QENS technique

The QENS technique has been used to study the diffusion of hydrogen in metals, of molecules on flat surfaces, and of ions in oxides or sohd electrolytes. Apart from zeolites, the method has been recently employed to characterize molecular diffusion in MCM-41 samples [25,26], or in microp-... 

The above examples demonstrate that for a microporous material system where only a simple, single diffusion process occurs, the diffusion coefficients can be easily obtained by fitting the FR experimental data with the single diffusion process model using the least-square fitting routines. Compared with the PFG NMR and QENS techniques, the FR method is simpler and of low-cost and can follow a much wider range of diffusivities. 

Lateral diffusion of phospholipids in model membranes at ambient pressure has been studied over the years by a variety of techniques including fluorescence recovery after photobleaching (FRAP), spin-label ESR, pulse field gradient NMR (PFG-NMR), quasielastic neutron scattering (QENS), excimer fluorescence and others.In general, the values reported for the lateral diffusion coefficient (D) range from 10 to 10 cm /s in the... 

While microscopic techniques like PFG NMR and QENS measure diffusion paths that are no longer than dimensions of individual crystallites, macroscopic measurements like zero length column (ZLC) and Fourrier Transform infrared (FTIR) cover beds of zeolite crystals [18, 23]. In the case of the popular ZLC technique, desorption rate is measured from a small sample (thin layer, placed between two porous sinter discs) of previously equilibrated adsorbent subjected to a step change in the partial pressure of the sorbate. The slope of the semi-log plot of sorbate concentration versus time under an inert carrier stream then gives D/R. Provided micropore resistance dominates all other mass transfer resistances, D becomes equal to intracrystalline diffusivity while R is the crystal radius. It has been reported that the presence of other mass transfer resistances have been the most common cause of the discrepancies among intracrystaUine diffusivities measured by various techniques [18]. 

NDIS techniques have been used for many years in the study of aqueous electrolyte solutions. Difrfaction measurements for two liquids which differ only in the isotopic composition of one of the components reduce the total number of correlations observed in the data from N(N+1)I2 in the pure liquid to N (corresponding to correlations to the substituted atom) in the first order diffnence function. By careful analysis of the first order difference function details of the geometric arrangement of molecules around the substituted atom can be established. The supplementary technique of QENS allows a more detailed knowledge of the exchange times of the water in the hydration shells of these ions to be established. 

In Fig. 18 the self-diffusivities obtained by different experimental techniques are compared. It appears that in both the absolute values and the trends in the concentration dependence, the QENS data, the PFG NMR results, and the data derived from sophisticated uptake experiments using the piezometric or single-step frequency-response techniques agree. Nevertheless, disagreement with some sorption results has to be stated. Additional information on the molecular reorientation of benzene in zeolite X has been obtained by QENS and NMR lineshape analysis. 

There are macroscopic (uptake measurements, liquid chromatography, isotopic-transient experiments, and frequency response techniques), and microscopic techniques (nuclear magnetic resonance, NMR and quasielastic neutron spectrometry, QENS) to measure the gas diffusivities through zeolites. The macroscopic methods are characterized by the fact that diffusion occurs as the result of an applied concentration gradient on the other hand, the microscopic methods render self-diffusion of gases in the absence of a concentration gradient [67]. 

Spectroscopic techniques have also been used to study aquaions, NMR and quasielastic neutron scattering (QENS) being particularly useful. Infrared (IR) visible and ultraviolet (UV) spectroscopies have... 

Results based on other techniques are certainly consistent with the preceding categorization. For example, QENS and NMR offer a means of dividing ions into labile and stable on the basis of the dynamic properties of water molecules. 

A very wide range of techniques can be used to probe atomic transport in solids, and these have been detailed in various books [204—208] and reviews [21, 209-212[ (see also Chapters 13, 8, 11 and 12). The most commonly used are tracer methods, ionic conductivity, and NMR measurements. Less commonly used (but more specialized) techniques include creep, quasi-elastic neutron scattering (QENS), and Mbssbauer spectroscopy (M S). An elegant survey ofthe methods that have been used on nanoionic materials has been made by Heitjans and Indris [210]. The principles, procedures, and limitations of the more common techniques are outlined in the following sections. 

QENS is a particularly powerful technique for the investigation of highly ordered metal hydrogen systems. A precondition is a single crystal as a sample, which for intermetallic compounds and their hydrides in most cases is not available up to now. The theoretical description is outlined in Section 26.4.1. QENS is... 

The techniques outlined above have been used to study diffusion in a wide range of zeolite systems. In general we find that there is reasonable agreement between the different macroscopic methods and also between the microscopic methods (QENS, and PFG NMR). However, although for several systems the macroscopic and microscopic measurements are also consistent, there are many systems for which we see significant discrepancies between the two classes of measurements. 

Fig. 16 Variation of diffusivity with carbon number for linear alkanes in silicalite at 300 K showing comparison between self-diffusivities and corrected transport diffusivities obtained by different techniques, o MD simulation [74] hierarchical simulation [75] + QENS [78] A PFG NMR [76] V single crystal membrane [65] A ZLC [77]. The ZLC values were calculated based on the assumption of isotropic diffusion in an equivalent spherical particle. The present figure has been modified by the addition of further experimental data from a figure originally presented by Jobic [78]...

Diffusion measurements fall into two broad classes. Under macroscopic equilibrium, i.e. if the overall concentration within the sample remains constant, molecular diffusion can only be studied by following the diffusion path of the individual molecules ( microscopic measurement by quasielastic neutron scattering (QENS) [48,183,184], nuclear magnetic relaxation and line-shape analysis, PFG NMR) or by introducing differently labelled (but otherwise identical) molecules into the sample and monitoring their equilibration over the sample ( macroscopic measurements by tracer techniques) [185,186]. The process of molecular movement studied under such conditions is called self-diffusion. 

Fig. 23 Variation of the diffusivity of n-alkanes in zeolite Na,Ca-A with the carbon number at 473 K as observed with different techniques [QENS spin-echo technique (NSE), 12 carbon atoms per cavity x PFG NMR, 1 molecule per cavity A, (more recent data), 2 molecules per cavity ZLC, limit of vanishing concentration , o (more recent data)]. From [176], with permission...

The derivation of Dt from coherent QENS is similar to a computation of Dt from the fluctuations in an equilibrium density distribution. This was accomplished by Tepper and co-workers for Ar in AIPO4-5 [6]. Using the Green-Kubo formahsm, they were able to extract this non-equilibrium quantity from just one equihbrium simulation. Moreover, the calculations being performed in reciprocal space, the variation of the diffusivity upon the wave vector was used to check when the system was in the linear regime [6]. The first application of non-equihbrium molecular dynamics (NEMD) to zeolites was performed by Maginn et al. on methane in sihcalite [7]. Standard equi-libriiun MD techniques were later used by Sholl and co-workers to determine the concentration dependence of diffusivities [8]. 

Despite extensive work in the last decade, large discrepancies still persist between the various experimental techniques which measure diffusion in zeohtes. One of the difficulties is that one has to compare self-diffusivities, obtained by PFG NMR or QENS methods, with transport diffusivities derived from macroscopic experiments. The transport diffusivity is defined as the proportionahty factor between the flux and a concentration gradient (Fick s first law)... 

Fig. 9 Chain-length dependence of the self-diffusion coefficients of n-alkanes in silicalite-1 (cf. [65]) at 303 K derived from the FR technique (- -) compared with the results measured by PPG NMR [50] at 298 K (-o-), QENS [51] (-A-) at 300 K and molecular dynamic calculations [52] (-0-) at 300 K...

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