Diffusion of Isobutane in Silicalite: A Neutron SpinâEcho and

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Diffusion of Isobutane in Silicalite: A Neutron SpinEcho and Molecular Dynamics Simulation Study Alexander J. O'Malley, C. Richard A. Catlow, Michael Monkenbusch, and Herve Jobic J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b08048 • Publication Date (Web): 04 Nov 2015 Downloaded from http://pubs.acs.org on November 11, 2015

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The Journal of Physical Chemistry

Diffusion of Isobutane in Silicalite: A Neutron Spin-Echo and Molecular Dynamics Simulation Study Alexander J. O’Malley*,a,b C. Richard A. Catlow,a,b Michael Monkenbusch,c and Hervé Jobic*d a

Department of Chemistry, Materials Chemistry, University College London, Third Floor, Kathleen Lonsdale Building, Gower Street, London WC1E 6BT, UK *a.j.o’[email protected] b The UK Catalysis Hub, Research Complex at Harwell, Rutherford Appleton Laboratory, Oxfordshire, OX11 0FA, UK c Jülich Centre for Neutron Science (JCNS-1) & Institute for Complex Systems (ICS-1), Forschungszentrum Jülich, D-52425 Jülich, Germany d Institut de Recherches sur la Catalyse et l’Environnement de Lyon, CNRS, Université Lyon 1, 2 Ave. A. Einstein, F-69626 Villeurbanne, France *[email protected] ABSTRACT: The diffusion of isobutane in silicalite was studied using neutron spin-echo (NSE) experiments and molecular dynamics (MD) simulations between 444 – 550 K. The experimental and simulated diffusion coefficients showed agreement well within an order of magnitude, as did the activation energies of diffusion which agreed to within 3.4 kJ mol-l (~15%). Jump diffusion was observed by NSE with a jump distance of 10 Å, also observed by the MD simulations showing that the residence time was spent in a small section of the sinusoidal channel, rather than the intersections between channels as reported in previous simulations. The level of sinusoidal trapping diminishes in the simulations with increasing temperature, where the isobutane develops isotropic diffusion through both channel systems, as observed by NSE experiments.

KEYWORDS: Diffusion, hydrocarbons, zeolites, molecular dynamics, neutron scattering

INTRODUCTION Understanding the diffusion behavior of hydrocarbons inside zeolites is important for the design of microporous catalysts and for applications in the petrochemical industry.1 The MFI framework is heavily utilized in the kinetic separation of alkane isomers for upgrading the octane number of gasoline, due to the steric effects imposed by the pore dimensions (width of 5.5 Å). For this reason, many studies of hydrocarbon dynamics in ZSM-5 and its siliceous analogue silicalite have been reported. Though the majority of work studying molecular diffusion in this framework focuses on n-alkanes,2,3,4,5,6 an understanding of branched alkane diffusion behaviour is crucial to gauge the effect of molecular shape on both catalytic cracking and molecular sieving characteristics. Experimental studies of isobutane in silicalite and ZSM-5 have employed a number of techniques, including the zero-length column method7,8 showing a strong dependence on loading. Supported membrane techniques have also been used, comparing straight and branched alkanes9, showing that self-diffusivity of isobutane is lower by a factor of 8 compared to n-butane. Microscopic techniques have rarely been used to study these systems, mainly due to the low resolution of instrumentation leading historically to significant errors in measured diffusion coefficients of slower moving branched sorbates. However, a comparative study of supported membrane and quasi-elastic neutron scattering (QENS) experiments gave diffusivities of an order of magnitude lower for QENS, consistent with literature differences between experimental techniques,10 supported by later QENS studies comparing n-alkanes with isobutane,11 though the error on the isobutane diffusion coefficient was a factor of 4 of the measured value due to low instrumental resolution. Computer simulations have also been used to study these systems including grand canonical Monte Carlo simulations showing preferred adsorption of isobutane in the straight/sinusoidal channel intersections at lower loadings.12 Infrequent hopping between intersections was calculated by

