Probing Mass Transfer in Mesoporous Faujasite-Type Zeolite Nanosheet Assemblies

DOI: 10.1002/cphc.201301133

Probing Mass Transfer in Mesoporous Faujasite-TypeZeolite Nanosheet AssembliesDirk Mehlhorn,[a] Alexandra Inayat,[b] Wilhelm Schwieger,*[b] Rustem Valiullin,[a] andJçrg K�rger*[a]

1. Introduction

The applicability of porous materials in numerous technolo-gies, including adsorption,[1] catalysis,[2] and separation,[3] isbased on the correct match between the size of the pores andthat of the molecules under consideration. The diffusional re-sistance of the pore network, however, is known to increasedramatically as the size of the guest molecule approaches thepore diameters.[4, 5] Mass transfer is, therefore, among the keyfactors that limit the technological performance of porous ma-terials.

As a promising strategy for overcoming this limitation,recent research activities have concentrated on the creation ofmaterials with hierarchical pore spaces.[6–8] In these materials,pores of larger diameters (the so-called transport pores) ensurethe required acceleration of mass transfer between the (tech-nology-relevant) purely microporous regions and the surround-ings. Together with the fabrication of these materials, the ex-ploration of various phenomena contributing to mass transferin such materials and their quantitation has thus become a keytopic of current research.[8–13]

Experimental techniques for measuring mass transfer arecommonly referred to as macroscopic if the information aboutmass transfer is deduced from the response of the wholesystem to well-defined changes in the surrounding atmos-phere, such as a stepwise pressure increase (or decrease) inconventional uptake (or release) experiments.[14–16] During thecourse of the experiments, the molecular diffusion paths covermacroscopic dimensions, that is, distances much larger than

the sizes of the crystals/particles of the sample, so that infor-mation about mass transfer within the individual crystals/parti-cles must always be based on model assumptions.

Microscopic techniques are, conversely, able to directly ob-serve molecular displacements over microscopic dimensions,that is, over distances that are notably smaller than the diame-ters of the crystals/particles under study. Being sensitive to dis-placements from hundreds of nanometers to hundreds of mi-crometers,[15, 17–19] pulsed field gradient (PFG) nuclear magneticresonance (NMR) spectroscopy has served as a particularly sen-sitive and universally applicable tool for the exploration ofmass transfer in complex systems,[16, 20–22] including mesoporouszeolites.[9–11, 13]

This paper reports the first application of PFG NMR spectros-copy to diffusion studies in hierarchical pore spaces formed byassemblies of zeolite nanosheets. The potential of this type ofporous materials has been impressively demonstrated inref. [23] by the catalytic activity of ultra-thin mordenite frame-work inverted (MFI) zeolites of single-unit-cell thickness. PFGNMR diffusion measurements of guest molecules in this mate-rial are complicated, however, by their relatively short nuclearmagnetic relaxation time in the medium-pore-size MFI zeo-lites.[24] In this repect, better prospects are provided by thelarge-pore zeolites of type NaX [Faujasite (FAU) structure] withnotably larger nuclear magnetic relaxation times and, corre-spondingly, the option of an at least one order-of-magnitudevariation in the observation time. Varying the observation timeis known to be an important prerequisite for the unambiguousinterpretation of the primary data of PFG NMR experiments incomplex systems.[13, 25, 26] Herein, we present the first results ofa systematic PFG NMR diffusion study in assemblies of meso-porous FAU-type zeolite nanosheets.[27] This was carried out byusing cyclohexane as a probe molecule at loadings corre-sponding to total micropore filling.

Pulsed field gradient nuclear magnetic resonance (NMR) diffu-sion studies are performed by using cyclohexane to probetransport properties in a NaX-type zeolite with a hierarchicalpore structure (house-of-cards-like assemblies of mesoporousnanosheets), which is compared with a purely microporoussample. With guest loadings chosen to ensure saturation ofthe micropores, and the meso- and macropores left essentially

unoccupied, guest diffusion is shown to be enhanced byalmost one order of magnitude, even at room temperature.Diffusivity enhancement is further increased with increasingtemperature, which may, therefore, be unambiguously attribut-ed to the contribution of mass transfer in the meso- and mac-ropores.

