Kerr constant, calculation

In table I we present the molar Kerr constants and mean square dipole moments of three fluorinated polymers, poly (trifluoroethylene) (PFjE), polylvinylidene fluoride) (PVF2) and poly(fluoromethylene) (PFM), dissolved in p-dioxane. The results show the sensitivity of mK to the degree and type of fluorination varying over an order of magnitude and also changing sign. Calculations of mK and for comparison are in progress (5). 

Dipole moment studies and molar Kerr constants, in C6Hi2 at 25 °C, have proved of much use in adducing the conformations of acylpyridines (73JCS(P2)l46l)..4-Formylpyridine is planar, but the acetyl group appears to be twisted about 25° from the plane of the pyridine ring in 4-acetylpyridine. The conformation of 4-benzoylpyridine must be defined by two angles 6 and 4> as in (262). The preferred conformation is calculated to be 6 = = 25°, consistent with the result for 4-acetylpyridine. 

Measurements of dipole moments, Kerr constants, and dielectric absorption have been employed (81RCR336) widely to obtain information on the conformational equilibrium in acyl heterocycles. Details on conformer structures and populations depend on the choice of additive scheme, group moments, or polarizability tensor in the case of Kerr constants. Several early conclusions, especially for furan- and thiophene-2-carboxaldehyde, appeared contradictory, owing to the choice of these quantities. A more precise definition of polarizability tensors for several heterocycles and a choice of group moments and additive schemes tested on a large amount of available experimental results and supported by accurate theoretical calculations have led to more confidence in the use of experimental dipole moments and Kerr constants in conformational analysis. A limitation of the method is that the... 

Based on comparison of calculation and experiment for the molar Kerr constants mK and the dipole moments squared of the a,o>-dibromoalkanes lx S 17) in cyclohexane. 

Molar Kerr constants mK and dipole moments squared of polytoxyethylene giycoils (POEG) and polyjoxyethylene dimethyl ether)s (POEDE) are reported in the isotropically polarizable solvents carbon tetrachloride, cyclohexane, and dioxane. Data for mK/x for POEG appear to reach an asymptotical value, Calculations of mK/x and /x based on the RIS model show good agreement with the experimental results. 

Two different RIS models are used to calculate dipole moments and molar Kerr constants for PVB oligomers. The obtained results are compared with experimental results. 

The optical anisotropies y and molar Kerr constants mK of model compounds, and of polylp-chlorostyrene) and polyfp-bromostyrene), are determined. Averages and over all conformations of the polymer chains are calculated as functions of the fraction wm of the meso diads using the RIS model originally developed for PS. 

Experimental values are presented of the molar Kerr constants /x and dipole moments squared, lx, for the copolymers poly(styrene-co-p-bromostyrene), where x is the degree of polymerization. Some results are also presented for poly(styrene-co-p-chlorostyrene) and related polymers. The RIS model of Yoon etal. (Yoon, D. Y. Sundararajan, P. R. Flory, P. J. Macromolecules 1975, 8, 776) is used to calculate mK/x and /x values as a function of tacticity and composition. The statistical weight matrices are identical with those used by Saiz etal. (Saiz, E. Mark, J. E. Flory, P. J. Macromolecules 1977, 10, 967), with the following parameters h = 0.8 exp 397/RT), co = o = 1.3 exp - 1987/RT) and m,= 1.B exp -(2186/RT), where T = 298 K is the temperature. 

The Kerr constant is related to the difference between the refractive indices of the medium parallel and perpendicular to an applied field, and these may be calculated for the assumed conformations. On this basis a 50 50 A-Meax lV-Meeq equilibrium was estimated for iV-methylpiperidine and an 80% N-Hai preference for piperidine in benzene solution.116 Some theoretical support117 was produced for this latter preference in terms of a more effective overall electron bonding in the iV-Hax conformer. These results are very much out of line with those estimates based on other methods and the Kerr-constant work has been criticized3 on the grounds of insufficient accuracy in the bond polarizabilities used in the calculations.118... 

Comparison with Experiment. The parameters and (.ri rj y of pairwise and triple radial correlations, as well as those of angular correlations (179)—(181), can be calculated numerically on making assumptions as to the model. Since the optical and electric parameters of atoms and molecules are known, the various contributions to the molecular Kerr constant can be calculated numerically from the above-derived formulae. The results of these calculations are compared with the experimental data in Table 14. 

Table 14 Theoretically calculated, and experimentally measured Kerr constants of some non-dipolar liquids (at room temperature)...

Based on dipole moments and Kerr constants, Arbusov and co-workers showed that the experimental and calculated data on 2-chloro-4-methyl-l,3,2-dioxarsinane are consistent with a chair conformation with axial chlorine and equatorial methyl <74mi 626-02,75izvi757>. 

Spectra and Theoretical Chemistry of Oxirans. - The use of conformational analysis, with the aid of torsion-angle notation, permits the interpretation and prediction of regioselective opening of epoxides/ Values for the molar refraction, electron polarization, and permanent electron dipole moments for oxiran and its simple derivatives have been calculated from literature data/ The molar Kerr constants for oxiran and its methyl derivatives in CCI4 were also calculated. The pericyclic reactivities of three-membered heterocycles have been rationalized, using the relaxation method. ... 

General discussion of intra- and intermolecular interactions 3 van der Waals interactions 3 Coulombic interactions 5 Medium effects on conformational equilibria 5 Quantum mechanical interpretations of intramolecular interactions 7 Methods of study 8 Introduction 8 Nmr and esr spectroscopy 8 Microwave spectroscopy (MW) 12 Gas-phase electron diffraction (ED) 12 X-ray crystallographic methods 13 Circular-dichroism spectroscopy and optical rotation 14 Infrared and Raman spectroscopy 18 Supersonic molecular jet technique 20 Ultrasonic relaxation 22 Dipole moments and Kerr constants 22 Molecular mechanic calculations 23 Quantum mechanical calculations 25 Conformations with respect to rotation about sp —sp bonds 27 Carbon-carbon and carbon-silicon bonds 28 Carbon-nitrogen and carbon-phosphorus bonds 42 Carbon-oxygen and carbon-sulphur bonds 48 Conformations with respect to rotation about sp —sp bonds Alkenes and carbonyl derivatives 53 Aromatic and heteroaromatic compounds 60 Amides, thioamides and analogues 75 Conclusions 83 References 84... 

Dipole moment measurements in conjunction with a knowledge of the molar Kerr constants and refractivities have been used (436) to calculate the rotation of the phenyl groups of triphenylarsine from their position in the ideal model (Section III, A, 1). In benzene solution, assuming a value of 96° for the C—As—C angle (435), the rotation is calculated to be 37° 3°. Using the more likely value of 102° the angle of rotation is found to be 40° 3° (437). Both values are in agreement with what could be expected from the available data (Section III, A, 1). 

Calculated for complete spherical symmetry, the Kerr constant has not yet been measured. 

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