Pulsed molecular displacements

When pulsed magnetic field gradients are applied to study diffusive processes, the MR technique is often referred to as pulsed field gradient or pulsed gradient spin echo (PGSE) MR. Application of PGSE MR techniques to quantify molecular diffusion was pioneered by Stejskal and Tanner 17,18), and the techniques typically probe molecular displacements of 10 -10 m over time scales of the order 10 M s. 

The movement of the fluid within the porous media is irregular in time and space, as it is dispersed by the walls and throats of the structure. In order to obtain a well-defined molecular displacement, it is advantageous to use intense gradient pulses whose pulse widths are much shorter than the time interval between them.26 If the pulse widths <5 are short enough to assume that molecular displacement is negligible, Eq. (28) simplifies to... 

Although the pulse sequences used to study phase transitions are usually quite simple in the examples presented in this review (one to maximum four pulses), the interpretation may be subtle. Solid-state NMR nevertheless remains a difficult technique since quantitative interpretation of the spectra rely on a profound knowledge of the chemical composition and structure of the sample analysis of NMR results also requires a model to relate the observed NMR spectral shapes or relaxation behavior to hypothesis concerning the structure and dynamics of the atoms or molecules carrying spins. That NMR motionally average the atomic and molecular displacements that occur on a time-scale faster than 10—8 10—9s is an important point that should be considered in the interpretation of data. In particular, the difference in perception between NMR and X-ray diffraction with regard to fast and slow dynamical disorder in molecular crystals undergoing phase transitions between different polymorphs was illustrated. In fact, the interpretation of NMR data almost always needs the support of other data obtained by different techniques. Therefore, we emphasized the different complementarities with X-ray (or neutron) diffraction, IQNS and other spectroscopic methods to provide, by cross-correlation of the different data, consistent picture of the phase transition. 

The alkaline earth metals form a host of unique monovalent free radicals. Most of these molecules can be formed by the laser-driven chemical reactions of metal vapors with a wide variety of organic and inorganic molecules. This photochemical production of new molecules has led to an extensive gas-phase inorganic chemistry and spectroscopy of alkaline earth derivatives. In recent years, the Broida oven source has been displaced by the pulsed molecular beam spectrometer. The chemical dynamics and photochemistry of these new molecules are still at a very early stage of investigation. 

Pulsed field gradient methods may be used in combination with a spin-echo pulse sequence to measure average molecular displacements in a time In liquids, PFG methods can therefore be used to measure self-diffusion coefficients (i.e. the rate of diffusion due to Brownian motion in the absence of a concentration gradient). In porous media, there is the possibility of obtaining information about the pore geometry because the pore boundaries will influence molecular transport. PFG techniques can measure restricted diffusion and thus provide valuable information on pore sizes in the range 5-100 (im. 

If the mean molecular displacements in the interval between the two field-gradient pulses are much larger than the crystalhte diameters, the diffusivity resulting from PFG NMR measurements reflects the rate of molecular propagation through the bed of crystalhtes. This coefficient of long-range diffusion may be shown to be determined by [84]... 

As a non-invasive technique being able to monitor directly molecular displacements of the order of micrometers [14,16,45], the pulsed held gradient... 

This situation applies to the case of restricted motion inside an emulsion droplet. In this case the molecular displacements cannot exceed the droplet size, which indeed often is in the micrometer regime. Until recently, no analytical expressions that describe the echo delay in restricted geometries for arbitrary gradient pulses have been available. However, Callaghan and coworkers have published two approaches that work for arbitrary gradient pulses (13, 14). This is a very important step, and will undoubtedly lead to an increased applicability of the method. Since the application of these approaches are somewhat numerically cumbersome, and since PFG work performed up until now rely on one of two approximative schemes, we will describe these schemes below. 

The molecular translations are spatially resolved by combining the velocity encoding sequence with the conventional spatial imaging encodings. In this velocity imaging", the phase shift of the spins reflects the information about their displacement as well as the spatial position. In this work, a flow-compensation [25] is implemented in the velocity imaging pulse sequence to eliminate the actifacts due to fluid flow. 

Abbreviations MD, molecular dynamics TST, transition state theory EM, energy minimization MSD, mean square displacement PFG-NMR, pulsed field gradient nuclear magnetic resonance VAF, velocity autocorrelation function RDF, radial distribution function MEP, minimum energy path MC, Monte Carlo GC-MC, grand canonical Monte Carlo CB-MC, configurational-bias Monte Carlo MM, molecular mechanics QM, quantum mechanics FLF, Hartree-Fock DFT, density functional theory BSSE, basis set superposition error DME, dimethyl ether MTG, methanol to gasoline. 

In this section, we provide an outline of the theoretical and practical aspects of diffusometry NMR experiments that are the core of chrom-NMR. This issue has been reviewed at large38,39 and thus only the key and most relevant aspects will be mentioned below. The displacement of a given molecular tracer is followed by a classical Stejskal-Tanner experiment. In this, pulses of magnetic field gradients are used to label the initial position of the tracer, and to follow its displacement along the direction of the gradient, Az. Indeed, in a spin-echo experiment, any displacement corresponds to a reduction of the efficiency of the echo formation. 

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