transition path sampling, giving significantly lower diffusion rates than experiment.13 Molecular dynamics (MD) simulations of n- and isobutane in a membrane concluded that separation of these isomers is possible as permeation was observed for n-butane after 200 ps unlike isobutane,14 µVT-non equilibrium molecular dynamics also showed preferred intersectional siting of isobutane.15 QENS and MD simulations are excellent complementary techniques for study of these systems,16 due to their measurement over nanosecond and nanometre scales. However it should be noted that due to approximations necessary historically (and in the referenced studies of these systems), such as the use of a rigid zeolite framework, a united-atom hydrocarbon model and shorter simulated MD times, discrepancies of 2-3 orders of magnitude in calculated diffusion coefficients are observed. These approximations can also affect behaviour such as preferred siting and the effect of molecular shape/length on diffusivity; as was reported in recent comparative studies employing more detailed models of the framework (including framework flexibility) and the hydrocarbon (with explicit atom-atom potentials) on longer n-alkane diffusion in silicalite.17 Greatly improved agreement was achieved between QENS and MD simulations to well within an order of magnitude and close to within experimental error when such models were implemented and loadings matching experiment were used.18 The effect of framework flexibility was actually investigated upon studying diffusion of n- and isobutane in silicalite (using a united atom hydrocarbon model), however the very short simulated time meant very little behavioural information on the branched alkane diffusion was obtained, especially in terms of experimental comparison.19

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Though QENS and MD simulations are ideally suited for complementary study of these systems, some sorbates as already mentioned move too slowly for conventional QENS instruments (time-of-flight and backscattering spectrometers), and a higher energy resolution is obtained using the neutron spin-echo (NSE) technique.20 We report here the very precise measurement of diffusion coefficients of isobutane in silicalite using the neutron spin-echo technique and molecular dynamics simulations using contemporary models, framework and hydrocarbon models, marking the first tandem microscopic experiment/computational study of slow moving branched alkanes in this zeolite. Close agreement between experimental and calculated diffusion coefficients and activation energies are achieved, along with new insight into the preferred siting of isobutane molecules.

METHODOLOGY NEUTRON SPIN-ECHO MEASUREMENTS The neutron spin-echo experiments were performed using the NSE spectrometer at the ELLA neutron guide hall at the FRJ-2 reactor in Jülich21 (which has been transferred to the MLZ in Garching). Data were collected using a neutron wavelength band of 10% FWHM centred at λ = 8 Å over a Fouriertime range from t = 0.1 – 22 ns, at wave-vector transfer values between Q = 0.08 - 0.3 Å-1, and sample temperatures between T = 300 K and 550 K. The incident neutron flux was of ~ 0.6×106 n/cm2/s on a sample area of 27 x 27 mm2. We used collection times of 200 s for each of the 27 countings to complete an echo and normalization scan for one (Q, t, T) combination. Sample data were normalized to data from an elastic reference scatterer, i.e. microporous carbon powder. Data evaluation was performed as described in reference 20, without subtraction of background scattering. Data from the full detector area were integrated, which leads to a wave-vector transfer width of about 0.025 Å-1 FWHM. The silicalite sample was activated at 770 K under oxygen flow, then pumped to 10-4 Pa at the same temperature. After cooling, the zeolite was loaded with 2 isobutane molecules per unit cell. The sample was transferred, inside a glovebox, into a cylindrical aluminium container. Since a larger intensity is obtained in NSE with coherent scatterers, deuterated isobutane was used. Coherent scattering measures, in principle, the transport diffusivity,16 but at low loading, which is the case here, the self- and transport diffusion coefficients have the same values.22

COMPUTATIONAL METHODS Our MD simulations employed a 2 x 2 x 2 orthorhombic silicalite supercell with Pnma symmetry23; the structure can be found in reference 17. Full ionic charges were assigned to the framework species. The potentials used to describe the flexible zeolite framework are widely used for simulations of silicalite but originate from work on SiO2.24 They include a Buckingham potential to describe Si-O and O-O interactions, along with a harmonic three-body potential to describe the O-Si-O

Fig 1. The starting configuration of isobutane in silicalite preproduction run at 450 K viewed down the (top) [010] direction and (bottom) [100] direction. triads. A cut-off distance of 10 Å was used. Forcefields employed to describe the hydrocarbon were derived from vibrational data.25 Each hydrogen atom was assigned a charge of +0.1, while the primary and tertiary hydrocarbons were given charges of -0.3 and -0.1 respectively to give an overall charge neutral isobutane molecule. The bonds and bond angle vibrations were described by harmonic potentials while the dihedrals were described by a cosine potential. The guest-host interactions and intramolecular sorbate interactions were modelled by a Lennard-Jones potential taken from the work of Kiselev et al26 with a 10 Å cut-off. All forcefield parameters are listed in reference 17. For the initial configuration, the isobutane molecules were placed in the intersections of the straight and sinusoidal channels, avoiding strong contact with the walls. The intersection was used as a starting location as it has been shown for nonlinear molecules to be an energetically favorable location.2728,28,29,30,31 This starting configuration for the MD runs is shown in figure 1, all methodological visualizations in this study were created using the visualization software package Aten1.8.32 The loading matched those of the NSE experiment at 2 molecules per unit cell.

