Orientational relaxation rate

All these features were observed experimentally for solutions of 3-amino-/V-methylphthalimide, 4-amino-/V-methylphthalimide, and for nonsubstituted rhoda-mine. The results were observed for cooled, polar solutions of phthalimides, in which the orientational relaxation is delayed. Exactly the same spectral behavior was observed [50] by picosecond spectroscopy for low viscosity liquid solutions at room temperature, in which the orientational relaxation rate is much higher. All experimental data indicate that correlation functions of spectral shifts Av-l(t), which are used frequently for describing the Time Dependent Stokes Shift, are essentially the functions of excitation frequency. 

Steady-state behavior and lifetime dynamics can be expected to be different because molecular rotors normally exhibit multiexponential decay dynamics, and the quantum yield that determines steady-state intensity reflects the average decay. Vogel and Rettig [73] found decay dynamics of triphenylamine molecular rotors that fitted a double-exponential model and explained the two different decay times by contributions from Stokes diffusion and free volume diffusion where the orientational relaxation rate kOI is determined by two Arrhenius-type terms ... 

With this procedure, as with the double-resonance methods in atomic physics, Zeeman and Stark splittings, hyperfine structures and A doublings in molecules can be measured with high precision, even if the observed level splittings are far less than the optical dopp-ler width. From the width of the rf resonance and from the time response of the pumped systems, orientation relaxation rates can be evaluated for individual v J") levels. Other possible applications of this promising technique have been outlined by Zare 30) Experiments to test some of these proposals are currently under investigation and their results will be reported elsewhere. 

Here the pre-exponential factor At is the product of a temperature-dependent constant (ksT/h) = 2 X 10 °Ts where ke and h are the Boltzmann and Planck constants, and a solvent-specific coefficient that relates to both the solvent viscosity and to its orientational relaxation rate. This coefficient may be near unity for very mobile solvent molecules but may be considerably less than unity for viscous or orientationally hindered highly stractured solvents. The exponential factor involves the activation Gibbs energy that describes the height of the barrier to the formation of the activated complex from the reactants. It also describes temperature and pressure dependencies of the reaction rate. It is assumed that the activated complex is in equilibrium with the reactants, but that its change to form the products is rapid and independent of its environment in the solution (de Sainte Claire et al., 1997). 

The dependence of C(B) on two parameters uoj /T1 and ujj>/T2 is of course connected to the fact that, as can be seen from (2.37) and (2.39), alignment is always created along with orientation under circularly polarized excitation. Hence, for the purpose of determining the orientation relaxation rate Ti, one has to register the intensity difference Ir — h... 

The information presented in Sections 5.1.1.1-5.1.1.4 and Table 5.1, although construed to pertain to the effects of ions on the structure of the solvent, in the sense of whether it is enhanced or loosened by the presence of ions, actually reflects the effects on the dynamics of the solvent in the immediate neighborhood of the ions. The mean residence times of water molecules in the vicinity of ions are indirectly measures of the effect of the ions on the structure of the water as described in Section 5.2.1. There are aspects of solvent dynamics that are not covered by these effects, such as the orientational relaxation rate and hydrogen-bond lifetimes. Two experimental methods have mainly been employed for obtaining such information ultrafast mid-infrared and dielectric relaxation spectroscopy on the fs to ps time scales. Some slower processes were studied by NMR relaxation studies. Computer simulations added additional information, since it could be applied to individual ions rather than salts. As for the ion effects dealt with in the previous sections, the vast majority of the studies dealt with ions in aqueous solutions and only few ones considered ions in nonaqueous solvents... 

This means that the theory may be applied only to dense media where rotational relaxation proceeds at a higher rate than does orientational relaxation. 

As one would expect, the rate of orientational relaxation in the jump model is activated, and the higher the libration barrier U0, the lower the rate. However, the Hubbard relation obtained as a result of Eq. (1.123) used in Eq. (2.96) does not involve this characteristic parameter of the solid-like model ... 