[a] D. Mehlhorn, Dr. habil. R. Valiullin, Prof. Dr. J. K�rgerFaculty of Physics and Earth Science, University of LeipzigLinn�straße 5, 04103 Leipzig (Germany)E-mail : [email protected]

[b] A. Inayat, Prof. Dr. W. SchwiegerInstitute of Chemical Reaction Engineering, University Erlangen-N�rnbergEgerlandstraße 3, 91058 Erlangen (Germany)E-mail : [email protected]

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2. PFG NMR Diffusion Measurements

PFG NMR diffusion studies are based on the measurement ofthe intensity, S, of an NMR signal (the spin echo) generated bya suitably chosen sequence of radiofrequency pulses as a func-tion of the intensity of pulsed field gradients applied duringthis sequence (see the Experimental Section and Refs. [16] ,[19] , [21] , [22] and [28] for more details). We represent this in-tensity by the term gdg in which d and g are the length andthe amplitude of the pulses, respectively, and where g (=2.67 � 108 T�1 s�1 for protons) denotes the gyromagnetic ratioof the nuclei under study. For sufficiently short field gradientpulses (as ensured throughout our studies), the primary dataof PFG NMR can be correlated with the dynamics of the mole-cules under study by the relationship [Eq. (1)]:[16, 21, 22]

S gdg; tð ÞS gdg ¼ 0; tð Þ �

S gdg; tð ÞS0

¼Z 1

�1Pðz; tÞ cosðgdgzÞdz ð1Þ

where P(z,t) (the mean propagator) denotes the probability(density) that, during time, t, an arbitrarily selected moleculewithin the sample is shifted over a distance, z, in a given direc-tion (namely that of the applied field gradient). The concept ofthe mean propagator was introduced in ref. [29] and exploitedfor attaining and presenting the complete information on mo-lecular dynamics in beds of zeolite crystals as accessible byPFG NMR spectroscopy. With Equation (1), the PFG NMR signalattenuation and the mean propagator are seen to be Fouriertransforms. Therefore, either of them can be used to deduceinformation about the governing parameters of mass transfer.

In an infinitely extended, homogeneous medium, completeinformation about molecular dynamics is contained in a singleparameter, the diffusivity (or, more strictly speaking, the coeffi-cient of self-diffusion or tracer diffusion), D. In this case, themean propagator is a simple Gaussian [Eq. (2)]:

Pðz; tÞ ¼ 1ffiffiffiffiffiffiffiffiffiffiffi4pDtp exp � z2

4Dt

� �ð2Þ

from which the mean-square displacement is found to obeythe Einstein relationship [Eq. (3)]:

z2ðtÞh i ¼Z 1

�1z2Pðz; tÞdz ¼ 2 Dt ð3Þ

predicting proportionality between the observation time andthe mean-square displacement. It is important to note that,completely equivalently, self-diffusivity can be introduced byFick’s first law, as the factor of proportionality between the fluxof labeled molecules and the gradient of labeling (within a uni-form overall concentration).[16, 30]

Inserting Equation (2) into Equation (1), yields Equation (4):

S gdg; tð ÞS0

¼ exp �g2d2g2Dtð Þ

¼ exp �g2d2g2 z2ðtÞh i=2ð Þð4Þ

with the second part of the equation resulting from Equa-tion (3). Thus, the self-diffusivity D (or the mean-square dis-placement <z2(t)>) which determines, in the propagator rep-resentation [Eq. (2)] , the widths of the distribution curves, isnow seen to appear as the slope in a semi-logarithmic plot ofthe PFG NMR signal attenuation versus the squared field-gradi-ent pulse intensity (gdg)2.

