tracing water and cation diﬀusion in hydrated zeolites...

Tracing Water and Cation Diffusion in Hydrated Zeolites of Type Li-LSX by Pulsed Field Gradient NMRSteffen Beckert,† Frank Stallmach,† Helge Toufar,‡ Dieter Freude,† Jorg Karger,*,† and Jurgen Haase†

†Faculty of Physics and Earth Sciences, Leipzig University, Linnestraße 5, 04103 Leipzig, Germany‡Clariant Corporation, P.O. Box 32730, Louisville, Kentucky 40232, United States

ABSTRACT: The pulsed field gradient (PFG) technique of NMR is exploited forrecording the time-dependent mean diffusion path lengths of both the water molecules(via 1H NMR) and the cations (via 7Li NMR) in hydrated zeolite Li-LSX. The observedpropagation patterns reveal, for both the water molecules and the cations, two types oftransport resistances, acting in addition to the diffusion resistance of the genuine porenetwork. They are attributed to the interfaces at the boundary between the purelycrystalline regions (crystallites) within the Li-LSX particles (intergrowths) under study andto the external surface of either the particles themselves or crystallite aggregates withinthese particles. The cation diffusivity is retarded by about 1 order of magnitude incomparison with the water diffusivity. This notably exceeds the retardation of cationdiffusion in comparison with water in free solution, reflecting the particular influence of thezeolite lattice on the guest mobility.

■ INTRODUCTION

The unique potentials of zeolites and related crystallinenanoporous materials for their technological use, notably formass separation,1 catalytic conversion,2 selective adsorption,3

sensing,4 and molecular ordering for generating opticalfunctionality5,6 are intimately correlated with the similarity inpore sizes and guest dimensions and with their content ofexchangeable cations.7,8 A wide variety of applications ofzeolites, ranging from water softening in detergency9 toselective removal of radionuclides,10 are based on the exchangeof these cations. Cation content is, moreover, known to deeplymodify the adsorption and diffusion behavior of zeolites11,12 aswell as their catalytic activity,13,14 prompting extensiveexperimental studies on cation locations15 and the developmentof computer simulation methods and theoretical models.16−19

However, exempt from in situ X-ray diffraction (XRD) andNMR studies of the variation of cation locations upondehydration20,21 and the measurement of cation exchangerates between the zeolite crystals and the surroundingsolution,22,23 cation migration used to remain beyond thefocus of both experimental and modeling studies.The advent of the pulsed field gradient (PFG) technique of

NMR24 and its first application to nanoporous host−guestsystems25,26 has provided us with clear and direct evidenceabout the rate of intracrystalline diffusion of the guestmolecules in such host materials.27,28 Equivalent informationon the cation mobility, however, is still missing. From cationexchange measurements, e.g., meaningful information aboutintracrystalline diffusivities only results if the overall exchangerate is indeed controlled by intracrystalline diffusion. The abilityto provide exactly this type of proof has made PFG NMR28−30

a powerful technique for probing molecular mass transfer incomplex systems over microscopic dimensions,31−35 whose

potentials for diffusion studies of cations in zeolites haverecently been demonstrated.36 It was due to the availability ofextra-large field gradient pulses35,37,38 as a prerequisite for themeasurement of small diffusivities39−43 that such measurementsbecame possible. These novel options are now exploited forcomparative diffusion studies of cations and water in zeolite Li-LSX and for unraveling correlations between guest propagationand host topology.

■ MATERIALS AND METHODS

Zeolite Synthesis. Zeolite LSX with particle diametersranging from about 3 to 10 μm was synthesized by D. Taschneras described in ref 36. The ion content after the 4-fold exchangewith lithium chloride solution amounts to 90.9% Li+, 3.4% K+

and 5.7% Na+, and the silicon-to-aluminum ratio is Si/Al =1.02. The zeolite was heated at 363 K for one hour in an openglass tube (outer diameter of 10 mm with a length of 50 mm)in an oven containing a water bed. Subsequently, the glass tubewas sealed off at room temperature, with the zeolite bed keptcooled in liquid nitrogen. After this treatment, the watercontent of the zeolite was about 20 wt %. This corresponds to171 molecules per unit cell. A scanning electron microscopy(SEM) picture of the LSX crystallites is presented in Figure 1.

