Simulations on 'Powder' Samples for Better Agreement with

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Simulations on ‘Powder’ Samples for Better Agreement with Macroscopic Measurements Angela Mary Thomas, and Yashonath Subramanian J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b02599 • Publication Date (Web): 02 Jun 2019 Downloaded from http://pubs.acs.org on June 2, 2019

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The Journal of Physical Chemistry

Simulations on ‘powder’ samples for better agreement with macroscopic measurements Angela Mary Thomas and Yashonath Subramanian∗ Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-560012,India E-mail: [email protected]

∗

To whom correspondence should be addressed

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ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Different experimental measurement techniques give widely differing values for the diffusivities (Ds ) and activation energies (Ea ) for the same sample. Values from molecular dynamics (MD) simulations agree with QENS measurements and not with those obtained from macroscopic techniques such as uptake or ZLC. We report molecular dynamics simulations on different zeolite samples with inter-crystalline space along 0-, 1-, 2- and 3-dimensions. The results on n-hexane in zeolite NaY samples with intercrystalline space along 3-dimensions exhibit values of Ds and Ea in excellent agreement with macroscopic techniques demonstrating the importance of ‘powder’ sample in simulations.

Keywords Zeolites, Diffusivity measurements, Molecular dynamics simulations, Uptake measurements, PFG-NMR, QENS

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Introduction Micro- and meso-porous materials are extensively used in chemical and consumer industries. In particular, petroleum refineries employ these substances for purification, extraction, refining, as well as separation of multi-component mixtures. A knowledge of diffusivity of various components of the mixture is sine qua non for all the above applications. Various experimental techniques such as uptake, ZLC (Zero Length Column chromatography), PFG-NMR (Pulsed Field Gradient- NMR), QENS (Quasi Elastic Neutron Scattering), etc are employed to measure the self-diffusivity (Ds ) of guest molecules in these substances. Computational methods such as molecular dynamics, Brownian dynamics, dissipative particle dynamics (DPD) have also been employed to compute diffusivities. 1–4 Unfortunately, different experimental techniques yield very different values of diffusivity of guests for the same sample under same conditions ( temperature and pressure). In Table 1, we list Ds values for the same system (n-hexane in silicalite) measured using different experimental techniques. The values vary over seven orders of magnitude. This is a typical case and such behaviour is seen across all guest species and different zeolitic systems. This makes it difficult for a chemical engineer to actually predict the behaviour on an industrial scale using these Ds values. In fact, the question would be : which is the ‘correct’ value for use in modelling for industries ? Kárger, Ruthven and several others have suggested possible reasons for the different Ds values obtained from different experimental techniques. 5–17 Uptake or chromatography techniques which probe diffusion for longer timescales (and therefore, probably, longer length scales) usually yield lower values for self-diffusivity compared to techniques which measure Ds for shorter periods. This is also evident from Table 1. Several groups have reported investigations to get insights into the underlying reasons for these differences between diffusivities. Zhang et al. have investigated the effect of crystal size distribution on diffusion of light olefins in ZSM-5. 13 Hashimoto and Yamashita measured the contact induced intercrystalline migration of aromatic molecules with the help of fluorescence microscopy. 11 In spite of several such investigations, a complete understanding of the processes at the microscopic level is lacking. Recently a molecular dynamics simulation of xenon in faujasite was reported on a purely 3



intra-crystalline system without any inter-crystalline space as well as a system with intercrystalline space along only one of the axes. 18 The values of Ds were lower for the latter while the values of activation energies for diffusion, Ea were higher. The basic idea is that the experimental sample is always a ‘powder’ sample and never a single crystal. Does diffusion in such a powder sample be very different from what one sees in a single crystal ? If so, in what way ? Also we shall attempt to answer the question : Can MD simulations ever provide estimates of Ds and Ea comparable to the experimentally measured values obtained from macroscopic measurement techniques such as uptake or chromatography ? We report extensive molecular dynamics (MD) simulations of n-hexane in zeolite Y on crystalline and powder samples. The crystalline sample consists of (a) large single crystal. The powder simulations have been carried out with inter-crystalline region (b) in x-, (c) xand y- as well as (d) x-, y- and z-directions. The results are compared with each other and also with experimental measurements.

