Diffusion anisotropy in molecular sieves

28 October 1994

ELSEVIER

CHEMICAL PHYSICS LETTERS

Chemical Physics Letters 229 (1994) 297-301

Diffusion anisotropy in molecular sieves. A Fourier transform PFG NMR study of methane in AlP&-5 Sriram S. Nivarthi, Department

Alon V. McCormick

*, H. Ted Davis

of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue S.E., Minneapolis, MN 55455, USA

Received 28 June 1994; in final form 19 August 1994

Abstract By analyzing the shape of the ‘H PFG NMR spin echo decay of methane in large crystals of AlPOd-5, we demonstrate that diffusion of methane is unidirectional but not single file. The intracrystalline diffusion coefficient is 2.9~ 10e9 m2 s-l. The same experiment, when performed on AIPO,-5 crystals of much smaller size, results in an isotropic diffusivity that is higher by nearly three orders of magnitude. This crystal size artifact emphasizes the importance of using large zeolite crystals in NMR measurements to obtain intracrystalline diffusivities.

1. Introduction In the literature there is substantial disagreement among the results of different techniques used to measure the diffusivity of gases in zeolites [ 11. In particular, gas uptake rate measurements and pulsed field gradient nuclear magnetic resonance (PFG NMR) measurements frequently give diffusivities differing by orders of magnitude. In several cases, agreement between NMR and uptake measurements was obtained when care was taken to eliminate external heat and mass-transfer resistances and when similar sample preparation and pretreatment procedures were employed [ l-3 1. However, there remain systems in which discrepancies are observed between NMR and uptake measurements of diffusivity [ 11. PFG NMR measurements are attractive, since they can provide more precise information, especially regarding diffusion anisotropy [4]. It is well recognized that inappropriately performed PFG NMR ex* Corresponding author.

periments could measure diffusivities corresponding to displacements over lengths larger than the size of the zeolite crystal. Here, we measure intracrystalline diffusion in large and perfect crystals of A1P04-5 (see Fig. la), where diffusion occurs in cylindrical channels extending along the length of the crystals. Furthermore, there are no interconnections between these channels that may allow the sorbate to escape along the smaller dimensions of the crystals. In this Letter, we report for the first time PFG NMR proof of unidirectional diffusion in a molecular sieve and we demonstrate in a controlled experiment how diffusivities by NMR can be much greater than the intracrystalline diffusivities. The system we studied is methane in the molecular sieve AlPO,-5. From the structure of A1P04-5 [ 51 it is expected that diffusion is along parallel channels without interconnections. Since the diameter of the channels is about 7.3 & diffusion is unidirectional in the time-scale of the PFG NMR measurements. If the diffusing molecule has a sufficiently large cross section, diffusion would be single file. In what follows,

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Letters 229 (1994) 297-301

for the powder average attenuation oft he NMR spinecho intensity in an isotropic medium f 71: .4=exp(

-1/%%‘ADf

~

12)

where A is the spin-echo intensity when G # 0 divided when G= 0. G is the magnitude of the magnetic field gradient pulse, 6 is the duration of the gradient pulse and 1_’the gyromagnetic ratio ofthe nucleus under observation. The factor LU in the exponent of Eq. (2) comes from the mean square displacement, (Y’), of the molecule during the observation time d. If molecular motion is ordinary diffusion (i.e. ( r2> ;cL)k) but is confined to one direction in the medium, Eq. (1) still applies for the propagator function. But in this case, the powder average spinecho attenuation obeys the expression [4,8 1 by the intensity

Fig. I _ SEM mkragraphs of A@%&-j c~slals: (a f ariginal caystak; (tr) smaller crystals obtained after grinding.

we will be able to test whether diffusion

is single file, since the single file propagator is different from the propagator due merely to unidirectional diffusion. Large crystals of AlPOr (about 30 pm long) were provided to us by M.E. Davis and 13. Young ( 1994). Some of the measurements were made on these crystals as received and were made on smaller crystals obtained by grinding some of the large crystals (see Fig. 1). In an isotropic medium, for an ensemble of spins undergoing Brownian motion, the normalized probability that a spin is displaced by z after a time lapse A, has the following Gaussian form [ 2,6]: P(zYd)=

