QENS measurements

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]. 

Diffusional motion. Many rotational and translational diffusion processes for hydrocarbons within zeolites fall within the time scale that is measurable by quasielastic neutron scattering (QENS). Measurements of methane in zeolite 5A (24) yielded a diffusion coefficient, D= 6 x lO" cm at 300K, in agreement with measurements by pulsed-field gradient nmr. Measurements of the EISF are reported to be consistent with fast reorientations about the unique axis for benzene in ZSM-5 (54) and mordenite (26). and with 180 rotations of ethylene about the normal to the molecular plane in sodium zeolite X (55). Similar measurements on methanol in ZSM-5 were interpreted as consistent with two types of methanol species (56). 

The results of QENS measurements for TaV2H [76] are consistent with this microscopic picture of H motion. First, on the frequency scale of tf the measured QENS spectra S(Q, co) are well described by the sum of a narrow elastic line and a broader quasielastic line having Q-dependent intensity, but Q-independent width. These features are typical of the case of spatially-confined (localized) motion [14]. 

As an example of the data, Eig. 26.6 shows the temperature dependences of zfi and obtained from QENS measurements for C14-type HfCr2Ho74 [84]. 

The dynamical properties of hydrogen in Sc are also quite remarkable. NMR measurements of the proton spin-lattice relaxation rate in a-ScH [132] have revealed a localized H motion with the characteristic jump rate tf of about 10 s at 50 K. This localized motion is evident from an additional frequency-dependent peak at low temperatures (35-80 K). The structure of the sublattice of tetrahedral interstitial sites in a h.c.p. metal suggests that the localized H motion corresponds to jumps between two nearest-neighbor sites separated by about 1.0 A in the c direction. QENS measurements on a-ScH [133, 134] have revealed the existence of a still faster localized motion with the jump rate passing through a minimum of approximately 7x10 ° s i near 100 K and increasing to 10 s at 10 K. 

Coherent QENS measurements and MD simulations have been performed for N2 and CO2 in silicalite [30,31]. It has been found that the self-diffusivities of the two gases decrease with increasing occupancy, while the transport diffusivities increase. For a comparison with other systems, it is appropriate to remove the influence of the thermodynamic correction factor and to discuss the collective mobility in terms of the corrected diffusivity (also called Maxwell-Stephan diffusivity). Dq(c) is directly obtained from the Simula-... 

Various experimental and theoretical methods have been used to determine the diffusivities of n-alkanes in silicahte or ZSM-5 zeoHtes. Branched alkanes are expected to be slower, but the ratio of the diffusivities between a normal alkane and a mono-methyl isomer may vary experimentally between a factor 5 to 1,000 [39,40]. With a rigid framework, the value of this ratio obtained from simulations varies between two and six orders of magnitude [41-43]. The first QENS measurements on hydrogenated isobutane in ZSM-5 were performed on a back-scattering instrument [40]. The broadenings were small, only 10-20% of the instrumental resolution. The self-diffusivities, which were extracted, were 2-5 x 10 m s , for temperatures ranging between 450 and 570 K [40]. 

QENS measurements on single crystals of the yttrium a-phase by Anderson et al. (1989) provides information on long-range and local diffusion rates. Fast hopping between neighbor t-sites are confirmed and an excellent discussion of data handling and interpretation is included. 

The HOMO-LUMO energy gap of a material is one of the properties that will influence its chemical reactivity. Data from NMR and QENS measurements of the ring rotation dynamics of ferrocene will reflect only effects of any interaction of the ferrocene molecule with the zeolite cage up to the HOMO level of the ferrocene molecule. This is because the LUMO is empty of electrons and any interaction of this level with the zeolite cage orbitals, to a first approximation, will have no effect on the QENS measured dynamic parameters, unless electron density flows into this orbital from the zeolite host. Such a transfer of a small amount of electron density will explain the slightly higher activation energy measured by QENS for ferrocene when encapsulated in zeolite. However, the jlSR measurements are made of a molecule of ferrocene with an additional electron introduced into the LUMO. Thus any interaction of the LUMO with the... 

This view is quite at variance with the direct interconversion between I and II proposed on the basis of NMR studies [41]. These different views correspond to measurements performed at different time scales. NMR and QENS measure only probabilities averaged over rather long time scales, compared to the transfer rate of a single proton. Only vibrational spectroscopy can probe the quantum regime and distinguish intermediate configurations. Similar double minimum potentials have... 

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