In many cases—and notably when considering porous host–guest systems—mass transfer does not proceed in a homoge-neous environment, so that molecular dynamics may occur asa succession of diffusion phenomena of a different nature.Mass transfer in such systems cannot be reflected adequatelyby a single diffusivity. In beds of porous crystals, for example,molecular displacements can occur in both the interior of theindividual crystals and throughout the intercrystalline spacewhich, depending on their interrelation, might lead to differentpatterns of mass transfer. In this case, the mean propagatornotably deviates from a simple Gaussian [Eq. (2)] , just as thesemi-logarithmic plot of the PFG NMR signal attenuation devi-ates from a straight line.

For diffusion in beds of porous crystals/particles, two cate-gories of molecules contribute to the mean propagator and,hence, to the PFG NMR signal attenuation, namely moleculesthat, during the observation time, have remained in the samecrystal/particle and those that did not. As a first-order approxi-mation, PFG NMR signal attenuation and mean propagator areapproached, therefore, by considering the superposition oftwo expressions of the type given by Equations (4) and (2) togive Equations (5) and (6):

S gdg; tð ÞS0

� pintra exp �g2d2g2Dintratð Þ

þplong�range exp �g2d2g2Dlong�ranget� �

¼ pintra exp �g2d2g2 z2ðtÞh iintra

2

� �

þplong�range exp �g2d2g2 z2ðtÞh ilong�range=2� �

ð5Þ

Pðz; tÞ� pintra

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4pDintratp exp � z2

4Dintrat

� �

þplong�range

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4pDlong�ranget

p exp � z2

4Dlong�ranget

� � ð6Þ

where we have used the notations pintra(t) for the relativenumber of molecules that, after time, t, are still within theirparticles and, correspondingly, plong-range(t) = 1�pintra(t) for thosethat have exchanged between different particles, with the re-spective mean-square displacements <z2(t)> intra(t) and<z2(t)> long-range, and with the effective diffusivities calculated,in analogy to Equation (3), from the ratio between the respec-tive mean-square displacements and the observation times. Anextensive discussion of these quantities and of their dependen-cies on the conditions, under which PFG NMR diffusion experi-ments in beds of porous particles/crystals are performed, canbe found in section 11.4 of ref. [16] .

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3. Results and Discussion

As an example of the primary data, Figure 1 provides a compar-ison between the PFG NMR attenuation curves observed at25 8C with cyclohexane at 100 % micropore loading in a purelymicroporous sample of zeolite NaX (NaX-micro) and ina sample of mesoporous NaX nanosheet assemblies (NaX-meso). Their scanning electron micrographs, at two differentmagnifications, are shown in Figure 2.

None of the attenuation curves are seen to follow the purelyexponential decay, as required by Equation (4) for diffusion inan ideally homogeneous system, because, in this case, in thesemi-logarithmic representation chosen in Figure 1 the signalattenuation would yield a straight line. Representing the famili-ar pattern of PFG NMR diffusion studies with porous crys-tals,[9, 16, 31, 32] the PFG NMR attenuation curves in Figure 1 a and1 b consist of a fast, first decay, followed by a notably slower,

second one. For this second decay, the slowly decaying part iseasily identified to correspond with the first term on the right-hand side of Equation (6), referring to those molecules that,during the observation time, have remained within the samecrystal/particle. Correspondingly, the first fast decay is causedby those molecules which did leave their crystals/particles, rep-resenting the second term on the right-hand side of Equa-tion (6). The contribution of this first, fast decaying part tooverall attenuation is seen to increase with increasing observa-

tion time. This observation is in agreement with theexpected behavior, as the relative number of mole-cules leaving their crystals (plong-range) must clearly beexpected to increase with increasing observationtime.

