Motionally averaged interactions, lineshape

Lineshape analysis and measurement of motionally averaged interactions 44... 

LINESHAPE ANALYSIS AND MEASUREMENT OF MOTION ALLY AVERAGED INTERACTIONS... 

In a fluid system, the spectrum structure is affected by molecular motions. In the limit of fast molecular motions (vQx << 1), the lineshape becomes insensitive to the type of individual motions, this is the so-called motional narrowing regime. What is observed in this regime is the time average of the quadrupolar interaction, i.e., of the tensor Hq. 

If there is some molecular motion with characteristic times on the order of ICT sec, the NMR spectrum will no longer have the Pake doublet lineshape discussed earlier. For example, in gel-phase bilayers a perdeuterated lipid acyl chain will have a broad, relatively featureless spectmm, as shown in Fig. 3. These spectra do not lend themselves to easy analysis The molecular motion in the membrane is not rapid enough to be axially symmetric (see the description of the fluid bilayer below) on the NMR time scale but is fast enough to influence the average value of the quadrupolar interaction and thus the splittings of the individual labels. 

When molecules undergo reorientation on a timescale of the order of the quadrupole interaction or faster (rapid exchange limit, correlation time of the motion < 10-7 s), the observed frequencies will be averaged and the resulting lineshape can be analysed to determine the type and the rate of the motion [7]. 

Conventional X-ray diffraction measures a space and time average of the electronic density. Therefore, any dynamical disorder will be transformed into spatial disorder between positions whose probabilities are determined by the average time spent on each position. Certainly, one of the most tremendous advantages of NMR compared to X-ray diffraction is its ability to measure the occurrence of motion at different time-scales. Whether the motion correlation time is on the Larmor frequency scale, the linewidth scale or much slower (exchange NMR) will affect differently the NMR parameters like relaxation rates, apparent anisotropy and asymmetry of the interaction and ID or 2D lineshape. With suitable sequences, the motion correlation times and site probabilities as a function of an external parameter (temperature or pressure) can be explicitly measured. 

The use of NMR spectroscopy for probing molecules adsorbed on alumina dispersions is briefly cited. Soderlind and Blum [66] used deuterium NMR to probe the dynamics and structure of a surfactant (an alkylbenzenesulfonate, SHBS) adsorbed onto alumina. The phenyl ring was deuterium-labeled, and from the analysis of the lineshapes of H spectra, valuable information on the degree of motional freedom in the adsorbed layer was obtained. As deuterium possesses a quadrupole moment, it is sensitive to the orientation of the molecule with respect to the external magnetic field. This sensitivity generates a quadrupolar splitting, which is defined as the separation between the two allowed transitions for the deuterium nucleus. In liquid systems, the quadrupole interaction is averaged out, but for static systems powder... 

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