Reorientational motion

In order to obtain a more realistic description of reorientational motion of intemuclear axes in real molecules in solution, many improvements of the tcf of equation Bl.13.11 have been proposed [6]. Some of these models are characterized in table Bl.13.1. The entry number of tenns refers to the number of exponential fiinctions in the relevant tcf or, correspondingly, the number of Lorentzian temis in the spectral density fiinction. 

Usually, nuclear relaxation data for the study of reorientational motions of molecules and molecular segments are obtained for non-viscous liquids in the extreme narrowing region where the product of the resonance frequency and the reorientational correlation time is much less than unity [1, 3, 5]. The dipolar spin-lattice relaxation rate of nucleus i is then directly proportional to the reorientational correlation time p... 

Here, the J terms are the spectral densities with the resonance frequencies co of the and nuclei, respectively. It is now necessary to find an appropriate spectral density to describe the reorientational motions properly (cf [6, 7]). The simplest spectral density commonly used for interpretation of NMR relaxation data is the one introduced by Bloembergen, Purcell, and Pound [8]. 

The largest correlation times, and thus the slowest reorientational motion, were shown by the three C- Fl vectors of the aromatic ring, with values of between approximately 60 and 70 ps at 357 K, values expected for viscous liquids like ionic liquids. The activation energies are also in the typical range for viscous liquids. As can be seen from Table 4.5-1, the best fit was obtained for a combination of the Cole-Davidson with the Lipari-Szabo spectral density, with a distribution parame-... 

Computer simulations therefore have several inter-related objectives. In the long term one would hope that molecular level simulations of structure and bonding in liquid crystal systems would become sufficiently predictive so as to remove the need for costly and time-consuming synthesis of many compounds in order to optimise certain properties. In this way, predictive simulations would become a routine tool in the design of new materials. Predictive, in this sense, refers to calculations without reference to experimental results. Such calculations are said to be from first principles or ab initio. As a step toward this goal, simulations of properties at the molecular level can be used to parametrise interaction potentials for use in the study of phase behaviour and condensed phase properties such as elastic constants, viscosities, molecular diffusion and reorientational motion with maximum specificity to real systems. Another role of ab initio computer simulation lies in its interaction... 

Normal vibrational spectroscopy generates information about the molecular frequency of vibration, the intensity of the spectral line and the shape of the associated band. The first of these is related to the strength of the molecular bonds and is the main concern of this section. The intensity of the band is related to the degree to which the polarisability is modulated during the vibration and the band shape provides information about molecular reorientational motion. 

Here the vector rj represents the centre of mass position, and D is usually averaged over several time origins to to improve statistics. Values for D can be resolved parallel and perpendicular to the director to give two components (D//, Dj ), and actual values are summarised for a range of studies in Table 3 of [45]. Most studies have found diffusion coefficients in the 10 m s range with the ratio D///Dj between 1.59 and 3.73 for calamitic liquid crystals. Yakovenko and co-workers have carried out a detailed study of the reorientational motion in the molecule PCH5 [101]. Their results show that conformational molecular flexibility plays an important role in the dynamics of the molecule. They also show that cage models can be used to fit the reorientational correlation functions of the molecule. 

As indicated, the power law approximations to the fS-correlator described above are only valid asymptotically for a —> 0, but corrections to these predictions have been worked out.102,103 More important, however, is the assumption of the idealized MCT that density fluctuations are the only slow variables. This assumption breaks down close to Tc. The MCT has been augmented by coupling to mass currents, which are sometimes termed inclusion of hopping processes, but the extension of the theory to temperatures below Tc or even down to Tg has not yet been successful.101 Also, the theory is often not applied to experimental density fluctuations directly (observed by neutron scattering) but instead to dielectric relaxation or to NMR experiments. These latter techniques probe reorientational motion of anisotropic molecules, whereas the MCT equation describes a scalar quantity. Using MCT results to compare with dielectric or NMR experiments thus forces one to assume a direct coupling of orientational correlations with density fluctuations exists. The different orientational correlation functions and the question to what extent they directly couple to the density fluctuations have been considered in extensions to the standard MCT picture.104-108... 