(4nDd)-1’2exp(

-z"/clDdf

,

(11

where P(z> 9) is the so-called propagator function, = is the nuclear spin displacement along the field direction in an NMR experiment, d is the time allowed for diffusion and D is the self-diffusion coefficient of the molecule carrying the nucleus. This probability leads to the following expression

Eq. (3) is obtained by averaging the echo attenuation over all solid angle in order to take into account the random orientation of the molecular sieve crystals. The unidirectional nature of diffusion results in Eq. (3 ) as opposed to Eq. (2) which is valid for isotropic systems. If the probe molecules, methane in our case, are too large to pass one another in the channels of AlPOd5, then the motion is single file diffusion. The propagator is still Gaussian [9] ~but the mean square displacement is proportional to the square root of the observation time rather than the observation time itself, i.e. ( r* ) x $ [ 9- 12 1. In the case of single file diffusion, therefore, the exponent in Eq. (3) would go as the square root of the observation time.

2. Experimental For the measurements, the AlPOd- samples were loaded with methane after outgassing under vacuum for 24 h at 450°C. A ceil-~librated quantity ofmethane was loaded into the zeotite. The loading corresponded to =: 0.7 molecule per periodic unit (8.4 a long) of the AIPO,-5 channels. In a sealed sample tube at 300 K, the ‘H transverse relaxation time, r,, of methane was determined by using the Hahn spin-echo

S.S. Nivarthi et al. /Chemical

sequence to be 5.2 It 0.3 ms. The longitudinal relaxation time, T,, was determined from the inversion recovery technique to be 22.4 + 2.7 ms. Both relaxation curves were single exponentials. The methane diffusivity was measured by using the NMR pulsed field gradient spin-echo technique [ 7,13,14]. Observation times (d) of 1, 4, 5 and 6 ms were employed for the large AlPOd- crystals. In the experiment with the ground A1P04-5 crystals, A was kept at 1 ms since no NMR signal was observed for higher observation times. Short observation times are desired in order to minimize the effect of T, relaxation on the echo decay and to minimize the number of sorbates escaping the crystals. The field gradient intensity G was varied from 0.5 to 5.8 T/m. The pulse width 6 was kept at 0.3 ms because longer values could result in eddy current distortion of the spin echo. Eq. (2) holds only if 6 CKA. Since 6 was finite in our experiments, we employed the effective observation time, A,=A- id, in our evaluation of the rhs of Eqs. (2) and (3). Signal averaging was carried out using about 1000 scans for each point. The relaxation delay used was 1 s. The measurements were made on a Nicolet NT-300 FT spectrometer at 300 MHz.

Physics Letters 229 (I 994) 297-301

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Fig. 2. ‘H NMR spin-echo attenuation (A) of methane in the large A1P04-5 crystals plotted versus y2G262d. Echo attenuations are obtained for observation times (d) of ( + ) 1 ms, (A ) 4 ms, (0) 5 ms and (0 ) 6 ms. Also shown are the least-squares best tits to the data using Eqs. (2) and (3 )_ The spin-echo attenuation for pure water (d = 4 ms) is also plotted ( * ) along with the best fit.

3. Results and discussion The spin-echo attenuation (A) is plotted versus y2G2d2A in Fig. 2 and versus y2G26’A’/2 in Fig, 3. The data in Fig. 3 strongly indicate that the diffusive motion of methane in A1P04-5 is not single file. On the other hand, the least-squares best fits of the methane data in Fig. 2 to Eqs. (2) and (3) strongly favor Eq. (3) and so establish that the diffusion is unidirectional but not single file. Thus, although methane molecules have a van der Waals diameter of 3.8 A [ 15 1, they are squishy enough to pass one another in pores 7.3 A wide. The diffusivity determined by the fit of the data to Eq. (3) is D=2.9~ lop9 m2 s-i. Note that the root mean square displacement corresponding to this diffusivity is on the order of 6 urn which is well below the average size of the crystallites used in the measurement. For comparison, also shown in Fig. 2 is the spinecho attenuation for pure water at 300 K. Diffusion in this case is of course isotropic and so, as expected, the attenuation obeys Eq. (2) and yields the known

Fig. 3. ‘H NMR spin-echo attenuation (d) of methane in the large AlPOd-5 crystals plotted versus y2G*62d’/*. Echo attenuations are plotted for observation times (d) of ( + ) 1 ms, (A ) 4 ms,(O)Smsand(O)6ms.

