Magnetic birefringence Cotton-Mouton

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]. 

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. 

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. 

Magnetic Circular Dichroism (MCD), Magnetic Linear Dichroism (MLD), Magnetic Linear Birefringence (Cotton-Mouton effect)... 

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. 

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... 

In the next section we summarize the theoretical background for coupled cluster response theory and discuss certain issues related to their actual implementation. In Sections 3 and 4 we describe the application of quadratic and cubic response in calculations of first and second hyperpolarizabilities. The use of response theory to calculate magneto-optical properties as e.g. the Faraday effect, magnetic circular dichroism, Buckingham effect, Cotton-Mouton effect or Jones birefringence is discussed in Section 5. Finally we give some conclusions and an outlook in Section 6. 

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],... 

This effect is related to the Cotton-Mouton effect of magnetic birefringence. 

The key is the Cotton-Mouton, or magnetically induced birefringence experiment. If the multipole analysis of induced effects, as outlined in 2 is justified then it may be shown ) that the Cotton-Mouton constant (jJZ) is proportional to g2 in fact... 

The quantity An/lP is called the Cotton-Mouton coefficient which is seen to diverge at T = Tc and to fall off as (T — Tc )" above Tc. Measurements of magnetic birefringence have been made for MBBA, and the inverse Cotton-Mouton coefficient was plotted as a function of temperature. The experimental behavior is in complete agreement with Eq. [127]. Analysis of the data yields Tc Tc — 1 K. 

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