Jobic, Hervé

Laloué, Nicolas

Laroche, Catherine

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 Concentration Dependence of Transport and Corrected Diffusivities of n-Hexane in Silicalite Measured by QENS Nicolas Laloué(1, 2), Catherine Laroche(1), Hervé Jobic(2)(1)Institut Français du Pétrole, BP 3, 69390 Vernaison, France (2)Institut de Recherches sur la Catalyse, 2 avenue A. Einstein, 69626 Villeurbanne, France E-Mail: nicolas.laloue@ifp.fr 1. Introduction Separation induced by kinetic effects using zeolite as a shape selective adsorbent is of great industrial concern. The control of diffusion process, requiring a precise knowledge of self-, transport and corrected diffusivities (Dself , Dt and DC, respectively), is essential for the design of industrial applications. Dself and Dt are usually measured directly by microscopic and macroscopic methods, respectively, while DC is extracted from the macroscopic quantity Dt using the Darken equation, Dt(θ) = DC(θ) ∂lnf / ∂lnθ. Those three diffusivities depend on loading θ and become only equal when θ → 0. However, longstanding discrepancies subsist on the diffusivity values measured by different techniques: indeed, different mass transfer resistances arise within the crystal since spatial observation ranges differ by several orders of magnitude. Moreover, controversies arise on the frequent, but erroneous, assumption of the independence of DC vs. loading that allows to relate Dself to Dt. Therefore, techniques that can provide multiple diffusion coefficients are of major interest. Besides atomically detailed simulation, Quasi-Elastic Neutron Scattering (QENS) is the only experimental technique so far that succeeds in estimating both Dself and Dt by using hydrogenated and deuterated compounds [1].  In this letter, the loading dependency of the transport and corrected diffusivities of linear hexane in silicalite close to saturation (8 molecules / u.c) is investigated by QENS. Using Dself also measured by QENS, the self-exchange coefficient Đ11(c) arising from the Maxwell-Stefan formulation for single component and the Đ11(θ) / DC(θ) ratio giving information about the influence of correlation effects, are calculated [2]. 2. Results and discussion The experiments were performed on hydrogenated and deuterated n-hexane at the Institut Laue-Langevin, Grenoble, France, by taking a 6.27 Ǻ incident wavelength. Details of sample preparation and Dt calculations can be found in [3]. DC was estimated using the thermodynamic factor based on a single-site Langmuir adsorption model.    As shown in Fig1 the transport diffusivity remains constant up to 5 molecules/u.c. after which it slightly decreases. The corrected diffusivity decreases linearly with increasing loading, diminishing by two orders of magnitude over the entire range of loading investigated. This behaviour of DC confirms the deviation from the Darken © 2005, N. Laloué The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and ApplicationDiffusion Fundamentals 2 (2005) 98.1 - 98.2 1 approximation observed experimentally for ethane [3], and is different from the atomically simulated behaviour of methane that remains constant [4] under the same conditions. DC extracted from macroscopic methods remains 1 or 2 order of magnitude lower but a quantitative comparison cannot be rigorous, as they are determined at various experimental conditions. Moreover, contrary to QENS they exhibit an increase for θ < 4 molecules/u.c [5].  The calculation of Đ11(θ) based on diffusivities provided by the same experimental technique has never been done so far.  molecules per unit cell0 2 4 6 810-1210-1110-1010-9iffusivities (m2 /s)D Fig1: Loading dependence of n-hexane diffusivities in silicalite: (   ) Dt, (O) DC and (+) DselfFor the linear hexane, activation energies of around 7.0 and 5.0 KJmol  are obtained for transport (1 molecule/u.c) and self-diffusion (2 molecules/u.c), respectively. This is in agreement with molecular dynamics simulation [6]. -13. Conclusions and perspectives Transport and corrected diffusivities of linear hexane in silicalite were measured by QENS. Dt remains constant up to 5 molecules/u.c. and then exhibits a slight decrease. DC was found to decrease linearly with increasing loading. The DC loading dependence confirms that the approximation of the Darken equation does not apply for the linear hexane in MFI-type zeolites. A Kinetic Monte Carlo (KMC) study based on a lattice model and jump frequencies provided either by experimental or other theoretical techniques is currently developed. It will allow to simulate experimental behaviours of Dself and DC regarding loading and topology, as well as the nearest neighbours’ influence that is considered by implementing a δE in the energy barrier to take into account repulsive or attractive effects [7]. References [1]   H. Jobic, J. Kärger, M. Bee, Phys. Rev. Lett. 82 (1999) 4260 [2]   A.I. Skoulidas, D.S. Sholl, R. Krishna, Langmuir 19 (2003) 7977 [3]   D.S. Sholl, H. Jobic, S. Chong, M. Plazanet, Chem Phys Lett. 408 (2005) 157-161 [4]   E.J. Maggin, A.T. Bell, D.N.Theodorou, J. Phys. Chem. 97 (1993) 4173-4181 [5] A.O. Koraibkina, A.M. de Jong, E.J.M. Hensen, R.A. van Santen, Micropor. Mesopor. Mater. 77 (2005) 119-129 [6]  E.J. Maggin, A.T. Bell, D.N. Theodorou, J. Phys. Chem., 100 (1996) 7155-7173  [7]  R. Krishna, D. Paschek, Chem. Phys. Lett. 342 (2001) 148-154   Diffusion Fundamentals 2 (2005) 98.1 - 98.2 2

Concentration dependence of transport and corrected diffusivities of n-Hexane in silicalite measured by QENS

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Concentration dependence of transport and corrected diffusivities of n-Hexane in silicalite measured by QENS

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