Crystals and Their Defects on Flat and Curved Surfaces

在平坦的表面上完美地铺上六边形瓷砖是很容易的，比如在公园、游乐场和浴室的地板上。但是当你试图平铺一个曲面时，六边形的平铺是失败的，而缺陷，例如五边形，对于减轻应力和应变是必不可少的。见证了12个五边形需要关闭一个六边形瓷砖的测地线圆顶，或一个足球或C60分子。本研究介绍了一个独特的系统，使粒子绑定到任意曲率的表面解决几何问题，并创建一个轻松的结构与缺陷的最佳安排。该研究涉及比人类头发小三十倍的胶体颗粒，它们排列在直径十分之一毫米的不同形状的水滴上。这些粒子在显微镜下成像，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指导各级学生和研究人员了解液体和固体基本性质的重要教学工具。由于几何结构是重要的，在所有的长度尺度这些结果将是重要的设计新的分子，为组装纳米和胶体粒子和工程新的建筑结构。技术摘要拓扑起着至关重要的作用，在几何形状和秩序的材料和拓扑缺陷，向错和位错，确定许多机械性能的晶体。曲率倾向于破坏周期性秩序，这里拓扑缺陷在缓解由此产生的应力和应变方面起着重要作用。一个六边形的测地线圆顶、一个足球或一个C60分子需要12个五边形来闭合，曲率需要引入拓扑缺陷，即五边形-向错，它迫使重定向。但是在过去的几年里，人们已经认识到，虽然拓扑结构限制了缺陷的净数量，但实际的排列是由能量决定的。本研究介绍了一种系统和多种技术来实验观察和操纵束缚在任意曲面油水界面上的移动的胶体颗粒。参与的学生将接受最新软物质和光学技术的培训。视频图像对各级学生和研究人员来说都是很好的教学方法。这些拓扑结果对于设计新的分子、组装纳米和胶体粒子以及设计新的建筑结构将是重要的。

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.