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The Journal of Physical Chemistry 1.0

160

(a)

140

Broadening (neV)

I(Q,t)/I(Q,0)

0.8 0.6 0.4 0.2 0.0 1.0

0.1

1

10

(b)

I(Q,t)/I(Q,0)

0.8

100 80 60 40 20 0.02

0.04 2

0.06

0.08

0.10

-2

Q (Å )

0.4

Fig 4. Broadenings obtained for isobutane in silicalite at: 444 K (), 491 K (), and 550 K (). The solid lines correspond to a jump diffusion model.

0.0

0.1

1

10

Time (ns)

Fig 2. Comparison between experimental and calculated normalized intermediate scattering functions obtained for isobutane in silicalite for Q = 0.2 Å-1 (a) and 0.3 Å-1 (b), at 444 K ( ), 491 K ( ), and 550 K (). The solid lines correspond to a 3D diffusion model. 1.0

(a) 0.8

I(Q,t)/I(Q,0)

120

0 0.00

0.6

0.2

0.6 0.4

The system was then equilibrated at the desired temperature for 1 ns in the canonical (NVT) ensemble. After the equilibration run, the production run of 10 ns in the microcanonical (NVE) ensemble was carried out at 450, 500 and 550 K. A timestep of 0.5 fs was used with atomic coordinates saved every picosecond (every 2000 steps). A Berendsen33 thermostat was used to maintain the temperature near a set point, with a time constant for thermal energy exchange set at 1 ps. All simulations were carried out using the DL_POLY_4 code.34 The production time of 10 ns is adequate to obtain a linear mean-squared displacement (MSD) plot, indicative of true diffusive motion. The changes in coordinates of the central carbon atom were used in calculating the MSD, and the Einstein relationship was then used to calculate the self-diffusion coefficient:

0.2 0.0 1.0

0.1

1

10

(b)

0.8

I(Q,t)/I(Q,0)

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0.6

where the term in braces is the ensemble average of the MSD of the hydrocarbon chain.

RESULTS AND DISCUSSION

0.4 0.2 0.0

0.1

1

10

Time (ns)

Fig 3. Comparison between experimental and calculated normalized intermediate scattering functions obtained for isobutane in silicalite at 491 K, for Q = 0.2 ( ) and 0.3 Å-1 ( ). The solid lines are calculated with: (a) a 3D diffusion model, and (b) a 1D diffusion model.

NEUTRON SPIN-ECHO MEASUREMENTS Normalized intermediate scattering functions obtained experimentally for isobutane in silicalite at different temperatures are shown in figure 2, at two Q values. The faster decay of the scattering functions which is observed with increasing temperature, at a given Q value, reflects the increase of the diffusivity. The experimental data are well fitted by an isotropic diffusion model. Figure 3 shows a comparison with experiment for both 3D and 1D diffusion models, from which it is clear that the 3D diffusion model fits better the experimental points than 1D diffusion. This finding implies that isobutane molecules are able to explore both straight and

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Table 1. Calculated Ds values in m2 s−1 for isobutane at all temperatures TK

Ds (NSE)

444

1.2 ×10

-11

450 491

2.1 ×10

3.9 ×10 -1

Ea (kJ mol )

22.6

9.1 x 10

-11

1.5 x 10

-10

2.2 x 10

-10

-11

500 550

Ds (MD)

-11

19.2

Fig 6. Comparison of diffusion coefficients of isobutane from NSE (), MD (◆) compared with previous simulation of noctane diffusion (Х).

