Liquid crystal diamagnetism

The order parameter can be directly related to certain experimentally determinable quantities - say, for example, the diamagnetic anisotropy of the liquid crystal.Let us choose a space-fixed cartesian coordinate system xyz with z parallel to n. If and are the principal diamagnetic susceptibilities of the molecule referred to its own principal axes, the average z component of the susceptibility per unit volume in the nematic phase is evidently... 

Fig. 4.6.3. Deformation of a planar structure due to a magnetic field acting along the helical axis of cholesteric liquid crystal composed of molecules of positive diamagnetic anisotropy. A similar deformation superposed in an orthogonal direction results in the square-grid pattern (see fig. 4.6.4). (Helfrich. )...

Thus, the anisotropy Ax of polyesters C and Cg pproached a nearly constant saturation value of 1.1.10 emu cgs g which corresponds to the diamagnetic anisotropy usually exhibited by conventional liquid crystals in the nematic phase. i he polymer with n = 9 reached a plateau value of 0.5 10 emu cgs g. For polyester with n = 12, i.e. the nematic phase of highest viscosity, no orientation effect was evidenced after 200 min. in the experimental magnetic field range 0 15 KG. 

Hence, the diamagnetic anisotropy of a uniaxial liquid crystal phase with orientational order S and molecules per unit volume can be found ... 

In both the cases considered, an optical contrast of the patterns observed in isotropic liquids is very small. Certainly, the anisotropy of Uquid crystals brings new features in. For instance, the anisotropy of (helectric or diamagnetic susceptibility causes the Fredericks transition in nematics and wave like instabilities in cholesterics (see next Section), and the flexoelectric polarizaticm results in the field-controllable domain patterns. In turn, the anisotropy of electric conductivity is responsible for instability in the form of rolls to be discussed below. All these instabilities are not observed in the isotropic liquids and have an electric field threshold controlled by the corresponding parameters of anisotropy. In addition, due to the optical anisotropy, the contrast of the patterns that are driven by isotropic mechanisms , i.e. only indirectly dependent on anisotropy parameters, increases dramatically. Thanks to this, one can easily study specific features and mechanisms of different instability modes, both isotropic and anisotropic. The characteristic pattern formation is a special branch of physics dealing with a nonlinear response of dissipative media to external fields, and liquid crystals are suitable model objects for investigation of the relevant phenomena [39]. 

Liquid crystals are anisotropic dielectric and diamagnetic media [1,25], Their resistivities are very high ( 10 °Q cm). Dipole moments are induced in them by external fields. They have different dielectric permittivities and magnetic susceptibilities along the directions parallel to and perpendicular to the liquid crystal director. 

The order parameter S can be measured in a number of ways. Usually a macroscopic property of the liquid crystal phase is measured, which then can be used to detemiine S if the molecular parameters that produce the macroscopic property are known. Diamagnetism, optical birefringence, nuclear magnetic resonance, and Raman scattering measurements are examples. 

Magnetic-Field-Induced Orientation. Liquid crystals may be oriented in magnetic fields, even though they are diamagnetic, due to the anisotropy in their diamagnetic susceptibility. The advantage of magnetic fields over surface-induced orientation or electric fields is that samples are not confined to thin films. 

If the directions x and y of the planar orientation of nematic liquid crystal molecules on opposite electrodes are perpendicular to each other and the material has a positive dielectric (or diamagnetic) anisotropy, then. 

Where po is the zero field pitch, A (m, the diamagnetic anisotropy of the liquid crystal, K22, the twist elastic constant. As the field increases the pitch is predicted to oncrease slowly at first and then diverge logarithmically as the critical field is ap>proached. The theory has been verified for lyotropic liquid crystals of PBG in a number of different solvents (Chandrasekhar, 1977, lizuka, 1973, DuPre Duke, 1974,1975, DuPre et al., 1976,1977, Patel DuPre, 1979). Molecules of liquid crystals orient themselves in the magnetic field so that their long chains are oriented parallel to the magnetic field lines (Miller, 1978). This orientation is associated with the molecular anisotropy of macromolecules rather than the existence of permanent magnetic moments. 

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