Methods Zeolite NaY with molecular formula Na56 Si136 Al56 O384 is used as the host in the simulations. It belongs to cubic space group Fd¯3m with a = 24.8536 ˚ A. The atom coordinates in the unit cell provided by Fitch and coworkers are employed in the simulations. 19 Each unit cell of this zeolite has eight α-cages or super-cages with a radius of ∼5.8 ˚ A. These super-cages are connected tetrahedrally via 12-membered windows of free diameter ∼ 7.0 ˚ A. There are in all 56 sodium ions as extra-framework cations which are distributed over SI, SI′ and SII sites in each unit cell. 19 4×4×4 unit cells of zeolite Y comprise the simulation cell. 128 n-hexane molecules (denoted as nC6 hereafter, 2 per unit cell) are introduced as guest molecules inside this zeolite host. Four different systems have been simulated in this study. (see Figure 1) (i ) 0d system Purely intra-crystalline system with no inter-crystalline region. The simulation cell length along each direction is uniform, 99.4144 ˚ A with 4×4×4 unit cells of zeolite Y. (Figure 1a) (ii ) 1d system - An inter-crystalline region of 40 ˚ A is introduced in the x-direction after each of the two crystallites of size 2×4×4 unit cells. The resulting simulation cell dimensions are 4


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179.4144×99.4144×99.4144 ˚ A3 . (see Figure 1b) (iii ) 2d system - The inter-crystalline regions are present along both x- and y-axes between four crystallites having 2×2×4 unit cells of A3 (Figure 1c). zeolite each. The simulation cell, thus, is of size 179.4144×179.4144×99.4144 ˚ (iv )3d system - Here, inter-crystalline regions are present along crystallographic x-, y- and z-directions after each crystallite of size 2×2×2 unit cells (comprising of 8 such crystallites). The simulation cell length is 179.4144 ˚ A along all the three directions. (Figure 1d) When the inter-crystalline space was introduced, there was no addition of hydroxyl groups to satisfy the unsaturated silicon atoms at the boundaries. All simulations are performed using LAMMPS package. 20 The simulations are equilibrated for 5 ns which is followed by a run of 20 ns during which positions, velocities and forces are stored for later analysis. Zeolite atom coordinates are excluded from the MD integration throughout the simulations. Intramolecular interactions for the nC6 molecules are modelled using OPLS parameters. 21 Intermolecular non-bonded interactions between the zeolite atoms (O and Na) and the guest atoms have been included using a Lennard Jones potential with self parameters for zeolite atoms taken from Wender et al. and for guest atoms from OPLS force field. 21,22 A spherical cut-off of 12 ˚ A is applied for these interactions. Periodic boundary conditions are imposed along the three directions. The total energy changes are less than 1 in 104 to ensure good energy conservation. Positions, velocities and forces are stored at an interval of 1 ps for the calculation of properties, although here the latter two have not been used. As discussed above, the Ds values for different experimental techniques can vary over several orders of magnitude for the same hydrocarbon-zeolite system. It has been suggested by Kárger, Ruthven and several others that this is due to differences in the length and timescale over which the probe measures diffusivities. 5–14 In order to examine if this is true, we carried out long simulations for four systems discussed above and the results are presented below.

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Results and Discussion In Figure 2a the plot of density distribution, ρ and potential of mean force (PMF, W = − ln RT ρ) at 200K are plotted along crystallographic x-axis by averaging over y- and zdirections. Similar plots are shown along y- and z-directions averaged over the other two directions in Figures 2b and 2c. It is seen that there is only a slight difference between different curves belonging to 1d, 2d and 3d systems. The density is higher in the intracrystalline region and essentially zero in the inter-crystalline region at 200 K. The PMF shows significant barrier in free energy in the inter-crystalline regions. Near the interface between the crystal and the inter-crystalline region, the density is negligible up to around 3˚ A within the crystal but increases gradually as one goes deep into the crystal. But the A from the boundary. This is density reaches values close to the maximum only around 12 ˚ not surprising since the interactions between the nC6 and the crystal is maximum only when all interactions exist. This happens only when the interactions have decayed to zero which occurs around 12 ˚ A. In Figure 3, the density and the PMF are shown at 800 K. The ρ(x) along x-direction for 1d, 2d and 3d are clearly different. Recall that all the 3 systems studied, namely 1d, 2d and 3d have inter-crystalline space along x-axis. Thus, even though all the three systems are all identical along x direction, the W (x) is maximum in the intra-crystalline space for 1d and minimum for 3d. In contrast, in the inter-crystalline space, the population density of 1d system is the least, whereas that of the 3d system is the highest. Similarly in the y-direction population density of nC6 is the highest in the inter-crystalline space in 3d as compared to 2d system. These differences are not seen at lower temperatures because inter-crystalline space in all three different powder samples studied are hardly populated. Instead nC6 populates almost exclusively the intra-crystalline space at lower temperatures. The density is almost uniform without variation within the inter-crystalline space whereas within the intra-crystalline space there are significant variations or oscillations. These may be attributed to variations in the interactions within the crystal. We have computed the time evolution of mean square displacement (MSD) of the centre of mass (COM) of nC6 over 6 ns for all the four systems at 3 different temperatures and these 6


