Experiment relaxation

The tenn slow in this case means that the exchange rate is much smaller than the frequency differences in the spectrum, so the lines in the spectrum are not significantly broadened. Flowever, the exchange rate is still comparable with the spin-lattice relaxation times in the system. Exchange, which has many mathematical similarities to dipolar relaxation, can be observed in a NOESY-type experiment (sometimes called EXSY). The rates are measured from a series of EXSY spectra, or by perfonning modified spin-lattice relaxation experiments, such as those pioneered by Floflfman and Eorsen [20]. 

Kr. In the B-emitting states, a slower stepwise relaxation was observed. Figure C3.5.5 shows the possible modes of relaxation for B-emitting XeF and some experimentally detennined time constants. Although a diatomic in an atomic lattice seems to be a simple system, these vibronic relaxation experiments are rather complicated to interiDret, because of multiple electronic states which are involved due to energy transfer between B and C sites. 

This is the fundamental differential equation for a shear stress relaxation experiment. The solution to this differential equation is an equation which gives a as a function of time in accord with experiment. 

It is interesting to note that the Voigt model is useless to describe a relaxation experiment. In the latter a constant strain was introduced instantaneously. Only an infinite force could deform the viscous component of the Voigt model instantaneously. By constrast, the Maxwell model can be used to describe a creep experiment. Equation (3.56) is the fundamental differential equation of the Maxwell model. Applied to a creep experiment, da/dt = 0 and the equation becomes... 

The purpose of this problem is to consider numerically the effect of including more than two Maxwell elements in the model for a relaxation experiment. Prepare a table analogous to Table 3.2 for a set of four Maxwell elements having the following properties ... 

Another way to describe deviations from the simple BPP spectral density is the so-called model-free approach of Lipari and Szabo [10]. This takes account of the reduction of the spectral density usually observed in NMR relaxation experiments. Although the model-free approach was first applied mainly to the interpretation of relaxation data of macromolecules, it is now also used for fast internal dynamics of small and middle-sized molecules. For very fast internal motions the spectral density is given by ... 

Atomic jump processes studied by order-order relaxation experiments, Acta Mater. 44 1573 (1996). 

The stress-relaxation behavior of a material is normally determined in either the tensile or the flexural mode. In these experiments, a material specimen is rapidly elongated or compressed to produce a specified strain level and the load exerted by the specimen on the test apparatus is measured as a function of time. Specimens of certain plastics may fail during tensile or flexural stress-relaxation experiments. 

The lines show data for the triphenyl methyl system, Eq. (3-30). The data represent the results of a relaxation experiment consisting of a concentration jump (i.e., a dilution) on a pre-equilibrated solution. The solid line shows the least-squares fit of the second data set in Table 3-2 according to Eq. (3-36). Panel A shows 5, itself, and panel B the quantity ln[S,/(a - 4K-- 5,)], as in Eq. (3-35). 

Relaxation experiments. Use the relaxation times for the equilibrium shown to calculate the forward and reverse rate constants. The values are expressed in terms of the total concentration of chromium(VI), or [Cr(VI)]i = [HCrOj] + 2[Cr202 ] ... 

Calculated with capacitance value from relaxation experiment. 

To conclude, we think that valuable information can ce obtained from such relaxation experiments. They could provide a direct, kinetic proof of the conjecture that the Berry mechanism is the most probable one, as is indicated by some recent experimental and theoretical work. The applicability of this model is however restricted to situations where the energy of the molecule does not depend on the distribution of the ligands on the skeleton and where, as a consequence, there is one rate constant for each process. If this is not true, the present description could be the first-order approximation of a perturbation calculation. Such a work will be undertaken soon. 

The second reason is related to the misconception that proton dipolar relaxation-rates for the average molecule are far too complicated for practical use in stereochemical problems. This belief has been encouraged, perhaps, by the formidable, density-matrix calculations " commonly used by physicists and physical chemists for a rigorous interpretation of relaxation phenomena in multispin systems. However, proton-relaxation experiments reported by Freeman, Hill, Hall, and their coworkers " have demonstrated that pessimism regarding the interpretation of proton relaxation-rates may be unjustified. Valuable information of considerable importance for the carbohydrate chemist may be derived for the average molecule of interest from a simple treatment of relaxation rates. 

In proton-relaxation experiments, R, values are used extensively, whereas 7, values are more frequently reported for C relaxation measurements. Although there is no special merit in this preference for C 7, values, the pairwise additivity of relaxation contributions in proton-relaxation experiments is more clearly apparent for the relaxation rates. 

As for nonselective-relaxation experiments, Eq. 15 can only be used for a three-spin system, because, for j>3, the problem is underdetermined. 

Fig. 2.—A. Normal, H-N.m.r. Spectrum of Asperlin (1) in Benzene-

From the previous discussion, it is clear that relaxation experiments constitute a very powerful tool for investigation of the structure and conformation of carbohydrate molecules in solution. However, the nature of the individual problem may determine which relaxation experiment should be chosen in order to extract interproton distances to the desired accuracy of < 0.2 A. Although the limitations and relative merits of all of the various relaxation methods have not yet been systematically studied, accumulated experience provides some direct knowledge about the range of errors associated with relaxation experiments. 

In addition to giving conformational information, solid state NMR relaxation experiments can be used to probe the thermal motion of polymers in the hydrated cell wall (5). The motion of the polymers can give us clues as to the environment of the polymer. When there are both rigid and mobile polymers within a composite material, NMR spin-diffusion experiments can be used to find out how far apart they are. 

Figure 2.7.2 illustrates two implementations of the diffusion-relaxation experiment using the pulsed field gradient. In the first implementation, a spin-echo... 

For the spin-echo diffusion-relaxation experiment, they showed... 

The stimulated echo diffusion-relaxation experiment exhibits a kernel that is similar to that of the one with the pulsed field gradients ... 

On macroscopic length scales, as probed for example by dynamic mechanical relaxation experiments, the crossover from 0- to good solvent conditions in dilute solutions is accompanied by a gradual variation from Zimm to Rouse behavior [1,126]. As has been pointed out earlier, this effect is completely due to the coil expansion, resulting from the presence of excluded volume interactions. 

Similar results were observed in the stress-relaxation experiments which are shown in Figure 2. The 5- and 10-day samples relax to the same stress level. The major difference in stress-relaxation behavior among the different samples occurs during the very beginning of the relaxation process. For that reason, and in order to better illustrate the first minutes of relaxation, the time scale is logarithmic. 

Relaxation Experiments (Jump Changes of Concentration of Oxygen, Temperature and Humidity) and Rate Constants of Respective Elementary Reaction Steps 482... 

---