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Microporous and Mesoporous Materials 105 (2007) 124–131

Mixture diffusion in zeolites studied by MAS PFG NMRand molecular simulation

Moises Fernandez a, Jorg Karger a, Dieter Freude a,*, Andre Pampel b,J.M. van Baten c, R. Krishna c

a Abteilung Grenzflachenphysik, Universitat Leipzig, Linnestraße 5, 04103 Leipzig, Germanyb Max Planck Institute for Human Cognitive and Brain Science, Stephanstraße 1a, 04103 Leipzig, Germany

c Van ‘t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands

Received 18 December 2006; received in revised form 15 April 2007; accepted 23 May 2007Available online 12 June 2007

Abstract

A combination of magic-angle spinning (MAS) and pulsed field gradient (PFG) NMR has been used to determine the self-diffusivitiesin MFI zeolite of n-butane, DnC4, in mixtures with iso-butane in which the total loading, q, is maintained constant at 4 molecules per unitcell. When the loading of iC4 in the mixture, qiC4, is increased from 0 to 2, the diffusivity DnC4 is observed to decrease dramatically by twoorders of magnitude. Snapshots obtained from molecular simulations indicate that the iC4 molecules are preferentially located at theintersections between the straight channels and zig-zag channels of MFI; these intersections serve as traffic junctions. At qiC4 = 2, themolecular traffic along the straight channels is brought to a virtual stand-still because of the obstructive influence of slow-diffusingiC4 ensconced at these junctions. Molecular dynamics (MD) simulations of DnC4 in nC4/iC4 mixtures show good qualitative agreementwith the observed experimental results.

In sharp contrast, both experimental measurements and MD simulations, of DnC4 and DiC4 in wide pore FAU zeolite yieldDnC4 � DiC4 and there is no influence of mixture composition on component diffusion.� 2007 Elsevier Inc. All rights reserved.

Keywords: Mixture diffusion; Zeolites; MFI; FAU; Butane isomers; Magic angle spinning; Pulse field gradient; Nuclear magnetic resonance; Moleculardynamics; Traffic junction effect

1. Introduction

NMR diffusiometry is a most powerful technique toinvestigate diffusion phenomena inside nanopores. It is ableto follow molecular displacements from some hundreds ofnanometers up to hundreds of micrometers. For diffusionwithin zeolites, NMR diffusiometry is able to provide directinformation on both intra-crystalline diffusion and theso-called long-range diffusion, i.e. the rate of molecularpropagation through beds of crystallites or in compactedparticles [1]. However, there are difficulties associated with

1387-1811/$ - see front matter � 2007 Elsevier Inc. All rights reserved.

doi:10.1016/j.micromeso.2007.05.042

* Corresponding author. Tel.: +49 341 9732503; fax: +49 341 9739349.E-mail address: freude@uni-leipzig.de (D. Freude).

NMR measurements of mixture diffusion within zeolites.Firstly, the heterogeneities in the magnetic susceptibilityof zeolite crystallites and the restricted molecular mobilityin the zeolite framework cause a broadening of the NMRsignal and make the resolution of the components in themixture difficult. Secondly, the shorter relaxation timeslimit the duration of the gradient pulses. Thirdly, thereduced molecular mobility in zeolite crystallites leads toshort diffusion paths during the observation time.

The combination of pulsed field gradient (PFG) NMRwith magic-angle spinning (MAS) NMR has advantagesin comparison with conventional PFG NMR, whenapplied to diffusion measurements in zeolites [2,3]. First,the increased resolution in the ppm scale allows us to mon-itor separately the different components of a mixture.

Notation

D self-diffusivity (m2 s�1)DnC4 self-diffusivity of nC4 (m2 s�1)DiC4 self-diffusivity of iC4 (m2 s�1)g field gradient (T m�1)pp duration of the p-pulse (s)q total mixture loading (molecules per unit cell)qiC4 loading of iC4 in mixture (molecules per unit

cell)T absolute temperature (K)

Greek letters

b factor define by Eq. (1) (dimensionless)c gyromagnetic ratio (dimensionless)d gradient pulse width (s)D diffusion time (s)s inter-gradient delay (s)

M. Fernandez et al. / Microporous and Mesoporous Materials 105 (2007) 124–131 125

Second, the longer transverse relaxation time upon MASallows more time for the application of magnetic field gra-dients and thus more sensitivity towards small moleculardisplacements.

