8. Textures of Liquid Crystals
The knowledge of the relations between structures and their textures are necessary for understanding of the liquid crystals structures from their optical microscopy textures.
Usually, for basic studying or practical application, liquid crystal is filled in between two glass substrates. As we already know, the certain treatment of the substrate surfaces allows one to obtain different types of LC orientation. In the case of heterogeneous planar orientation of nematics, the director n is parallel to substrates but points in different directions. Such a structure appears as a schlieren texture between crossed polarizers in a polarizing microscope (Fig.21).
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Figure 21. Schlieren texture in nematic liquid crystal |
The schlieren texture
shows dark brushes, which correspond to the extinction orientation of
the nematic LC. Accordingly, the director n lies either parallel or perpendicular to
the polarizer or analyzer axes. The points, where two or four brushes meet,
correspond to the director singularities and are called disclinations in the structure.
The disclination is characterized by its strength s, which shows how much the
director rotates in each point on the closed curve around the singularity
point. The disclinations with s=±1/2,±1 can be found in nematics.
The points where four brushes meet correspond to the disclinations
with s=±1, and, the points with two brushes correspond to
the disclinations with s=±1/2.
To distinguish between the disclinations of different sign, one can use
the rotation of the sample with schlieren texture between the crossed polarizers.
When the LC sample is rotated, the black brushes move continuously indicating
a continuous change of the director n. At points with positive sign, the brushes
rotate in the same sense as the sample (Fig.22a), but at the points with negative
sign of the strength brushes move in the opposite direction (Fig.22b).
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(b) |
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Figure 22. Rotation of nematic liquid crystal sample between crossed polarizers to distinguish the sign of disclinations with s=±1 | |
Usually, neighboring singularities which are connected by brushes have opposite signs (Fig.23).
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Figure 23. Rotation of nematic liquid crystal sample between crossed polarizers to distinguish the sign of disclinations s=±1/2 |
Electric fields applied along the homeotropically aligned nematic LC with the negative dielectric anisotropy also can produce schlieren textures (Fig.24) where the defects with s=±1/2 do not appear.
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Figure 24. Schlieren texture caused by electric field applied to homeotropically aligned nematic liquid crystal with Δε<0 |
In the case when the nematic LC sample with the homogeneous planar alignment placed between two crossed polarizers, the texture appears completely black when the director direction is either parallel or perpendicular to the transmission axis of the polarizer or analyzer (Fig.25).
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Figure 25. Uniform nematic liquid crystal cell between crossed polarizers |
The intensity of the transmitted light through a system polarizer - planar nematic - analyzer depends on the angle β between the LC optical axis and polarizers as I∝sin22β and reach the maximum when β=45o (Fig.25).
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LCs in external fields
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Textures of cholesterics