Diffusion spectrum

The strongest, most easily discerned set of lines were called the principal spectrum. After the principal spectrum, there are two series of lines, the sharp spectrum and the diffuse spectrum. In addition, there was a fourth series of lines, the Bergmann or fimdamental spectrum. 

The wide range of diffusivity magnitudes evident in the diffusivity spectrum in Fig. 9.1 may be expected intuitively as the atomic environment for jumping becomes progressively less free, the jump rates, T, decrease accordingly in the sequence rs > rB rD(undissoc) > rD(dissoc) > VXL. The activation energies for these diffusion processes consistently follow the reverse behavior,... 

The dominant mechanism and transport path—or combinations thereof—depend upon material properties such as the diffusivity spectrum, surface tension, temperature, chemistry, and atmosphere. The dominant mechanism may also change as the microstructure evolves from one sintering stage to another. Sintering maps that indicate dominant kinetic mechanisms for different microstructural scales and environmental conditions are discussed in Section 16.3.5. 

Fig. 3. The phase spectrum for PGSE sequence and the diffusion spectrum (dotted) for the Uhlenbeck time-dependent self-diffusion.

Fig. 4. Frequency-domain modulated gradient NMR rf and gradient pulse sequences, showing the (actual) gradient modulation wave form Git), the time integral of the effective gradient wave form Fit), and the spectrum of Fit). H )P directly samples the diffusion spectrum. The wave forms and spectra are for (a) double lobe/dc rectangular modulation, (b) single lobe/ac rectangular modulation, and (c) single lobe/ac sawtooth-shaped phase modulation. Note that pulse sequences (b) and (c) sample the diffusion spectrum at a single frequency.

Peptides. The correlation of deuterium quadrupolar tensors by spin diffusion under slow magic-angle-spinning conditions can provide accurate measurements of their relative orientation. This work showed the technique applied to the cyclo-P-peptide cyclo[(5)- 3-homoalanyl-(R)-P-homoalanyl-(S)-P-homoalanyl-(i )-P-homoalanyl] with its amide hydrogens labeled by deu-terons. From the 2D spin-diffusion spectrum, the mutual orientation of the amide deuteron quadrupolar coupling tensors were found. Eight conformations that are all consistent with the NMR measurement were determined. 

Fig. 4.6. Spin-diffusion spectrum (or TOSSY spectrum) of uniformly labeled calcium acetate monohydrate. Intramolecular as well as intermolecular cross-peaks are detected. The mixing time in the presence of a RIL mixing sequence with Lee-Goldburg proton decoupling was 20 ms. 512 ti experiments were performed with 16 scans each. Contour levels are shown for constant intervals between 2 and 15% of the maximal signal intensity. The signals marked by a star are assigned to a second crystal form present as a contamination. (Figure adapted from Ref. [2]).

The application of proton-driven CSA correlation spectroscopy to amino-acid specifically carboxylic-labeled spider silk [63] is shown in Fig. 4.11. Spider silk is known to consist of alanine- and glycine-rich domains [64, 65] and is known to be semicrystalline. The assignment of alanine to the (crystalline) /3-sheet domains [66] is clearly supported by the chemical-shift correlation spectrum of Fig. 4.11. Because the tensors in a j8-sheet structure are almost parallel, or antiparallel, with the tensors in spatial proximity, a diagonal spin-diffusion spectrum is expected for that structure and is indeed found. In contrast, the glycine spectrum shows considerable off-diagonal intensity. Simulations have shown that the spectrum is compatible with a local 3i-helical structure [63]. 

Fig. 4.12. (a) 2D quasi-equilibrium proton-driven spin-diffusion spectrum at 295 K of amorphous, atactic polystyrene C-enriched at the aromatic carbon Ci. The mixing time was set to 10 s. Within this time frame, a completely disordered environment is sampled (see Fig. 4.8(c)). (b) Rate-constants for r.f.-driven spin-diffusion obtained from mixing times smaller than 4 ms from the same compound, (c) Structure of a microstructure, constructed by Rapold et al. [71] to describe amorphous atactic polystyrene. The rate constants in (b) can be well explained by a set of such microstructures. From the microstructures, in turn, the weighted distributions p( 8)/sin /3 can be extracted. The result is given in (d). (Figure adapted from Refs. [30, 70]). 