The narrowing of signals achieved by MAS is demon-strated for a mixture of n-butane (nC4) and iso-butane(iC4) adsorbed in FAU zeolite (in the form of NaX, withSi/Al = 1.2) in Fig. 1. Without sample rotation, the spec-trum consists of one broad peak with an full width at halfmaximum (fwhm) of 1275 Hz, without any possibility of

2.0δ / ppm

24δ / ppm

*****

withoutspinning

1 kHz

10 kHz

Fig. 1. 1H MAS NMR spectra of an equimolar mixture of nC4 and iC4 adso300 K, upper spectrum without sample spinning, middle spectrum with a MAAsterisks denote spinning side bands.

differentiating between the two contributions. At a rotationfrequency of 10 kHz, the spectra of nC4 and iC4 are wellresolved in the peaks of the CH2 and CH groups. Eventhe signal of the CH3 groups shows a splitting of0.1 ppm, the fwhm of the CH3 signals is about 15 Hz.

The major objective of the current work is to investigateself-diffusion in nC4/iC4 mixtures in two types of zeolitesFAU (wide pore) and MFI (medium pore) using MASPFG NMR. We aim to demonstrate that the diffusioncharacteristics of these two zeolites are markedly different,

0.51.01.5

0.02 ppm

-20

* ** *

rbed in FAU (NaX, with Si/Al = 1.2). Measurements were performed atS frequency of 1 kHz, lower spectrum with a MAS frequency of 10 kHz.

126 M. Fernandez et al. / Microporous and Mesoporous Materials 105 (2007) 124–131

and that within the intersecting channels of MFI, the ‘‘traf-fic-junction’’ effect prevails. Molecular simulations are usedto provide insights in the mixture diffusion characteristics.

2. Experimental procedure

MFI zeolite (in the all-silica form, silicalite-1) with acrystallite size in the range from 10 lm · 10 lm · 100 lmto 20 lm · 20 lm · 200 lm was kindly provided by Dr.Wolfgang Schmidt, MPI Mulheim. FAU zeolite (in theform NaX) was provided by Dr. Xiaobo Yang, Universityof Hannover. It has a crystallite size of about 50 lm and aSi/Al ratio of 1.2. The samples for the NMR measurementswere prepared by heating 20 mg of the zeolite sample inglass tubes of 3 mm outer diameter. The temperature wasincreased under vacuum at a rate of 10 K h�1. The sampleswere maintained at 673 K for 24 h under vacuum (less than10�2 Pa). The zeolites were loaded with nC4 and iC4 atroom temperature with a total loading, q, of 4 and 16 mol-ecules per unit cell for the zeolites MFI and FAU, respec-tively. Then the glass tube (8 mm length) was sealed off.

NMR experiments were performed on a BrukerAVANCE spectrometer operating at 750 MHz with awide-bore magnet. A Bruker 4 mm MAS probe with pulsedfield gradient capabilities was used. The typical 90�-pulse-length was 10 ls. The maximum gradient strength in thissystem, gmax = 0.54 T m�1. Diffusion measurements wereperformed using the stimulated-echo sequence with bipolargradient pulses and eddy current delay before detection, see

Fig. 2. A pictorial representation of the MAS design combined with anti-Helmprobe is shown at the top. The orientation of the spinning axis with respect to(r.f.) and gradient pulse scheme of the MAS PFG NMR experiment is shown bpulse strength g, eddy current delay secd, inter-gradient delay s. Two weak rec

Fig. 2. The signal attenuation for single-component isotro-pic diffusion is given by

S ¼ S0 exp �D4dgc

p

� �2

D� dþ s2� d

6� pp

� �" #

¼ S0 exp½�Db� ð1Þ

where D denotes the self-diffusion coefficient, c the gyro-magnetic ratio, d the gradient pulse width, D the diffusiontime, s the inter-gradient delay, and pp the duration ofthe p-pulse. The factor b is defined by Eq. (1). The delaybetween gradient pulse and subsequent r.f. pulse was500 ls, in order to ensure that the duration of the dephas-ing and rephasing period is a multiple of the rotor period.Sinusoidal gradients with 2 ms duration were applied.

