5. Main types of Liquid Crystals
In smectic A (SmA) phases, on average, the molecules are parallel to one another and are arranged in layers, with the long axes perpendicular to the layer plane (Fig.12). Within the layers, the centers of gravity of the molecules are ordered at random. Thus, smectics A possess the one-dimensional quasi long-range positional order and within the layers molecules show a relatively high mobility. The layer thickness is equal to the molecule length. SmA LCs are optically positive and uniaxial with the optic axis parallel to the molecular long axes.
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Figure 12. Structure of smectic A liquid crystals |
Deformation of the SmA structure is also possible. One can bend the layers (Fig.13), causing the splay deformations of the director n, and the splay distortion free energy density may be described by
Fd = 1/2 K1(div n)2.
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Figure 13. Deformation of SmA
liquid crystal: |
The bend and twist deformations of the director field in the SmA structure are prohibited. The energy for curving layers is much lower than energy needed to change the interlayer spacing 1/2Bγ2, where B is a compression modulus and γ is a relative layer thickness change. Taking the displacement of the layer plane u as a variable, the distortion free energy density is given by
where the first term corresponds to splay of the director,
and the second corresponds to the dilation/compression contribution.
Interesting to note, that according to coarse-grained description,
the cholesteric LCs also can be treated as the layered, smectic-like,
LC if the size of distortions is much larger than the layers periodicity.
The layer thickness in cholesterics is equal p/2 as the directions of the
director +n and -n are equivalent. Then the distortion free energy density
of cholesterics can be expressed by the same equation as for
smectics A, but K=3K3/8 and B =K2·qo2.
The structure of the smectic C (SmC) liquid crystals is closely related to the structure of the SmA. The molecules are arranged in layers, but the long axes of the molecules are tilted to the layers planes (Fig.14).
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Figure 14. Structure of SmC liquid crystals: n is director; z is normal to layers |
For some materials the tilt angle is constant but for others it is temperature dependent. The centers of gravity of the molecules are randomly ordered and the molecules are free to rotate around their long axes. SmC phases are optically biaxial.
The SmC* phase is similar to the SmC phase but consists of the chiral molecules (Fig.15), which rotate the direction of the director projection on the layer plane from one layer to the next. The twist axis of the SmC* is perpendicular to the layers. Therefore, these phases appear optically positive uniaxial, and show optical activity and selective reflection similar to the cholesterics.
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Figure 15. Helical structure of SmC* liquid crystals: n is director; z is twist axis; μ is dipole moment |
If the molecules in SmC* have the permanent dipole moments perpendicular to their long axes than such phase exhibits ferroelectric properties.
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