Relaxation rate spectrum

The full-time dependence of the stress relaxation modulus ot randomly branched unentangled polymers is best derived from the fractal dynamics of Section 8.8 using the relaxation rate spectrum P( ) ... 

Looney J. P., Rosasco G. J., Rahn L. A., Hurst W. S., Hahn J. W. Comparison of rotational relaxation rate laws to characterize the Raman Q-branch spectrum of CO at 295 K, Chem. Phys. Lett. 161, 232-8 (1989). 

Thus, identification of all pairwise, interproton relaxation-contribution terms, py (in s ), for a molecule by factorization from the experimentally measured / , values can provide a unique method for calculating interproton distances, which are readily related to molecular structure and conformation. When the concept of pairwise additivity of the relaxation contributions seems to break down, as with a complex molecule having many interconnecting, relaxation pathways, there are reliable separation techniques, such as deuterium substitution in key positions, and a combination of nonselective and selective relaxation-rates, that may be used to distinguish between pairwise, dipolar interactions. Moreover, with the development of the Fourier-transform technique, and the availability of highly sophisticated, n.m.r. spectrometers, it has become possible to measure, routinely, nonselective and selective relaxation-rates of any resonance that can be clearly resolved in a n.m.r. spectrum. 

Selective, spin-lattice relaxation-rates are measured by the inversion-recovery technique. A rather weak, 180° pulse of very long duration (10-50 ms) inverts a multiplet (single-selective) or two multiplets (double-selective) in the spectrum of asperlin (1 see Fig. 2 ) and the recovery of the... 

Thus, the starting parameters for the computer-simulation of spectrum IB were chosen to agree with the value of hyperfine fields at 613 K as measured by Rlste and Tenzer, using neutron scattering measurements (36). In addition, the magnetic relaxation rate depends on temperature, as discussed in the Theory section of this paper. 

At higher temperatures, the two-phonon (Raman) processes may be predominant. In such a process, a phonon with energy hcOq is annihilated and a phonon with energy HcOr is created. The energy difference TicOq — ha>r is taken up in a transition of the electronic spin. In the Debye approximation for the phonon spectrum, this gives rise to a relaxation rate given by... 

When, however, phonons of appropriate energy are available, transitions between the various electronic states are induced (spin-lattice relaxation). If the relaxation rate is of the same order of magnitude as the magnetic hyperfine frequency, dephasing of the original coherently forward-scattered waves occurs and a breakdown of the quantum-beat pattern is observed in the NFS spectrum. 

Slowly tumbling large molecules, such as proteins, undergo rapid transverse relaxation, which causes line broadening in the NMR spectrum. This imposes an upper limit on the size of molecules whose structures can be usefully interpreted by NMR. Small molecules tumble at high rates and have much slower relaxation rates, and therefore a sharper well-resolved NMR spectrum. 

Because of the NOE and differences in relaxation rates, the intensity differences for carbon signals in a broad-band decoupled spectrum are extremely large, so that quantitative information is not available. 

The long-range coupling via the flow field which only decreases with 1/r leads to a qualitatively different behavior from that of the Rouse model. Equation (75) is approximately solved by transformation to Rouse normal coordinates. Its solution [6,91] leads to the spectrum of relaxation rates... 

Figure 12 The C responses (bottom) obtained by selectively inverting H5 (bound to a car on 12), they lead to the cross-relaxation rates erH C6 and cl1. A reference carbon-13 spectrum is shown at the top.

Quantitative solid state 13C CP/MAS NMR has been used to determine the relative amounts of carbamazepine anhydrate and carbamazepine dihydrate in mixtures [59]. The 13C NMR spectra for the two forms did not appear different, although sufficient S/N for the spectrum of the anhydrous form required long accumulation times. This was determined to be due to the slow proton relaxation rate for this form. Utilizing the fact that different proton spin-lattice relaxation times exist for the two different pseudopolymorphic forms, a quantitative method was developed. The dihydrate form displayed a relatively short relaxation time, permitting interpulse delay times of only 10 seconds to obtain full-intensity spectra of the dihydrate form while displaying no signal due to the anhydrous... 

The difference between equilibrium and non-equilibrium systems exists in the time-dependence of the latter. An example of a non-equilibrium property is the rate at which a system absorbs energy when stirred by an external influence. If the stirring is done monochromatically over a range of frequencies an absorption spectrum is generated. Another example of a non-equilibrium property is the relaxation rate by which a system reaches equilibrium from a prepared non-equilibrium state. 

The ultrasonic absorption spectrum for a series of inorganic salts with /i-CD showed one relaxation process.166 No absorption was observed for solutions only containing /i-CD. The equilibrium constants determined from competitive binding isotherms were relatively low (2-30 M-1). The relaxation frequency (/, ) was related to the observed relaxation rate constant, which is equal to the sum of the association and dissociation processes. The association rate constants for all salts with the exception of perchlorate were similar and this result was interpreted to mean that... 

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