Crystals and Their Defects on Flat and Curved Surfaces

平面和曲面上的晶体及其缺陷

• 批准号: 1105417
• 负责人: Paul Chaikin
• 金额: $ 43.5万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1105417&HistoricalAwards=false
• 关键词: Crystals; Their; Defects; Flat; Curved

Non-Technical AbstractIt is easy to perfectly tile a flat surface with hexagons, as in parks and playgrounds and bathroom floors. But when you try to tile a curved surface, the hexagonal tiling is frustrated and the defects, for example pentagons, are essential for relieving the stresses and strains. Witness the 12 pentagons required to close an otherwise hexagonally tiled geodesic dome, or a soccer ball or a C60 molecule. The present study introduces a unique system whereby particles bound to a surface of arbitrary curvature solve the geometric problem and create a relaxed structure with defects arranged optimally. The study involves colloidal particles, thirty times smaller than a human hair, which arrange themselves on different shaped water droplets a tenth of a millimeter in diameter. The particles are imaged microscopically and added or moved with focused light, optical tweezers. Students working on this project are trained in the latest optical techniques. The video imaging of defects and their dynamics in crystals is a great pedagogical tool for instructing students and researchers at all levels as to the basic properties of liquids and solids. Since geometry is important for structures at all length scales these results will be important for designing new molecules, for assembling nano and colloidal particles and for engineering new architectural structures.Technical AbstractTopology plays a crucial role in the geometry and order of materials and topological defects, disclinations and dislocations, determine many of the mechanical properties of crystals. Curvature tends to frustrate periodic order, and here topological defects play an important role in relieving the resulting stresses and strains. Witness the 12 pentagons required to close an otherwise hexagonally tiled geodesic dome, or a soccer ball or a C60 molecule, curvature requires the introduction of topological defects, pentagons - disclinations, which force reorientation. But within the past several years it has been realized that although topology constrains the net number of defects it is energetics that dictates the actual arrangements. The present study introduces a system and a number of techniques to experimentally observe and manipulate mobile colloidal particles which are bound to an arbitrarily curved surface oil-water interface. Students involved will be trained in the latest soft matter and optical techniques. The video images are great pedagogically for students and researchers at all levels. These topological results will be important for designing new molecules, for assembling nano and colloidal particles and for engineering new architectural structures.

非技术摘要用六边形完美地铺设平坦表面很容易，例如公园、游乐场和浴室地板。但是，当您尝试在弯曲表面上铺瓷砖时，六边形瓷砖就会受挫，而缺陷（例如五边形）对于缓解应力和应变至关重要。看看需要 12 个五边形来闭合一个六边形平铺的测地圆顶，或者一个足球或一个 C60 分子。本研究引入了一种独特的系统，通过该系统，颗粒结合到任意曲率的表面上可以解决几何问题，并创建具有最佳排列的缺陷的松弛结构。这项研究涉及比人的头发小三十倍的胶体颗粒，它们排列在直径为十分之一毫米的不同形状的水滴上。颗粒在显微镜下成像，并用聚焦光、光镊添加或移动。从事该项目的学生接受了最新光学技术的培训。晶体中缺陷及其动力学的视频成像是一个很好的教学工具，可以指导各级学生和研究人员了解液体和固体的基本性质。由于几何形状对于所有长度尺度的结构都很重要，因此这些结果对于设计新分子、组装纳米和胶体颗粒以及设计新的建筑结构也很重要。技术摘要拓扑在材料的几何形状和顺序以及拓扑缺陷中起着至关重要的作用，向错和位错决定了晶体的许多机械性能。曲率往往会破坏周期顺序，而拓扑缺陷在缓解由此产生的应力和应变方面发挥着重要作用。以闭合六角形平铺测地圆顶、足球或 C60 分子所需的 12 个五边形为例，曲率需要引入拓扑缺陷、五边形 - 旋错，这会迫使重新定向。但在过去的几年里，人们已经认识到，尽管拓扑结构限制了缺陷的净数量，但能量学决定了实际的排列。本研究介绍了一种系统和多种技术来实验观察和操纵与任意弯曲表面油水界面结合的移动胶体颗粒。参与的学生将接受最新软物质和光学技术的培训。这些视频图像对于各个级别的学生和研究人员来说在教学上都非常有用。这些拓扑结果对于设计新分子、组装纳米和胶体颗粒以及设计新的建筑结构非常重要。