Diffusion 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]. 

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]. 

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...

Before the introduction of measuring techniques such as pulsed field gradient (PEG) NMR ([14,16,45], pp. 168-206) and quasielastic neutron scattering (QENS) [49,50], which are able to trace the diffusion path of the individual molecules, molecular diffusion in adsorbate-adsorbent systems has mainly been studied by adsorption/desorption techniques [ 16]. In the case of singlefile systems, adsorption/desorption techniques cannot be expected to provide new features in comparison to the case of normal diffusion [51,52]. In adsorption/desorption measurements it is irrelevant whether or not two adjacent molecules have exchanged their positions. But it is this effect which makes the difference between normal and single-file diffusion. 

Similar to the PPG NMR method, neutron scattering techniques are successfully employed for the determination of diffusivities under equihbrium conditions. These techniques and their apphcation are discussed in Chapter 5 by H. Jobic. Particularly efficient is a novel combination of quasi-elastic neutron scattering (QENS) and a neutron spin-echo technique (NSE), which considerably expands the range of accessible diffusivities, viz. down to 10... 

The reversible step may be related to the dynamic crossover in protein hydration water at To 345 5K. NMR self-diffusion results [19] indicate that at this temperature a sudden change in hydration water dynamics occurs and the inverse diffusion constant switches from low-temperature super-Arrhenius behavior to high-temperature Arrhenius behavior. Neutron techniques (QENS) have also been used to study protein hydration water at this high-r crossover. Figure 21 shows the atomic MSD of protein hydration water at the low-r crossover measured using MD simulation. These crossovers can also be shown theoretically. Whenever the slope of an Arrhenius plot of the D T) changes, the specific heat has a peak. The well-known Adam-Gibbs equation (AGE) shows this as... 

For several reasons the reliable measurement of micropore-diffusion has proved to be far more difficult than expected. A wide range of different experimental techniques have been applied (see Table 3). We now know that when the diameter of the diffusing molecule is even slightly smaller than the pore diameter, diffusion within an ideal micropore is surprisingly fast and difficult to measure by macroscopic methods since the size of available zeolite crystals is limited. Such fast processes can, however, be measured relatively easily by PFG NMR and QENS. As the molecular diameter of the sorbate approaches (or even exceeds) the minimum diameter of the pore the diffusional activation energy increases and the diffusivity drops by orders of magnitude. Slow transport-diffusion (for example ethane, propane, etc. in CHA or Zeolite A - see Fig. 7) is easily measured macroscopically but inaccessible to microscopic techniques. The range of systems and experimental conditions where reliable measurements can be made by both macroscopic and microscopic methods is therefore quite restricted. 

Figure 13. Diffusivities for n-alkanes in silicalite at 300K measured by different techniques. , 0 MD simulations +, QENS V, single crystal membrane A, PFG NMR A, ZLC. From Jobic [72].

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