Slow molecular motion

ELDOR has been employed to study a number of systems such as inorganic compounds, organic compounds, biologically important compounds and glasses. The potential of ELDOR for studying slow molecular motions has been recognized by Freed and coworkers [29, 30]. 

Spin-spin relaxation of nuclei is accelerated when the nuclei participate in a dipolar bond (O — H, N — H, 13C—1H). Spin-spin relaxation involving dipole-dipole interaction is very effective in solids and viscous liquids with slow molecular motion, since the magnetic fields caused by slowly tumbling dipoles change very slowly. 

Very slow molecular motion (tc > 10 9 s/rad at B0 x 2.1 Tesla) leads to an increase in T, while T2 decreases (Fig. 3.20). The signals then broaden (line width at half-maximum intensity zlv1/2 1/7V). Therefore, the more sluggish macromolecules usually give poorly resolved 13C NMR spectra having a bandlike shape. 

Exchange experiments are invaluable for studying slow molecular motions (with correlation times of the order of milliseconds or slower) in solids,20 and accordingly have seen many applications in polymers, for instance, as discussed in Section 5. The essential concept of a two-dimensional exchange experiment is straightforward and is illustrated in Fig. 19. 

Fig. 25. Schematic pulse sequence for the reduced four-dimensional experiment to probe the spatial heterogeneity of molecular motions.54" 5 As for the experiment in Fig. 24, part A of the sequence selects out only signal from any slow components in the system. This experiment differs from that in Fig. 24 only in that the central mixing time, rmb, provided to allow the motional timescale to change if it can, now allows H- H spin diffusion instead, so that the size of the region with slow molecular motions may be estimated. The two other mixing times rma and rmc are equal.

T2 ofprotons onmolecules are dependent on molecular motion. Large molecules such as membranes and proteins with slow molecular motion have a very short T2 (<1 ms). As a result, the linewidth of these molecules is very broad compared to free water. The relationship betw een linewidth (full width at half maximum) and the T2 of molecules is given by ... 

Here T2 is the effective transverse relaxation time, and the Larmor frequency wl is taken to be time dependent in order to account for effects of slow molecular motion as well as for the effects of time-dependent magnetic field gradients. The initial magnetization before the 90° excitation pulse at f = 0 is taken to be Mz which can be different from the thermodynamic equilibrium value Mo as a result of incomplete relaxation or the use of a filter for longitudinal magnetization. 

If the orientation dependence of the resonance frequency of a spin 5 is determined by just one interaction, it can be exploited for use as a protractor to measure angles of molecular orientation. In powders and materials with partial molecular orientation, the orientation angles and, therefore, the resonance frequencies are distributed over a range of values. This leads to the so-called wideline spectra. From the lineshape, the orientational distribution function of the molecules can be obtained. These lineshapes need to be discriminated from temperature-dependent changes of the lineshape which result from slow molecular reorientation on the timescale of the inverse width of the wideline spectrum. The lineshapes of wideline spectra, therefore, provide information about molecular order as well as about the type and the timescale of slow molecular motion in solids [Sch9, Spil]. 

NMR can provide detailed information about type and timescale of slow molecular motion. Slow molecular reorientational processes can be probed by making use of the angular dependence (3.1.23) of the resonance frequency. Slow molecular translation can be investigated with NMR by measuring the particle diffusion and flow in magnetic field gradients (cf. Section 7.2.6) [Call, Cal2, Karl, Kiml, Stil]. 

The expression for Tip equals that for T2 in the limit as a>i approaches zero, although the spin-lock condition breaks down with decreasing a). Nevertheless, from the experimental point of view Tip is a very handy parameter for the characterization of slow molecular motion on the time scale of caj", because coi can be adjusted via the spin-lock power so that Tip can be determined as a function of frequency. 

Similar to transverse relaxation longitudinal relaxation in the rotating frame is also sensitive to slow molecular motion (cf. Fig. 7.1.3) and is thus a good probe for elastomer... 

Typical values of coil diameter. Therefore, 7 ip relaxation is particularly useful for generating contrast based on differences in slow molecular motion, such as in elastomers and in solids. 

Space encoding is achieved most conveniently through magic-echo techniques [Hafl]. Parameter contrast is introduced by suitable filters, which generate a signal decay under an effective Hamiltonian that is sensitive to slow molecular motion. Such filters are the... 

Just as in the relation of the FID to the spectrum as discussed in I.D.2., G(t) and J(ui) have an inverse relationship such that for slow molecular motion in which xc is long its J(u>) is all bunched up for small ui and vice versa. 

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