Pleats in crystals on curved surfaces
Pleats in crystals on curved surfaces
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DOI：
10.1038/nature09620
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发表时间：
2010-12-16
期刊：
影响因子：
64.8
通讯作者：
Chaikin, Paul M.
中科院分区：
文献类型：
--
作者：
Irvine, William T. M.;Vitelli, Vincenzo;Chaikin, Paul M.
障碍物可以很容易地平铺一个平面，但不是一个曲面。引入七边形和五边形（带拓扑电荷的缺陷）使曲面更容易拼接;例如，基于巴克·富勒的测地线圆顶（1）的足球正好有12个五边形（正电荷）。在平面上总是形成六方晶体的相互作用粒子在球体上表现出迷人的疤痕缺陷图案（2-4）。在这里，我们表明，对于更一般的曲面，曲率可以放松褶皱：不带电的线的位错（拓扑偶极子），消失在表面上，并发挥相同的作用，织物褶皱。我们的实验研究晶体的顺序与空间变化的积极和消极的曲率表面。在圆柱形毛细管桥，拉伸产生负曲率，我们观察到一系列的过渡与我们的精力充沛的计算一致，从没有缺陷孤立的位错，随后增殖和组织成褶皱，最后，疤痕和孤立的七边形（以前看不见的）出现。这种用曲率对晶体有序的精细控制，将使我们能够探索弯曲空间中缺陷的一般理论（5-11）。从实际的角度来看，有可能设计出具有曲率的结构（例如腰形纳米管和拱形结构），并开发出用于软光刻（12）和定向自组装（13）的新方法。
Hexagons can easily tile a flat surface, but not a curved one. Introducing heptagons and pentagons (defects with topological charge) makes it easier to tile curved surfaces; for example, soccer balls based on the geodesic domes(1) of Buckminster Fuller have exactly 12 pentagons (positive charges). Interacting particles that invariably form hexagonal crystals on a plane exhibit fascinating scarred defect patterns on a sphere(2-4). Here we show that, for more general curved surfaces, curvature may be relaxed by pleats: uncharged lines of dislocations (topological dipoles) that vanish on the surface and play the same role as fabric pleats. We experimentally investigate crystal order on surfaces with spatially varying positive and negative curvature. On cylindrical capillary bridges, stretched to produce negative curvature, we observe a sequence of transitions-consistent with our energetic calculations-from no defects to isolated dislocations, which subsequently proliferate and organize into pleats; finally, scars and isolated heptagons (previously unseen) appear. This fine control of crystal order with curvature will enable explorations of general theories of defects in curved spaces(5-11). From a practical viewpoint, it may be possible to engineer structures with curvature (such as waisted nanotubes and vaulted architecture) and to develop novel methods for soft lithography(12) and directed self-assembly(13).