Diffusion experiments were carried out by varying thestrength of gradient pulses between 10% and 90% of theirmaximum value that amounts to gmax = 0.54 T m�1. Wedid not use the full gradient range for two reasons. First,linearity between the adjusted value and the gradientstrength is only ensured between 4% and 90%. Second,for bipolar gradients and a 16-phase-cycle, in addition tothe stimulated echo, the signal contains further contribu-tions which are not averaged out by the phase cycle, butthey disappear under the influence of the applied field gra-dients. Hence, experimental data for too small gradientintensities may assume values exceeding the actual onesand therefore have to be omitted. Therefore, the correctvalue of S0 is not accessible by direct measurement. In case

holtz-coils for the pulsed field gradients in a high-resolution MAS NMRthe external magnetic field is hm = arccos 3�1/2 � 54.7�. Radio frequency

elow. The parameters are diffusion time D, gradient pulse width d, gradienttangular shaped spoiler gradients average undesirable coherences.

g2 / T2 m-2

0.00 0.05 0.10 0.15 0.20 0.25

S/S 0

0.1

1.0

nC4iC4

nC4/iC4 equimolar mixture;Total loading, q = 16 molecules/uc;FAU (Si/Al=1.2); 300 K;Δ = 200 ms; δ = 0.5 ms

Fig. 4. Semi-logarithmic plot of the decay of the CH2 and CH signals ofthe single components nC4 and iC4 in FAU (NaX, with Si/Al = 1.2) at300 K. The diffusion time D = 200 ms and a gradient pulse lengthd = 0.5 ms.

CH3 (n-but)

CH3 (iso)

CH2 (n-but)CH (iso)

1.02.0 δ / ppm

gradient strength

CH3

1.01.52.0

CH3

CH

CH2

δ / ppm

iC4

nC4

nC4/iC4

Fig. 3. (a) 1H MAS NMR spectra of pure nC4, iC4 and nC4/iC4 mixturediffusion in FAU. The spectra refer to iC4 (top), nC4 (middle) and nC4/iC4 mixture (bottom). (b) Stack plot of the 1H MAS PFG NMR spectra ofthe equimolar nC4/iC4 mixture absorbed in FAU as function of increasingpulsed gradient strength for a diffusion time D = 100 ms. The total mixtureloading, q = 16.

M. Fernandez et al. / Microporous and Mesoporous Materials 105 (2007) 124–131 127

of sufficient signal-to-noise ratio, the value S0 has been esti-mated by extrapolating the first three experimental points(with gradient strengths above the 10% limit).

A short transverse relaxation time T2 limits the durationof the gradient pulses and decreases the signal-to-noiseratio. MAS extends T2 by a factor of 100 for FAU andwe obtain T2 � 40 ms, see line narrowing in Fig. 1. FornC4 and iC4 in MFI, at 363 K, values of T2 under MASconditions are about 5 ms and 3 ms, respectively. At300 K, the T2 of iC4 drops to 2 ms. However, as a conse-quence of the low diffusivity (and of the given upper valueof the gradient intensity) gradient pulse durations that aretwo times larger are needed, so that a dramatic reduction ofthe MAS NMR signal even without the effect of the pulsedfield gradient is inevitable. In order to reduce this effect, thenumber of accumulations is varied from 16 to 1024.

Eq. (1) is valid for isotropic one-component diffusion.For diffusion anisotropy the attenuation is more compli-cated. As an example, for two-dimensional diffusion [4]with Dz = 0 and Dx = Dy = D2D = (3/2) Deff, we have

S=S0 ¼ exp½�D2Db�Z 1

0

exp½D2Dbt2�dt ð2Þ

One may define an effective diffusion coefficient in the caseof anisotropic diffusion; see chapter 7.2 of Karger andRuthven [5]

D ¼ ðDx þ Dy þ DzÞ=3 ð3Þ

which directly results from the first part of the echo atten-uation, where it may be approached by a single exponentialcurve. As expected, there was no anisotropy effect of diffu-sion in FAU. By contrast, the well-known diffusion anisot-ropy in the MFI is known to cause a deviation from thesingle-exponential decay [6]. Under the given experimentalconditions (low diffusivity, small signal intensities) it wasimpossible to use the experimental data for the determina-tion of the principal elements Dx, Dy and Dz of the diffusiontensor, as it was realized for example in Hong et al. [6]. Insuch cases (notable deviations from a single-exponentialbehavior) we used only the first five points of our experi-mental curves for the determination of the effectivediffusivity.

