Theories of orientation

Emsiey J W, Luckhust G R and Stockley C P 1982 A theory of orientational ordering in uniaxial liquid-crystals composed of molecules with alkyl chains Proc. R. See. A 381 117-28... 

K. Fukui in, Theory of Orientation and Stereose-leclion, Springer, Heidelberg 1979. 

Of course, knowledge of the entire spectrum does provide more information. If the shape of the wings of G (co) is established correctly, then not only the value of tj but also angular momentum correlation function Kj(t) may be determined. Thus, in order to obtain full information from the optical spectra of liquids, it is necessary to use their periphery as well as the central Lorentzian part of the spectrum. In terms of correlation functions this means that the initial non-exponential relaxation, which characterizes the system s behaviour during free rotation, is of no less importance than its long-time exponential behaviour. Therefore, we pay special attention to how dynamic effects may be taken into account in the theory of orientational relaxation. 

Markovian theory of orientational relaxation implies that it is exponential from the very beginning but actually Eq. (2.26) holds for t zj only. If any non-Markovian equations, either (2.24) or (2.25), are used instead, then the exponential asymptotic behaviour is preceded by a short dynamic stage which accounts for the inertial effects (at t < zj) and collisions (at t < Tc). 

Comparison of formulae (2.51) and (2.64) allows one to understand the limits and advantages of the impact approximation in the theory of orientational relaxation. The results agree solely in second order with respect to time. Everything else is different. In the impact theory the expansion involves odd powers of time, though, strictly speaking, the latter should not appear. Furthermore the coefficient /4/Tj defined in (2.61) differs from the fourth spectral moment I4 both in value and in sign. Moreover, in the impact approximation all spectral moments higher than the second one are infinite. This is due to the non-analytical nature of Kj and Kf in the impact approximation. In reality, of course, all of them exist and the lowest two are usually utilized to find from Eq. (2.66) either the dispersion of the torque (M2) or related Rq defined in Eq. (1.82) ... 

Fukui K (1975) Theory of orientation and stereoselection, Springer, Berlin Heidelberg New York... 

The theory of orientation measurements by linearly polarized Raman spectroscopy has been developed in detail by Bower in 1972 [44]. The Raman intensity, I, is given by... 

K. Fukui, Theory of Orientation and Stereoselection, Springer, Berlin, 1975. 

The book thus embraces an extended study on a variety of issues within the theory of orientational ordering and phase transitions in two-dimensional systems as well as the theory of anharmonic vibrations in low-dimensional crystals and dynamic subsystems interacting with a phonon thermostat. For the sake of readability, the main theoretical approaches involved are either presented in separate sections of the corresponding chapters or thoroughly scrutinized in appendices. The latter contain the basic formulae of the theory of local and resonance states for a system of bound harmonic oscillators (Appendix 1), the theory of thermally activated reorientations and tunnel relaxation of orientational... 

Fukui, K. Theory of orientation stereoselection, Berlin, Heidelberg, New York Springer 1975... 

On the strict theory of orientation the data in the first horizontal series must be interpreted on the assumption that the substituent groups are all in the vapour phase the hydrogen being in the liquid, a conclusion quite opposite to that usually obtained. In the second... 

The mode coupling theory of molecular liquids could be a rich area of research because there are a large number of experimental results that are still unexplained. For example, there is still no fully self-consistent theory of orientational relaxation in dense dipolar liquids. Preliminary work in this area indicated that the long-time dynamics of the orientational time correlation functions can show highly non-exponential dynamics as a result of strong in-termolecular correlations [189, 190]. The formulation of this problem, however, poses formidable difficulties. First, we need to derive an expression for the wavevector-dependent orientational correlation functions C >m(k, t), which are defined as... 

K. Fukui, Theory of Orientation and Stereoselection (Reactivity and Structure - Concepts in Organic Chemistry, Vol. 2), Springer-Verlag, Weinheim, 1975 (a) ibid., p. 54. 

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