Pulsed Field Gradient (PFG) NMR Diffusion Measure-ments. Under the influence of a pair of field gradient pulses,applied in addition to the sequence of radio frequency pulsesgiving rise to the formation of the NMR signal, the intensity ofthe spin echo, M, is known to obey the relation29,30,44,45

Received: August 28, 2013Revised: November 1, 2013Published: November 1, 2013

Article

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© 2013 American Chemical Society 24866 dx.doi.org/10.1021/jp408604y | J. Phys. Chem. C 2013, 117, 24866−24872

pubs.acs.org/JPCC

∫δγδ γδ≡ Ψ =

−∞

∞M gM

g,t P z,t gz z( )(0)

( ) ( )cos( )d(1)

with g and δ denoting, respectively, the amplitude and durationof the gradient pulses. t stands for the observation time of thePFG NMR experiment, i.e., the time interval between the twogradient pulses (where, for simplicity, the pulse width δ isimplied to be negligibly small in comparison with t). Thesymbol γ (= 2.67 × 108 T−1 s−1 for protons and 1.04 × 108 T−1

s−1 for 7Li) denotes the gyromagnetic ratio of the nucleusunder study. P(z,t) stands for the probability that, during time t,an arbitrarily selected molecule within the sample is shifted overa distance z, i.e., in the direction of the applied field gradient.This interrelation between the signal attenuation curveΨ(γδg,t) and the “mean propagator” P(z,t)29,30,44,45 gives riseto the matchless versatility of PFG NMR for the exploration ofmolecular mass transfer in complex systems.The present measurements were carried out by means of a

home-built NMR spectrometer at a proton resonancefrequency of 400 MHz. The spectrometer is equipped with apulsed field gradient (PFG) unit35,37 allowing field gradientamplitudes g up to a value of 39 T/m. The field gradient widths

δ were varied between 0.5 and 1.5 ms. Diffusion measurementswere performed using the stimulated24 and (for shortobservation times) the Hahn-echo sequences.46

For molecules in an infinitely extended, isotropic medium thepropagator is a Gaussian28

π= −

⎧⎨⎩⎫⎬⎭P z t

DtzDt

( , )1

4exp

4

2

(2)

with the mean square width (molecular mean squaredisplacement) given by the Einstein formula

∫⟨ ⟩ = =−∞

∞z t z P z,t z Dt( ) ( )d 22 2

(3)

with the self-diffusivity D. Inserting eqs 2 and 3 into eq 1 leadsto the familiar expressions

γδ γ δ γ δΨ = − = − ⟨ ⟩⎜ ⎟⎛⎝

⎞⎠g t g Dt g r t( , ) exp( ) exp

16

( )2 2 2 2 2 2 2

(4)

For normal diffusion in infinitely extended homogeneoussystems, one may even abandon the requirement of pulsegradient widths δ to be negligibly small in comparison with thedistance t between the two field gradient pulses. In this case oneobtains, quite generally, a relation of the form of eq 4 in whichonly the separation between the two gradient pulses t isreplaced by t − δ/3.24 Throughout this study, we haveconsidered the thus corrected pulsed separation as theobservation time.On considering diffusion in nanoporous materials and, in

particular, in zeolites, one must be aware that some of theprerequisites for deriving eq 4 are not strictly fulfilled anymore(see chapter 11 of ref 28 for details). This concerns, inparticular, the fact that one cannot assume absolute uniformityof the material. As a consequence, we have to expect adistribution of diffusivities so that the observable PFG NMRsignal attenuation is not a single exponential anymore. It ratherresults as the weighted mean over many exponentials of thetype of eq 4 with the (different) diffusivities corresponding tothe differences in material structure and/or composition.

Figure 1. SEM pictures of the parent material of type Na,K-LSX.Reprinted from Freude et al.36 with permission.

