Correlation times, NMR

Equally Informative are the deuterium spin-spin relaxation times l2 (usually obtained from line width measurements), especially when studying low deuterltim concentrations. Due to the sensitivity of line widths to subtle changes In correlation times, NMR can give a detailed picture of rotational motion of specifically deuterlumr-labeled reporter groups. This technique has, for Instance, been used to study Internal motions of deuterium-labeled molecules bound to proteins (2.9.11,13). 

N-protonation the absolute magnitude of the Ad values is larger than for Af-methylation <770MR(9)53>. Nuclear relaxation rates of and have been measured as a function of temperature for neat liquid pyridazine, and nuclear Overhauser enhancement has been used to separate the dipolar and spin rotational contributions to relaxation. Dipolar relaxation rates have been combined with quadrupole relaxation rates to determine rotational correlation times for motion about each principal molecular axis (78MI21200). NMR analysis has been used to determine the structure of phenyllithium-pyridazine adducts and of the corresponding dihydropyridazines obtained by hydrolysis of the adducts <78RTC116>. 

MT McMahon, E Oldfield. Determination of order parameters and correlation times m proteins A comparison between Bayesian, Monte Carlo and simple graphical methods. I Biomol NMR 13 133-137, 1999. 

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

Turning from chemical exchange to nuclear relaxation time measurements, the field of NMR offers many good examples of chemical information from T, measurements. Recall from Fig. 4-7 that Ti is reciprocally related to Tc, the correlation time, for high-frequency relaxation modes. For small- to medium-size molecules in the liquid phase, T, lies to the left side of the minimum in Fig. 4-7. A larger value of T, is, therefore, associated with a smaller Tc, hence, with a more rapid rate of molecular motion. It is possible to measure Ti for individual carbon atoms in a molecule, and such results provide detailed information on the local motion of atoms or groups of atoms. Levy and Nelson " have reviewed these observations. A few examples are shown here. T, values (in seconds) are noted for individual carbon atoms. 

Pulsed deuteron NMR is described, which has recently been developed to become a powerftd tool for studying molectdar order and dynamics in solid polymers. In drawn fibres the complete orientational distribution function for the polymer chains can be determined from the analysis of deuteron NMR line shapes. By analyzing the line shapes of 2H absorption spectra and spectra obtained via solid echo and spin alignment, respectively, both type and timescale of rotational motions can be determined over an extraordinary wide range of characteristic frequencies, approximately 10 MHz to 1 Hz. In addition, motional heterogeneities can be detected and the resulting distribution of correlation times can directly be determined. 

In presence of molecular motion the NMR line shape will change. A particularly simple situation arises, if the motion is rapid on timescale defined by the inverse width of the spectrum in absence of motion 6 1. In this fast exchange limit, which in 2H NMR is reached for correlation times tc < 1CT7 s, the motion leads to a partially averaged quadrupole coupling and valuable information about the type of motion can directly be obtained from analysis of the resulting line shapes. The NMR frequency is then given by... 

Fig. 7. Theoretical line shapes resulting from an interchange between two NMR frequencies

In Fig. 7 actual numbers for the correlation times of the motion are included that apply for 2H NMR of deuterons in C—H bonds. It is evident that the line shape analysis of deuteron spectra should, in principle, provide a means to determine accurate values for the correlation times in a range of at least three orders of magnitude, the limits... 

Fig. 8. Calculated solid echo 2H NMR powder spectra for jumps between two sites related by the tetrahedral angle for ij =0, i.e. true absorption spectrum and Tj = 200 ps. xc is the correlation time of motion. R is the reduction factor, giving the total normalized intensity of the spectra for x, = 200 ps. (For x, = 0 all the spectra have total intensity 1)...

