Diamagnetic Properties of Nematic Liquid Crystals

Common nematic liquid crystals represent diamagnetic fluids. Molecular diamagnetism in non-ordered isotropic materials in general, as well as the mean diamagnetic polarizability in ordered materials, is temperature independent. However, due to thermal expansion of the material the volume susceptibility X is constant but decreases with increasing temperature. It is therefore sometimes convenient to introduce the temperature independent quantities susceptibility per mole, or the mass susceptibility, which are related to X by 

The anisotropic magnetic properties of nematics and the interactions of the director with external magnetic fields are described by a symmetric second rank diamagnetic susceptibility tensor /. The magnetic moment per volume induced in the nematic liquid crystal by an external magnetic field H is 

The susceptibility tensor / can be split into an isotropic contribution 

In the isotropic state, the orientational anisotropy is zero and the susceptibility reduces to its isotropic value Xoso)- As mentioned above, is weakly temperature dependent, decreasing by approximately 0.1 % with increasing temperature. The molar and mass susceptibilities and are temperature invariant. 

The orientation-dependent part of the magnetic free energy density of a uniaxial nematic liquid crystal is found from Eqs. (1) and (2)  

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When an electric or magnetic field is applied to a liquid crystal cell, a texture transition occurs to minimize the free energy of the system. These texture changes in cholesteric liquid crystals are physically similar to the Frederiks transition in a nematic liquid crystal and result in a significant change in the optical properties of the layer. Texture transitions have been reviewed previously [8, 9] with allowance made for the sign of the dielectric or diamagnetic anisotropy, the initial texture, and the direction of the applied field. Here, we consider only the instability of the planar cholesteric texture, which has been widely discussed in recent literature. 

The coupling of the axis of rod-shaped molecules is the basic characteristic that leads to a liquid which displays many of the. properties of a crystalline solid, such as birefringence and electric and diamagnetic anisotropy. The response of liquid crystals to applied forces may be weakly elastic but, in nematics at least, true flow is retained. This combination of anisotropy and liquid flow leads to some interesting properties of liquid crystals, since it becomes possible to reorient the director by imposing an external electric field. 

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