Figure 2. PFG NMR attenuation plots for water diffusion at 25 °C (a) and for the diffusion of the lithium cations at 100 °C (b) in hydrated zeoliteLi-LSX.

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp408604y | J. Phys. Chem. C 2013, 117, 24866−2487224867

However, even under these conditions, by a series expansion ofthe cosine in eq 1, eq 4 is easily seen to be still correct for smallenough gradient pulse intensities gδ, with the mean squaredisplacement taken over the total system (and the diffusivity,correspondingly, denoting the weighted mean over alldiffusivities in the sample). It is this diffusivity to which werefer in our study. If distinction from the genuine self-diffusivityas introduced with eq 2 is needed, the diffusivity as resultingfrom the PFG NMR measurements is referred to as Deff.A second deviation from the ideal case of an infinitely

extended medium originates from the finite size of the particleunder study, including the presence of a possible substructure.The confinement of the guest molecules to certain regions willobviously lead to a decrease in their propagation rates. In theResults and Discussion section, exactly this consequence isexploited for estimating the sizes of the regions to which guestpropagation is confined, using the adequate analytical solutions.There is, however, also a second consequence of the finiteparticle size. As soon as a perceptible number of molecules areable to leave the individual crystallites, the mean squaredisplacement shall be dramatically affected by their contributionwhen the rate of mass transfer through the intercrystalline spacenotably exceeds the rate of intracrystalline diffusion. Since thelong-range diffusivity is, essentially, given by the productpinterDinter of the relative amount of molecules in theintercrystalline space and their diffusivity, it is easily seen tonotably exceed, at sufficiently high temperatures, thediffusivities of the remaining part of molecules, corresponding,with eq 4, to a much larger decay of the contribution of thesemolecules to the overall PFG NMR signal attenuation curve. Itmay, therefore, be easily subtracted.

■ RESULTS AND DISCUSSION

Figures 2a and b show selected PFG NMR attenuation curvesas the primary data of our diffusion studies with water and thelithium cations in hydrated zeolite Li-LSX. The full linesrepresent the best fit of eq 4 to our attenuation data. Theresulting diffusivities are plotted, as a function of the squareroot of the observation time, in Figures 3a and b.The resulting diffusivities are immediately seen to depend on

the observation time. Not unexpectedly, the diffusivities

decrease with increasing observation time, indicating theexistence of transport resistances on the diffusion paths ofthe species (the water molecules and lithium cations,respectively) under study. Judging from the micrographs ofthe crystals, see Figure 1, there are two sources of transportresistances which one might expect: at the outer surface of thezeolite particles and at the boundary between the individualcrystallites out of which the particles are, obviously, composed.Figures 3a and b are seen to exhibit, for both species, twodistinctly differing regimes of time dependence. They are,tentatively, expected to be correlated with the two types ofresistances. For quantitatively correlating the effective diffusiv-ities experimentally determined with relevant structural andtransport parameters, we are going to distinguish between theresults of “short-range” and “long-range” measurements. Short-range measurements refer to displacements smaller than thedistance between transport resistances within the zeoliteparticles, most likely correlated with barriers formed at theinterfaces between the individual crystallites which are found toform the zeolite particles. They are thus expected to reflectmolecular diffusion within the genuine micropore space,affected by confinement effects at the boundaries between theindividual crystallites. Long-range measurements refer todisplacements exceeding the sizes of the individual crystallitesbut still within the interior of the individual zeolite particles.They are, correspondingly, expected to reflect mass transferunder the combined effect of the micropores and transportresistances at their mutual interfaces, subject to the confine-ment by the size of the particles, i.e., by the surface of theagglomerates seen in Figure 1.For quantitative analysis we refer to the well-known

analytical expression28,47−49

π= −D t D

RD t( )

43eff

3/2

(5)

which correlates the “effective” diffusivity Deff(t), resulting fromthe application of eq 4 to the PFG NMR attenuation curves,with the genuine, intrinsic diffusivity D if mass transfer isconfined to spheres of radius R. The straight lines in the long-time part of the Deff(t)-vs-√t plots in Figures 3a and brepresent the best fits to the Deff data points for the long-range

