Liquid crystal helical ribbons as isometric textures

Liquid crystal helical ribbons as isometric textures
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作为等距纹理的液晶螺旋带

DOI：
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发表时间：
2004
期刊：
The European Physical Journal E : Soft matter
影响因子：
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通讯作者：
H. Nguyen
H. Nguyen
中科院分区：
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文献类型：
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作者：
M. Achard;M. Kleman;Y. Nastishin;H. Nguyen

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摘要。保持平行度和距离的变形- 层，在近晶相;柱之间，在柱状相-是 在液晶中很常见。生成的等距变形纹理 显示特定的几何特征。对应的顺序参数 奇点在相当大的宏观距离上延伸，例如， 共焦二次曲线这幅著名的图画被修改了， 叠加到1D或2D周期性，结构是螺旋形的。 然而，等距可以被保留。本文讨论了一种介质的情况， 其结构由1D调制层（层状-柱状相）制成， 假设调制从一层到下一层螺旋旋转。 付出的代价是任何等距纹理都必然会受挫;它 由折叠成一组平行螺旋面的层组成， 螺旋位错（宏观Burgers矢量），调制是 沿着螺旋，即双绞。奇点集由两个 螺旋向错线我们通过一个粗略的 计算螺旋带的能量。建议由 在香蕉样分子的B7相中观察到的螺旋带是这样的 等距纹理。作为一个附带的结果，让我们提到， 双捻，传统上是按照导演的分区制作的 场到嵌套圆柱体，可以比往往是有利可图的测试， 对着一个隔板分成嵌套的螺旋面。
Abstract.Deformations that conserve the parallelism and the distances – between layers, in smectic phases; between columns, in columnar phases – are commonplace in liquid crystals. The resulting isometric deformed textures display specific geometric features. The corresponding order parameter singularities extend over rather large, macroscopic, distances, e.g., cofocal conics in smectics. This well-known picture is modified when, superimposed to the 1D or 2D periodicities, the structure is helical. However isometry can be preserved. This paper discusses the case of a medium whose structure is made of 1D modulated layers (a lamello-columnar phase), assuming that the modulations rotate helically from one layer to the next. The price to pay is that any isometric texture is necessarily frustrated; it consists of layers folded into a set of parallel helicoids, in the manner of a screw dislocation (of macroscopic Burgers vector), the modulations being along the helices, i.e. double-twisted. The singularity set is made of two helical disclination lines. We complete this geometric analysis by a crude calculation of the energy of a helical ribbon. It is suggested that the helical ribbons observed in the B7 phase of banana-like molecules are such isometric textures. As a side result, let us mention that the description of double-twist, traditionally made in terms of a partition of the director field into nested cylinders, could more than often be profitably tested against a partition into nested helicoids.