3. Experimental results for diffusion in FAU

Three samples of zeolite FAU were used with a totalloading, q, of 16 molecules per unit cell; this amounts to2 molecules per cavity of FAU. The first sample was loadedwith nC4, the second with iC4, and the third with an equi-molar mixture of nC4 and iC4. 1H MAS NMR spectra arepresented in Fig. 3a. A stack-plot of the 1H MAS PFGNMR spectra of the nC4/iC4 equimolar mixture absorbedin FAU as function of the increasing pulsed gradientstrength is presented in Fig. 3b. We used a diffusion timeof D = 200 ms and a gradient pulse length of d = 0.5 msand performed the measurements at 300 K and at 363 K.Fig. 4 shows the decay of the CH2 and CH signals of the

mixture. The values of the self diffusivities for pure nC4,iC4 and in nC4/iC4 mixtures at 300 K and 363 K are sum-marized in Figs. 5a and b. The values of DnC4 and DiC4

Loading of iC4, qiC4 / molecules per unit cell

0 4 8 12 16

Self

diffu

sivi

tivie

s, D

nC4 an

d D

iC4

/ 10

-9 m

2s-1

0

1

2

nC4iC4

Experiments at 300 K;nC4-iC4 mix diffusion; FAU (Si/Al=1.2),Total loading, q = 16 molecules/uc;

Loading of iC4, qiC4 / molecules per unit cell0 4 8 12 16

Self

diffu

sivi

tivie

s, D

nC4

and

DiC

4 /

10-9

m2

s-1

0

1

2

3

4

nC4iC4

Experiments at 363 K;nC4-iC4 mix diffusion; FAU (Si/Al=1.2),Total loading, q = 16 molecules/uc;

Loading of iC4, qiC4 / molecules per unit cell

0 4 8 12 16

Self

diffu

sivi

tivie

s, D

nC4

and

DiC

4 /

10-9

m2

s-1

0

2

4

6

8

nC4iC4

MD simulations at 300 K;nC4-iC4 mix diffusion; FAU (Si/Al=1),Total loading, q = 16 molecules/uc;

b

c

Fig. 5. Experimentally determined self diffusivities of nC4 and iC4, bothfor pure components and in equimolar mixture, in FAU (NaX, Si/Al = 1.2) at (a) 300 K and (b) 363 K. (c) MD simulations of self-diffusivities in FAU (Si/Al = 1) at 300 K. The total mixture loading,q = 16.

128 M. Fernandez et al. / Microporous and Mesoporous Materials 105 (2007) 124–131

show no significant influence of the diffusion time. At300 K we obtain for D = 20 ms the value DiC4 = 1.09 ·10�9 m2 s�1, whereas for D = 200 ms we have DiC4 =1.37 · 10�9 m2 s�1. At 363 K we obtain for D = 50 ms thevalue DnC4 = 2.89 · 10�9 m2 s�1, whereas for D = 200 mswe get DnC4 = 2.68 · 10�9 m2 s�1. It should be notedthat the accuracy of the experimentally determined self-diffusion coefficients can be given only within ±10% despitethe fact that the error bar of individual points in graphssuch as Fig. 4 is less than ±10%. It can therefore be con-cluded that the data on D is not influenced significantlyby choice of the D.

Karger et al. [7] obtained by PFG NMR in FAU (NaX)at qnC4 = 8, a value of DnC4 = 1.3 · 10�9 m2 s�1 at 300 K.Our value of DnC4 = 1.17 · 10�9 m2 s�1 at qnC4 = 16 is inreasonable agreement with their results.