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are shown in Figure 4. At 200K, the distance traversed over 6 ns decreases with increase in the dimensionality. In contrast at 800 K, the distance traversed increases with increase in dimensionality. To understand these contrasting trends we need to look at the earlier plots of density and PMF. At 200 K, there is little or no sampling of inter-crystalline region since there is a large free energy barrier for passage through the inter-crystalline region (see W (x) in Figure 2). As a result, when inter-crystalline space is present along several directions n-hexane is more and more confined leading to reduced displacement. This explains why when we go from 1d- to 3d- there is a reduction in the slope of the MSDs. At higher temperature (800 K), n-hexane samples the inter-crystalline region in addition to intracrystalline region leading to significant increase in density in the inter-crystalline regions. Motion in the inter-crystalline region is more facile than in the intra-crystalline region and availability of the inter-crystalline region increases with increased dimensionality. This leads to higher diffusivity with increase in the dimensionality of the system at 800 K. One of the consequences of this is the pronounced increase in the diffusivity with temperature in the higher dimensional systems (2d and 3d). This as we shall see leads to what is seen in the macroscopic measurements (where the guest molecules sample both the intra-crystalline and inter-crystalline space: a higher activation energy. Further, it will be seen that the macroscopic measurements invariably report lower diffusivity ( see Table 1). In fact, the longer the sampling duration of the experimental technique, the lower will be the diffusivity (at lower temperatures). This arises from the fact that the diffusing molecules typically sample the intra-crystalline region and they therefore remain confined to the crystallites and are unable to leave these crystallites to sample the inter-crystalline regions, leading to lower diffusivity of the diffusing or adsorbed molecules. This is because experimental measurements are made at lower temperatures where the guest molecules sample largely the intra-crystalline region and less frequently the inter-crystalline region. In Table 2, the overall self diffusivities, Ds at 3 different temperatures for all the 4 systems are listed. It is seen that at 200 K diffusivities are in the order Ds (0d) > Ds (1d) > Ds (2d) > Ds (3d). At 800K, the order is reversed, namely, Ds (0d) < Ds (1d) < Ds (2d) < Ds (3d). From Table 2 it is seen that the diffusivity varies only by one order of magnitude between 0d (0.88 × 10−9 m2 /s) and 3d (0.09 × 10−9 m2 /s) systems at 200 K. At 800 K, it is seen that 7



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the diffusivity between the 0d and 3d systems differ by several (between 2 and 3) orders of magnitude : 0d (16.14 × 10−9 m2 /s) and 3d (7720.0 × 10−9 m2 /s). These findings may be compared with the PFG-NMR investigation by Kárger and Spindler who have made measurement of mean square displacements(MSDs) as a function of observation times. 23 Thus, they could obtain diffusivities for short times which correspond to intra-crystalline diffusivity or Ds for 0d system of the present study as well as MSDs from long observation times corresponding to motion both within the crystallites and the intercrystalline regions. They observed that while the Ds is higher at lower temperatures for intra-crystalline motion as compared to inter-crystalline motion, at higher temperatures, the Ds is higher for inter-crystalline motion as compared to intra-crystalline motion. In other words, the present study confirms their finding and there is a one-to-one correspondence between the experimental findings and the findings from our study here. The reasons for the rather large value of Ds at higher temperatures is due to the relatively large increase in the population in the inter-crystalline space. Indeed, this has been pointed out in several experimental studies by Kárger and coworkers who studied single component adsorption and Rittig et al who investigated multi-component mixtures. 23–25 They proposed that the effective diffusivity, Def f can be written as,

