Two-dimensional exchange

Figure 5.47 Two-dimensional exchange spectrum of N,Af-dimethylacetamide and its generation, (a) The first set of spectra results from the first series of Fourier transformations with respect to The modulation of signals as a function of t is observed, (b) The second set of spectra is obtained by the second series of Fourier transformations. The unmodulated signals appear on the diagonal at (v, v ), (vx, Vx), and (v, v ), whereas the modulations due to exchange show up as crosspeaks on either side of the diagonal at (vx, Vx) and (vx, Vx). (c) A contour plot representation of (b). (Reprinted from Science 232, A. Bax, et ai, 960, copyright (1986), with permission from Science-AAAS, c/o Direct Partners Int., P.O. Box 599, 1200 AN Hilversum, The Netherlands)...

In addition to X-ray crystallographic studies, two-dimensional NMR solution experiments (i.e., COSY, 1D-NOE, and NOESY, discussed in Sections 3.5.9 and 3.5.10) have been carried out on many lanthanide(III), Ln(ffl), chelate complexes to confirm that the structure of the MRI imaging agent, used in aqueous solution, will correspond to the solid-state X-ray crystallographic structure. Two-dimensional exchange spectroscopy (2D-EXSY) has been applied to lanthanide chelates to study the dynamics of conformational equilibria (how acetate arms chelate and how... 

In fact, two-dimensional solid-state NMR is far superior to one-dimensional techniques for studying structure and dynamics123. In particular, the two-dimensional exchange NMR spectrum124 of a static sample is identical with a two-time distribution function125. Thus a two-dimensional NMR spectrum, which is detected for a fixed mixing time, is an image of the state of the dynamic process under study at that time. 

The NMR characteristic time depends, however, on the type of experiment. Figure 12.8 shows the result of a two-dimensional exchange experiment [13], for which the characteristic time can be varied from a value of the order of T2 to a value of the order of the spin-lattice relaxation time Tx, for Xe usually several seconds (depending for example on the amount of oxygen in the Xe gas used). The presence of cross-peaks in the 2-dimensional spectrum indicates that Xe atoms move during the mixing time (here 5 seconds) from the rubbery EP phase into the iPP matrix and vice versa. The cross peaks first appear already after a mixing time of 50 milliseconds. 

In Section 12.3 it was described how, with the help of a two-dimensional exchange spectrum, domain sizes in the iPP/EP blend are estimated. There an estimated value for the Xe diffusion coefficient was used. Now with experimental data from Table 12.2 the average EPDM domain size for the iPP/EPDM blend can be calculated. It was assumed that the structure of the EPDM in the blend is the same as in the pure material, (i.e., the Xe diffusion coefficient in the EPDM domains in the blend is equal to the measured D for pure EPDM and likewise for iPP), then for Xe in the EPDM domain during A = 1.2 seconds is 20 grn. In the same time for Xe in the iPP matrix is approximately 5 grn. These distances for a diffusion time of 1.3 milliseconds, the inverse of the frequency difference 770 Hz of the two lines in the Xe NMR spectrum of the blend, are 0.6 and 0.2 grn, respectively. The average size of the EPDM domains in the iPP/EPDM blend is... 

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. 24. The basic scheme of the reduced four-dimensional exchange experiment as performed on l3C.53 All pulses are 90° pulses. Part A of the experiment is simply a two-dimensional exchange experiment with l set equal to U. The effect of this part of the pulse sequence is to select out only those spins that did not reorientate significantly during the mixing period of part A, rma. The remainder of the experiment then serves to examine whether the motional timescale of these selected components subsequently changes during the second mixing time, rmb- The experiment thus probes the timescale of motional heterogeneity.

Each of the intermediate steps in the mechanistic sequence involved in spillover can differ. As an example, surface transport may occur as a two-dimensional gas, as species associated with an activated site, or as two-dimensional exchange (via hydroxyls). The literature has suggested a variety of mechanisms for spillover and mechanisms induced by spillover. The studies have not assumed that all of the mechanisms are possible and have not focused on discriminating between the alternative possibilities. This more open (albeit more disconcerting) approach is suggested to understand the phenomena of spillover. Further, novel experimental techniques are needed to isolate the catalytic effects occurring on the source of spillover (usually the metal) from the effects induced by spillover on the acceptor surface, and to access the relative contribution of each. Both the numbers of species involved and the relative rates need to be quantified. 

It is important to recognize that the two-dimensional exchange area... 

Two-dimensional exchange spectroscopy (2D EXSY) offers an enormous extension of accessible rates towards slow and very slow exchange processes. Extending the timescale is not the only merit of 2D EXSY methods before discussing some practical examples, there should be a few general remarks. The basic pulse sequence used is shown in scheme 4. 

Two-dimensional exchange spectroscopy might also be a valuable tool in the study of the metal skeleton. No example has been found in the literature. Preferably for nuclei with 100% natural abundance, homonuclear COSY or double-quantmn filtered (DQF)-COSY spectra can give the connectivity pattern of the different metal atoms in a cluster. This holds even, in some cases, for quadnipolar nuclei such as Co [21]. 

One way by means of which the structural and dynamic information inherent to the anisotropic interactions can be probed in a site-selective fashion involves the investigation of samples where specific isotopic labels, e.g., 2H, 13C, 15N, are introduced. 2H is a spin 1= 1 nucleus, and the quadrupolar interaction dominates 2H NMR. By an analysis of onedimensional line shapes, fast dynamic processes (10-4 to 10-7 s) can be quantitatively probed, while two-dimensional exchange experiments allow the inves-... 

---