The slope of the further decay is, in the chosenrepresentation versus (gdg)2t, seen to remain essen-tially unchanged, within the limits of accuracy. Thevalues of the diffusivities and of the root-mean-square displacements determined from these slopesby using Equation (4) for the shortest and largest ob-servation times are shown in the insets (Figure 1).They refer to those molecules that, during the obser-vation time, did not leave their crystals/particles. Thediffusivities of about 10�12 m2 s�1, as observed withthe purely microporous sample (NaX-micro, Fig-ure 1 a), are of the order of magnitude as obtained inprevious studies with cyclohexane in zeolite NaX.[33]

The value of about 0.5 mm for the mean displace-ment during the maximum observation time is com-patible with the finding that, during this time,a 1�pintra fraction of about 30 % is able to leave eachindividual crystal. The fact that the crystal diametersof about 3 mm did notably exceed the root-mean-square displacements also explains why, given thesubstantial scattering in the attenuation curves, anyconfinement-caused decrease in the diffusivities withincreasing observation time[26, 32, 34] remains unobserv-able.

In the PFG NMR attenuation data for cyclohexanein NaX-meso, shown in Figure 1 b, the slope of thesecond decay is seen to be significantly enhanced incomparison with NaX-micro, giving rise to intraparti-cle diffusivities increased by a factor of about five.We note that the displacements exceed the thicknessof the nanosheets (ca. 50 nm) significantly, so thatthe trajectories of the cyclohexane moleculesthrough the nanosheet assemblies may be concludedto consist of displacements alternating betweenmicro-, meso-, and macropores. Assuming that the

mean lifetimes spent by the diffusing molecules within eachindividual type of pore space (before entering the next one) ismuch smaller than the observation time (fast-exchange condi-tion[16]), one might note Equation (7):[28, 35]

Dintra ¼ pmicroDmicro þ pmesoDmeso þ pmacroDmacro ð7Þ

Figure 1. PFG NMR attenuation curves for cyclohexane at 100 % micropore-filling ina) NaX-micro and b) NaX-meso for different observation times at 25 8C. Explicitly indicat-ed are the mean-square displacements of intracrystalline/intraparticle diffusion and thecorresponding diffusivities resulting from Equation (3), which have been determinedfrom the slopes of the dashed lines for the shortest and largest observation times.

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where pmicro(meso, macro) and Dmicro(meso, macro) denote the relativenumber of molecules in the micro-, meso-, macropores andtheir diffusivities, respectively, as defined, on the basis of Equa-tion (3), for the molecules in the respective pore spaces. Underthe conditions of complete micropore filling, as considered inour experiments, we know pmeso and pmacro ! pmicro�1. Asa first-order approximation, the diffusivities in the meso- andmacropores can be represented by a Knudsen-type relation[Eq. (8)]:[16, 28, 36]

DmesoðmacroÞ �13

uh idmesoðmacroÞ ð8Þ

in which uh i and dmesoðmacroÞ denote the mean velocity of themolecules in the gas phase and the mean diameter of themeso- or macropores, respectively. As the Knudsen diffusivityin the meso- and macropores exceeds the micropore diffusivi-ties by several orders of magnitude,[11, 13, 37] its contribution toDintra can exceed that of Dmicro, irrespective of the factthat pmeso and pmacro is negligibly small in comparisonwith pmicro. This becomes immediately apparent fromcomparison with the values of Dmicro resulting fromthe representations in Figure 1 a for the purely micro-porous sample. Diffusion in zeolite NaX of hierarchi-cal pore structure (NaX-meso) is thus seen to notablyexceed the diffusivity in microporous NaX.