Fig 5. The average mean squared displacement as a function of time for isobutane at all 3 temperatures. sinusoidal channels, while previous QENS and NSE measurements showed that linear n-alkanes longer or equal to C8 diffuse mainly along the straight channels.11,35 Temporal decays extracted from the curves in figure 2 can be expressed as energy broadenings as depicted in figure 4. When plotted as a function of Q2, one expects a linear variation of the energy broadening in the case of continuous or Fickian diffusion. It appears from figure 4 that the experimental points deviate from straight lines, and the trend is characteristic of jump diffusion. The jump model with a fixed jump length of 10 Å, which was previously used in the case of benzene in ZSM-5,36 was found to fit satisfactorily the broadenings to the solid lines in figure 4. The diffusivities are extracted from the low-Q range.16 The experimental diffusion coefficients are reported in table 1 and plotted in figure 6. The activation energy obtained from an Arrhenius representation (figure 7) is 22.6 kJ mol-1. Previous QENS measurements were performed on a back-scattering spectrometer on the same system, using however ZSM-5 instead of silicalite.10 The diffusion coefficients were about one order of magnitude lower in ZSM-5, with an estimated activation energy of 17 kJ mol-1. Since the broadenings were small, compared with the instrumental resolution, the errors were much larger than in the present work.

Fig 7. Arrhenius plots from the MD simulations (◆) and NSE experiments ().

MOLECULAR DYNAMICS SIMULATIONS The linearity of the average MSD plot (figure 5) was confirmed before calculating the diffusion coefficient for each temperature; listed in table 1. Simulated diffusion coefficients are all within a factor of 7.5 of experimental results. At 550 K where the temperatures match exactly we obtain agreement to a factor of 5. It is difficult to obtain the statistical errors of these diffusion coefficient values; however the very linear nature of the MSD plots in figure 5 suggests that these errors are low. All calculated diffusion coefficients are in the upper limit of experimental results. This, as with previous studies can be attributed to the use of a perfect periodic silicalite crystal structure in these simulations. The experimental sample of silicalite would possess defects within the crystallite, and grain boundaries on the scale of several nanometres which would lower the average diffusion coefficient. The absence of these in the simulation could account for the higher diffusion coefficients measured. The activation energy of diffusion was calculated from the Arrhenius plot shown in figure 7, with a value

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(a)

MSD Å2

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MSD Å2

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ϕ

+ ∆ *

(b)

Fig 8. Average directional MSD of all isobutane molecules (a) and an individual isobutane molecule (b) in silicalite at 450 K.

Fig 9. Trajectory plot of isobutane in silicalite at 450 K between 3000 ps and 5000 ps of the MD simulation run.

of 19.2 kJ mol-1, 3.4 kJ mol-1 (~15%) lower than that observed by the NSE experiments. It is notable that the diffusion coefficients obtained for isobutane are significantly lower than those obtained for nalkanes in reference 18. The Ds of n-octane (also plotted in figure 6) at 400 K is higher by a factor of 12 than of isobutane at 450 K, illustrating the effect of alkane branching on the diffusion in the 5.5 Å silicalite pore, even when framework flexibility is taken into account. This hindrance is also illustrated by the much higher activation energy, compared to that of n-octane (5.8 kJ mol-1). To gain a greater understanding of the diffusion of isobutane in the silicalite framework, the mean squared displacement plot in the possible directions can be examined to observe preference for a specific channel system. These can also be illustrated by the use of a trajectory plot to show specific locations of molecules. The average directional MSD plot of all isobutane molecules at 450 K is shown in figure 8 (a). The plot shows that the molecules are diffusing in both channel systems, but show preference for the 100 direction (the sinusoidal channels). Though this contrasts with previous studies

into n-alkane diffusion, where the 010 channel is preferred, the ability to explore both the straight and sinusoidal channels would agree with the 3D diffusion observed by NSE. This behavior is detailed in the directional MSD of an individual isobutane molecule at 450 K in figure 8 (b). This particular MSD plot shows that the molecule spends prolonged periods diffusing in the 100 channel system between much shorter periods of time in the 010 channel system. The trajectory plot of this molecule between 3000 and 5000 ps is shown in figure 9. The trajectory plot shows that the molecular diffusion in the 100 direction is actually molecular trapping in the very small section of the sinusoidal channel between intersections (c. 3 Å in length), then movement between two adjacent sinusoidal channel segments via the straight channel segment connecting them. The movement in the 010 direction is rapid as illustrated in the MSD plot in figure 8 (b), taking place back and forth between the two trapping sinusoidal segments, indicative of a jump diffusion mechanism. The 10 Å jump length between sinusoidal segments matches that observed in the NSE experiments. However, it is not possible from experiment to.

