Fujara, Franz

Geil, Burkhard

Kruk, Danuta

Pahlke, Hannes

English

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 The working range of static field gradient NMR illustrated by measurements of the intracrystalline diffusion of water in NaA-zeolites Hannes Pahlke, Burkhard Geil, Danuta Kruk, Franz Fujara Technische Universität Darmstadt, Institut für Festkörperphysik, Hochschulstraße 6, 64289 Darmstadt, Germany, E-mail: hannes.pahlke@physik.tu-darmstadt.de  1. Introduction Measuring diffusion in zeolites is a long-lasting challenge. For more than 70 years many efforts have been made to determine the diffusion coefficient of host molecules in the porous framework of zeolites [1]. Actually the different techniques, which were applied, observed different processes and provided dissenting diffusion coefficients. Precisely, there are methods observing diffusion on a macroscopic or a microscopic scale, under equilibrium or non-equilibrium conditions. We are interested in the molecular dynamics of water inside a crystallite, i.e. the intracrystalline self-diffusion coefficient. Common zeolites, as used in our experiments, have crystallite radii of about 0.5 μm, therefore we need a high spatial resolution to determine the diffusion coefficient of the molecules inside the crystallites. Static field gradient NMR can provide such a high resolution under certain conditions. In our contribution we discuss the potential and limitations of this method. 2. The working range of SFG-NMR Field gradient NMR uses stimulated echo experiments with three-pulse sequences “(pulse) – τ – (pulse) – t – (pulse) – τ – (echo)” to measure the echo height Secho(τ,t). During the first time interval τ the spins are dephasing, during the second interval τ they are rephasing. In an inhomogeneous magnetic field, the dominant dephasing mechanism arises from a spacially varying Larmor frequency ω [r (t)] = γ B [r (t)] = γ g r(t), where γ is the gyromagnetic ratio, g is the magnetic field-gradient, and r(t) is the time dependent spin position. For the limit t » τ  one can introduce the “generalized scattering vector“ Q = γ τ g [2], so that one obtains for isotropic free diffusion not affected by any boundary conditions, considering T2-relaxation in the de- and rephasing periods and T1-relaxation in the storage period, the measured echo height Secho(τ,t) is given by Fig. 1 Schematic representation of the working range (shaded area) of FG-NMR in confined geometries. Secho(τ,t) = exp[-Q2D t] exp[-2τ/T2] exp[-t/T1]  (1) with D being the self diffusion coefficient. Figure 1 shows the trajectories of two particles performing free diffusion represented in a log(t) vs. log(Q) plot by arrows of slope -2. According to eq. 1 the competing relaxation induced cofactors and the given maximum gradient strength lead to The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application© 2005, H. PahlkeDiffusion Fundamentals 3 (2005) 26.1 - 26.2 1 an upper bound tmax≈ T1 of accessible storage times and an upper bound Qmax ≈ τmax γ gmax, where τmax≈ T2 has been used. The lower bound tmin is, roughly speaking, determined by the condition of applicability of eq. 1, that is tmin≈ τmax. This limit implies tmin≈ T2 at Qmax, whereas smaller Q-values permit correspondingly smaller tmin. The essential limitation in our context is given by the crystallite size R within which the diffusion can be considered to be free. From this follows the lower bound Qmin ≈ 2 π R-1.  3. The intracrystalline diffusion of water in NaA-zeolites The experiments have been carried out in a specially designed static magnetic field gradient at the 1H frequency of 99.55 MHz at gradient values of 58, 135 and 185 T/m. The  stimulated echo height Secho was recorded as a  function of the diffusion time t at fixed dephasing times τ. The results (Fig. 2) show an extremely strong Q-dependence of Dapp, turning over toward a Q-independent plateau value. The transition takes place roughly at a Q-value of  10-3 Å-1, which is consistent with the crystallite size. At smaller Q-values the increasingly high apparent diffusion coefficients coincide with deviations of the experimental Secho(t) from a behaviour predicted by eq. 1, maybe due to partly intercrystalline diffusion or to surface relaxation effects. However, at larger Q-values the Q-independent plateau value of D is indeed the intracrystalline diffusion coefficient.   Fig. 2Q-dependence of the apparent diffusioncoefficient Dapp of H2O in polycrystalline NaA-zeolites as obtained by fits of eq. 1 to experimentalecho decay curves in a magnetic field gradient(open symbols: 58 T/m; half-filled: 135 T/m,filled: 185 T/m). 4. Conclusion From  NMR stimulated echo experiments in very high static magnetic field gradients it has been possible to obtain intracrystalline diffusion coefficients for water diffusion in μm-size NaA-zeolites. Based on the experimental results, we are going to show in our poster contribution further considerations on the effective working range of SFG-NMR. Acknowledgement Aleksander Gutsze, who passed away at 28th april 2004, had proposed this work. We thank Włodzimierz Masierak for the sample preparation [3]. References [1] J. Kärger, Adsorption 9 (2003) 29-35.  [2] G. Fleischer, F. Fujara,  in: P. Diehl et al. (Eds.), NMR - Basic Principles and Progress, Vol. 30, Springer, Berlin, 1994, pp. 159-207. [3] A. Gutsze, W. Masierak, B. Geil, D. Kruk, H. Pahlke, F. Fujara, Solid State Nuclear Magnetic Resonance, submitted. Diffusion Fundamentals 3 (2005) 26.1 - 26.2 2

The working range of static field gradient NMR illustrated by measurements of the intracrystalline diffusion of water in NaA-zeolites

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The working range of static field gradient NMR illustrated by measurements of the intracrystalline diffusion of water in NaA-zeolites

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