Figure 3. Effective diffusivities of water at 25 °C (a) and of the lithium cations at 100 °C (b) in hydrated zeolite Li-LSX. The straight lines representthe best fit of eq 5 to the experimental data in the short- and long-time ranges.



measurements. With eq 5, the corresponding diffusivities andradii of confinement result to be DH2O,long‑range = 1.1× 10−11 m2

s−1, Rparticle(H2O) = 1.3 μm, and DLi,long‑range = 1.3 × 10−11 m2 s−1,Rparticle(Li) = 2.41 μm.For mass transfer affected by both the diffusion resistance of

the genuine pore space and transport resistances at the interfacebetween the subunits (crystallites) within the zeolite particles,effective medium theory provides an expression of thetype28,50−52

α= +‐D D1/ 1/ 1/( )long range (6)

with D denoting the diffusivity within the genuine pore spaceand α and denoting, respectively, the permeability and theseparation of additional transport barriers.The resulting radii reproduce the sizes of the smaller and

medium particles, in agreement with the expected behavior.Given the large distribution of the particle sizes, one cannotexclude that the larger particles are, in reality, agglomerates ofsmaller particles so that it is not unexpected that their particlesizes may exceed the Rparticles values determined in our diffusionstudies.For rationalizing the origin of the time dependence of the

effective diffusivities in the short-time range, it is helpful to referto the influence of spherical boundaries on the PFG NMRsignal attenuation in a more general way. With eq 3, the meandiffusion path lengths during t in a given direction (we choosethat perpendicular to the boundary) are seen to be ⟨z2(t)⟩1/2 =(2Dt)1/2.The effect of confinement by a sphere of radius R may thus,

in first-order approximation, be assumed to affect a shell ofthickness (2Dt)1/2, while the remaining part of the sphereremains unaffected. Within this approximation, the effectivediffusivity results as

π π

ππ

π=

−+D

R R Dt

RD

R DtR

D4 (2 ) 4 (2 )

eff

43

3 2 1/2

43

3

2 1/2

43

3 red(7)

where the confinement by the boundary of the sphere, whichthe molecules within this layer are able to experience, is takeninto account by introducing a “reduced” diffusivity Dred < D. Ifthe “ reduced ” d iffus i v i ty D r e d i s s e t equa l toD(1 − 4/(9(2π)1/2)), eq 7 is seen to coincide with eq 5. Wenote that, also in this more general approach, the effectivediffusivity decreases linearly with the square root of time. As afirst-order approach, we are therefore going to use eq 5 for alsoanalyzing the effective diffusivities in the short-time range. Nowthe corresponding diffusivities and radii of confinement resultto be DH2O,micro = 3.45 × 10−11m2 s−1, Rmicro(H2O) = 0.28 μm andDLi,micro = 4 × 10−11m2 s−1, Rmicro(Li)= 0.44 μm. Just as theparticle sizes resulting from analyzing the effective diffusivitiesin the long-time range, now also the sizes of the individualconstituents, i.e., the sizes of the “crystallites” as resulting fromthe short-time analysis, are seen to be of the order of magnituderevealed by the SEM picture in Figure 1.Confinement by an impermeable boundary (as implied for

the external particle surface) on the mean square displacementclearly exceeds the effect of confinement by the boundariesbetween the subunits within one zeolite particle which, at leastto some degree, allow a passage of the diffusants. Dred musttherefore be expected to be even closer to the genuineintracrystalline diffusivity D so that the prefactor of the√t termin eq 5 becomes smaller. Correspondingly, the radii R

calculated on the basis of eq 5 may exceed the real ones. Anestimate of the extent of this shift is in the focus of ongoingsimulation work.The increase in the genuine micropore diffusivities Dmicro for

both the cations and the water molecules in comparison withthe long-range diffusivities Dlong‑range within the zeolite particleshas been seen to be the immediate consequence of theadditional impediment of propagation on the boundariesbetween the different crystallites which the diffusants have toovercome on their diffusion paths over larger distances, with eq6 providing a quantitative expression of this interrelation. Theinfluence of internal surface barriers is known to decrease withincreasing temperature.53−56 This may be easily referred to thefact that the activation energy for barrier permeation exceeds, ingeneral, the activation energy for diffusion in the genuine porenetwork. Also in the present case, the genuine intracrystallinediffusivities Dmicro of both the lithium ions and the watermolecules are seen to differ by not more than a factor of about3 from the intraparticle long-range diffusivities.In ref 36, the diffusivity of the lithium ions in hydrated zeolite

