Directed self-assembly of a colloidal kagome lattice
TL;DR: This paper shows how colloidal spheres can be induced to self-assemble into a complex predetermined colloidal crystal—in this case a colloidal kagome lattice—through decoration of their surfaces with a simple pattern of hydrophobic domains, and encodes the target supracolloidal architecture.
Abstract: A challenging goal in materials chemistry and physics is spontaneously to form intended superstructures from designed building blocks. In fields such as crystal engineering and the design of porous materials, this typically involves building blocks of organic molecules, sometimes operating together with metallic ions or clusters. The translation of such ideas to nanoparticles and colloidal-sized building blocks would potentially open doors to new materials and new properties, but the pathways to achieve this goal are still undetermined. Here we show how colloidal spheres can be induced to self-assemble into a complex predetermined colloidal crystal-in this case a colloidal kagome lattice-through decoration of their surfaces with a simple pattern of hydrophobic domains. The building blocks are simple micrometre-sized spheres with interactions (electrostatic repulsion in the middle, hydrophobic attraction at the poles, which we call 'triblock Janus') that are also simple, but the self-assembly of the spheres into an open kagome structure contrasts with previously known close-packed periodic arrangements of spheres. This open network is of interest for several theoretical reasons. With a view to possible enhanced functionality, the resulting lattice structure possesses two families of pores, one that is hydrophobic on the rims of the pores and another that is hydrophilic. This strategy of 'convergent' self-assembly from easily fabricated colloidal building blocks encodes the target supracolloidal architecture, not in localized attractive spots but instead in large redundantly attractive regions, and can be extended to form other supracolloidal networks.
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TL;DR: This review discusses efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions, and explores the unique possibilities offered by leveraging nontraditional surface chemistries and assembly environments to control superlattice structure and produce nonbulk assemblies.
Abstract: Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self-assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micro...
1,376 citations
TL;DR: This work demonstrates a general method for creating the colloidal analogues of atoms with valence: colloidal particles with chemically distinct surface patches that imitate hybridized atomic orbitals, including sp, sp2, sp3, sp 3d, sp4d2 and sp3d3.
Abstract: The ability to design and assemble three-dimensional structures from colloidal particles is limited by the absence of specific directional bonds. As a result, complex or low-coordination structures, common in atomic and molecular systems, are rare in the colloidal domain. Here we demonstrate a general method for creating the colloidal analogues of atoms with valence: colloidal particles with chemically distinct surface patches that imitate hybridized atomic orbitals, including sp, sp2, sp3, sp3d, sp3d2 and sp3d3. Functionalized with DNA with single-stranded sticky ends, patches on different particles can form highly directional bonds through programmable, specific and reversible DNA hybridization. These features allow the particles to self-assemble into ‘colloidal molecules’ with triangular, tetrahedral and other bonding symmetries, and should also give access to a rich variety of new microstructured colloidal materials. A general method of creating colloidal particles that can self-assemble into ‘colloidal molecules’ is described: surface patches with well-defined symmetries are functionalized using DNA with single-stranded sticky ends and imitate hybridized atomic orbitals to form highly directional bonds. Chemists routinely use atoms that can form directional bonds to assemble complex and useful molecular structures. But larger colloidal particles have proved less conducive to rational assembly because they lack specific directional bonds. David Pine and colleagues now report a way around this problem that could lead to the creation of a rich variety of new micro-structured colloidal materials with technologically useful properties. Using microsphere clusters as intermediates, they create colloidal particles with chemically distinct and precisely located 'sticky patches' on the surface — up to 7 per particle — that enable specific and highly directional bonding. Using this system, they assemble 'colloidal molecules' exhibiting a wide range of bonding symmetries.
954 citations
TL;DR: Research in electronic nanomaterials, historically dominated by studies of nanocrystals/fullerenes and nanowires/nanotubes, now incorporates a growing focus on sheets with nanoscale thicknesses, referred to as nanomembranes, which have practical appeal because their two-dimensional geometries facilitate integration into devices, with realistic pathways to manufacturing.