Def f = pinter Dinter

(1)

where pinter is the population in the inter-crystalline region and Dinter is the diffusivity of the guest molecule in the inter-crystalline region. The temperature dependence of the Ds is of interest as they are obtainable from experimental data as well. Arrhenius plots of ln Ds vs. 1/T were plotted and activation energy Ea were derived for each system (see Figure 5). These are listed in Table 3. We have also listed Ea from different experimental measurements. The value of Ea for 0d system consisting of purely intra-crystalline motion is 6.6 kJ/mol. With introduction of inter-crystalline region along x-direction, Ea value obtained from total MSD increases to 23.7 kJ/mol. For 2d-system one obtains an activation energy of 34.6 kJ/mol which increases to 38.9 kJ/mol for 3d-system. 8


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Also listed in Table 3 are the values of activation energies from various experimental techniques obtained from literature. Usually, QENS measurements which probe for short duration (ps to ns), will give values of activation energies which are close to values derived from MD. 26 However, in the present case, there are no QENS measurements for n-hexane in zeolite NaY. They have reported a value of 14.6 kJ/mol for nC6 in NaX. 27 (see Table 3). PFG-NMR probe for milliseconds and the n-hexane molecules are likely to sample both intra and inter-crystalline regions, but predominantly the intra-crystalline region. Thus, the activation energy appears to be between 6.6 kJ/mol and 23.7 kJ/mol. Bobok et al. have reported Ds values at different temperatures with the help of gas chromatography from which we have obtained an Ea value of 30.9 kJ/mol for nC6 in NaY. 28 Also listed are the values of Ea for nC6 in three other systems: MgA (uptake), 5A (PFG, SE) and FER (ZLC). Both these techniques probe for seconds to hours and therefore their values sample adequately the inter-crystalline region even at low temperature giving higher values for Ea . The Ea values for nC6 in these zeolites are in the range between 27 and 50 kJ/mol. Kárger and Volkmer found that the Ea value lies between 40 and 75 kJ/mol for n-hexane in NaX. Our estimate here 38.9 kJ/mol is in good agreement with their measurements. 29 Thus, the simulations on 3d-systems appear to yield values of activation energy which are in the right range and appear to yield values close to those obtained from macroscopic measurements.

Conclusions The results on ‘powder’ sample here provide several interesting insights into the diffusion in inhomogeneous systems. The variation of diffusivity within an inhomogeneous system over a certain temperature range is far wider than in the homogeneous system (0d-system). At low temperatures, the guest species preferentially populates the intra-crystalline regions while at sufficiently high temperatures the inter-crystalline regions are preferentially populated. Before we discuss some of interesting results obtained in the present study, we like to emphasize the following. In Table 2, we see the diffusivities obtained from our simulations for 0d- to 3d-systems listed. 0d-system has only intra-crystalline region and the diffusivity computed for this system actually corresponds to short time measurements by techniques 9



such as normal MD on non-powder samples or QENS. Diffusivity obtained for 3d-systems really corresponds to long probe times by techniques such as uptake or ZLC. We have seen that (see Table 1) that the diffusivity of the guest molecule, n-hexane, is lower when the experimental measurement technique probes the sample for longer periods. Thus, we see that uptake measurements which can take seconds to hours to measure give very low diffusivity values (of the order of 10−16 ). Other techniques such as ZLC or PFGNMR have diffusivities which are of the order of 10−13 and 10−11 respectively. This trend – where longer the probe time lower the diffusivity is so well known that it is taken for granted. The present study, in contrast, suggests that the diffusivity obtained from a technique such as uptake can yield values that are greater than the value obtained from a technique such as PFG-NMR (see Table 2) at somewhat higher temperatures. This is evident from Table 2 : both at 400 and 800 K the values for 3d-system are greater than the values for 0d-system. As the former would correspond to macroscopic measurement techniques such as uptake or chromatography and the latter to QENS, it proves that this is the case at higher temperatures. The present investigation provides activation energies in good agreement with Ea values obtained from macroscopic measurement techniques. Present study uses very small crystallites (≈50 ˚ A) while the crystal sizes used in experimental sample might be of the order of micrometers or 10,000 ˚ A. This could lead to differences in the results but we do not understand how this could alter the results as yet. Similarly, the magnitude or size of the inter-crystalline region employed in the simulation is likely to be quite different from those in the found in the samples used in the experiments. We have no measure of the intercrystalline region in the experiment. Use of more appropriate sizes for the crystal and the inter-crystalline region might lead to better agreement between the simulation and experimental Ds as well as Ea values. The results obtained here raise new questions. (a) How do the dynamics and the activation energy barriers depend on the crystal size? (b) What will be the effect of variation of inter-crystalline region on these properties? (c) What is the influence of a small crystallite that is not an integral number of unit cells ? Note that previous studies by Liu and coworkers have actually quantified the influence of surface barriers on mass transfer. 16 They have also investigated how channels of different sizes play different 10


