The Faraday effect

The phenomenon of the rotation of the plane of polarization of light by substances when placed in a magnetic field is called the Faraday effect. The angle of rotation (a) depends on the nature of the substance  

V is called the Verdet-constant it depends only slightly on the temperature, but varies markedly with the wavelength of the light measurements are normally carried out 

Absolute determinations of V are extremely difficult. For routine measurements relative methods have been worked out29 31, in which the experimental material is compared directly with a standard liquid ( e.g. water) these methods also require a relatively complicated apparatus and skilled operators to obtain a reasonable accuracy ( °-°5%)- 

The method can also be applied to aromatic- and olefin-free hydrocarbon mixtures (cf. Table III) in these cases Nc can be calculated from the average molecular weight M by means of the formula 

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Waveguides are coimnonly used to transmit microwaves from the source to the resonator and subsequently to the receiver. For not-too-high-frequency radiation (<10 GHz) low-loss MW transmission can also be achieved usmg strip-lines and coaxial cables. At the output of a klystron an isolator is often used to prevent back-reflected microwaves to perturb the on-resonant klystron mode. An isolator is a microwave-ferrite device that pemiits the transmission of microwaves in one direction and strongly attenuates their propagation in the other direction. The prmciple of this device involves the Faraday effect, that is, the rotation of the polarization... 

Other physical methods were also applied to the elucidation of the isomerism of diazocyanides, e. g., determination of diamagnetic susceptibility, the Faraday effect (optical rotation in a magnetic field), and electronic and infrared spectra. Hantzsch and Schulze measured ultraviolet spectra at a remarkably early date (1895 a). Unfortunately, their results and later work (Le Fevre and Wilson, 1949 Freeman and Le Fevre, 1950) did not allow unambiguous conclusions, except perhaps the observation that the molar extinction coefficients of the band at lowest frequency are consistently larger in all types of (i -compounds Ar — N2 - X than in the corresponding (Z)-iso-mers (Zollinger, 1961, p. 62). 

An answer to the problem of determining the electronic structure in the ground state of cyclophosphazenes (NPX2)n has been supplied by a concerted use of quantum chemistry (79) and the Faraday effect (20), the results of which unambiguously support Dewar s island model (18). 

In recent several years, super-capacitors are attracting more and more attention because of their high capacitance and potential applications in electronic devices. The performance of super-capacitors with MWCNTs deposited with conducting polymers as active materials is greatly enhanced compared to electric double-layer super-capacitors with CNTs due to the Faraday effect of the conducting polymer as shown in Fig. 9.18 (Valter et al., 2002). Besides those mentioned above, polymer/ CNT nanocomposites own many potential applications (Breuer and Sundararaj, 2004) in electrochemical actuation, wave absorption, electronic packaging, selfregulating heater, and PTC resistors, etc. The conductivity results for polymer/CNT composites are summarized in Table 9.1 (Biercuk et al., 2002). 

Much simpler than the use of active isolators, such as rotators making use of the Faraday effect, is again a saturable absorber cell which can easily be adjusted in length, dye composition and concentration to give the desired low light level attenuation and high light level transmission 46>. 

The signs of optical activity or of the Faraday effect (magnetically induced optical activity see Appendix) used by physicists are frequently opposite to the chemically defined ones. Furthermore, the handness in liquid crystals, such as cholestric or chiral smectic ones, often has been defined erroneously and thus confused. 

Bishop has recently been studying the magnetic properties of small systems (including the Cotton-Mouton effect and the Faraday effect), once again providing accurate values with which the experiments can be judged. As well, his concerns with the effects of magnetic fields on vibrations have received widespread attention. 

The Faraday effect refers to the induction of circular birefringence following the... 

The coefficient K is a measure of the Faraday effect and is proportional to the applied... 

Measure of the Faraday effect, (8.23) Jeffery orbit constant, (7.108)... 

These models offer no explanation of the Faraday effect. 

Apart from subtle exceptions, an isolated molecule differs from a molecule in a crystal in that the isolated molecule has no shape, whereas in a crystal it acquires shape, but loses its identity as an independent entity. This paradoxical situation is best understood through the famous Goldstone theorem, which for the present purpose is interpreted to state that any phase transition, or symmetry broken, is induced by a special interaction. When a molecule is introduced into an environment of other molecules of its own kind, a phase transition occurs as the molecule changes its ideal (gas) behaviour to suit the non-ideal conditions, created by the van der Waals interaction with its neighbours. An applied electric or magnetic field may induce another type of transformation due to polarization of the molecular charge density, which may cause alignment of the nuclei. When the field is switched off the inverse transformation happens and the structure disappears. The Faraday effect (6.2.3) is one example. 

Most chemists would accept the general statement that optically active molecules are those without an alternating axis of symmetry, as adequate. This is perhaps a reliable diagnostic of natural optical activity, but it offers no explanation of the Faraday effect, which shows that achiral molecules become optically active in an applied magnetic held. 

The classic solution is the application of current and voltage transformers, usually as a cast resin embedded type. As a certain disadvantage of inductive transducers, their small frequency range may be considered. Other solutions for current sensors are Rogowski coils (with active or passive integrators) or the fibre-optic current sensor, based upon the Faraday effect [20]. 

The elusive relationship between molecular chirality and optical activity, as well as the Faraday effect, likewise reduce to the minimization of orbital angular momentum as a function of molecular symmetry. 

The second part of this paper describes how we have studied the behaviour of what were previously called aromatic molecules relative to the Faraday effect (or magnetic rotatory power), with particulary emphasis on the experimental and theoretical information which has led us to discard the notion of aromaticity in favour of a new, well-defined and easily measured phenomenon. 

This equation has recently appeared also in the framework of a simplified theory of the Faraday effect ). 

It is not surprising that such currents may be detected by means of the Faraday effect, this effect being a magnetic property of matter to the same extent as, for instance, diamagnetism or N.M.R., in connection with which, as we have seen, the concept of ring current was mentioned for the first time. 

To come back to the Faraday effect It might be expected from the preceding discussion that any molecule characterized by a given 2/, value should... 

Strobilism will then either be measured experimentally by means of the Faraday effect (measure of ), or calculated theoretically from the (o + it) electronic structure (determination of G at equal bond character). 

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