7. Liquid Crystals in External Fields
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Liquid Crystals in Electric Field
LC materials may consist of polar or non-polar molecules. The polar molecules possess the permanent dipole moments caused by slight charge separation in the molecule. In the case of non-polar molecules, the induced electric dipoles are created by an applied electric field causing the slight separation of positive and negative charges in the molecules. The induced electric dipoles are much weaker than permanent electric dipoles. However, they experience the same forces in an electric field. The LC molecules can possess the permanent or induced dipole along or across the long molecular axis. If the dipole moment is parallel (or nearly parallel) to the long molecular axis then Δε>0 and the molecules tend to orient along the electric field direction (Fig.18a). If the molecules carry dipole moments that are more or less normal to the long molecular axis then Δε<0 and molecules tend to orient perpendicular to the electric field direction (Fig.18b). (a)   (b) Figure 18. Liquid crystal molecules with positive Δε (a) and negative Δε (b) in electric field The orientational order of LC molecules does not change in an applied electric field. The electric field causes the director n reorientation. The LC molecules respond to the applied electric field E collectively that causes the distortions of the director n. The electric contribution should be added to the free energy density Fe = - 1/2 εoΔε (E⋅n)2 where εo is the electric permittivity of vacuum. The larger the dielectric anisotropy the smaller electric field is needed to reorient the LC molecules.
Liquid Crystals in Magnetic Field
Most LC organic molecules are diamagnetic. The induced magnetic dipoles are responsible for the reorientation of the LC molecules in a magnetic field H. The LC molecules tend to orient themselves parallel to the magnetic field decreasing the distortion of the magnetic field flux when they are perpendicular to H (Fig.19). Figure 19. Liquid crystal molecule in magnetic field The magnetic contribution to the distortion free energy density is given by FB = - 1/2 μo-1Δχ (B⋅n)2 where B is the magnetic induction, μo is the magnetic permeability of vacuum, Δχ = χII - χ⊥>0 is a diamagnetic anisotropy, χII and χ⊥ are diamagnetic susceptibilities measured parallel and perpendicular to the director, respectively, Iχ⊥I>IχIII. In nematics, the positive anisotropy of susceptibility proportional to the number of aromatic rings is expected. Comparing the relative efficiencies of the electric and magnetic fields should be noted that, roughly, the torque exerted on the LC molecules by one Volt/μm is equivalent to the magnetic torque exerted by 10,000 Ga.
Frederiks Transition
The Frederiks transition means the deformation of a uniform director pattern in an external field. If the external, electric or magnetic, field is applied to the LC sample with some uniform director structure, there is a gradual change of the director structure once the field strength exceeds some threshold or critical value. It is possible to create basic deformations in nematics by applying the external field, electric or magnetic (Fig.20). (a)   (b) Figure 20. Splay (a) and bend (a) deformations of nematic liquid crystals in electric field The critical value for deformations of the director n in the electric field is given by Eci = π/d (Ki/εoΔε)1/2, and in the magnetic field is given by Bci = π/d (Ki/μo-1Δχ)1/2, where Ki is an elastic constant, i = 1,2,3 corresponds to splay, twist, and bend deformations, respectively. The helical structure of the cholesteric LC can be untwisted in strong enough field applied to the helix axis normally.
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