It is interesting to note that both temperatures the DnC4

and DiC4 are nearly equal to one another in the mixture. At363 K the measured data show DiC4 to have a slightlyhigher diffusivity than DnC4. To rationalize these data, weperformed MD simulations for diffusivities DnC4 and DiC4

in FAU (Si/Al = 1.0) at 300 K; the details of the MD sim-ulation methodology are given in the Supplementary Mate-rial. The MD simulation results in Fig. 5c show that thediffusivities of either isomer are within ±10% of each other.It is also to be noted that the MD simulations predict aslightly higher diffusivity for the branched isomer, becausethe configuration of this molecule is more compact thanthat of nC4.

4. Experimental results for diffusion in MFI

Samples of MFI were used at a total loading, q = 4 mol-ecules per unit cell. Pure nC4, and iC4, along with nC4/iC4mixtures of varying compositions were used. 1H MASNMR spectra (not shown here) allow an examination ofthe loading of the mixtures by comparison of the CHand CH2 peaks.

For diffusion of pure iC4, Fig. 6 shows the decays of theCH3 signals at 300 K and 363 K. The self-diffusion coeffi-cients measured for a diffusion time of D = 400 ms areDiC4 = 1.63 · 10�12 m2 s�1 and DiC4 = 2.32 · 10�12 m2 s�1

for 300 K and 363 K, respectively. Additional measure-ments with D = 200 ms at 363 K did not yield a significantdifference in the value obtained with D = 400 ms for DiC4.

Banas et al. [8] were the first to determine DiC4 in MFIusing PFG NMR. At 363 K, they report a valueDiC4 = 2 · 10�12 m2 s�1, which was obtained, however, ata very poor signal-to-noise ratio. Millot et al. [9] usedQENS to determine a value DiC4 = 2.1 · 10�12 m2 s�1 at398 K. Our value of 2.32 · 10�12 m2 s�1, at qiC4 = 4, is inreasonable agreement with their QENS data.

Also for nC4 a variation of the diffusion time D does notsignificantly affect the values of DnC4; we obtained at 363 Kvalues of DnC4 = 6.42 · 10�9 m2 s�1 and 9.87 · 10�9 m2 s�1

for D = 20 and 200 ms, respectively. At 300 K, the value ofDnC4 = 3.55 · 10�1 m2 s�1 was obtained with D = 30 ms.

g2 / T2 m-2

0.00 0.05 0.10 0.15 0.20 0.25

S/S 0

1

363 K300 K

pure iC4 diffusion;Loading, qiC4 = 4 molecules/ucMFI; 300 K and 363 K;Δ = 200 ms; δ = 2 ms

0.85

0.90

0.95

Fig. 6. Semi-logarithmic plot of the signal attenuation of the signalattenuation of the CH3 group of iC4 adsorbed in MFI at T = 300 K and363 K. The diffusion time is D = 400 ms and gradient pulse length isd = 2 ms.

M. Fernandez et al. / Microporous and Mesoporous Materials 105 (2007) 124–131 129

Pampel et al. [2] measured by MAS PFG NMR at 300 Kthe value of DnC4 = 3.17 · 10�1 m2 s�1, in reasonableagreement with our results.

Heink et al. [10] obtained by PFG NMR at 290 K thevalue of DnC4 = 5.7 · 10�1 m2 s�1 for MFI. Values whichare lower up to two orders of magnitude were obtainedby other techniques, see Nijhuis et al. [11]. Banas et al.[8] found also by PFG NMR at 303 K a significant lowervalue of DnC4 = 1.4 · 10�11 m2 s�1.

Self diffusivities of nC4 were determined in nC4/iC4 mix-tures with varying proportions of nC4 and iC4, keeping thetotal loading constant at q = 4. For the higher diffusivitiesin the mixtures we used smaller values of D. Higher diffu-sivities are obtained when the loading of iC4 in the mixture,

g2 / T2 m-2

0.00 0.05 0.10 0.15 0.2

S/S 0

0.1

1.0

nC4-iC4 mixture diffusion;Total loading, q = 4 molecules/ucMFI; 363 K

Fig. 7. Attenuation of the CH2 signals of nC4 in pure nC4 and in nC4/iC4 mixtuthe total mixture loading q = 4.

qiC4 < 2.5; for these cases, D = 20 ms. Significantly lowerdiffusivities were obtained for qiC4 > 2.5; for these casesD = 200 ms was used. Pure iC4 was measured atD = 400 ms.

