Magnetic fields Cotton-Mouton effect

The optical properties of semicrystalline polymers are often anisotropic. On the other hand, amorphous polymers are normally isotropic unless directional stresses are frozen in a glassy specimen during fabrication by a process such as injection molding. Anisotropy can often be induced in an amorphous polymer by imposing an electric field (Kerr effect), a magnetic field (Cotton-Mouton effect), or a mechanical deformation. Such external perturbations can also increase the anisotropy of a polymer that is anisotropic even in the absence of the perturbation. 

The ability of anisotropic and anisometric particles to assume some co-orientation in external force fields is not only responsible for significant changes in scattering properties but also causes birefringence (double refraction), i.e., the average refractive indexes of two beams polarized in perpendicular planes happen to be different. The specific orientation of particles and birefringecne may be caused by the action of electric field (Kerr effect), magnetic field (Cotton-Mouton effect), or in the case of anisotropic particles by flow of medium (Maxwell effect) [25]. 

Finally, let us mention the experimental methods that use other physical effects to measure molecular polarizability. These methods use the birefringence effects [15] in any magnetic field (Cotton-Mouton effect) and flow (dynamic optical effect of Maxwell), the acoustic birefiingence effect, absorption spectra induced by the electric field [16] and so on. It should be noted that last group of methods have the greater errors compared to the methods discussed above. 

Polymer solutions are isotropic at equilibrium. If there is a velocity gradient, the statistical distribution of the polymer is deformed from the isotropic state, and the optical property of the solution becomes anisotropic. This phenomena is called flow birefringence (or the Maxwell effect). Other external fields such as electric or magnetic fields also cause birefringence, which is called electric bire ingence (or Kerr effect) and magnetic birefiingence (Cotton-Mouton effect), respectively. 

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. 

Rizzo reviews in a unitary framework computational methods for the study of linear birefringence in condensed phase. In particular, he focuses on the PCM formulation of the Kerr birefringence, due to an external electric field yields, on the Cotton-Mouton effect, due to a magnetic field, and on the Buckingham effect due to an electric-field-gradient. A parallel analysis is presented for natural optical activity by Pecul Ruud. They present a brief summary of the theory of optical activity and a review of theoretical studies of solvent effects on these properties, which to a large extent has been done using various polarizable dielectric continuum models. 

The birefringence in external electric and magnetic fields (the Kerr and Cotton-Mouton effects) can be explained by the anisotropy of the properties of the medium that is due to either the orientation of anisotropic molecules in the external field (the Langevin-Bom mechanism) or the deformation of the electric or magnetic susceptibilities by this field, i.e., to hyperpolarizabilities (Voight mechanism). The former mechanism is effective for molecules that are anisotropic in the absence of the field and... 

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. 

Cotton-Mouton effect. (magnetic double refraction). Double refraction produced in some pure liquids by a magnetic field transverse to the hght beam. 

The poor sister of electric-field-induced non-linear optics is that of magnetic-field-induced non-linear optics, of which the Cotton-Mouton effect is the most important example attention is drawn to this in Section 4. Finally, some thoughts on the future of quantum chemistry in this subject are given in Section 5. It is an area which is a tough test of computational quantum chemistry but recent achievements show it to be one well worth pursuing. 

Here, pa and ma are the electric and magnetic dipole moment functions, aap, Papy> YapyS 81 the polarizability and first and second hyperpolarizabilities, is the magnetizability, and, of the other terms, only the hypermagnetizability will be of interest (it relates to the Cotton-Mouton effect). The Greek subscripts a, p,... denote vector or tensor quantities and can be equal to the Cartesian coordinates x, y, or z. Einstein summation over these subscripts is implied both here and elsewhere. Differentiation of this expression with respect to F (or B) leads to an expression for the dipole moment (or polarization) of the species in the presence of the perturbing fields and it is clear that P, y, t), etc. will govern the non-linear terms in the induced electric (or magnetic) dipole moment - hence, non-linear optics. 

On the other hand, a phase gap, 8, between the linear polarizations parallel (In) and perpendicular (I ) to the magnetic field may be induced when a transparent medium, placed in a magnetic field which can cause a Zeeman effect, is irradiated with light propagating perpendicularly to the lines of magnetic force. This phenomenon is known as the Cotton-Mouton effect (Voigt effect). The phase gap is given by Eq. (4.37),... 

The experimental parameter that may give quantitative information on the magnetizability polarizability to second order in the electric field is the Cotton-Mouton constant, responsible for the Cotton-Mouton effect (CME), i.e., the birefringence of light in gases in a static magnetic field [15-19],... 

A magnetic field dependent splitting of some of the doubly degenerate zone center optical phonons was found in RCh (Schaack 1975, 1977). The effects result from the CEF-splitting of the RE-ions. It can be shown that they are the analogues of the Cotton-Mouton effect and the Faraday rotation of acoustic phonons. For a microscopic theory see Thalmeier and Fulde (1977). 

Electric and magnetic fields Linear dichroism produced as a result of applying an electric field is known as electric dichroism (Kerr effect). The effect is usually quite small for normal-sized molecules, although polymers such as DNA can be oriented very well. The orientation imposed by a magnetic field is even smaller, and therefore its practical use is limited to large molecular ensembles (Cotton-Mouton effect). 

Fig. II.3. Effect of fluorine substitutions on the out-of-plane minus average in-plane component of the magnetic susceptibility are shown for several aromatic rings. The difference between the Cotton-Mouton and the rotational Zeeman effect data is probably due to the neglect of the field dependence of the electric polarizability in the analysis of the Cotton-Mouton data. Note that the difference in the results for 1,2- and 1,3-difluorobenzene indicates that the ring current quenching effects of substituents strongly depend on their position...

Fig. 23. The geometry of the propagation (k), polarization (e) and magnetic field (5) vectors for the Voigt or Cotton-Mouton (CM) and Faraday (FA) effects. The change of polarization state of transverse C44 modes is indicated. For clarity the polarization is not shown in perspective. 0 is the CM or FA rotation angle.

Particular nonlinear optical phenomena arise also when static electric or magnetic fields are applied. The molecular states and selection rules are thereby modified, leading, for instance, to higher-order, nonlinear-optical variants of the linear (Pockels) and quadratic (Kerr) electro-optical effect, or of the linear (Faraday) and quadratic (Cotton-Mouton) magneto-optical effect. 

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