Journal ArticleDOI
A counter-example to Kelvin's conjecture on minimal surfaces
Denis Weaire,R. Phelan +1 more
TLDR
The β-tungsten structure as mentioned in this paper has a surface area that is approximately 0.3% less than that of Kelvin's structure, which is a counter-example of a structure analogous to that of some clathrate compounds.Abstract:
Kelvin's conjecture, that a b.c.c. arrangement of his minimal tetrakaidecahedron divides space into equal cells of minimum surface area, has stood for over one hundred years. We have found a counter-example, in the form of a structure analogous to that of some clathrate compounds and also related to the β-tungsten structure. Its surface area is approximately 0.3% less than that of Kelvin's structure.read more
Citations
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Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials
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.
Journal ArticleDOI
Nanoemulsions: formation, structure, and physical properties
TL;DR: In this article, the authors summarize procedures for producing nanoemulsions comprised of nanoscale droplets, methods for controlling the droplet size distribution and composition, and interesting physical properties of nanoEMulsions.
PatentDOI
Multivascular networks and functional intravascular topologies within biocompatible hydrogels
TL;DR: The Grigoryan et al. show that natural and synthetic food dyes can be used as photoabsorbers that enable stereolithographic production of hydrogels containing intricate and functional vascular architectures, and establish intravascular and multivascular design freedoms with photopolymerizablehydrogels.
Journal ArticleDOI
TOPICAL REVIEW: Nanoemulsions: formation, structure, and physical properties
TL;DR: In this article, the authors summarize procedures for producing nanoemulsions comprised of nanoscale droplets, methods for controlling the droplet size distribution and composition, and interesting physical properties of nanoEMulsions.
Journal ArticleDOI
Density Functional Theory of Adsorption in Spherical Cavities and Pore Size Characterization of Templated Nanoporous Silicas with Cubic and Three-Dimensional Hexagonal Structures
TL;DR: In this paper, the authors compared the performance of cavities with ordered nanoporous materials with cubic Pm3n (SBA-1, HMM-3), cubic Im3m (S BA-16), and 3D hexagonal P63/mmc cagelike structures, and showed that in sufficiently small cavities (pore diameters 3 ca. 6 nm), the condensation step corresponds to the theoretical limit of the metastable adsorption film.
References
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Journal ArticleDOI
The surface evolver
TL;DR: The Surface Evolver is a computer program that minimizes the energy of a surface subject to constraints that is represented as a simplicial complex.
Journal ArticleDOI
Soap, cells and statistics – random patterns in two dimensions
Denis Weaire,Nicolas Rivier +1 more
TL;DR: A survey of random two-dimensional patterns, paying particular attention to soap cell networks, metallurgical grain structures and the Giant's Causeway.
Journal ArticleDOI
Clathrate Structure of Silicon Na8Si46 and NaxSi136 (x < 11)
TL;DR: The crystal structure of two new cubic phases in the silicon-sodium system have been solved from their x-ray diffraction patterns and there is strict correspondence between the silicon positions and the oxygen positions of the hydrate structures.
Journal ArticleDOI
LXIII. On the division of space with minimum partitional area
TL;DR: In this article, the division of space with minimum partitional area is discussed, and the authors propose a solution to the problem of partitioning space with a minimum number of partsitional areas.