Evidence complementary to these model consider-ations was provided by supplementary measure-ments at 60 8C. Figure 3 shows, for the chosen obser-vation time of 10 ms, a comparison of the PFG NMRattenuation plots of the samples under study at bothtemperatures. Also indicated are the resulting diffu-sivities. By assuming Arrhenius dependency,DðTÞ ¼ D0 exp � EA

RT

� �, the measured diffusivities have

been used to estimate the respective activation ener-gies, E, of diffusion, which are also presented. Where-as in the purely microporous zeolite NaX the estimat-ed activation energy is of the order of the literaturevalue [(15.5�2.5) kJ mol�1][33] for intracrystalline diffu-sion in zeolite NaX, the activation energy for the in-traparticle diffusivities in the mesoporous zeolite ismuch greater than this value. With Equation (8), the

Dmeso and Dmacro diffusivities only weakly depend on the tem-perature (namely with v/

ffiffiffiTp

) ; therefore, the temperature de-pendence of the two further terms on the right-hand side ofEquation (7), pmesoDmeso and pmacroDmacro, are seen to be dominat-ed by of pmeso and pmacro. In PFG NMR measurements withclosed sample tubes, as considered in these studies (see theExperimental Section), the relative population in the meso-and macropores scales with pressure, giving rise to a tempera-ture dependence with an activation energy of the order of theisosteric heat of adsorption. From the literature, the heat of ad-sorption of cyclohexane in NaX is known to take values of theorder of (60�5) kJ mol�1.[37, 38] The activation energies of Dintra

of cyclohexane in NaX-meso, being intermediate between theheat of diffusion in the micropores and the heat of adsorption,are thus seen to provide additional evidence that the termspmesoDmeso and pmacroDmacro, appearing on the right-hand side ofEquation (7), do in fact contribute to the overall diffusivityDintra.

4. Conclusions

PFG NMR diffusion measurements with cyclohexane in zeoliteNaX were performed for evidencing transport enhancement insamples with a hierarchical pore structure (particularly in as-semblies of mesoporous NaX nanosheets), which were com-pared with purely microporous samples. Transport enhance-ment is found to be further intensified with increasing temper-ature. This behavior is the immediate consequence of the in-crease of the fraction of molecules in the meso- and macro-pores with increasing temperature.

It is important to note that the diffusivities of saturated hy-drocarbons in the micropores of zeolite NaX are known to de-crease by up to two orders of magnitude with increasing con-

Figure 2. SEM images of the zeolite NaX samples under study.

Figure 3. PFG NMR attenuation curves for cyclohexane at 100 % micropore-filling in NaX-micro (squares) and NaX-meso (triangles) for different temperatures (filled symbols:25 8C, open symbols : 60 8C) at an observation time of 10 ms. Also indicated are the intra-crystalline/intraparticle diffusivities resulting, using Equation (4), from the dashed straightlines and estimates of the activation energies of diffusion, which follow from the diffusiv-ities at the two temperatures considered.

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centration.[5, 33, 39] For attaining the utmost effect of transportenhancement, the experiments of this study have, therefore,been performed with guest loadings sufficient to saturate themicropores, leaving, however, the meso- and macropores es-sentially unoccupied, with only the gas phase present. Furtherexploration of the mechanisms of mass transfer within and be-tween the three pore spaces shall be based on experimentswhere, following previous studies of guest diffusion in Vycorporous glasses[40] and activated carbon,[41] the PFG NMR mea-surement is performed with the samples connected with a re-servoir of the guest molecules. In this way, by varying theguest molecule pressure, loadings both below micropore fillingand with mesopore filling should be possible. Under such con-ditions, transport enhancement in comparison with the purelymicroporous samples is expected to be moderated at bothlow pressure (owing to the increasing values of Dmicro, simulta-neously with decreasing values of pmeso (macro) with decreasingpressure) and high pressure (owing to a blockage of the trans-port (i.e. meso- and macro-) pores by a liquid phase). Such ex-periments are in progress.

Experimental Section

The zeolite sample with a hierarchical pore system was synthesizedin the presence of the organosilane template 3-(trimethoxysilyl)-propylhexadecyldimethylammonium chloride (TPHAC; synthesizedaccording to ref. [27]). For comparison, a conventional sample ofpurely microporous zeolite NaX (NaX-micro) was synthesized byusing the same procedure, but without the addition of TPHAC. Allsamples were calcined at 650 8C for 12 h in air. Further details ofthe synthesis procedure can be found in ref. [27] and specific con-ditions are given in Table 1.

