Kerr effect temperature dependence

The following section contains a more detailed treatment of the theory behind the nonresonant spectroscopy of liquids. This will be followed by a description of the experimental implementation and data analysis techniques for a common OKE scheme, optical-heterodyne-detected Raman-induced Kerr-effect spectroscopy (22). We will then discuss the application of this technique to the study of the temperature-dependent dynamics of simple liquids composed of symmetric-top molecules. 

In the expressions (184) and (184b) the second, temperature-dependent term defines the Born effect due to superposition of the two non-linear processes of second-order distortion and reorientation of permanent dipole moments in the electric field. Buckingham et al. determined nonlinear polarizabflities If and c for numerous molecules by Kerr effect measurements in gases as a function of temperature and pressure. It is here convenient to use the virial expansion of the molar Kerr constant, when the first and second virial coefficients Ak and Bk result immediately from equations (177), (178), and (184). Meeten et al. determined nonlinear molecular polarizabilities by measuring K in liquids as a function of temperature. 

Hu Z H, Huang X H, Annapureddy H V R, et al. Molecular dynamics study of the temperature-dependent optical kerr effect spectra and intermolecular dynamics of room temperature ionic liquid 1-methox-yethylpyridinium dicyanoamide. /. Phys. Chem. B. 2008. 112, 7837-7849. 

It follows from the preceding results that the electro-optical properties of molecules in degenerate electronic states should have unusual temperature dependence, which is absent in the case of nondegenerate states. Even for nondipolar degenerate electronic states (e.g., for states in which the reduced matrix elements of the dipole moment are zero) for certain relationships between the vibronic constant and the temperature, there may be a quadratic dependence of the Kerr effect on p, similar to that observed in the case of molecules that are simultaneously anisotropic polarizable and possess a proper dipole moment. The nonlinear dependence on p under consideration is due exclusively to the vibronic interaction that redetermines the vibronic spectrum and leads to different polarizability in different vibronic states. This dependence on p has to be distinguished from that which arises due to the nonzero value of the dipole moment in the initial ground electronic state (e.g., as in the case of the E term in molecules with D3h symmetry). The two sources of the... 

It can easily be seen that in the absence of the vibronic coupling all the parameters 0G3/2(r, p), Q%n(T, /3), and Q n(T, P) are equal to one, and the Cotton-Mouton constant in this approximation is a quadratic function of the inverse temperature, similar to that inherent to molecules with nonzero magnetic moments and with anisotropic polarizability and magnetic susceptibility. The vibronic interaction modifies the temperature dependence by means of the temperature-dependent reduction factors, a part of which was discussed in the investigation of the Kerr effect. 

Fig. 34. Concentration dependence of

The temperature dependence of the Faraday and Kerr rotation in a number of amorphous Gd1 xFex alloys was studied by Hartmann (1982). Results obtained for the latter alloys are reproduced in fig. 53. These results have to be compared with the temperature dependence of the magnetization shown for Gd0 2Fe0 8 in fig. 52. It follows from the results of Hartmann that all the Gdt xFex alloys shown in fig. 53 have a compensation temperature, which decreases with increasing Fe concentration. However, no such features are seen in the magneto-optical effect in the sample is merely due to one of the two sublattice magnetizations. In accordance with this feature is the observation by means of hysteresis loops at temperatures above Tcomp but inverted types of hysteresis loops at temperatures... 

The liquid-crystalline mesophases of cholesteryl benzoate and p-phenylbenzoate provide useful stationary phases for the gas chromatography of steroids, giving separations largely on the basis of molecular shape. These steroidal materials have distinct advantages over the more conventional stationary phases for certain applications, including separations of the isomeric androstane-3,17-diols or pregnane-3,20-diols, and of cholest-4-ene from the 5-ene. The dicho-lesteryl esters of some dicarboxylic acids are reported to exhibit liquid-crystalline properties. The temperature-dependence of the Kerr effect has been measured for a series of liquid-crystalline esters of cholesterol. 

The second approach is indirect and involves the measurement of the stress-temperature coefficient of a solid polymer. For the measurement, the polymer must be in the rubbery state. Crosslinking a thermoplastic polymer at room temperature and then heating it above its melting point accomplishes this. Chapter 3 describes the mathematics involved in calculating stress-temperature coefficients. Other approaches use the birefringence dependence on temperature or the Kerr Effect to measure the stress-temperature coefficient. 

N is the Loschmidt number while 0i and 02 are complex functions of the dipole moments and polarizabilities belonging to the molecule. The Kerr constant itself can be split into two terms of which one (Ki) merely expresses the anisotropy of the optical and electrical polarizability and is named the anisotropy term K, while the other represents the effect of possibly existing electric moments. This is called the dipole term K2. The two terms differ from each other in their dependence upon temperature the Kerr effect of dipole-free molecules is proportional to 1/T, that of dipole molecules is proportional to 1/T. ... 

Let us go back to the discussion of the Frederiks transition in a homogeneously oriented nematic with positive dielectric anisotropy (splay distortion). A conventional sandwich cell is used which is very convenient in this case, because the Kerr effect is not observed when the light wave vector coincides with the field direction. Let us imagine that we are measuring the temperature dependence of the anchoring energy of the nematic using the saturation field for the complete director reorientation. For 5CB we have the left part of Fig. 4.39 [226]. 

Xiao, D., Rajian, J. R., Cady, A., Li, S., Bartsch, R. A., and Quitevis, E. L. 2007. Nanostructural organization and anion effects on the temperature dependence of the optical Kerr effect spectra of ionic liquids. J. Phys. Chem. B 111, 4669-4677. 

Loughnane, B., Scodinu, A. and Fourkas, J.T. (2006). Temperature-dependent optical Kerr effect spectroscopy of aromatic liquids. J. Phys. Chem. B 110 5708-5720. 

Hu, Z. Huang, X. Armapureddy, H. V. R. Margulis, C. J. (2008). Molecular dynamics study of the temperatme-dependent optical Kerr effect spectra and intermolecular dynamics of room temperature ionic liquid 1-methoxyethylpyridinium dicyanoamide. Journal of Physical Chemistry B, 112, 7837-7849 Hunt, N. T. Jaye, A. A. Meech, S. R. (2007). Ultrafast dynamics in complex fluids observed through the ultrafast optically-heterodyne-detected optical-Kerr-effect (OHD-OKE), Physical Chemistry Chemical Physics, 9, 2167-2180 Hyun, B.-R. Dzyuba, S. V. Bartsch, R. A. Quitevis, E. L. (2002). Intermolecular dynamics of room-temperature ionic liquids femtosecond optical Kerr effect measurements on l-alkyl-3-ethylimidazoliinn bis((trifluoromethyl)sulfonyl)imides. Journal of Physical Chemistry A, 106, 7579-7585. 

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