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:
影响因子:
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通讯作者:
H. Nguyen
中科院分区:
文献类型:
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作者:
M. Achard;M. Kleman;Y. Nastishin;H. Nguyen
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.