Magnetic and electric birefringence

The free energy per mole of the isotropic phase in the presence of an external field (magnetic or electric) may be written as 

7/a is the anisotropy of optical polarizability of the molecule, and V the molar volume. The magnetic birefringence varies essentially as (7—r ) since the dependence of C on temperature is relatively small. Experimentally this is found to be the case, with T j —7 1 K (fig. 2.5.2). As we shall see later a (7— J )- law implies a classical mean field. 

The behaviour is slightly more complicated in the case of electric birefringence because, as explained in 2.3.4, the orientational energy in an electric field E arises from the anisotropy of low frequency polarizability and also from the net permanent dipole moment p. An interesting example is that of PAA in which the Kerr constant actually changes sign at about T -I-5K (fig. 2.5.3). The sign reversal is easily understood. The 

A e can be positive or negative depending on the sign of the quantity in the square brackets of (2.5.14). The polarizability anisotropy is always 

If) = 0, A e given by (2.5.14) varies essentially as T— In such materials, the electric and magnetic birefringence may be expected to exhibit the same type of behaviour over a wide temperature range. Measurements on pure samples of hexylcyanobiphenyl, a nematogen 

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EDNA see Ethylene diniCroaniinc Electric birefringance ef arv>matic nitro compounds see Magnetic and electric birefringance... 

Fig. 2.5.4. Reciprocals of the magnetic and electric birefringence in the isotropic phase of 4-hexyl-4 -cyanobiphenyl versus temperature. Both give the same value of T T = 28 °C, = 1.1 C). (After reference 130.)...

Magnetic birefringance (Cotton-Mounton effect) and electric birefringance (Kerr effect) of nitrobenzene, p-dinitrobenzene and 1,3.5-trinitrobcnzene was... 

Birefringance, magnetic and electric see Magnetic and electric hircfrineaiiec EISA 610 BIIA 609.61(1... 

Before giving analytical expressions for the director deformations in Freedericksz cells, we will summarize the magnetic and electrical methods. The advantage of electro-optical measurements is that the cell thickness does not enter the equations and is therefore ruled out as an error source. Furthermore, the electric field can always be considered strictly perpendicular to the sample plane. On the other hand, in the electric method conductivity effects can influence the measurements and exact knowledge of and is required to extract the second elastic constant from the birefringence or capacitance characteristics. Moreover, the electric measurement is restricted... 

The main part of this chapter will deal with birefringence caused by flow (streaming birefringence). Other possibilities i.e. magnetically and electrically induced birefringence) are also possible, but will not be discussed. 

Shah, D. O., and Hamlin, R. M. J. (1971), Structure of water in microemulsions Electrical birefringence and nuclear magnetic resonance studies, Sciences, 111, 483 485. 

The birefringence of liquid crystalline solutions of polypeptides is time dependent (Fig. 12) it takes more time for the solutions to attain the equilibrium orientation of the same degree in tl magnetic field than in the electric field. A time lag is observed in some cases and the birefringence increases patently in two steps. 

In the previous section we discussed pure electric-dipole hyperpolarizabilities, in particular second harmonic generation. Another important class of NLO processes includes birefringences and dichroisms which can be rationalized (at least to lowest orders in perturbation theory) in terms of response functions involving, besides the electric-dipole, also magnetic-dipole and electric-quadrupole operators. Prominent examples related to quadratic response functions are ... 

Fig. 2.5.3. The electric birefringence (Tsvetkov and Ryumtsev," open circles) and the reciprocal of the magnetic birefringence (Zadoc-Kahn," full circles) in the isotropic phase of PAA versus temperature. The lines represent the theoretical...

Fig. 3.11 Electro-optic device configurations, (a) Mach-Zehnder interferometer, (b) birefringent modulator. TM and TE denote transverse magnetic and transverse electric polarization, respectively.

In addition to the substantial literature on solvent and small-molecule translational diffusion, there is also a significant literature on small-molecule rotational diffusion. Experimental methods that report rotational diffusion behavior include VH tight scattering, as examined in different time domains with Fabry-Perot interferometry and photon correlation methods, nuclear magnetic resonance, oscillatory electrical birefringence, and time-resolved optical spectroscopy. 

Fig. 1. Representative device configurations exploiting electrooptic second-order nonlinear optical materials are shown. Schematic representations are given for (a) a Mach-Zehnder interferometer, (b) a birefringent modulator, and (c) a directional coupler. In (b) the optical input to the birefringent modulator is polarized at 45 degrees and excites both transverse electric (TE) and transverse magnetic (TM) modes. The appHed voltage modulates the output polarization. Intensity modulation is achieved using polarizing components at the output.

The rotational diffusion coefficient Dr of a rodlike polymer in isotropic solutions can be measured by electric, flow, and magnetic birefringence, dynamic light scattering, and dielectric dispersion. However, if the polymer has some flexibility, its internal motion makes it difficult to extract Dr for the end-over-end rotation of the chain from data of these measurements. In other words, Dr can be measured only for nearly rodlike polymers. 

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