Up to now it has been tacitly assumed that each molecular motion can be described by a single correlation time. On the other hand, it is well-known, e.g., from dielectric and mechanical relaxation studies as well as from photon correlation spectroscopy and NMR relaxation times that in polymers one often deals with a distribution of correlation times60 65), in particular in glassy systems. Although the phenomenon as such is well established, little is known about the nature of this distribution. In particular, most techniques employed in this area do not allow a distinction of a heterogeneous distribution, where spatially separed groups move with different time constants and a homogeneous distribution, where each monomer unit shows essentially the same non-exponential relaxation. Even worse, relaxation... 

Polycarbonate (PC) serves as a convenient example for both, the direct determination of the distribution of correlation times and the close connection of localized motions and mechanical properties. This material shows a pronounced P-relaxation in the glassy state, but the nature of the corresponding motional mechanism was not clear 76 80> before the advent of advanced NMR techniques. Meanwhile it has been shown both from 2H NMR 17) and later from 13C NMRSI) that only the phenyl groups exhibit major mobility, consisting in 180° flips augmented by substantial small angle fluctuations about the same axis, reaching an rms amplitude of 35° at 380 K, for details see Ref. 17). 

Fig. 29. Observed and calculated 2H NMR spectra for the mesogenic groups of a) the nematic (m = 2), b) the smectic (m = 6) liquid crystalline polymer in the glassy state, showing the line shape changes due to the freezing of the jump motion of the labelled phenyl ring. The exchange frequency corresponds to the centre of the distribution of correlation times. Note that the order parameters are different, S = 0.65 in the frozen nematic, and S = 0.85 in the frozen smectic system, respectively...

H NMR 38,39,42, 50-55 Hole capacity constant 205 Homogeneous distribution of correlation times 37 Humic acids 17 Humidity of plastics 119 Humins 17 Hydrogen bond 200 Hydrophilic 191, 194, 206... 

Gillen K. T., Douglas D. S., Malmberg M. S., Maryott A. A. NMR relaxation study of liquid CCI3F. Reorientational and angular momentum correlation times and rotational diffusion, J. Chem. Phys. 57, 5170-9 (1972). 

Lowering the temperature has a similar effect on the deuterium spectra as does increased loadings. In Figure 3, spectra for benzene-d6/(Na)X at 0.7 molecules/supercage over the temperature range 298 to 133 K are shown. It is observed that both benzene species are detected simultaneously between 228 and 188 K. Below this temperature the oriented benzene species becomes the predominant form. A similar situation occurs for polycrystalline benzene-dg in which two quadrupole patterns, one static and the other motionally narrowed due to C rotation, are observed to coexist at temperatures between 110 and 130 K (7). This behavior has been attributed to sample imperfections (8) which give rise to a narrow distribution in correlation times for reorientation about the hexad axis. For benzene in (Na)X and (Cs,Na)X such imperfections may result from the ion/benzene interaction, and a nonuniform distribution of benzene molecules and ions within the zeolite. These factors may also be responsible for producing the individual species. However, from the NMR spectra it is not possible to... 

PGSE-NMR provides direct information on the translational mobility of a liquid medium capable of swelling a given CFP. The self-diffusion coefficient of the swelling agent is found to be related to the nanoporosity of the matrix as determined from ISEC and to the rotational correlation time of a suitable paramagnetic probe (ESR) [22]. 

Accurate interpretation of the formation properties (porosity, permeability and irreducible water saturation) requires reliable estimates of NMR fluid properties or the relationship between diffusivity and relaxation time. Estimation of oil viscosity and solution-gas content require their correlation with NMR measurable fluid properties. These include the hydrogen index, bulk fluid relaxation time and bulk fluid diffusivity [8]. 

Figure 1 Schematic representation of the 13C (or 15N) spin-lattice relaxation times (7"i), spin-spin relaxation (T2), and H spin-lattice relaxation time in the rotating frame (Tlp) for the liquid-like and solid-like domains, as a function of the correlation times of local motions. 13C (or 15N) NMR signals from the solid-like domains undergoing incoherent fluctuation motions with the correlation times of 10 4-10 5 s (indicated by the grey colour) could be lost due to failure of attempted peak-narrowing due to interference of frequency with proton decoupling or magic angle spinning.

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