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Defect-Driven Shape Instabilities of Bundles

机译：缺陷驱动的捆绑形状稳定性

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Topological defects are crucial to the thermodynamics and structure of condensed matter systems. For instance, when incorporated into crystalline membranes like graphene, disclinations with positive and negative topological charge elastically buckle the material into conical and saddlelike shapes, respectively. A recently uncovered mapping between the interelement spacing in 2D columnar structures and the metric properties of curved surfaces motivates basic questions about the interplay between defects in the cross section of a columnar bundle and its 3D shape. Such questions are critical to the structure of a broad class of filamentous materials, from biological assemblies like protein fibers to nanostructured or microstructured synthetic materials like carbon nanotube bundles. Here, we explore the buckling behavior for elementary disclinations in hexagonal bundles using a combination of continuum elasticity theory and numerical simulations of discrete filaments. We show that shape instabilities are controlled by a single material-dependent parameter that characterizes the ratio of interfilament to intrafilament elastic energies. Along with a host of previously unknown shape equilibria—the filamentous analogs to the conical and saddlelike shapes of defective membranes—we find a profoundly asymmetric response to positive and negative topologically charged defects in the infinite length limit that is without parallel to the membrane analog. The highly nonlinear dependence on the sign of the disclination charge is shown to have a purely geometric origin, stemming from the distinct compatibility (or incompatibility) of effectively positive- (or negative-)curvature geometries with lengthwise-constant filament spacing.
机译：拓扑缺陷对冷凝物系的热力学和结构至关重要。例如，当掺入如石墨烯等结晶膜中时，具有正拓扑电荷的公开和阴性拓扑电荷分别弹性地将材料缠绕成圆锥形和致死的形状。最近在2D柱状结构中的时隙间距和弯曲表面的度量特性之间的映射，这激励了关于柱状束的横截面中的缺陷与其3D形状之间的相互作用的基本问题。这些问题对于广泛的丝状材料的结构至关重要，从蛋白质纤维等生物组合物到纳米结构或微结构化的合成材料如碳纳米管束。在这里，我们使用连续丝的组合和离散长丝的数值模拟来探索六边形束中的基本披露的屈曲行为。我们表明，形状不稳定性由单一材料相关参数控制，该参数表征渗透到血管内弹性能量的比率。除了先前未知的形状平衡 - 丝状模拟与透明膜的锥形和致死的膜形状 - 我们发现对膜类似物的无限长度极限的正和阴性拓扑电荷缺陷的深刻不对称反应。对所公开电荷的符号的高度非线性依赖性被示出具有纯几何来源，源于具有纵向恒定长丝间距的有效正（或负）曲率几何形状的不同的兼容性（或不相容性）。

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