Birefringence orientational contribution

The classical ideas about the isotropy of electrical properties of spherical-top molecules are usually extrapolated to the magnetic properties. This leads to the conclusion about the isotropy of the magnetic susceptibility in high-symmetry molecules and hence about the disappearance of the orientational contribution to the birefringence in magnetic fields (the Cotton-Mouton effect). In the case of degenerate electronic terms or in the pseudodegeneracy situation, these conclusions are incorrect and have to be reconsidered. 

Hence in the case of linear vibronic coupling the orientational contribution to the birefringence in the inhomogeneous electric field can be described by the expression... 

Figure 4.6. Schematic of the different gratings that are formed during illumination of an azo sampie. (a) SRG. (b) DG. (c) Birefringence (orientational) grating, (d) Chemicai (trans/cis) grating. Aii the gratings contribute to the observed diffraction efficiency, to varying extents. Gratings (b), (c) and (d) are all refractive-index gratings.

Physical properties of liquid crystals are generally anisotropic (see, for example, du Jeu, 1980). The anisotropic physical properties that are relevant to display devices are refractive index, dielectric permittivity and orientational elasticity (Raynes, 1983). A nematic LC has two principal refractive indices, Un and measured parallel and perpendicular to the nematic director respectively. The birefringence An = ny — rij is positive, typically around 0.25. The anisotropy in the dielectric permittivity which is given by As = II — Sj is the driving force for most electrooptic effects in LCs. The electric contribution to the free energy contains a term that depends on the angle between the director n and the electric field E and is given by... 

C0Pi6 (137) was the first to give an expression for the contribution of the form birefringence to the Maxwell constant. His theory is based on the elastic dumb-bell model, which has been used in early theories on flow birefringence and viscosity and which is identical with the model used in Sections 2.6.1 and 2.6.2. The ratio of Maxwell constant to intrinsic viscosity is probably unaffected by this simplification, when also the viscosity is calculated with the same model, as Copi6 did. For the absence of the form effect, this has strictly been shown in the mentioned Sections. In fact, in the case of small shear rates the situation is rather simple To a first approximation with respect to shear rate, the chain molecules are only oriented, their intramolecular distances which are needed for the calculation of form birefringence, being unaffected. 

It is evident that the contributions due to angular movements are caused by diffusion forces corresponding to the state of orientation, whereas the radial component is a hydrodynamic contribution. The radial force, as exerted by the flowing solvent, is balanced by the rigidity of the rod and has no consequences for the birefringence of orientation. According to eqs. (5.15), one obtains for rigid dumb-bells ... 

Crystalline polymers, and especially oriented crystalline polymers show birefringence that is made up of two contributions ... 

Next we expand Eq. (77) in a power series with respect to field S by assuming that this field is small and cannot result in an orientational saturation. Then, after averaging over the orientations of the molecule, we obtain for the Langevin-Born contribution to the birefringence the expression... 

By means of Eqs. (85a)-(85c), (92), (93), (104), and (106) for the three contributions to the molecular Cotton-Mouton constant arising from the orientational mechanism of birefringence in the magnetic field, we obtain... 

Molecular quadrupole moments may be obtained directly by observing the optical birefringence induced in a gas by an electric field-gradient Exx = —Eyy <35—37 The birefringence nx -ny, like the dielectric polarization in Debye s treatment, is comprised of a temperature-independent contribution due to distortion of the molecule and an orientation term proportional to T l 35 ... 

---