The second separation method involves n.O.e. experiments in combination with non-selective relaxation-rate measurements. One example concerns the orientation of the anomeric hydroxyl group of molecule 2 in Me2SO solution. By measuring nonselective spin-lattice relaxation-rat s and n.0.e. values for OH-1, H-1, H-2, H-3, and H-4, and solving the system of Eq. 13, the various py values were calculated. Using these and the correlation time, t, obtained by C relaxation measurements, the various interproton distances were calculated. The distances between the ring protons of 2, as well as the computer-simulated values for the H-l,OH and H-2,OH distances was commensurate with a dihedral angle of 60 30° for the H-l-C-l-OH array, as had also been deduced by the deuterium-substitution method mentioned earlier. 

Now the expectation (mean) value of any physical observable (A(t)) = Yv Ap(t) can be calculated using Eq. (22) for the auto-correlation case (/ = /). For instance, A can be one of the relaxation observables for a spin system. Thus, the relaxation rate can be written as a linear combination of irreducible spectral densities and the coefficients of expansion are obtained by evaluating the double commutators for a specific spin-lattice interaction X in the auto-correlation case. In working out Gm x) [e.g., Eq. (21)], one can use successive transformations from the PAS to the (X, Y, Z) frame, and the closure property of the rotation group to rewrite D2mG(Qp ) so as to include the effects of local segmental, molecular, and/or collective motions for molecules in LC. The calculated irreducible spectral densities contain, therefore, all the frequency and orientational information pertaining to the studied molecular system. 

The above spectral densities can be modified for the occurence of chain flexibility, and for the director being oriented at dLD w.r.t. the external BQ field in the L frame. For CD bonds located in the flexible chain, the effect of DF is reduced due to an additional averaging of the time dependent factor (/f g) by conformational transitions in the chain. Consequently, the spectral densities given in Eqs. (60)-(62) are modified by replacing Soc%0(Pm,q) by the segmental order parameter YCD of the C-D bond at a particular carbon site on the chain.146,147 As observed experimentally,148,149 the spectral densities in a flexible chain show a SqD dependence when DF dominate the relaxation rates. The general expression of Jm(co 0LD) due to DF in uniaxial nematic phases is given by... 

Furthermore, the method of orientation selection can only be applied to systems with an electron spin-spin cross relaxation time Tx much larger than the electron spin-lattice relaxation time Tle77. In this case, energy exchange between the spin packets of the polycrystalline EPR spectrum by spin-spin interaction cannot take place. If on the other hand Tx < Tle, the spin packets are coupled by cross relaxation, and a powder-like ENDOR signal will be observed77. Since T 1 is normally the dominant relaxation rate in transition metal complexes, the orientation selection technique could widely be applied in polycrystalline and frozen solution samples of such systems (Sect. 6). 

Orientational relaxation measurements have also been performed on this system. Earlier papers showed no frequency dependence to the decay rate [48, 57, 58], but a recent study by the Fayer group [59] showed that the very short-time decay has a frequency dependence, in agreement with our theoretical calculations for... 

The DD-CSA cross-correlated relaxation, namely that between 13C-1H dipole and 31P-CSA, can also be used to determine backbone a and C angles in RNA [65]. The experiment requires oligonucleotides that are 13C-labeled in the sugar moiety. First, 1H-coupled, / - DQ//Q-II CP spectra are measured. DQ and ZQ spectra are obtained by linear combinations of four subspectra recorded for each q-increment. Then, the cross-relaxation rates are calculated from the peak intensity ratios of the doublets in the DQ and ZQ spectra. The observed cross-correlation rates depend on the relative orientations of CH dipoles with respect to the components of the 31P chemical shift tensor. As the components of the 31P chemical shift tensor in RNA are not known, the barium salt of diethyl phosphate was used as a model compound with the principal components values of -76 ppm, -16 ppm and 103 ppm, respectively [106]. Since the measured cross-correlation rates are a function of the angles / and e as well, these angles need to be determined independently using 3/(H, P) and 3/(C, P) coupling constants. 

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