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MSD Å 2

(a)

MSD Å

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(b)

Fig 10. Average directional MSD of all isobutane molecules (a) and an individual isobutane molecule (b) in silicalite at 550 K. determine whether the jumps occur between the intersections or between sinusoidal channels Previously referenced simulations have all shown that the preferred siting is the intersections between channels, where it is assumed the molecule would spend the residence time between jumps. . This simulation however suggests that the molecule spends the residence time in a 3 Å sinusoidal channel section. This preference can be attributed to the favorable interactions between the molecule and channel walls, enabled by the increased access and geometric freedom offered by the use of a flexible silicalite framework. However, in previous simulations the rigid framework, used due to computational restrictions, would have prevented sustained access to this region due to steric hindrance and associated instability, thus the lowest potential energy region in the rigid framework would be the intersections. The breathing of the framework in this simulation allows for both sustained access, and framework relaxation around the isobutane accommodating this preferred siting. The isobutane then makes the 10 Å jumps between adjacent sections of sinusoidal channel. The passage via the straight channel segments is sufficient to make the diffusion appear isotropic from an experimental point of view. To decipher the dependence of this siting preference on temperature, the average directional MSD plot of all isobutane

Fig 11. Trajectory plot of isobutane in silicalite at 550 K between 7000 ps and 9000 ps of the MD. molecules at 550 K is shown in figure 10 (a). This behavior differs from that at 450 K, as the isobutane molecule is preferentially diffusing in the 010 direction (the straight channel system), suggesting that less time is spent residing in the small section of sinusoidal channel system, illustrated by the directional MSD plot of an individual molecule in figure 10 (b). The plot shows two distinct types of behavior before and after 5000 ps: the first is that of long term residence in either channel, consistent with the experimentally observed 3D diffusion, in that the molecule is prone to translating along either channel system freely. The increased gradient of the diffusive motion in the 100 direction is more indicative of unhindered diffusion along the channel than molecular trapping. This is consistent with behavior exhibited by n-octane in reference 18, suggesting that the higher temperatures allow behavior more like an n-alkane to take place. After 5000 ps however, regular and frequent switching between the two channel systems is observed, as illustrated by the trajectory plot in figure 11 suggesting that two modes of diffusion are available to isobutane at higher temperatures: that of prolonged, highly mobile diffusion in either channel

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system, or frequent switching between the two channel systems (both of which would agree with the 3D diffusion observed by NSE). This behavior is in contrast with that of nalkanes such as octane, which upon switching to another channel system would remain there for extended periods as the molecular length was a hindrance to the channel switching process which is not the case for the more spherical isobutane. The molecular sinusoidal trapping is diminished in both diffusion modes exhibited at higher temperatures, suggesting that trapping is inversely proportional to temperature, as would be expected for an activated process such as jump diffusion. This observation supports the proposal that the level of trapping is temperature dependent, and that the increase in average diffusion coefficient is related to the lower level of trapping in small sinusoidal sections. The initial observation of prolonged periods of unidimensional diffusion (though allowed in both 100 and 010 directions) also agrees with the decline in this trapping at higher temperatures, despite the confinement of the movement to one channel system for a period. Summary and Conclusions The diffusion of isobutane in silicalite was measured using neutron spin-echo experiments and molecular dynamics simulations between 444 and 550 K. The NSE measurements showed jump diffusion with a jump length of 10 Å, with the intermediate scattering functions showing the isobutane molecules are able to explore both 010 and 100 channel systems, unlike n-alkanes in previous studies of silicalite diffusion. The diffusion coefficient values were between 1.2 and 3.9 x 10-11 m2s-1, with an activation energy of 22.6 kJ mol-1. Agreement with the molecular dynamics simulations was well within an order of magnitude (between a factor of 5 and 7.5), with diffusion coefficients ranging from 9.1 – 22 x 10-11 m2s-1 and an activation energy of 19.2 kJ mol-1. Discrepancies were attributed to the use of a perfect periodic silicalite crystal structure. The MD simulations agreed with the 10 Å jump length; however the preferred residence time was spent in small sections of the sinusoidal channel system, rather than the intersections between channels shown to be favorable sites in previous simulations. This difference in preferred siting is attributed to favorable interactions between the molecule and the channel walls, and the access granted by the use of a flexible silicalite framework. However, in previous simulations the rigid framework would have prevented sustained access to this region due to steric hindrance and associated instability, thus the lowest potential energy region in the rigid framework would be the intersections. The breathing of the framework in this simulation allows for both sustained access, and framework relaxation around the isobutane accommodating this preferred siting. At higher temperatures the isotropic diffusion observed in experiment is observed as dominant in the simulations. The sinusoidal trapping diminishes significantly, suggesting that the diffusion of isobutane in silicalite may be governed by the temperature dependent trapping in small sinusoidal channel sections, becoming increasingly isotropic with temperature where exploring of both channel systems is allowed.