Scanning electron microscopy (SEM) images were recorded with anULTRA55 electron microscope (Carl Zeiss SMT AG) with a workingdistance of 7 mm and acceleration voltage of 1.5 kV. Samples wereadhered to a conducting carbon pad and non-sputtering measure-ments were made. The fractions of non-nanosheet crystal and zeo-lite P impurities in the samples were determined from the SEMimages by observing 100 particles. SEM images of the samples atdifferent magnifications are shown in Figure 2.

Nitrogen physisorption measurements were performed at 77 K ona QuadraSorb SI instrument (Quantachrome Instruments, BoyntonBeach, USA). Prior to measuring, the samples were outgassed at300 8C for 12 h under vacuum. The specific surface area (ABET) wasobtained from the Brunauer–Emmett–Teller (BET) equation in thelinear range between 0.004 and 0.012 p/p0 (where p/p0 is the rela-tive pressure). The total pore volume (Vtot) was calculated from theadsorption point at p/p0 = 0.99. The calculation of all other texturaldata and the pore-size distribution curves were based on the non-localized density functional theory (NLDFT) method, using the

kernel for nitrogen adsorption in cylindrical silica pores; the specif-ic volumes of micro-, meso-, and macropores were determined asthe cumulative volumes of pores with diameter below 2 nm (Vmicro),between 2 and 50 nm (Vmeso), and above 50 nm (Vmacro). The exter-nal surface area was calculated as the difference between totalNLDFT surface area and the cumulative surface area of pores withdiameter below 2 nm. The nitrogen physisorption results can befound in Figure 4 and Table 2.

The PFG NMR self-diffusion measurements were performed withthe 13-interval stimulated echo–pulse sequence by use of the in-house-built PFG NMR spectrometer FEGRIS[18, 19] with a field gradi-ent amplifier allowing the application of field gradient pulses withamplitudes up to 35 Tm�1. The host–guest systems under studywere contained in fused glass tubes (diameter 7 mm) with a fillingheight of about 10 mm. Earlier, the zeolite material had been acti-

Table 1. Molar gel composition [mol] and reaction conditions for the syn-thesis of the NaX samples.

Sample Al2O3 SiO2 Na2O K2O H2O TPHAC Crystallization

NaX-micro 1.00 3.00 3.50 0.00 180 – 80 8C, 4 dNaX-meso 1.00 3.00 3.70 0.30 180 0.06 80 8C, 3 d

Figure 4. Nitrogen physisorption isotherms (a) and pore-size distributioncurves (b) of the investigated NaX samples.

Table 2. Textural and morphological characteristics of the zeolite NaXsamples.

Analysis Property NaX-micro NaX-meso

SEM P content [%] 0 ca. 1X compact [%] 100 5–10dmean nanosheets [nm] – ca. 50dmean crystal/assembly [mm] ca. 3 4–5

N2 sorption ABET [m2 g�1] 908 696Aext [m2 g�1] 14 84Vmicro [cm3 g�1] 0.36 (95 %) 0.26 (61 %)Vmeso [cm3 g�1] 0.02 (5 %) 0.16 (37 %)Vtot [cm3 g�1] 0.38 (100 %) 0.43 (100 %)

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vated by heating at a rate of about 20 K per hour up to 400 8Cunder evacuation and kept at the final temperature for about 20 h.Subsequently, by cooling the sample with liquid nitrogen, theguest molecules were transferred into the sample from a calibratedvolume, where the number of molecules was chosen according tothe total micropore volume of the samples, as given in Table 2.

Acknowledgements

Financial support by Deutsche Forschungsgemeinschaft, Fondsder Chemischen Industrie and Cluster of Excellence “Engineeringof Advanced Materials” is gratefully acknowledged.

Keywords: diffusion · hierarchical pore systems ·nanostructures · nmr spectroscopy · zeolites

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