Spin diffusion

The characteristic time of the tliree-pulse echo decay as a fimction of the waiting time T is much longer than the phase memory time T- (which governs the decay of a two-pulse echo as a function of x), since tlie phase infomiation is stored along the z-axis where it can only decay via spin-lattice relaxation processes or via spin diffusion. 

Because both spins are in the transverse plane and transition energy levels are matched, energy can be transferred from the protons to the nuclei. In this manner the rate of repolarization is controlled by rather than by Because the protons can interchange energy by spin-diffusion only a single-proton exists and its value is usually on the order of 1 s. As a result the preparation delay can be reduced from 10 s to about 5 s increasing the number of transients, which can be acquired by two or more orders of magnitude. 

In an isolated two-spin system, the NOE (or, more accurately, the slope of its buildup) depends simply on where d is the distance between two protons. The difficulties in the interpretation of the NOE originate in deviations from this simple distance dependence of the NOE buildup (due to spin diffusion caused by other nearby protons, and internal dynamics) and from possible ambiguities in its assignment to a specific proton pair. Mofec-ufar modeling methods to deaf with these difficulties are discussed further below. 

Usually, simplified representations of the data are used to obtain preliminary structures. Thus, lower and upper bounds on the interproton distances are estimated from the NOE intensity [10], using appropriate reference distances for calibration. The bounds should include the estimates of the cumulative error due to all sources such as peak integration errors, spin diffusion, and internal dynamics. 

Structure calculation algorithms in general assume that the experimental list of restraints is completely free of errors. This is usually true only in the final stages of a structure calculation, when all errors (e.g., in the assignment of chemical shifts or NOEs) have been identified, often in a laborious iterative process. Many effects can produce inconsistent or incorrect restraints, e.g., artifact peaks, imprecise peak positions, and insufficient error bounds to correct for spin diffusion. 

Depending on experimental parameters, NOE intensities will be affected by spin diffusion (Eig. 8). Magnetization can be transferred between two protons via third protons such that the NOE between the two protons is increased and may be observed even when the distance between the two protons is above the usual experimental limit. This is a consequence of the distance dependence of the NOE. Depending on the conformation, it can be more efficient to move magnetization over intennediate protons than directly. The treatment of spin diffusion during structure refinement is reviewed in more detail in Refs. 31, and 71-73. 

Figure 8 Effects of spin diffusion. The NOE between two protons (indicated by the solid line) may be altered by the presence of alternative pathways for the magnetization (dashed lines). The size of the NOE can be calculated for a structure from the experimental mixing time, and the complete relaxation matrix, (Ry), which is a function of all mterproton distances d j and functions describing the motion of the protons, y is the gyromagnetic ratio of the proton, ti is the Planck constant, t is the rotational correlation time, and O) is the Larmor frequency of the proton m the magnetic field. The expression for (Rjj) is an approximation assuming an internally rigid molecule.

The well-known difficulties in calculating tliree-dimensional structures of macromolecules from NMR data mentioned above (sparseness of the data, imprecision of the restraints due to spin diffusion and internal dynamics) also make the validation of the structures a challenging task. The quality of the data [88] and the energy parameters used in the refinement [89] can be expected to influence the quality of structures. Several principles can be used to validate NMR structures. 

ROESY Rotating frame NOESY, detection of NOE in the HH COSY format with suppressed spin-diffusion, detects closely spaced protons also in smaller molecules... 

Thus, for the investigation of buried polymer interfaces, several techniques with molecular resolution are also available. Recently NMR spin diffusion experiments [92] have also been applied to the analysis of a transition zone in polymer blends or crystals and even the diffusion and mobility of chains within this layer may be analyzed. There are still several other techniques used, such as radioactive tracer detection, forced Rayleigh scattering or fluorescence quenching, which also yield valuable information on specific aspects of buried interfaces. They all depend very critically on sample preparation and quality, and we will discuss this important aspect in the next section. 

It may be concluded that during the contact time in the competing process for the energy in the various spin systems, the carbon atoms are trying to reach thermal equilibrium with the proton polarization, which is in itself decreasing with a time constant, (Tig, H). In fact the protons undergo spin diffusion and can be treated together, whereas the carbon atoms behave individually. Therefore one implication is that we can also expect to obtain a C-13 spin polarization proportional to the proton polarization. 