value of 2.3~ 1O-9 m’s_’ for the self-diffusion coefficient of water. Consider next the PFG NMR experiment on the smaller crystallites of .41P04-5 obtained by grinding the larger ones. From Fig. lb it is apparent that the ground crystallites are of the order of 1 pm in lateral dimension. If the diffusivity is 2.9~ 10e9 m* s-’ in the crystal, then during a millisecond the root mean square displacement (J2Dd) of a methane molecule is on the order of a couple of microns. Thus, if spinecho attenuation is observed during 1 ms, we expect

S.S. Nivarthr et al. I Chewucal Physics Letters 229 (1994) 297-301

300

the methane molecules to spend some time outside the crystallites, where diffusion is isotropic and the diffusivity is high. This hypothesis is tested in Fig. 4. Aside from a couple of points near the origin, the data tit the isotropic diffusion expression, Eq. (3), very well with a diffusion coefficient D= 1.3~ 10u6 m* s- ‘, more than two orders of magnitude higher than the diffusion coefftcient in the large crystallites. Note the change of scale necessary to display the data for the case of higher diffusivity. The comparison between the results on the large and small AlPOdcrystallites demonstrates how critical it is to have sufficiently large crystals in an NMR diffusion measurement to measure the intracrystalline diffusivity. When the root mean square displacement of the sorbates is greater than the mean crystallite radius, Karger et al. [ 16,171 have shown that the diffusivity is described by 4, = ,%nte$)inter + ( 1- %rcr)Dintra x

(4)

where D,, is the ‘long-range’ diffusivity, J)inter the diffusivity in the intercrystalline space, Dintra is the intracrystalline diffusion coefficient and ~Z,,,, is the fraction of the moIecules in the intercrystalline space. The terms in Eq. (4) can be estimated following the procedure of Karger and Volkmer [ 16 ] . D,, is the diffusivity measured for the smaller AlPOd- crystallites, which is 1.3~ 10m6 m” s-l. For methane in AlPOd-5, Qntra is 2.9x low9 m2 s-l. The quantity from the adsorption iso%“I,, can be determined -1

therm. In an independent adsorption experiment, the gas pressure in equilibrium with the sorbate concentration was determined to be 140 Torr. Assuming the intercrystalline void fraction to be 0.5, $“ter was calculated to be 0.07. The intercrystalline diffusion coefficient, assuming Knudsen diffusion, can be estimated from the expression [ 161 &ter zfud,,

(5)

where u is the mean velocity of the sorbate molecules and dk is the effective intercrystalline pore diameter. Here, u=,,/w, where k is Boltzmann’s constant, Tis the absolute temperature and m is the mass of the sorbate molecule. Assuming dk to be of the order of 0.1 urn, Dinter is z 2.1 x 10M5 m2 s-’ at 300 K for methane. The rhs of Eq. (4) is equal to 1.5 X 10d6 m* s- ‘, Considering the approximations involved in calculating the quantities in Eq. (4), the agreement between the measured and the computed values of diffusivity is remarkable, and shows that the model proposed by Karger and Volkmer is valid.

Acknowledgement This work was supported by a grant from the Dow Chemical Company and by an NSF-PYI grant (CTS9058387). The authors would like to thank Dr. Michael J. Annen (PPG Industries) for helpful discussions and Dr. Juan M. Garces and Dr. Michael M. Olken (Dow Chemical Company). We also thank Professor M.E. Davis (Caltech) and Dr. D. Young (University of Toronto) for providing the AlPOdsamples.

References \

I

\ i

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[ 1 ] J. Karger and D.M. Ruthven, Zeolites 9 (1989) 267. [ 21J. Karger and D.M. Ruthven, Diffusion in zeolites and other microporous solids (Wiley-Interscience, New York, 1992).

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0.02 0.03 0.04 y2G2s2d x lo-*, s mw2

0.01

0.05

Fig. 4. ‘H NMR spin-echo attenuation (A) of methane in the small AlPO,-5 crystals plotted versus y2G%12d.Note the change in scale in comparison to Fig. 2. The data are for an observation time (d) of I ms. Also plotted is the least-squares best Iit to the linear portion of the data using Eq. (2).

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