Double lineshape

Fig. 60. Crossover from single-chain to many-chain relaxation at T = 343 K. Lineshape analysis for PDMS/d-benzene at c = 5 and 18% double logarithmic plot of — ln/S(Q,t)/S(Q,0) vs. t/s. (Reprinted with permission from [116]. Copyright 1982 J. Wiley and Sons, Inc., New York)...

We describe in some detail the techniques of nuclear magnetic resonance which are used for studying alumina-supported platinum catalysts. In particular, we describe the spin-echo technique from which the Pt lineshape can be obtained. We also discuss spin echo double resonance between surface Pt and chemisorbed molecules and show how the NMR resonance of the surface Pt can be separately studied. We present examples of experimental data and discuss their interpretation. 

Fig. 46. Double-logarithmic plot of the lineshapes of the specular He intensity from a Ni( 113) surface along the (3,3,2) direction with the temperature as parameter. (After Ref. 117.)...

Fig. 47. Double-logarithmic plot of the lineshape of the purely elastic specular He intensity from a Pt(lll) surface along the F M azimuth. The primary beam energy was 18.3 meV.

The distribution of cations in a hydrated zeolite is mainly controlled by their sizes and can be described by a statistical model. In the dehydrated state, most of the cations are located on the intraframework sites their occupancies are governed by mutual repulsions and cation—framework interactions [1]. By which, the environments of the framework silicon atoms and their corresponding ssi NMR spectra are affected [2,3]. The chemical shift and lineshape of Si NMR have been found to depend on the nature and the distribution of cations in the small sodalite and double hexagonal prism (D6R) cavities of the dehydrated Y zeolites [3] The irreversible migration of La3 ions from the supercages to the small sodalite and/or D6R cavities by... 

The double quantum filter eliminates or at least suppresses the strong signals from protons that do not experience J-coupling, e.g. the solvent signal, which would otherwise dominate the spectrum and possibly be a source of troublesome tl noise. Compared to a phase-sensitive but non-DQ-filtered COSY with pure absorption lineshapes for the cross peaks but mixed lineshapes for the diagonal peaks, the phase-sensitive, DQ-filtered COSY has pure absoiption lineshapes throughout. 

To observe a 7s — 9 transition requires that there be a 9p admixture in the 9 state. For odd this admixture is provided by the diamagnetic interaction alone, which couples states of and 2, as described in Chapter 9. For even states the diamagnetic coupling spreads the 9p state to all the odd 9( states and the motional Stark effect mixes states of even and odd (. Due to the random velocities of the He atoms, the motional Stark effect and the Doppler effect also broaden the transitions. Together these two effects produce asymmetric lines for the transitions to the odd 9t states, and double peaked lines for the transitions to even 9( states. The difference between the lineshapes of transitions to the even and odd 9i states comes from the fact that the motional Stark shift enters the transitions to the odd 9( states once, in the frequency shift. However, it enters the transitions to the even 9( states twice, once in the frequency shift and once in the transition matrix element. Although peculiar, the line shapes of the observed transitions can be analyzed well enough to determine the energies of the 9( states of >2 quite accurately.25... 

PCI differs from the disturbances of electron spectrometry treated above, because it is an inherent property of photon-induced two-step double ionization, and not an external disturbance. Nevertheless, PCI is included here because the effects on lineshape, line broadening and line position belong to the present discussion (for more details on PCI see Section 5.5). 

At low density (< 1012 cm-3) and temperatures > 100 /jK the two-photon lineshape is a double exponential, exp(- p /<5p0) [3], as expected for Doppler-free two-photon excitation by a Gaussian laser beam of a thermal gas [29]. Here v is the laser detuning from resonance and 8v0 is the linewidth due to the finite interaction time of the atom with the laser beam. At low temperature, lines as narrow as 3 kHz (FWHM at 243 nm) have been observed. A detailed discussion of this lineshape in the trap and the appearance of sidebands due to coherence effects for repeated crossing of the laser beam can be found in [30]. 

For CqS in the MHz range dynamical effects on the single-quantum (SQ) and double-quantum (DQ) 14N coherences were compared. Hereby it was demonstrated that the DQ lineshape was not broadened as much as the SQ lineshape as the DQ transition is not affected by the first-order quadrupolar Hamiltonian. 

In contrast to n-paraffins, which exhibit no or only a slight C NMR CSA, aromatics or hydrocarbons with double or triple bonds show a much larger anisotropy. Therefore, benzene (57) and 2-butyne 14) were chosen as suitable probe molecules to study molecular motions by C NMR lineshape analysis. Theoretical lineshapes for different motional states of benzene and 2-butyne molecules are depicted in Figs. 3 and 4. The proton-decoupled C NMR spectra were recorded by means of the homemade NMR spectrometer UDRIS (University of Leipzig) and a BRUKER MSL 400 (Central Institute of Physical Chemistry, Berlin) at frequencies of 22.6 and 100.6 MHz (9,14,57). 

From the relative area of the Pt spectrum that is sensitive to the double resonance, the fraction of Pt atoms that are bonded to a CO can be found. This fraction was 40% for a sample with a dispersion of 0.26 measured by hydrogen adsorption [0.22 from transmission electron microscopy (TEM)] (Fig. 40a), and it was 81% for a sample with dispersion of 0.76. No clean-surface Pt, NMR spectra have been published for these samples, but it was stated that the change in Pt lineshape upon CO chemisorption is similar to that caused by hydrogen chemisorption (see Section VI.C). 

In the interpretation of these spectra it is assumed that the geometry (i.e., the layer statistics in the NMR layer model) of the particles does not change as a result of chemisorption but that the surface LDOS and the healing length are affected. In principle, this suggestion can be tested experimentally by comparing the lineshape in a double-resonance experiment on... 

The dipolar coupling is also central to many schemes for magnetisation transfer between nuclei using double resonance techniques such as cross-polarisation. The data become more difficult to unravel when a nucleus experiences numerous different dipolar interactions at the same time. Even an increase to just three spins causes the lineshape... 

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