Anisotropic diamagnetic susceptibility

Crystals, except those belonging to the cubic system, are anisotropic in this respect the force of repulsion varies with the orientation of the crystal with respect to the direction of the field. The graph representing vectorialiy the diamagnetic susceptibility in all directions in a crystal is an ellipsoid, whose orientation with respect to the unit cell is restricted by symmetry in exactly the same way as that of the optical indicatrix. Thus, for uniaxial crystals the magnetic ellipsoid an ellipsoid of revolution whose unique axis coincides with the threefold, fourfold, or sixfold axis of the crystal for orthorhombic crystals the ellipsoid has three unequal axes which necessarily coincide with the three axes of the crystal for monoclinie crystals the only restriction is that one of the principal axes of the magnetic ellipsoid must coincide with the b axis of the crystal while for triclinic crystals the orientation of the ellipsoid is not restricted in any way. 

The b s quoted (from Mortensen and Smith, 1960) represent the two bonds as being more anisotropic than they appear in Table 22, but Ziircher comments that the Mortensen-Smith polarizabilities should be taken with caution. He stresses that his own calculations have an approximate character and involve quantities and equations of varying precision. Nevertheless their interest lies in the indication that the directions of greatest diamagnetic susceptibility in bonds should be perpendicular to those of greatest electronic polarizability and vice-versa. Such an inverse relationship is in accord with empirical (Bothner-By and Naar-Colin, 1958) and theoretical (Pople, 1957) deductions to date rough predictions of the shielding of a proton by a remote bond... 

As the dielectric constant and diamagnetic susceptibility of many mesogens are anisotropic, the orientation of side-chain LCPs in the nematic state can also be changed by the application of a magnetic... 

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]. 

The isotropic part of Xa(3 is given by the average x = Xxx + Xyy + Xzz)-To define an order parameter that vanishes in the isotropic phase, the anisotropic part of the diamagnetic susceptibility is extracted ... 

The diamagnetic susceptibility of a liquid crystal is anisotropic. This is a result of shape anisotropy in the molecules that form the liquid crystal. In a uniaxial phase, the susceptibility tensor has two principal components, X and x 5 the susceptibilities per unit volume along and perpendicular to no, respectively. If Ax = X X >0, the director will align along the magnetic field B The presence of a magnetic field leads to an additional term in / [6.28],... 

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... 

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