Motion, correlation

The 13C NMR sensitivity can sometimes be a problem, but for the kind of samples studied here the effective concentration of monomer units is several molar which does not place excessive demands on present Fourier transform NMR spectrometers. In addition to the sensitivity of the chemical shift to structure (9), the relaxation of protonated carbons is dominated by dipole-dipole interaction with the attached proton (9). The dependence of the relaxation parameters T, or spin-lattice, and Tor spin-spin, on isotropic motional correlation time for a C-H unit is shown schematically in Figure 1. The T1 can be determined by standard pulse techniques (9), while the linewidth at half-height is often related to the T2. Another parameter which is related to the correlation time is the nuclear Overhauser enhancement factor, q. The value of this factor for 13C coupled to protons, varies from about 2 at short correlation times to 0.1 at long correlation... 

Since the molecular motion correlation time, Xc, depends on the temperature, the T1 curves, plotted in semilogarithmic coordinates, go through a minimum, Ti mm (Figure 4.19) which can be expressed as... 

Lee et al. evolved a comprehensive analytical-theoretical treatment, based on the solution of the reorientational isotropic diffusion equation, for an ensemble of high-spin systems under motion. These authors developed an analytical expression for the slow-tumbling motional region that relates the orientational-motion correlation time t (in s), or the corresponding tumbling rate t, with the step separation bB, of the ESR fine structure of a quartet by Eq. 8,... 

Figure 14.1. Dependence of the spin-spin relaxation time (T2) and spin-lattice relaxation time (7)) on the motional correlation time xc. Approximate values of the expected line widths for small organic molecules, proteins, and lipids in a bilayer are indicated.

It is well known that 2D NOESY is an effective method to study the three-dimensional (3D) structure of large molecules, such as proteins which have long motional correlation times.70-71 Cross-dipolar interaction peaks in a NOESY spectrum rely on the cross-relaxation of the longitudinal magnetization during the mixing time. One can extract valuable information about intermolecular distances from the intensity of the NOESY cross-peaks. The appearance of... 

Kemp, Comparison of Particle Motion Correlations for Cascading Rotary Dryers, Drying 2004—Proceedings of the 14th International Drying Symposium (IDS 2004), Sao Paulo, Brazil, Aug. 22-25, 2004, vol. B., pp. 790-797. 

The criterion for such motional narrowing is Zl- r 1, where A is the static linewidth of the relevant species and ris its motional correlation time. "" We reasonably substitute the... 

Prompers and Briischweiler showed by quasiharmonic analysis that the conformational partition function of a globular protein sampled on the ns time scale can be factorized in good approximation into purely reorientational part, which determines heteronuclear NMR spin relaxation, and a remaining part that includes other types of intramolecular motions. Thus a thermodynamic interpretation of NMR relaxation parameters in proteins in the presence of motional correlations can be given. 

An application of the saturation-recovery filter to the suppression of signal from rigid components in bisphenol-apoly(carbonate) is shown in Fig. 7.2.2 [Hanl]. The wideline solid-echo spectrum of the phenyl deuterons exhibits a range of broad and narrow components (a) as a result of a distribution of motional correlation times. The mobile components are characterized by a shorter T than the more rigid components. Consequently the rigid components can be suppressed by partial saturation. After application of the saturation-recovery filter the shape of the wideline spectrum is dominated by the narrow signal in the centre from the mobile ring deuterons (b). 

Fig. 7.2.2 [Hanl] Solid-echo wideline spectra of the ring deuterons of bisphenyl-a polycarbonate-d at 253 K. The phenyl rings undergo a 180° flip motion with a wide distribution of motional correlation times, (a) Spectrum with signals from fast and slow flipping rings.

Very slow motions (correlation times, tc>103s) may be studied via exchange methods. Such techniques are often two (or higher) dimensional. The strength of a particular nuclear spin interaction is monitored during the ti period of the experiment, usually by allowing transverse nuclear spin... 

Fig. 25. Random walk simulations for static 2H NMR powder lineshapes arising from a quadrupole echo 90°x-t-90°v-t-FID pulse sequence for the model of an isotropic 3° jump.36 (a) Jump correlation time, tj = 411 gs correlation time for the motion, xc = 100 ms, echo delays x as given in the figure. Dotted line is the spectrum for an isotropic random jump with xj = xc = 100 ms and an echo delay x — 200 gs. (b) Jump correlation times xj and motional correlation times xc as given in the figure, echo delay x = 100 gs.

More typically, relaxation data is analyzed in the form of a Ta versus temperature curve, where Ta denotes a relaxation time constant, derived from one of the experiments in Fig. 28. The motional process is either assumed to be known, or is a choice between a very restricted set. The knowledge of the form of the motional process and the spin interaction, which governs the relaxation then allows the correlation functions of Eq. (12) to be determined as a function of the motional correlation time, and this ultimately allows the determination of an equation for the characteristic relaxation time constant for the motional process as a function of its correlation time. The experimental Ta versus temperature curves are then fitted to the equation by varying the motional correlation time. The resulting variation in motional correlation time as a function of temperature then means that an activation energy for the motional process can be derived. 

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