In contrast to measurements in FAU, signal broadeningin MFI inhibits resolution of the two CH3 signals in themixture. The intensity of the CH-signal is very low andcould not be used for the determination of DiC4 in thenC4/iC4 mixture. Therefore, in mixtures we measuredthe attenuation of the CH2-signal of nC4 molecules, seeFig. 7. The DnC4 are obtained by linear regression ofthe experimental data. Due to the diffusion anisotropy,the decay is not linear; the extent of non-linearity increaseswhen qiC4 < 2.5; see Fig. 7. In order to determine the DnC4

in the mixtures we consider the initial portion of the decaycurve and the first five experimental points; this gives theeffective value of DnC4, see Eq. (3). Fig. 8 presents a semi-log plot of DnC4 in the mixture as a function of qiC4; alsoincluded in this figure is the data for DiC4 at qiC4 = 4.The data is remarkable because we notice that DnC4 reducesby two orders of magnitude when qiC4 is increased from 0to 2. This dramatic reduction is best appreciated by plot-ting the same data on linear axes, as shown in Fig. 8b.We note that the DnC4 reduces to near-zero values in a lin-

ear fashion as the loading qiC4 is increased from 0 to 2. Inorder to understand and explain the reason for the reduc-tion of DnC4 to near-zero values at qiC4 = 2, we resort tomolecular simulations.

5. Molecular simulations

We performed two types of simulations. Firstly, Config-urational-Bias Monte Carlo (CBMC) simulations were per-formed in order to determine the equilibrium spatialdistribution of nC4 and iC4 within the channels of MFIzeolite. Secondly, molecular dynamics (MD) simulations

0 0.25

qiC4=4; qnC4=0qiC4=3.2; qnC4=0.8

qiC4=2.68; qnC4=1.32qiC4=2; qnC4=2qiC4=1.32; qnC4=2.68qiC4=0.8; qnC4=3.2qiC4=0; qnC4=4

res and of the CH3 signal of pure iC4 in MFI at T = 363 K. In all samples,

Loading of iC4, qiC4 / molecules per unit cell

0 1 2 3

Self

diffu

sivi

ty o

f nC

4, D

nC4 /

10-9

m2

s-1

0

2

4

6

MD spatiallyaveragedexpt

Loading of iC4, qiC4 / molecules per unit cell

0 1 2 3 4

Self

diffu

sivi

tivie

s, D

nC4 an

d D

iC4

/ 10

-9m

2s-1

10-3

10-2

10-1

100

101

nC4, exptiC4, expt

nC4-iC4 mixture diffusion;Total loading, q = 4;MFI; 363 K

nC4-iC4 mixture diffusion;Total loading, q = 4;MFI; 363 K

Loading of iC4, qiC4 / molecules per unit cell0.0 0.5 1.0 1.5 2.0 2.5

Self

diffu

sivi

ty o

f nC

4, D

nC4 /

10-9

m2s-1

0

2

4

6

MD xMD yMD z

nC4-iC4 mixture diffusion;Total loading, q = 4;MFI; 363 K

b

c

Fig. 8. (a) Experimental data on self-diffusion coefficients of nC4 in nC4/iC4 mixtures in MFI at 363 K as a function of the loading of iC4 in themixture. Also shown is the self-diffusivity of pure iC4. (b) Spatiallyaveraged value of DnC4 from MD simulations compared with experimentaldata for DnC4. (c) MD simulations of the DnC4 in nC4/iC4 mixtures in MFIat 363 K in x-, y- and z-directions as a function of the loading of iC4 in themixture. The total mixture loading, q = 4 in all cases.

130 M. Fernandez et al. / Microporous and Mesoporous Materials 105 (2007) 124–131

were performed to determine DnC4 in nC4/iC4 mixture withvarying composition keeping a total loading, q = 4. TheCBMC and MD simulation methodologies are describedin the Supplementary Material accompanying this publica-tion; this also contains a variety of snapshots and detailedsimulation results. A selection of these results is discussedbelow.