Abstract: Research in electronic nanomaterials, historically dominated by studies of nanocrystals/fullerenes and nanowires/nanotubes, now incorporates a growing focus on sheets with nanoscale thicknesses, referred to as nanomembranes. Such materials have practical appeal because their two-dimensional geometries facilitate integration into devices, with realistic pathways to manufacturing. Recent advances in synthesis provide access to nanomembranes with extraordinary properties in a variety of configurations, some of which exploit quantum and other size-dependent effects. This progress, together with emerging methods for deterministic assembly, leads to compelling opportunities for research, from basic studies of two-dimensional physics to the development of applications of heterogeneous electronics.
661 citations
References
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TL;DR: In this article, the modularity of a network is expressed in terms of the eigenvectors of a characteristic matrix for the network, which is then used for community detection.
Abstract: Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as “modularity” over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times. I illustrate the method with applications to several published network data sets.
10,137 citations
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
Abstract: The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries --- stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for decomposition have been proposed, including the method of frames (MOF), Matching pursuit (MP), and, for special dictionaries, the best orthogonal basis (BOB).
Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP, and BOB, including better sparsity and superresolution. BP has interesting relations to ideas in areas as diverse as ill-posed problems, in abstract harmonic analysis, total variation denoising, and multiscale edge denoising.
BP in highly overcomplete dictionaries leads to large-scale optimization problems. With signals of length 8192 and a wavelet packet dictionary, one gets an equivalent linear program of size 8192 by 212,992. Such problems can be attacked successfully only because of recent advances in linear programming by interior-point methods. We obtain reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver.
9,950 citations
"Directed self-assembly of a colloid..." refers methods in this paper
...Relaxing a combinatorial problem into a convex one is another instantiation of the general strategy, used for example to recover spike trains [50, 51] and sparse images from a few Fourier modes [52] by minimizing l1-norm....
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TL;DR: This work has shown that highly porous frameworks held together by strong metal–oxygen–carbon bonds and with exceptionally large surface area and capacity for gas storage have been prepared and their pore metrics systematically varied and functionalized.
Abstract: The long-standing challenge of designing and constructing new crystalline solid-state materials from molecular building blocks is just beginning to be addressed with success. A conceptual approach that requires the use of secondary building units to direct the assembly of ordered frameworks epitomizes this process: we call this approach reticular synthesis. This chemistry has yielded materials designed to have predetermined structures, compositions and properties. In particular, highly porous frameworks held together by strong metal-oxygen-carbon bonds and with exceptionally large surface area and capacity for gas storage have been prepared and their pore metrics systematically varied and functionalized.
8,013 citations
Book•
01 Jan 1982
TL;DR: In this article, exactly solved models of statistical mechanics are discussed. But they do not consider exactly solvable models in statistical mechanics, which is a special issue in the statistical mechanics of the classical two-dimensional faculty of science.
Abstract: exactly solved models in statistical mechanics exactly solved models in statistical mechanics rodney j baxter exactly solved models in statistical mechanics exactly solved models in statistical mechanics flae exactly solved models in statistical mechanics dover books exactly solved models in statistical mechanics dover books exactly solved models in statistical mechanics dover books hatsutori in size 15 gvg7bzbookyo.qhigh literature cited r. j. baxter, exactly solved models in exactly solvable models in statistical mechanics exactly solved models in statistical mechanics dover books okazaki in size 24 vk19j3book.buncivy exactly solved models of statistical mechanics valerio nishizawa in size 11 b4zntdbookntey fukuda in size 13 33oloxbooknhuy yamada in size 19 x6g84ybook.zolay in honour of r j baxter’s 75th birthday arxiv:1608.04899v2 statistical mechanics, threedimensionality and np beautiful models: 70 years of exactly solved quantum many exactly solved models in statistical mechanics (dover solved lattice models: 1944 2010 university of melbourne exactly solved models and beyond: a special issue in the statistical mechanics of the classical two-dimensional faculty of science, p. j. saf ́arik university in ko?sice? a one-dimensional statistical mechanics model with exact statistical mechanics department of physics and astronomy statistical mechanics principles and selected applications graph theory and statistical physics yaroslavvb chapter 4 methods of statistical mechanics ijs thermodynamics and an introduction to thermostatistics potts models and related problems in statistical mechanics methods of quantum field theory in statistical physics statistical mechanics: theory and molecular simulation exactly solvable su(n) mixed spin ladders springer statistical field theory : an introduction to exactly
7,761 citations
"Directed self-assembly of a colloid..." refers methods in this paper
...The approach followed in this thesis is to study exactly solvable models, in the sense of Baxter [1]....
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