ACKNOWLEDGMENTS The authors would like to acknowledge the Engineering and Physical Sciences Research Council, grant no. EP/G036675/1 for financial support under their Centres for Doctoral Training scheme, the STFC and the ISIS neutron source for funding and sponsorship, J. Saßmannshausen for maintenance and use of the Faraday computer cluster.

References 1. Auerbach, S. M.; Carrado, K. A.; Dutta, P. K., Handbook of Zeolite Science and Technology; CRC press, 2003. 2.Jobic, H.; Theodorou, D. N., Diffusion of Long N-Alkanes in Silicalite. A Comparison between Neutron Scattering Experiments and Hierarchical Simulation Results. J. Phys. Chem. B 2006, 110, 1964-1967. 3. Maginn, E. J.; Bell, A. T.; Theodorou, D. N., Dynamics of Long N-Alkanes in Silicalite: A Hierarchical Simulation Approach. J. Phys. Chem 1996, 100, 7155-7173. 4. Talu, O.; Sun, M. S.; Shah, D. B., Diffusivities of N‐ Alkanes in Silicalite by Steady‐State Single‐Crystal Membrane Technique. AIChE J. journal 1998, 44, 681-694. 5. Leroy, F.; Rousseau, B.; Fuchs, A., Self-Diffusion of NAlkanes in Silicalite Using Molecular Dynamics Simulation: A Comparison between Rigid and Flexible Frameworks. Phys. Chem. Chem. Phys. 2004, 6, 775-783. 6. van Well, W. J.; Wolthuizen, J. P.; Smit, B.; van Hooff, J. H.; van Santen, R. A., Commensurate Freezing of N-Alkanes in Silicalite. Angew. Chem.(Int. Ed.) 1995, 34, 2543--2544. 7. Hufton, J. R.; Ruthven, D. M., Diffusion of Light Alkanes in Silicalite Studied by the Zero Length Column Method. Ind. Eng. Chem. Res 1993, 32, 2379-2386. 8. Zhu, W.; Malekian, A.; Eić, M.; Kapteijn, F.; Moulijn, J., Concentration-Dependent Diffusion of Isobutane in Silicalite1 Studied with the Zlc Technique. Chem. Eng. Sci. 2004, 59, 3827-3835. 9. Millot, B.; Methivier, A.; Jobic, H.; Moueddeb, H.; Dalmon, J., Permeation of Linear and Branched Alkanes in Zsm-5 Supported Membranes. Microporous Mesoporous Mater. 2000, 38, 85-95. 10. Millot, B.; Méthivier, A.; Jobic, H.; Moueddeb, H.; Bée, M., Diffusion of Isobutane in Zsm-5 Zeolite: A Comparison of Quasi-Elastic Neutron Scattering and Supported Membrane Results. J. Phys. Chem. B 1999, 103, 1096-1101. 11. Jobic, H., Diffusion of Linear and Branched Alkanes in Zsm-5. A Quasi-Elastic Neutron Scattering Study. J. Mol. Catal. A: Chem. 2000, 158, 135-142. 12. Vlugt, T.; Zhu, W.; Kapteijn, F.; Moulijn, J.; Smit, B.; Krishna, R., Adsorption of Linear and Branched Alkanes in the Zeolite Silicalite-1. J. Am. Chem. Soc. 1998, 120, 55995600. 13. Vlugt, T. J.; Dellago, C.; Smit, B., Diffusion of Isobutane in Silicalite Studied by Transition Path Sampling. J. Chem. Phys. 2000, 113, 8791-8799. 14. Takaba, H.; Koshita, R.; Mizukami, K.; Oumi, Y.; Ito, N.; Kubo, M.; Fahmi, A.; Miyamoto, A., Molecular Dynamics Simulation of Iso-and N-Butane Permeations through a Zsm-5 Type Silicalite Membrane. J. Membr. Sci. 1997, 134, 127-139.

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