Mesoscale structure of wrinkle patterns and defect-proliferated liquid crystalline phases
Mesoscale structure of wrinkle patterns and defect-proliferated liquid crystalline phases
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皱纹图案和缺陷扩散液晶相的介观结构
DOI：
10.1073/pnas.1916221117
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Davidovitch, Benny
中科院分区：
文献类型：
--
作者：
Tovkach, Oleh;Chen, Junbo;Ripp, Monica M.;Zhang, Teng;Paulsen, Joseph D.;Davidovitch, Benny
薄固体往往发展弹性不稳定和随后复杂的，多尺度的变形模式。揭示这种空间复杂性的组织原理对我们理解植物叶片和动物上皮的形态发生过程，甚至可能对人类指纹的形成产生影响。我们阐明了这种形态复杂性的主要来源——均匀间隔皱纹的弹性有利“微观结构”与通过皱纹指示器传递并由约束力决定的“宏观结构”之间的不相容。我们的理论是根据实验和模拟的浮动板受到径向拉伸。通过分析粗径向皱褶的形态，我们发现了两种截然不同的形态：皱褶数量固定且间距不均匀的无缺陷图案和由富含缺陷的缓冲区分隔的均匀间距皱褶图案。我们展示了这些形态类型如何反映金兹堡-朗道函数的不同最小值——弹性能量的粗粒度版本，它惩罚了不均匀的皱纹间距和振幅，以及由约束施加的实际方向与轴的偏差。我们的结果扩展了皱纹图案作为液晶的有效描述[H]。Aharoniet, Nat。我们强调了几何-能量相互作用之间的有趣类比，这种相互作用是限制片的机械平衡以及超导体和手性液晶的热力学相中缺陷扩散的基础。
Thin solids often develop elastic instabilities and subsequently complex, multiscale deformation patterns. Revealing the organizing principles of this spatial complexity has ramifications for our understanding of morphogenetic processes in plant leaves and animal epithelia and perhaps even the formation of human fingerprints. We elucidate a primary source of this morphological complexity—an incompatibility between an elastically favored “microstructure” of uniformly spaced wrinkles and a “macrostructure” imparted through the wrinkle director and dictated by confinement forces. Our theory is borne out of experiments and simulations of floating sheets subjected to radial stretching. By analyzing patterns of grossly radial wrinkles we find two sharply distinct morphologies: defect-free patterns with a fixed number of wrinkles and nonuniform spacing and patterns of uniformly spaced wrinkles separated by defect-rich buffer zones. We show how these morphological types reflect distinct minima of a Ginzburg–Landau functional—a coarse-grained version of the elastic energy, which penalizes nonuniform wrinkle spacing and amplitude, as well as deviations of the actual director from the axis imposed by confinement. Our results extend the effective description of wrinkle patterns as liquid crystals [H. Aharoniet al.,Nat. Commun.8, 15809 (2017)], and we highlight a fascinating analogy between the geometry–energy interplay that underlies the proliferation of defects in the mechanical equilibrium of confined sheets and in thermodynamic phases of superconductors and chiral liquid crystals.
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影响因子：
16.6
作者：
Aharoni H;Todorova DV;Albarrán O;Goehring L;Kamien RD;Katifori E
通讯作者：
Katifori E
影响因子：
2.4
作者：
Davidovitch, B.;Schroll, R. D.;Cerda, E.
通讯作者：
Cerda, E.
影响因子：
5.5
作者：
Chang, Jooyoung;Toga, Kamil B.;Russell, Thomas P.
通讯作者：
Russell, Thomas P.
影响因子：
2.5
作者：
Ian Tobasco
通讯作者：
Ian Tobasco
影响因子：
8.6
作者：
Klein, Yael;Venkataramani, Shankar;Sharon, Eran
通讯作者：
Sharon, Eran