Crystals and Their Defects on Flat and Curved Surfaces

非技术摘要很容易用六边形完美地铺平平面，比如在公园、游乐场和浴室地板上。但是，当您尝试平铺曲面时，六角形平铺会受挫，缺陷(例如五边形)对于缓解应力和应变是必不可少的。以12个五边形为例，闭合一个六角形的测地圆屋顶，或者一个足球或一个C60分子。本研究介绍了一种独特的系统，通过该系统，粒子绑定到任意曲率的表面上，解决了几何问题，并创建了一个松弛的结构，缺陷以最佳方式排列。这项研究涉及比人类头发小30倍的胶体颗粒，它们在直径十分之一毫米的不同形状的水滴上排列。这些颗粒被显微成像，并用聚焦的光和光钳进行添加或移动。参与这个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。由于几何对所有长度尺度的结构都很重要，这些结果将对设计新的分子、组装纳米和胶体粒子以及设计新的建筑结构具有重要意义。技术摘要拓扑在材料的几何和顺序以及拓扑缺陷、位错和位错中起着至关重要的作用，决定了晶体的许多力学性质。曲率往往会阻碍周期有序，而在这里，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12个五边形为例，闭合一个原本为六角瓷砖的测地圆顶，或者一个足球或一个C60分子，曲率需要引入拓扑缺陷，即五边形倾斜，这会迫使重新定向。但在过去的几年里，人们已经意识到，尽管拓扑限制了缺陷的净数量，但实际的安排是由能量学决定的。本研究介绍了一种实验观察和操纵结合在任意曲面油水界面上的可移动胶体颗粒的系统和一些技术。参与的学生将接受最新软物质和光学技术的培训。这些视频图像对所有级别的学生和研究人员都具有很好的教学意义。这些拓扑结果将对设计新分子、组装纳米和胶体粒子以及设计新的建筑结构具有重要意义。

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.