Li-LSX at 100 °C was determined to be (2.0 ± 0.8) × 10−11 m2

s−1. The order of magnitude of these measurements, whichhave been performed with an observation time of t = 2 mswithout any further variation, has been confirmed in the presentstudy using the identical samples. In addition, by an extensivevariation of the observation time, it has been revealed that anobservation time of even as short as the considered 2 ms is notyet short enough to exclude corruption by confinement withinthe individual crystallites. By extrapolation to zero observationtime via eq 5 the true (i.e., unperturbed by boundary effects)value of DmicroLi+ is now estimated to be (4.0 ± 0.9) × 10−11 m2

s−1.A comparison between the magnitudes of the water and

cation diffusivities is complicated by the difference in themeasuring temperature. Their choice, however, was aconsequence of the measuring conditions. A dramatic decreasein the cation mobility with decreasing temperature, togetherwith an accompanying reduction in the transverse relaxationtimes, excluded any meaningful 7Li PFG NMR measurementwith hydrated Li-LSX at temperatures below the chosen 100°C. On the other hand, with temperatures higher than thechosen room temperature, the increasing water diffusivities giverise to increasing diffusion path lengths. With eq 3, the root-mean-square displacements are thus, for even the shortestpossible observation time of 2 ms, found to amount to 1.7 μm,notably exceeding the size of the individual crystallitesappearing from both the micrograph (see Figure 1) and theconfinement effects as traced by the short-range PFG NMRmeasurements (see Rmicro data in Figure 3). PFG NMRmeasurements of water diffusion at 100 °C do allow, therefore,reliable measurement of only intraparticle long-range diffusivity.Since the diffusivities of genuine micropore diffusion have todefinitely exceed the intraparticle long-range diffusivities andare, moreover, known to be approached by them at sufficientlyhigh temperatures, a comparison with the cation diffusivitiesmay clearly be also based on the intraparticle long-rangediffusivities of the water molecules.Figure 4 shows the PFG NMR signal attenuation curve for

water in the hydrated Li-LSX samples, corresponding to thoseshown in Figure 2a for 25 °C, measured now at 100 °C for theshortest possible observation time, i.e., t = 2 ms. In thebeginning of the attenuation curve we note a very fast decaywhich has to be correlated with those water molecules which, at



this high temperature, are able to leave the crystals, even duringthis shortest possible observation time. For considering theeffective diffusivity within the zeolite particles, their contribu-tion to the overall signal has to be subtracted. The resultingsignal attenuation curve is shown by the broken line. From thevery first part of this attenuation curve, the mean diffusivityresults to be (2.5 ± 0.5) × 10−10 m2 s−1. Also this diffusivity is,strictly speaking, an effective diffusivity, Deff, resulting fromdiffusion within a finite, spherical volume. For an order-of-magnitude estimate of the difference between this value and thetrue intraparticle diffusivity, we consider the magnitude of thesecond term on the right-hand side of eq 5. For this estimatewe approach the value of the true diffusivity appearing in thisterm by the value of the effective diffusivity, 2.5 × 10−10 m2 s−1,and the particle radius R = 1.3 μm as resulting from the long-range data analysis given in Figure 3a. In this way, the secondterm is estimated to 10−10 m2 s−1, yielding a water diffusivity in

