Dipolar Pake doublet

A special case occurs if the solid contains nuclear spin pairs that are sufficiently far apart from each other such that intrapair coupling dominates interpair coupling. In this situation, instead of a featureless broad lineshape, we observe a well-defined powder pattern known as a Pake doublet (Figure 15.15). Since the dipolar coupling between two nuclei... 

For an isolated pair of nuclei in a polycrystalline system the band shape shows a Pake doublet. When the number of interacting nuclei becomes larger and a polycrystalline material is analyzed, the resulting spectrum is much more complex and much less informative. Nevertheless an expression for the dipolar second moment (or mean square width) of the NMR spectrum in a polycrystalline sample has been suggested by Van Vleck [12] ... 

The disordered nature of the amorphous phase has prevented the direct determination of the structural parameters by the usual structural techniques such as X-ray diffraction. Solid-state NMR can give us those parameters even for amorphous samples. Yannoni and Clark [14] applied nutation NMR spectroscopy, which is specifically designed to measure interatomic distances, to determine the bond lengths in both the cis- and tran -polyacetylenes. They used polyacetylene polymerized from a mixture of 4% doubly C-enriched acetylene and doubly depleted acetylene. In Fig. 7.6, the observed and simulated proton decoupled nutation spectra of the cis sample are shown. The sharp peak in the centre arises from the isolated nuclei in the sample. The remainder of the spectrum is a Pake-doublet arising from the dipolar coupling of adjacent nuclei in the polyacetylene. The best fit to the observed spectrum corresponds to a distribution of bond length with... 

The basic principles are well established isolated pairs of nuclei in a rigid solid experience a mutual dipolar interaction directly proportional to the average of the inverse cube of the internuclear distance. For a powder sample of an H2 complex, a normal Pake doublet line shape results (Fig. 20.3C), which can be used to calculate internuclear H-H distances within 1%. The patterns are quite sensitive to anisotropic motion, that is hindered rotation or torsion of the side-bound H2 about the M-H2 axis. This will not affect the H2 dipolar splitting when this axis is parallel to the applied magnetic field. One pair of temperature-independent... 

The dipolar pattern for polystyrene shown in Figure 3 (left) is not a Pake doublet reflecting only the CH static dipolar coupling (as scaled by WAHUHA irradiation of the protons). 

Rg. 2. Comparison between a Gaussian (dashed line) and a Pake "doublet" (solid line) for the broadening comparable to the dipolar splitting, p/a = 2/3. The... 

In QE experiments, a wiggle can be noticed due to the classic Pake doublet of dipolar coupled spin pairs (Pake 1948). This mainly occurs when a high amount of solid-like protons is probed or for specific time-domain data. Figure 7.21 shows an example of this phenomenon that has occured... 

In the NMR spectrum, the dipolar interaction represents itself as a line splitting. For isolated pairs of unlike spins, the i and j spin resonances are each split into a doublet with a splitting of 2d , for like spins a doublet with a splitting of 3d is found. For powder samples a so called Pake powder pattern is found instead of the doublet. Resolved splittings are only observable for fairly well isolated spin systems consisting of two or a very few spins (e.g., the proton pair of the crystal water in gypsum [9]). For extended spin systems, a broad and rather featureless resonance line is observed. 

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