Dynamics of reorientation

Dynamics of Reorientation. The approach of Impey, Madden and McDonald is used to consider the dynamics of reorientation for water molecules. The time autocorrelation function of the second Legrendre polynomial P2 of the angle subtended by the intramolecular H-H bond vector at time t with respect to its position at time t = 0 is calculated ... 

The time dependence of the anisotropy r(t) depends on the underlying dynamics of reorientational motion. For rotational diffusion (tumbling) of a spherical object, the expected anisotropy decay is exponential with a rotational diffusion time given in the hydrodynamic limit by the Stokes-Einstein-Debye equation. For nonspherical molecules, more complex time dependence may be detected. (For more on these topics, see the book by Cantor and Schimmel in Further Reading.)... 

The dynamics of reorientation in static fields was studied by Pieranski et o/. Durbin et investigated the dynamic behaviour of the optical Freedericksz... 

The results above show that the Frank moduli are determined mainly by the structure of mesogenic units which are similar for conventional nematics and thermotropic polymers (the situation changes considerably for the lyotropic solutions of long rod-like polymeric molecules, see the next section). On the other hand, the dynamics of reorientation are strongly influenced by the backbone. Field response and relaxation times depend dramatically on the molecular mass of a polymer though, in the first approximation, obey the same equations (4.30, 4.31). Figure 4.42 shows field-response times as a function of temperature for a comb-like acryl polymer H... 

Before turning to dynamics, we should hke to point out that, because no solvent is explicitly included, the Rouse model [37,38] (rather than the Zimm model [39]) results in the dilute limit, as there is no hydrodynamic interaction. The rate of reorientation of monomers per unit time is W, and the relaxation time of a chain scales as [26,38]... 

Models for description of liquids should provide us with an understanding of the dynamic behavior of the molecules, and thus of the routes of chemical reactions in the liquids. While it is often relatively easy to describe the molecular structure and dynamics of the gaseous or the solid state, this is not true for the liquid state. Molecules in liquids can perform vibrations, rotations, and translations. A successful model often used for the description of molecular rotational processes in liquids is the rotational diffusion model, in which it is assumed that the molecules rotate by small angular steps about the molecular rotation axes. One quantity to describe the rotational speed of molecules is the reorientational correlation time T, which is a measure for the average time elapsed when a molecule has rotated through an angle of the order of 1 radian, or approximately 60°. It is indirectly proportional to the velocity of rotational 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. 

The vibrational dynamics of water solnbilized in lecithin-reversed micelles appears to be practically indistingnishable from those in bulk water i.e., in the micellar core an extensive hydrogen bonded domain is realized, similar, at least from the vibrational point of view, to that occurring in pure water [58], On the other hand, the reorientational dynamics of the water domain are strongly affected, due to water nanoconfmement and interfacial effects [105,106],... 

In addition to the described above methods, there are computational QM-MM (quantum mechanics-classic mechanics) methods in progress of development. They allow prediction and understanding of solvatochromism and fluorescence characteristics of dyes that are situated in various molecular structures changing electrical properties on nanoscale. Their electronic transitions and according microscopic structures are calculated using QM coupled to the point charges with Coulombic potentials. It is very important that in typical QM-MM simulations, no dielectric constant is involved Orientational dielectric effects come naturally from reorientation and translation of the elements of the system on the pathway of attaining the equilibrium. Dynamics of such complex systems as proteins embedded in natural environment may be revealed with femtosecond time resolution. In more detail, this topic is analyzed in this volume [76]. 

Solid-state 9Be and 13C NMR studies have been used to characterize the structure and dynamics of the methyl-substituted beryllocenes. The isotropic 9Be chemical shift has been found to vary with the coordination of the Cp rings, from —19.8ppm in 11 (rf/rf) to — 24.4ppm in 10 (rf/rf). The Cp rings of 11 display comparatively little motion from —100 to 80°C, whereas the rate of reorientation of the CsMes rings decreases substantially at low temperatures in 10.50... 

NMR 13C spin-lattice relaxation times are sensitive to the reorientational dynamics of 13C-1H vectors. The motion of the attached proton(s) causes fluctuations in the magnetic field at the 13C nuclei, which results in decay of their magnetization. Although the time scale for the experimentally measured decay of the magnetization of a 13C nucleus in a polymer melt is typically on the order of seconds, the corresponding decay of the 13C-1H vector autocorrelation function is on the order of nanoseconds, and, hence, is amenable to simulation. 

G. B. Dutt and S. Doraiswamy, Picosecond reorientational dynamics of polar dye probes in binary aqueous mixtures, J. Chem. Phys. 96, 2475-2491 (1992). 

Observation of reorientational dynamics of dipolar groups surrounding the fluorophore in response to changes in the dipole moment of the fluorophore occurring upon electronic excitation. Such dynamics result in the appearance of spectral shifts with time,(1 ) in changes of fluorescence lifetime across the fluorescence spectrum,(7,32) and in a decrease in the observable effects of selective red-edge excitation.(1,24 33 34) The studies of these processes yield a very important parameter which characterizes dynamics in proteins— the reorientational dipolar relaxation time, xR. 

Antony, J. H., Mertens, D., Dolle, A., Wasserscheid, R, and Carper, W. R., Molecular reorientational dynamics of the neat ionic liquid l-butyl-3-methyl-imidazolium hexafluorophosphate by measurement of C nuclear magnetic relaxation data., Chem. Phys. Chem., 4, 588-594, 2003. 

In Fig. 3, the orientational diffusion time constants ror of the first solvation shell of the halogenie anions CD. Br, and D are presented as a function of temperature. From the observation that ror is shorter than rc, it follows that the orientational dynamics of the HDO molecules in the first solvation shell of the Cl ion must result from motions that do not contribute to the spectral diffusion, i.e. that do not affect the length of the O-H- -Cl hydrogen bond. Hence, the observed reorientation represents the orientational diffusion of the complete solvation structure. Also shown in Fig. 3 are fits to the data using the relation between ror and the temperature T that follows from the Stokes-Einstein relation for orientational diffusion ... 

An important signature of the dynamics of water molecules is the reorientation of its dipole vector that can be probed by dielectric and NMR measurements. We have calculated the single molecule dipole-dipole time correlation function (TCF), defined as,... 

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