Reorientational relaxation times

Tabic I. Reorientational relaxation times Tf (in psec) of the Q (r) for two-body and three-body liquid water models. The value of is taken from Jonas, J. deFries, T. Wilbur, D. J. J. Chem. Phvs. 1976, 582. 

Reorientational relaxation times, tJ can be estimated from the assumed exponential decay of the orientational correlation functions cf(/), defined as the average of the / I.egendre polynomial of cos 0, ... 

It is important from a practical viewpoint to predict the shear viscosity of mixtures from those of pure melts. For alkali nitrate melts, a linear dependence has been found between the reorientational line width obtained by Raman measurements and the ratio of temperature divided by shear viscosity.For NO3 ions, the depolarized Raman scattering from 1050cm" total stretching vibrational mode (Al) has a contribution to the line width L, which is caused by the reorientational relaxation time of the Csv axis of this ion. The Stokes-Einstein-Debye(SED) relation establishes a relation between the shear viscosity r of a melt and the relaxation time for the reorientation of a particle immersed in it ... 

The shapes of both /w and 7hv lines are assumed to be represented by simple Lorentzians. For a totally symmetric vibration with a low polarization ratio as in the present case, the vibrational and reorientational relaxation times Tv and can be determined from the half-widths of the isotropic and anisotropic spectra. Since the value of /hv is much smaller than that of /w for the 1050 cm" line, the contribution of /gv to the isotropic intensity can be neglected ... 

Even if we consider a single solvent, e g., water, at a single temperature, say 298K, depends on the solute and in fact on the coordinate of the solute which is under consideration, and we cannot take xF as a constant. Nevertheless, in the absence of a molecular dynamics simulation for the solute motion of interest, XF for polar solvents like water is often approximated by the Debye model. In this model, the dielectric polarization of the solvent relaxes as a single exponential with a relaxation time equal to the rotational (i.e., reorientational) relaxation time of a single molecule, which is called Tp) or the Debye time [32, 347], The Debye time may be associated with the relaxation of the transverse component of the polarization field. However the solvent fluctuations and frictional relaxation occur on a faster scale given by [348,349]... 

Figure 2. Reorientational relaxation time of SN vs. the inverse of the temperature (9).

Figure 3. Viscosity dependence of the reorientation relaxation time of I.

REORIENTATIONAL RELAXATION TIME AT THE ONSET OF INTERMOLECULAR COOPERATIVITY... 

Presently, the empirics is ahead of the theory the model mechanisms that we propose we have only been able to quantitate in one instance, that of the dependence of protein reorientational relaxation time on protein concentration. Nonetheless, we have been able to clarify the distinction between macroscopic and microscopic viscosity to measure protein-protein interactions within cells and to demonstrate magnetization transfer from protein protons to solvent protons all of this is consistent with the dynamics of water-protein interactions that we infer and have discussed. 

Carbon-13 NMR has been used to study anisotropic rotational motion in liquids, as have combinations of techniques. Gillen and Griffiths (1972) have obtained the two reorientational relaxation times for benzene (a symmetric top) by combining reorientation relaxation times obtained from Raman band shapes and deuterium spin-lattice NMR relaxation times. The most extensive series of measurements probing anisotropic molecular reorientations have been made by Pecora and co-workers (Alms et al., (1973a, b)), who combined Carbon-13 spin lattice relaxation times with those obtained from depolarized Rayleigh spectra. 

Fig. 7.8.1. Reorientational relaxation time t versus solution viscosity for benzene solutions O and neat benzene. (From Alms et al., 1973b.)...

Bauer et al. (1974) have studied reorientational relaxation times of a wide variety of molecules in organic solvents and find that the single particle rotational reorientation time about a given molecular axis is of the form... 

Fig. 12.3.1. Reorientational relaxation times for chloroform versus chloroform concentration at constant viscosity (0.56 CP). The line is a least-squarefit of the tt data (O). The squares denote values of zs = tnmr. The g] also denotes relaxation times for neat chloroform for other techniques (see Table 12.3.1).

The corresponding reorientational relaxation times for these linear anions were also studied by the infrared pump/probe technique by Li et al. [162]. However, NMR spin-lattice relaxation times have been employed for other polyatomic ions, using the nuclei NforNOj" [162], forClO " [163], N for NH/ [164], and C for several tetraalkylammonium cations [165] according to Masuda and coworkers. The results are shown in Table 5.10. It was concluded that these times do not follow the expected (Stokes-Einstein-Debye) hydrodynamic solvent sequences according to the solvent... 

The top panel of Figme 10 shows the reorientational relaxation time Ti as a function of the solute s electric dipole moment, when the solute s center of mass is constrained to a slab of width 4 A centered at the Gibbs surface (labeled G), 3.5 A above the Gibbs smface (S), and in bulk water (B). As expected, in every location the relaxation time increases with the increase of the solute dipole moment, reflecting the increase in the dielectric friction. For relatively small solute dipole moments fi < 6D), the friction is dominated by the mechanical density-dependent contribution, and the relaxation in the higher density bulk region is much slower than the relaxation at the interface. However, as the dipole moment is increased, the bulk and the surface reorientation relaxation times become similar. This behavior, which mirrors that of the... 

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