Oil and 0)2, and (b) 2D shift-correlation spectra, involving either coherent transfer of magnetization [e.g., COSY (Aue et al, 1976), hetero-COSY (Maudsley and Ernst, 1977), relayed COSY (Eich et al, 1982), TOCSY (Braunschweiler and Ernst, 1983), 2D multiple-quantum spectra (Braun-schweiler et al, 1983), etc.] or incoherent transfer of magnedzation (Kumar et al, 1980 Machura and Ernst, 1980 Bothner-By et al, 1984) [e.g., 2D crossrelaxation experiments, such as NOESY, ROESY, 2D chemical-exchange spectroscopy (EXSY) (Jeener et al, 1979 Meier and Ernst, 1979), and 2D spin-diffusion spectroscopy (Caravatti et al, 1985) ]. 

In addition to giving conformational information, solid state NMR relaxation experiments can be used to probe the thermal motion of polymers in the hydrated cell wall (5). The motion of the polymers can give us clues as to the environment of the polymer. When there are both rigid and mobile polymers within a composite material, NMR spin-diffusion experiments can be used to find out how far apart they are. 

E. O. Stejskal, J. E. Tanner 1965, (Spin diffusion measurements Spin echoes in the presence of a time-dependent field gradient),/. Chem. Phys. 42 (1), 288—292. 

Multidimensional and heteronuclear NMR techniques have revolutionised the use of NMR spectroscopy for the structure determination of organic molecules from small to complex. Multidimensional NMR also allows observation of forbidden multiple-quantum transitions and probing of slow dynamic processes, such as chemical exchange, cross-relaxation, transient Over-hauser effects, and spin-diffusion in solids. 

The NOE is really quite complicated, and in fact even small molecules can show negative NOEs, which are due to a phenomenon known as spin diffusion. 

FIGURE 4.2 (See color insert following page 336.) Alkyl chain organization of a C30 phase. (From Raitza, M. et al., Investigating the Surface Morphology ofTriacontyl Phases with Spin-Diffusion Solid-State NMR Spectroscopy, John Wiley Sons Ltd., 3489, 2000. With permission.)... 

Raitza, M., Wegmann, J., Bachmann, S., and Albert, K. 2000. Investigating the surface morphology of triacontyl phases with spin-diffusion solid-state NMR spectroscopy. Angew. Chem. 112 3629-3632, Angew. Chem. Int. Ed. 112 3486-3489. 

Proton-driven spin diffusion Pulsed field gradient spin-echo Pleckstrin homology Poly(hydroxyethylmethacrylate)... 

Taking into account spin diffusion among the proton spin system (multiple proton-proton cross-relaxation rates), one obtain order... 

The fact that dynamic 13C polarization is only possible through the indirect way via tire 1H spins suggests the mechanism of polarization transfer. Since the polarization transfer between the electrons and nuclei are driven by the dipolar interactions between them, and the fraction of the guest triplet molecules was small, it would be natural to assume that the polarization of the electron spins in the photo-excited triplet state is given to those H spins which happen to be close to the electron spins, and then the 1H polarization would be transported away over the whole volume of the sample by spin diffusion among the 1H spins. 

For the dilute aH spins surrounded by a large number of the 2H spins, the heteronuclear aH-H dipolar interaction is dominant, lifting the spectral overlap between the 1H packets. H spin diffusion is driven by the flip-flop term of the 1H-1H dipolar interaction, which becomes secular in the presence of spectral overlap. Thus, spin diffusion would be accelerated if it had not been for the 1H-2H dipolar interaction. In order to confirm this prediction, they used another RF channel of the OPENCORE... 

Spin-Diffusion and Third-Spin-Assisted Recoupling. 25... 

Magnetization transfer via proton-driven-spin-diffusion (PDSD) in MAS NMR is not by any means a new experiment. It was introduced in the early 1980s by Maciel and coworkers [136] and later used, described, and analyzed by numerous groups in relation to, e.g., biological solid-state NMR. In its original form, the experiment consists of a couple of oppositely phase n/2 pulses bringing the low-y... 

---