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roles in diffusion and reaction. However, the introduction of inter-crystalline regions within the system mimicking the ‘powder’ sample appears to already provide a value for Ea that is quite close to the experimentally derived value even with modest system size and simulation duration. The dramatic improvement and better agreement with macroscopic measurements in the Ea values from the simulations suggests that it may not be necessary to use the actual sizes of the crystallites present in the actual laboratory sample of zeolites on which experiments such as uptake or chromatographic measurements are carried out. Such samples typically contain Avogadro number of molecules (∼ 1024 ). This is similar to the use of rather small sizes of the system (∼ 103 to 106 atoms) on which simulation is carried out as compared to much larger number of atoms in experimental samples. The use of periodic boundary conditions (PBC) along the three perpendicular directions ensure the powder nature of the sample and excellent agreement in the various properties computed. The present study suggests that the presence of the inter-crystalline region by which the single crystal sample becomes a powder sample might be a significant advance in the computational approach or strategy akin to that achieved by the use of PBC. These results augur well for the future of computational approaches. It will be interesting to study the effect of the presence of the inter-crystalline regions on other properties such as adsorption isotherms. We plan to carry out studies to compute other properties.

Acknowledgements Authors thank Department of Science and Technology, New Delhi and Nano-mission, DST, New Delhi for support. Authors also thank the reviewers for their useful comments giving experimental references which agree with the results reported here which has improved the discussion.

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Tables Table 1: Diffusivity values of n-hexane in silicalite with MFI structure measured using different experimental and computational techniques. 30–34 Method Uptake ZLC PFG-NMR QENS MD

Timescale >s >s 10-100 ms ps - ns fs - ns

Temperature (K) 298 303 298 298 314

Ds (m2 /s) 7.5 × 10−16 5.3 × 10−13 5.0 × 10−11 4.5 × 10−10 1.42 × 10−9

Table 2: Diffusivities of nC6 in zeolite Y without inter-crystalline space (0d) and with inter-crystalline space along x (1d), along x and y (2d), and along x-, yand z axes (3d) from the slopes of MSDs obtained over the time range of 0-6 ns. Simulations are done for 20 ns at 200 K, 400 K and 800 K. Activation energies are calculated for the total diffusion from Arrhenius plots. T (K) 200 400 800

0d 0.88(0.05) 9.23(0.25) 16.14(0.34)

Ds (×10−9 m2 /s) 1d 2d 0.61(0.08) 0.22(0.07) 7.95(0.32) 12.48(1.79) 4.37×102 (30.1) 2.28×103 (106.8)

3d 0.09(0.03) 36.17(4.77) 7.72×103 (439.6)

Table 3: Activation energies, Ea , calculated for the total diffusion using Arrhenius relations. System nC6 in NaY (this study) nC6 in NaY (gas chromatography) 28 nC6 in NaX (PFG-NMR) 27 nC6 in NaX (PFG-NMR) 29 nC6 in MgA (uptake) 35 nC6 in 5A (PFG,SE) 36 nC6 in FER (ZLC) 37

0d 6.6 -

12

1d 23.7 -


Ea (kJ/mol) 2d 3d Experiments 34.6 38.9 30.9 14.6±2.5 40-75 42-50 28.1-27.6 32

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Figures Figure 1: Various types of zeolite NaY systems under study.

(b) 1d system with inter-crystalline region along x-axis only.

(a) 0d system with no inter-crystalline region.

(c) 2d system with inter-crystalline region along x- and y-axes.

(d) 3d system with inter-crystalline region in all three directions, x-, y- and z-axes.

