7. Liquid Crystals in External Fields
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 orientational order of LC molecules does not change
in an applied electric field. The electric field causes the director
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.
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).
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.
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.
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.