Geometrical birefringence

It should be noted that Eq. (55) contains a factor b which becomes zero when the molecule is spherical (p = 1). Hence, the contribution to the birefringence of a solution is provided only by molecules adopting conformations in which the molecule is not only optically anisotropic but also geometrically aspherical. 

FIGURE 15.3 Crystal systems. Shown is the shape of the unit cell for each system, the number N of different Bravais lattices in each system, geometrical characteristics of the unit cell, and optical anisotropy (birefringence). Some examples of crystals of various materials are given. 

Fig. 5. Illustration showing one possible geometrical arrangement of isotropic (or anisotropic) elements that can lead to form birefringence.

The time course of orientational changes induced by electric fields contains information on the orientation mechanism, and on the electrical and geometrical properties (main dipole axis, length) of the aligning and deorienting molecules. For instance, permanent dipole orientation of a given particle type in the presence of a constant electric field builds up with zero slope and has two modes, whereas the build-up of induced dipole orientation starts with maximum slope and is characterized by only one time constant. The deorientation relaxation of a system of identical particles, after termination of the step pulse, is monophasic, independently of the presence of permanent or induced dipoles. Table 3 summarizes the characteristic features of the rotational kinetics indicated by electric dichroism and birefringence for small perturbations. We see that there are a number of specific relationships to differentiate between permanent and induced dipole mechanism. In particular, the technique of field-reversal is a sensitive indicator for the relative contributions of permanent or induced dipoles. 

For higher refractive index anisotropy n, the geometrical requirements on the nematic structure which need to be satisfied in order to achieve compensation of birefringence become more stringent. Thus, the transmission versus voltage curve for normal incidence shifts toward higher voltages and becomes less steep. 

The exponent 2/3 in eq. (VI.77) does not reflect excluded volume effects but expresses simply a geometric property of three-dimensional convergent flows. Birefringence measurements on such convergent flows donor give profound insight into the chain behavior they measure principally p or t. 

FIGURE 2.54 Geometrical phenomenon of birefringence optical axes (O.A.) are in the direction of the 1-5 arrows after (Optical Mineralogy, 2003,2013). 

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