The measured spin relaxation parameters (longitudinal and transverse relaxation rates, Ri and P2> and heteronuclear steady-state NOE) are directly related to power spectral densities (SD). These spectral densities, J(w), are related via Fourier transformation with the corresponding correlation functions of reorientional motion. In the case of the backbone amide 15N nucleus, where the major sources of relaxation are dipolar interaction with directly bonded H and 15N CSA, the standard equations read [21] ... 

For reorientational motions the hole in the embedding medium does not change and Eq. 4.29 is valid for arbitrary reorientations. In the case of translational... 

High-symmetry systems discussed in the previous section are scarce. In systems with lower symmetry and S > 1, we must expect a static ZFS, which can have a profound effect on both the electron spin relaxation and the PRE. The treatment of the PRE in systems with static ZFS requires caution. The reorientational motion of the complex modulates the ZFS which can cause the breach of both the Redfield condition for the electron spin relaxation and the assumption that electron spin relaxation and molecular reorientation are statistically independent (the decomposition approximation). One limit where the decomposition approximation is valid is for slowly rotating systems. 

When the reorientational motion is rapid and the ZFS averaged over rapid motions (distortions, collisions) is non-zero, the validity of the decomposition... 

Abernathy and Sharp employed a similar idea, although in a more simplified form 130). They also worked in terms of a spin Hamiltonian varying with time in discrete steps and let the Hamiltonian contain the Zeeman and the ZFS interactions. They assumed, however, that the ZFS interaction was constant in the molecule-fixed (P) frame and that variation of the Hamiltonian originated only from fluctuation of the P frame with respect to the laboratory frame. These fluctuations were described in terms of Brownian reorientational motion, characterized by a time interval, x, (related to the rotational correlation time x ) and a Gaussian distribution of angular steps. 

The Orbach-type process as well as the collisional process (inducing either ZFS, g anisotropy or hyperfine coupling modulation) are mechanisms that can provide electron relaxation independently on reorientation. Electron relaxation is certainly not modulated by reorientational motions... 

The largest correlation times, and thus the slowest reorientational motion, were shown by the three vectors of the aromatic ring, with values of between... 

No single model can exactly describe molecular reorientation in plastic crystals. Models which include features of the different models described above have been considered. For example, diffusion motion interrupted by orientation jumps has been considered to be responsible for molecular reorientation. This model has been somewhat successful in the case of cyclohexane and neopentane (Lechner, 1972 De Graaf Sciesinski, 1970). What is not completely clear is whether the reorientational motion is cooperative. There appears to be some evidence for coupling between the reorientational motion and the motions of neighbouring molecules. Comparative experimental studies employing complementary techniques which are sensitive to autocorrelation and monomolecular correlation would be of interest. 

One of the most direct methods of examining reorientational motion of molecules is by far infrared absorption spectroscopy or dielectric absorption. In the absence of vibrational relaxation, the relaxation times obtained by IR and dielectric methods are equivalent. In both these techniques we obtain the correlation function, [Pg.209]

A 3H and 2H NMR study of single crystals of [Ag(NH3)2][Ag(ONO)2] has been reported.32 Rapid reorientational motions of the ammine groups around their C3 axes were found. The orientations of the C3 axes within the crystal corresponded with the Ag—N bond directions of the [H3N—Ag—NH3]+ unit. The deuterium quadrupole coupling constant was determined and found to be identical to that of solid ND3. It was concluded that the electronic configuration and the geometric structure of ammonia were changed only very slightly upon coordination to silver ions. 

In principle, solvent trapping is also included in the vibrational overlap intergral in equation (25). As noted above, the solvent dipole reorientational motions associated with solvent trapping can be treated as a series of collective vibrations of the medium using approaches devised for treating the collective vibrations of ions or atoms that occur in a crystalline lattice.32-33 However, the problem is mathematically intractable because of the many solvent molecules involved which lead to many normal modes and the existence of a near continuum of energy levels. In addition,... 

The carbonyl motions of the carbonate group can be accounted for by considering jumps between two sites, corresponding to a rotation around an axis perpendicular to the C = O bond in the plane formed by the three oxygen atoms, with an angle of 40° between the two sites, over which is superimposed a rotation of 15° about the C = O bond. This latter motion requires a main-chain reorientation motion. 

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