hydrated zeolite Li-LSX at 100 °C of about (3.5 ± 0.5) × 10−10

m2 s−1.This value confirms the estimate of the water diffusivity at

100 °C in ref 36 which has been based on the rate of waterexchange with the surrounding atmosphere. This value isslightly smaller than the water diffusivity in zeolite Na-X (D ≈ 5× 10−10 m2 s−1) determined in the very first PFG NMRmeasurement of intracrystalline zeolitic diffusion 40 years ago,25

which, quite recently, was confirmed by molecular dynamics(MD) simulations and quasi-elastic neutron scattering experi-ments.57 In addition to the influence of transport resistances atthe crystallite boundaries, the difference between the waterdiffusivities in zeolites Na-X and Li-LSX can easily be referredto the different amount and nature of the cations.Figure 5 shows the diffusivities in aqueous lithium chloride

solution at both room temperature and 100 °C. In comparisonwith these data, the diffusivities in hydrated zeolite Li-LSX foreither component (Figure 3) are seen to be significantly (byabout 2 orders of magnitude) reduced. This reduction is morepronounced for the cations. Their diffusivity in Li-LSX is seento be nearly 1 order of magnitude smaller than the waterdiffusivities, while in aqueous lithium chloride solution, theydiffer by not more than a factor of about two. Both effects maybe easily referred to the existence of the zeolite lattice. It isexpected to slow down the random motion of all guests and is,in addition, the carrier of the negative charges whichincontrast to the mobile anions in solutionare now fixed inspace, leading to an additional slowing down of the positivelycharged cations.

■ CONCLUSIONS AND OUTLOOK

For the first time, PFG NMR diffusion measurements areshown to provide a complete view on cation self-diffusion inhydrated zeolite particles. By varying the observation times and,hence, the diffusion path lengths covered in the experiments,the propagation patterns are found to be closely related withthe morphology of the zeolite specimens under study. The viewon guest dynamics is completed by the PFG NMR results ofwater diffusion, yielding diffusivities exceeding the cationdiffusivities by about 1 order of magnitude. This is a remarkable

Figure 4. 1H PFG NMR signal attenuation curve for water diffusion inhydrated zeolite Li-LSX at 100 °C for an observation time of 2 ms.The diffusivity, D (H2O, long-range) = (2.5 ± 0.5) × 10−10 m2 s−1, hasbeen determined, via eq 4, from the slope of the broken line shown inthe representation which approaches the slope in the attenuation curvefor small values of (γδg)2t if one omits the very first steep decay whichhas to be attributed to water molecules which exchange, during theobservation time, between different particles.

Figure 5. Diffusivities of water (●) and of lithium ions (■) in an aqueous solution of LiCl at 25 °C (a) and at 100 °C (b) determined by 1H and 7LiPFG NMR, respectively, (this study) and comparison with literature data for the lithium diffusivities (□).58



difference since, in the free aqueous solution, water diffusivitiesare found to exceed the cation diffusivities by not more than afactor of 2. Diffusivities in the hydrated zeolite are notablyreduced in comparison with aqueous solution, by more than 2orders of magnitude for the cations and slightly less than 2orders of magnitude for water. The time dependence of thediffusivities of both the cations and the water molecules revealstwo types of additional transport resistances which may beattributed to the interfaces between the individual crystallitesforming the zeolite particles and to the external surface of theseparticles or of larger subunits within the particles.With the entity of diffusion data in hydrated zeolite Li-LSX as

provided by the present PFG NMR studies we dispose of ascenario of the dynamics of exchangeable cations and guestmolecules in zeolites of unprecedented completeness. Thesenovel options are, notably, accompanied by a recent break-through in the modeling of cation exchange isotherms inzeolites which, following previous studies of water andhydrogen adsorption,59−61 have been based on grand ensembleMonte Carlo simulations.62 The combination of these twooptions for an in-depth study of the laws of the exchangedynamics of the cations in hydrated zeolites is, doubtlessly,among the most attractive tasks of future zeolite research.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported by Deutsche Forschungsgemeinschaftunder the projects AVANCE 750, HA 1893/9-1 and GK 1056/2 and by the Fonds der Chemischen Industrie.

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tracing water and cation diﬀusion in hydrated zeolites...

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