Correlation time distribution

At high temperatures above Tb 617 K PMN behaves Hke all other simple perovskites. The dynamics of the system is determined by the soft transverse optical (TO) phonon which exhibits a normal dispersion and is imderdamped at all wave vectors. Below Tb, in addition to the soft mode—which becomes overdamped—a new dielectric dispersion mechanism appears at lower frequencies which can be described by a correlation time distribution function /(t). 

For the investigation of the molecular dynamics in polymers, deuteron solid-state nuclear magnetic resonance (2D-NMR) spectroscopy has been shown to be a powerful method [1]. In the field of viscoelastic polymers, segmental dynamics of poly(urethanes) has been studied intensively by 2D-NMR [78, 79]. In addition to ID NMR spectroscopy, 2D NMR exchange spectroscopy was used to extend the time scale of molecular dynamics up to the order of milliseconds or even seconds. In combination with line-shape simulation, this technique allows one to obtain correlation times and correlation-time distributions of the molecular mobility as well as detailed information about the geometry of the motional process [1]. 

Continuoas wave output, laser, IQS CMwdudon inlB ral, 103,179,409 COPA, 341-342 Co, 238,239,269 CorDnene.86.87.247,248 Corrected emissions spectra, 51.637 Correlation time distributions, 330-331 Correlation times, 304-306 Cortisol. 563-564 Cosyntropin, 497 Cottmarin,388... 

Fig. 18.6. Correlation time distributions at 0 °C for protons in (a) PWA. 2IH2O, (b) water in charcoal and (c) water in zeolite 13-X. The correlation times have been calculated from Ti and measurements with permission. The correlation times for ice (d) and water (e) are also shown.

Where M2 is the second moment of the NMR lineshape, J the spectral density function, with (Dq the Larmor frequency, and (0i the frequency of the spin-locking field. The spectral density can be written in terms of the molecular correlation time, x, and the overall shape of the Tjp - temperature dispersion and the relatively shallow minima arc due to the correlation time distribution, although the location of the minimum is unaffected by this distribution. We have examined several models for the distribution, all of which give essentially the same results. One of the more simple is the Cole-Davidson function (75), which has also been applied to the analysis of dielectric relaxations. The relevant expression for the spectral density in this case is given by Equation 4. 

The relatively small value of 8 in each case indicates a fairly broad distribution of correlation times. The same value of 0.17 is obtained for 73R and 73M, which suggests that the small amount of crystallinity induced by the annealing of the 73M has no effect on the distribution. The value for the 30R is somewhat lower, at 0.12, which implies that increasing the number of naphthalene units in the chain broadens the correlation time distribution. 

The spectral density represented by Eq. (25) can be used in place of any of the spectral densities discussed so far to provide a correlation time distribution however, the appropriate geometric factors A, B, and C in Eq. (21) or Co, C], and C2 in Eq. (22) would need to be coefficients to spectral density terms formed by Eq. (25). The effect of imposing a correlation time distribution is to (a) broaden the NMR resonance regardless of correlation time (b) raise the Tj minimum with a diminished slope (T, versus Tc plot) and (c) decrease the NOE from its maximum in the extreme narrowing limit (t l/cu) while maintaining a measurable NOE at longer correlation times. 

Shindo (1980) measured the linewidth, T, and NOE of poly(U) at 109.3 and 24.3 MHz. Because poly(U) in solution has a random-coil conformation, a motional model with a log correlation time distribution about a single average correlation time t value was utilized [see Eqs. (24) and (25)]. 

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