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Figure 2: Density distribution, ρ and potential of mean force (W ) of the COM of n-hexane along the three crystallographic directions. The inter-crystalline (indicated by IC) and crystalline region (C) are shown with the vertical dashed lines indicating the boundaries. There are shown for the three systems investigated (1d-, 2d- and 3d-) along (a) x-axis, (b) y-axis and (c) z-axis at 200 K.

-4

1d 2d 3d

-8 -12

-8 6

ρ(x) (kJ/mol)

IC

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C -4

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90

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(c) along z-axis

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Figure 3: Density distribution, ρ and potential of mean force (W ) of the COM of n-hexane along the three crystallographic directions. The inter-crystalline (indicated by IC) and crystalline region (C) are shown with the vertical dashed lines indicating the boundaries. There are shown for the three systems investigated (1d-, 2d- and 3d-) along (a) x-axis, (b) y-axis and (c) z-axis at 800 K.

C

C -4 -8

0 C

C -5 -10

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90

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(c) along z-axis

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0 180

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Figure 4: Mean square displacement of COM of nC6 in zeolite Y without inter-crystalline space (0d) and with inter-crystalline space along x-axis (1d), along x and y-axes (2d) and along x-,y- and z-axes (3d) at temperatures (a) 200 K, (b) 400 K and (c) 800 K calculated with the trajectories from 20 ns runs.

4000

1.5e+05

0d 1d 2d 3d

0d 1d 2d 3d

1.25e+05 1e+05

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(Å )

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Figure 5: Activation energies obtained from MD simulations on 0d system and 3d system obtained from self-diffusivity data between 200 and 800 K. The activation energy for the 3d system is comparable to that obtained from macroscopic measurement on ‘powder’ samples.

-9 0d 3d -12

2

ln [Ds (m /s)]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-15

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0.002

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1/T (K )

16


0.005

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(31) Guimarães, A. P.; Möller, A.; Staudt, R.; de Azevedo, D. C. S.; Lucena, S. M. P.; Cavalcante, C. L. Diffusion of linear paraffins in silicalite studied by the ZLC method in the presence of CO2 . Adsorption 2010, 16, 29–36. (32) Heink, W.; Kärger, J.; Pfeifer, H.; Datema, K. P.; Nowak, A. K. High-temperature pulsed field gradient nuclear magnetic resonance self-diffusion measurements of nalkanes in MFl-type zeolites. J. Chem. Soc., Faraday Trans. 1992, 88, 3505–3509. (33) Jobic, H.; Bee, J., and M. Caro Proc. Sixth Intl. Zeol. Conf.; Guildford : Butterworths, 1993; p 121. (34) Hernandez, E.; Catlow, C. R. A. Molecular Dynamics Simulations of N-Butane and N-Hexane Diffusion in Silicalite. Proc. Math. Phys. Scie. 1995, 448, 143–160. (35) B¨ ulow, M.; Struve, P.; Finger, G.; Redszus, C.; Ehrhardt, K.; Schirmer, W.; Kärger, J. Sorption kinetics of n-hexane on MgA zeolites of different crystal sizes. Study of the rate-limiting transport mechanism. J. Chem. Soc., Faraday Trans. 1 1980, 76, 597–615. (36) Jobic, H.; Paoli, H.; Méthivier, A.; Ehlers, G.; Kärger, J.; Krause, C. Diffusion of nhexane in 5A zeolite studied by the neutron spin-echo and pulsed-field gradient NMR techniques. Microporous Mesoporous Mater. 2003, 59, 113–121. (37) Voogd, P.; van Bekkum, H.; Shavit, D.; Kouwenhoven, H. W. Effect of zeolite structure and morphology on intracrystalline n-hexane diffusion in pentasil zeolites studied by the zero-length column method. J. Chem. Soc., Faraday Trans. 1991, 87, 3575–3580.

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Graphical TOC Entry The introduction of inter-crystalline regions between the zeolite single crystals, making the sample ‘powder’, gives better agreement of transport properties with the macroscopic experimental measurements.

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The introduction of inter-crystalline regions between the zeolite single crystals, making the sample `powder', gives better agreement of transport properties with the macroscopic experimental measurements. 167x90mm (300 x 300 DPI)


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Simulations on 'Powder' Samples for Better Agreement with

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