Relaxation time translation

Zi(Air, x) and 7)(N2, x) are spin-lattice relaxation times of nitroxides in samples equilibrated with atmospheric air and nitrogen, respectively. Note that W(x) is normalized to the sample equilibrated with the atmospheric air. W(x) is proportional to the product of the local translational diffusion coefficient D(x) and the local concentration C(x) of oxygen at a depth x in the membrane, which is in equilibrium with the atmospheric air ... 

Jonas et al. measured the proton rotating frame spin-lattice relaxation time (Tip) at pressures from 1 bar to 5000 bar and at temperatures of 50 to 70 °C for DPPC and at 5 to 35 °C for POPC. If intermolecular dipolar interactions modulated by translational motion contribute significantly to the proton relaxation, the rotating frame spin-lattice relaxation rate (1/Tip) is a function of the square root of the spin-locking field angular frequency... 

When a chain has lost the memory of its initial state, rubbery flow sets in. The associated characteristic relaxation time is displayed in Fig. 1.3 in terms of the normal mode (polyisoprene displays an electric dipole moment in the direction of the chain) and thus dielectric spectroscopy is able to measure the relaxation of the end-to-end vector of a given chain. The rubbery flow passes over to liquid flow, which is characterized by the translational diffusion coefficient of the chain. Depending on the molecular weight, the characteristic length scales from the motion of a single bond to the overall chain diffusion may cover about three orders of magnitude, while the associated time scales easily may be stretched over ten or more orders. 

Relaxation is then generally governed by the equations of Freed (9). In the special case where the translational diffusion correlation time is much shorter than the Neel relaxation time, tq is dominated by diffusion and the equations of Freed reduce to the earlier equations of Ayant (10). 

The first method consists in mechanical translation of the sample between areas with different field intensities (15,16,50-64). However, such mechanical shuttling methods are inherently slow. It follows that they are applicable only to samples with long relaxation times, limited essentially by the shortest possible time it takes to move the sample from one position to another which is typically about 50 ms. 

As discussed in Section II, the Adam-Gibbs [48] model of relaxation in cooled liquids relates the structural relaxation times x, associated with long wavelength relaxation processes (viscosity, translational diffusion, rates of diffusion-limited... 

Figure 7 presents z as a function of the reduced temperature variable 87a T — 7a /7a- The different curves of Fig. 7 refer to the F-F and F-S polymer classes and the same M as in Fig. 6. Evidently, the calculated z grows much faster with 87a for the F-S polymer class and increases somewhat with M within each polymer class. These trends, taken in conjunction with the AG model, again translate into the prediction that polymer chains with bulky stiff side groups (F-S class) have a stronger dependence of the relaxation time on temperature (i.e., they are more fragile) than flexible chains with...

The rotational relaxation times of these nitrocompounds have not been measured. Comparison with the studies of perylene by Klein and Haar [253] suggests that most of these nitrocompounds have rotational times 10—20 ps in cyclohexane. For rotational effects to modify chemical reaction rates, significant reaction must occur during 10ps. This requires that electron oxidant separations should be <(6 x 10-7x 10-11)J/2 2 nm. Admittedly, with the electron—dipole interaction, both the rotational relaxation and translational diffusion will be enhanced, but to approximately comparable degrees. If electrons and oxidant have to be separated by < 2 nm, this requires a concentration of > 0.1 mol dm-3 of the nitrocompound. With rate coefficients 5 x 1012 dm3 mol-1 s 1, this implies solvated electron decay times of a few picoseconds. Certainly, rotational effects could be important on chemical reaction rates, but extremely fast resolution would be required and only mode-locked lasers currently provide < 10 ps resolution. Alternatively, careful selection of a much more viscous solvent could enable reactions to show both translational and rotational diffusion sufficiently to allow the use of more conventional techniques. 

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