4. Anisotropy in Liquid Crystals



Dielectric Anisotropy in Liquid Crystals

Dielectric properties of LCs are related to the response of LC molecules to the application of an electric field. Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. In the LC materials consisting of non-polar molecules, there is only an induced polarization, which consists of two parts: the electronic polarization (which is also present at optical frequencies) and the ionic polarization. In the LCs with polar molecules, there is in addition to the total induced polarization, the orientation polarization, due to the tendency of the permanent dipole moments to orient themselves parallel to the field.
Considering the uniaxial LC phases in a macroscopic coordinate system x, y, z, with the z axis parallel to the director n, it is possible to distinguish two principal permittivities, parallel to the director εII = εzz, and perpendicular to the director ε = 1/2(εxx + εyy). Then the dielectric anisotropy Δε = εII - ε can take positive and negative values. The graph of temperature dependence of dielectric permittivities for a typical LC (Fig.8) shows that magnitude of Δε usually depends on temperature, Δε∝S(T).


Figure 8. Temperature dependence of dielectric permittivity in liquid crystals with Δε > 0: Tc - clearing temperature; εiso - permittivity of isotropic liquid

For non-polar LCs the situation is relatively simple but in the case of polar molecules with permanent dipole moments, the orientation polarization must be added, which, by Maier and Meier, leads to an expression for the dielectric anisotropy


where Δα is a polarizability anizotropy, μ is a molecular dipole moment, F is parameter depending on the reaction field factor, kB is a Boltzmann constant and T is temperature. Then Δε is determined by the angle β between the molecule axis and the direction of the off-axis molecular dipole moment μ. The dipole contribution to Δε is positive for β < 54.7o and negative for β > 54.7o, which may result in negative Δε depending on the relative magnitude of two contributions. The larger the anisotropy the smaller electric field is needed to make the LC respond to it.



Optical anisotropy of LCs


Main types of LCs