Initial relaxation-rate

The tube dilation may be seen in, for example, the relaxation of birefringence from the highly oriented state the initial relaxation rate is larger than the final one. A theoretical analysis of this effect has been done in ref. 2... 

This brief outline of electron spin-lattice relaxation processes has assumed that all vibrational modes of the lattice are in thermal equilibrium with the large thermal reservoir provided by the surrounding cryogenic fluid or other thermal bath. However, these vibrational modes may not be in equilibrium with the spin system, as such equilibrium requires a certain time to become established. The situation can arise in which some vibrational modes absorb energy from the spin system faster than they can transfer it to other modes or to the thermal reservoir. This situation is referred to as the phonon bottleneck, and the spin lattice relaxation is said to be bottlenecked. In this case, the initial relaxation rate can be shown to be faster than the unbottlenecked rate, followed by a transition to a slower than normal rate. The overall behavior therefore cannot be described by a single exponential process. Detailed treatments of all aspects of phonon bottlenecking and its dependence on the nature of the particular ionic species involved may be found in the general references cited above. 

The extra term means that the relaxation is no longer exponential. However, the perturbation of I, for example by a 180° pulse, will not normally depend on the spin state of S, and in this case /ii = j and 2 = 4 initially. Thus the initial relaxation rate of I is the same as in the previous case, where S was continuously irradiated, with... 

In the case of dipolar relaxation (see below) and of relatively rapid motion, it can be shown that Wq IV2 Wi = 2 12 3, which means that the initial relaxation rate after full homonuclear spin inversion is 3/2 times that following selective inversion. The irradiation of the S spins has the effect of driving the relaxation of the I spins. If the experimental ratio is less than 3/2 then the presence of competing relaxation mechanisms is indicated. Therefore the 3/2 test is a useful check before any attempt to convert H relaxation data into structural information. ... 

Due to the retractive forces in stretched mbber, the aldehyde and zwitterion fragments are separated at the molecular-relaxation rate. Therefore, the ozonides and peroxides form at sites remote from the initial cleavage, and underlying mbber chains are exposed to ozone. These unstable ozonides and polymeric peroxides cleave to a variety of oxygenated products, such as acids, esters, ketones, and aldehydes, and also expose new mbber chains to the effects of ozone. The net result is that when mbber chains are cleaved, they retract in the direction of the stress and expose underlying unsaturation. Continuation of this process results in the formation of the characteristic ozone cracks. It should be noted that in the case of butadiene mbbers a small amount of cross-linking occurs during ozonation. This is considered to be due to the reaction between the biradical of the carbonyl oxide and the double bonds of the butadiene mbber [47]. 

The initial sealing force, item 4, should be roughly known from initial design studies, but it may be subject to considerable uncertainty and must be based on an assumption of the worst combination of seal-housing tolerance variables. The residual sealing force may be estimated if there is knowledge of the stress-relaxation rate of the elastomer, using... 

To lessen experimental time, the null-point method may be employed by locating the pulse spacing, tnun, for which no magnetization is observed after the 180°-1-90° pulse-sequence. The relaxation rate is then obtained directly by using the relationship / , = 0.69/t n. In this way, a considerable diminution of measuring time is achieved, which is especially desirable in measurements of very low relaxation-rates, or for samples that are not very stable. In addition, estimates of relaxation rates for overlapping resonances can often be achieved. However, as the recovery curves for coupled spin-systems are, more often than not, nonexponential, observation of the null point may violate the initial-slope approximation. Hence, this method is best reserved for preliminary experiments that serve to establish the time scale for spin-lattice relaxation, and for qualitative conclusions. 

Fig. 3.—A. Initial Slope Approximation to Determine the Initial, Nonselective, Spin-Lattice Relaxation Rate of H-S of 2,3 S,6-Di-0-isopropylidene-a-D-mannofuranose (2) in Me2SO-d Solution. (Points between 0.01 and l.SS s were selected for tracing the best straight line.) B. The Same as in A for H-1 of a Partially Deuterated Sample of 1,6-Anhydro- -cellobiose Hexaacetate (3). [Note that the relaxation of H-1 is strongly dependent on the choice of I value. An R (ns) value of 0.24s was obtained from the data points 0 t 5s, where a value of 0.18 s was obtained from the terminal decay 5 lOs (see text).]...

The simulations can be made to reproduce the initial ratio of fits in Equation 9.27 using the measured 7j (ps) and fitting the distance r (nm), which is the only adjustable parameter. For canthaxan-thin and BI the experimental fits and the integrated values showed the best match in a very narrow temperature range ( 10 K) in the vicinity of the maximum enhancement in the relaxation rate. The distances obtained from the curve fits were similar to those determined from l/rM - 1/7 M0 difference, namely, 13.0 2.0 A for canthaxanthin and 10.0 2.0 A for BI. It was found for canthaxanthin, which shows no prominent peak in the relaxation rate, that the distance does not depend on l/rM -l/rM0. Using the ratio of curve fits, we can estimate the value of r for canthaxanthin as 9. 0+3.0 A in TiMCM-41 in the temperature range of 110-130K. 

Equation (44) is that the cross-relaxation rate can be deduced from the initial slope of the plot of as a function of tm. This initial slope is... 

Felli et al. [23] and Pelupessy et al. [24] have developed a method that measures dipole, dipole cross-correlated relaxation by transferring an initial operator to another operator by the evolution of the desired cross-correlated relaxation rate. 

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