CBMC simulations show that whereas nC4 can locatealong either straight or zig-zag channels of MFI, iC4locates preferentially at the intersections because of config-urational considerations [12]. The intersections providemore ‘‘leg-room’’ for iC4 molecules to locate; the branchedisomer finds it difficult to locate within either the straight orzig-zag channels. For an equimolar mixture with a total

Fig. 9. Snapshots showing the location of nC4 (blue) and iC4 (green)molecules in silicalite-1, viewed (a) from the top, in the x–z plane, and (b)from the side, in the x–y plane. The total loading in this simulationsnapshot is 4 molecules per unit cell, with equal amounts of each isomer.The side view is one unit cell deep. The top view is two unit cells deep. (Forinterpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

M. Fernandez et al. / Microporous and Mesoporous Materials 105 (2007) 124–131 131

loading, q = 4, Fig. 9 shows snapshots, viewed from (a) thetop, and (b) along the sides. At the chosen componentloadings, qnC4 = qiC4 = 2, only half the total number ofintersections are occupied by iC4. Since the occupancy ofthe intersections is distributed randomly, each one of thestraight channels has an iC4 molecule ensconced some-where along the y-direction; this is evident from Fig. 9a,a view that is 2 unit cells deep, showing all intersectionshave at least one iC4 molecule. Our experimental data, pre-sented in Fig. 8a, shows that the pure component DiC4 isabout three orders of magnitude lower than DnC4. Conse-quently, the occupation of iC4 at the intersections of thechannels is tantamount to blockage, leading to severereduction in the molecular traffic of the more mobile nC4along the straight channels in the y-direction.

For quantification of the traffic junction effect weperformed MD simulations of the DnC4 various mixturecompositions. Fig. 8c shows the MD simulation resultsfor DnC4 in x-, y- and z-directions as function of iC4 load-ing, qiC4. Diffusion along the straight channels is the maincontributor to diffusion and the increasing occupation ofintersection sites by iC4 has a significant negative effecton the diffusivity. We see that DnC4,y is reduced to practi-cally zero as qiC4 is increased from 0 to 2. It is also interest-ing to note that for qiC4 > 1.5, DnC4,y < DnC4,x, suggestingthat nC4 has to worm its way along the zig-zag channelsbecause the traffic in the y-direction is at a practicalstand-still at qiC4 = 2. The spatially averaged DnC4 =(DnC4,x + DnC4,y + DnC4,x)/3 is compared in Fig. 8b with

the experimental value; both sets of results show a lineardecline in DnC4 with increasing qiC4. The MD simulatedDnC4 is about half of the experimental value; such a devia-tion is not uncommon [13] and is due to the extreme sensi-tivity of the MD simulations to the choice of the forcefields.

6. Conclusions

Magic-angle spinning and pulsed field gradient NMRhave been combined to study the intra-crystalline self-diffu-sion of nC4/iC4 mixtures in MFI and FAU. Using theMAS PFG combination the detrimental line broadeningdue to inevitable susceptibility heterogeneities in MFIwhich so far has prohibited highly resolved measurementshas been dramatically reduced. This enabled selective diffu-sion measurements of species with chemical shift differ-ences of less than 0.1 ppm.

Experimental measurements of DnC4 and DiC4 in widepore FAU zeolite show DnC4 � DiC4 and there is no influ-ence of mixture composition on component diffusion.These results are in agreement with MD simulations.

In MFI, it was found that DnC4 in the mixture decreaseswith increasing loading of iC4. As qiC4 increases to a value

of 2 molecules per unit cell, the DnC4 reduces by about twoorders of magnitude. Molecular simulations have shownthat at qiC4 = 2, the molecular traffic of nC4 is brought toa virtual stand-still because of blocking of the intersectionsites by iC4 molecules.

Acknowledgments

This work was supported by the Deutsche Forschungs-gemeinschaft under the projects Pa 907/3-1 and GRK1056/1 (International Research Training Group ‘‘Diffusionin Porous Materials’’) and by the Max-Buchner-Stiftung.RK acknowledges the grant of a TOP subsidy from theNetherlands Foundation for Fundamental Research(NWO-CW) for intensification of reactors and NWO/NCF for provision of high performance computingresources.

Appendix A. Supplementary data

Appendix A gives details of the CBMC and MD simula-tion methodologies. Snapshots showing location of themolecules in MFI and FAU, along with detailed simulationresults are also included. Supplementary data associatedwith this article can be found, in the online version, atdoi:10.1016/j.micromeso.2007.05.042.

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