A comparison can be made between Table 7 and Table 6 (mineral suspensions). In both cases, the presence of coarse particles is characterised by a diffusion spectrum with a relatively flat shape due to the very light dependence of absorbance versus wavelength (diffraction). On the contrary, the presence of colloids is responsible for a high variation of absorbance with wavelength (Mie diffusion). The main difference between the two sets of spectra is the presence of structured elements (i.e. shoulders) on the spectra of wastewater, related to the chemical absorption of organic compounds bound to the particles (i.e. surfactants). 

Figure 5. Contour plot of the 2D spin diffusion spectrum of the hydroxyl protons of SAPO-5.

The behaviour of Sn in chromium is rather unusual. At temperatures below the Neel temperature one does not see a single unique magnetic field as expected, but rather a broad distribution of fields which results in a diffuse spectrum [247]. Examples are shown in Fig. 14.14. The narrow central line is due to precipitated metallic tin and is not part of the Sn/Cr... 

Spectral spin diffusion in the solid state involves simultaneous flipflop transitions of dipolar-coupled spins with different resonance frequencies 11,39,63-76], whereas spatial spin diffusion transports spin polarization between spatially separated equivalent spins. In this review we deal only with the first case. The interaction of spins undergoing spin diffusion with the proton reservoir provides compensation for the energy imbalance (extraneous spins mechanism) [68,70,73,74]. Spin diffusion results in an exchange of magnetization between the nuclei responsible for resolved NMR signals, which can be conveniently detected by observing the relevant cross-peaks in the 2D spin-diffusion spectrum [63-65]. This technique, formally analogous to the NOESY experiment in liquids, is already well established for solids and can also be applied to the study of catalysts. 

Figure 11 C NMR spin-diffusion spectrum of products of the conversion of meth-...

Table 3 Assignment of the 2D C NMR Spin-Diffusion Spectrum Shown in Fig. 11 [10]...

Fig. 4 proton-driven spin diffusion spectrum of OmpG-GAFY recorded at 900 MHz... 

The spectrum of the meso form of a, -diaminopimelic acid displays some sharp bands from 1667 to 1250 cm . The L form has a more diffuse spectrum in this region. Between 1250 and 667 cm" there is no resemblance between the spectra. 

FIGURE 12.16 (a) 2D H- H spin-diffusion spectrum of thymol. Boxes indicate the regions used for integration of each cross-peak. Asterisks indicate the carrier frequency artifacts (b) H- H spin-diffusion build-up curves. Experimental data points are represented by circles the best fit from the rate matrix analysis using the X-ray structure is shown using solid lines. Adapted with permission from Ref. [71]. Copyright 2009, RSC Publishing. 

Figure 19 (A) CRAMPS NMR spectrum of the slow-spin unannealed thin film P3HT PCBM blend. Also, CRAMPS NMR spin diffusion spectrum representing a physical P3HT-PCBM (50-50 by mass) mixture at tm = 2 ms (B), and that of the slow-spin unannealed thin film blend for f,n=(C)2, (D) 30, (E) 60, and (F) 240 ms. All experiments were performed at 7.0 T using a spinning frequency of 2525 Hz. Copyright 2012 Wiley. Used with permission from Ref. [55].

Figure 8. NMR spin diffusion spectrum of products of methanol conversion into gasoline over zeolite ZSM-5 with the projection onto the F2 axis (corresponding to a conventional spectrum) at the top [51]. Carbon atoms to which individual resonances are assigned are highlighted. For signal assignment see Table 2.

Table 2. Assignment of the 2D NMR spin-diffusion spectrum in Figure 8.

---