest known arrangements of these polyhedra and set a new world record for the packing density (i.e., fraction of space covered by the particles) of the tetrahedral packing. Moreover, through theoretical analysis of the Platonic solids and Archimedean solids (semi-regular polyhedra) (see figure), the researchers discovered a unifying organizing principle that explains how these polyhedra Densely pack space. Namely, particles with a special type of symmetry (central symmetry) like to be arranged in an ordered way such that the packing density is maximized.

The only Platonic and Archimedean solids that lack of central symmetry are the tetrahedron and truncated tetrahedron, respectively, must be arranged in more jumbled way to achieve high packing densities. Their simulation results together with derived rigorous upper bounds and theoretical arguments led them to the conjecture that the densest packings of the Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This is the analogue of Kepler’s famous four-century old sphere conjecture for these solids.

Dense packings of the Platonic and Archimedean solids, S. Torquato, Y. Jiao, Nature, 2009, 460, 876-879

Natural Quasicrystals
MRSEC Investigators - Paul Steinhardt
06.05.09

Text Box:Fig. 1. (A) The original khatyrkite-bearing sample used in the study. The lighter-colored material on the exterior contains a mixture of spinel, augite, and olivine. The dark material consists predominantly of khatyrkite (CuAl2) and cupalite (CuAl) but also includes granules, like the one in (B), with composition Al63Cu24Fe13. The diffraction patterns in Fig. 4 were obtained from the thin region of this granule indicated by the red dashed circle, an area 0.1 µm across. (C) The inverted Fourier transform of the HRTEM image taken from a subregion about 15 nm across displays a homogeneous, quasiperiodically ordered, fivefold symmetric, real space pattern characteristic of quasicrystals.
Quasicrystals are solids whose atomic arrangements have symmetries that are forbidden for periodic crystals, including configurations with fivefold symmetry. All examples identified to date have been synthesized in the laboratory under controlled conditions. Here we present evidence of a naturally occurring icosahedral quasicrystal that includes six distinct fivefold symmetry axes. The mineral, an alloy of aluminum, copper, and iron, occurs as micrometer-sized grains associated with crystalline khatyrkite and cupalite in samples reported to have come from the Koryak Mountains in Russia. The results suggest that quasicrystals can form and remain stable under geologic conditions, although there remain open questions as to how this mineral formed naturally.

Natural Quasicrystals, L. Bindi, P. J. Steinhardt, N. Yao, P. J. Lu, Science, 2009, 324, 1306 - 1309

 



Text Box: Figure C.4.1. Schematic representation of polymerase-catalyzed generation of DNA scaffolds with pendant monomers from nucleoside-monomer substrates (B = nucleotide; two monomers here depicted as blue and green pendant groups). The knot structure, enforced by the oligonucleotide sequence, contains a sequence-specific ordering of the monomers along the scaffold. Polymerization of the monomers attached to the knotted scaffold by a second enzyme, followed by cleavage from the scaffold, produce a copolymer with a knot topology and a sequence encoded by the oligonucleotide sequence.

Investigators at the New York University MRSEC and the University of Minnesota MRSEC have reported the growth of glycine nanocrystals inside aligned cylindrical nanopores of a polymer monolith that was derived from an ordered block polymer precursor. The size confinement imposed by the nanopores stabilizes the least stable beta polymorph, and the crystals grow with their native fast-growth direction aligned parallel with each pore.Furthermore, selective binding of racemic auxiliaries (circled) to the crystal face (red) perpendicular to this direction results in faster growth along a different crystal direction, which changes the crystal orientation. 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. See the article at J. Am. Chem. Soc. 2009, 131, 2588-2596. Supported by NYU MRSEC Award DMR#0820341 and UMN MRSEC Awards DMR#0212302 and DMR#0819885

Listen to JACS podcast of Marc Hillmyer and Mike Ward discussing this research: http://pubs.acs.org/JACSbeta/coverartpodcasts/index.html#podcast6"







 
 
 
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