Reorientation rates

The density dependence of however, is not trivial since one must take into account the density dependence of the monomeric friction [41] given by the monomer reorientation rate W. If a scaling plot of the correct ratio DN/iyVl /N) is attempted, one again finds poor scaling in terms of the variable (Fig. 24(a)), and a good collapse of data if instead... 

It is well known [11] that the reorientation rate in the jump model... 

Loutfy and coworkers [29, 30] assumed a different mechanism of interaction between the molecular rotor molecule and the surrounding solvent. The basic assumption was a proportionality of the diffusion constant D of the rotor in a solvent and the rotational reorientation rate kOI. Deviations from the Debye-Stokes-Einstein hydrodynamic model were observed, and Loutfy and Arnold [29] found that the reorientation rate followed a behavior analogous to the Gierer-Wirtz model [31]. The Gierer-Wirtz model considers molecular free volume and leads to a power-law relationship between the reorientation rate and viscosity. The molecular free volume can be envisioned as the void space between the packed solvent molecules, and Doolittle found an empirical relationship between free volume and viscosity [32] (6),... 

Molecular rotors are useful as reporters of their microenvironment, because their fluorescence emission allows to probe TICT formation and solvent interaction. Measurements are possible through steady-state spectroscopy and time-resolved spectroscopy. Three primary effects were identified in Sect. 2, namely, the solvent-dependent reorientation rate, the solvent-dependent quantum yield (which directly links to the reorientation rate), and the solvatochromic shift. Most commonly, molecular rotors exhibit a change in quantum yield as a consequence of nonradia-tive relaxation. Therefore, the fluorophore s quantum yield needs to be determined as accurately as possible. In steady-state spectroscopy, emission intensity can be calibrated with quantum yield standards. Alternatively, relative changes in emission intensity can be used, because the ratio of two intensities is identical to the ratio of the corresponding quantum yields if the fluid optical properties remain constant. For molecular rotors with nonradiative relaxation, the calibrated measurement of the quantum yield allows to approximately compute the rotational relaxation rate kor from the measured quantum yield [Pg.284]

It has recently been demonstrated that the analysis of MAS sidebands patterns can be used to study molecular dynamics in the solid state [85-88]. Indeed, the line narrowing effect of MAS can be partly offset, or completely eliminated, if the 2H quadrupole tensor is reoriented due to motion on a time scale comparable to (first-order quadrupolar broadening, such motion-induced effects should be less evident in the DQMAS spectrum, as has indeed been observed by Wimperis and colleagues in several deuterated solids [87, 88]. For example, the simulation of the SQ spectrum of tetrathionate dihydrate-cfi yielded the same reorientational rate constant as the previously described quadrupolar echo approach (Fig. 6). 

For a single subbarrier level we have A0(f) = 1, B0(4) = C0(4) = 0, and the halfwidth of the spectral function is determined solely by the reorientation rate, which is equal to the transition rate to the first excited state of deformation vibrations 164... 

The dielectric constant values in Table 2.8 also suggest that, while hydrate water molecules reorient rapidly compared to molecules in other solids, reorientation rates are only one-half those in ice. The hydrate value is lower than that of ice due to the lower density of hydrogen-bonded water molecules. 

In the dynamic triplet model a similar dependence of polarization magnitude on plane-polarized light is predicted, provided that the ISC rate exceeds the molecular reorientation rate. 

Fig.6Tcmpcr tufe dependence of fcorieouiionalraie constants Fjj.7 Temperature dependence of reorientational rate constants of HNMA ID PMMA. (—) e-ftlaxanoo (dielectric relaxation) cyclophane in PMMA.(—) P-relaxation (dielectric relaxation) f—) y-relaxation ( CP / MAS CNMR) For cotnparisoo. For comparison, the relaxation frequencies of these data have the reluation frequencies of these dau have been shifted been shifted by an appropriate amount along the ordinate, by an appropriate amount along tbe ordinate. 

The still faster ( nsec) dynamics of local motions of polymer molecules in dilute solutions have been investigated by Ediger and coworkers (Zhu and Ediger 1995, 1997). They find that the rates of these local motions of a few bonds are not proportional to the solvent viscosity, unless the solvent reorientation rate is fast compared to the polymer local motion. Thus, for local motions (such as bond reorientations) of polymer molecules, Stokes law of drag does not always hold. 

In Fig. 7 we depict the mean square displacement of the director as a function of time for the prolate ellipsoids. At this state point it is very low. After ten time units, the square root of the MSD is only 4°. It is important to keep this figure in mind. This low reorientation rate means that a director-based coordinate system is an inertial frame to a very good approximation even if one does not apply the constraint equation, Eq. (2.31). This MSD was obtained from a simulation of 256 molecules. If the system size increases the MSD will be even smaller. 

There is one major technical problem that must be overcome In a liquid crystal most properties are best expressed relative a to a director based coordinate system. This is not a problem in a macroscopic system where the reorientation rate of the director is virtually zero but it can be a problem in a small system such as a simulation cell where the director is constantly diffusing on the unit sphere. When NEMD methods are applied the fictitious mechanical field exerts torques that twist the director and might make it impossible to reach a steady state. This problem has been solved by devising a Lagrangian constraint algorithm that fixes the director in space so that a director based coordinate system becomes an inertial frame. 

This interaction is removed by high-power decoupling above and below Tg. When the reorientation rate of nuclei in the amorphous phase becomes near to the frequency corresponding to the amplitude of the proton decoupling field, the motion in the amorphous phase reduces the efficiency of the decoupling and leads to a maximum linewidth [30]. From this point of view, the methylene carbons in the amorphous phase are undergoing transition between the trans- and gawc/ie-conformations at frequency of about 60 kHz. 

Distances in solution at physiological temperatures can at least be estimated under conditions where the reorientation rate of the spin-spin-vector is reduced by other mechanisms, e.g., embedding the proteins in membranes or upon addition of viscosity agents [79]. In this case the dipole-dipole interaction is partly averaged out, making accurate distance measurement difficult. Quantitative... 

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