Colloids and Surfaces, 36 (1989) 209-219 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

209

The Diffusion of Benzene in High Silica Zeolite ZSM5 Studied by PFGNMR and QUENS

MARK MORGAN, TERENCE COSGROVE* and ROBERT RICHARDSON

School of Chemistry, University of Bristol, Bristol BS8 1 TS (United Kingdom)

(Received 3 August 1988; accepted 22 August 1988)

ABSTRACT

The diffusion of benzene in the high silica zeolite ZSM5 has been studied at various coverages by pulsed field gradient nuclear magnetic resonance (PFGNMR) and quasi-elastic neutron scat- tering (QUENS ) .

The PFGNMR technique has probed inter- and intra-crystalline diffusion over the millisecond timescale giving intra coefficients of the order lO_” m2 s-l and inter coefficients in the range from lo-’ to lo-’ m2 s-l with increasing coverage. This suggests a ‘viscous’ liquid-like environ- ment inside the zeolite but rather faster diffusion between crystallites.

QUENS has probed intra-crystalline diffusion on the nanosecond timescale giving results in the range lo-‘” to 10m9 m2 s-l at high coverages. A jump activation energy for this process of 5.0 + 0.4 kJ mol-’ has been estimated over the temperature range of 213 to 343 K.

INTRODUCTION

In previous studies of sorbed species in zeolite ZSM5 by pulsed field gradient NMR (PFGNMR), the molecules studied have had typical dimensions less than that of the ZSM5 channels. These have included paraffins, water [ 11 and methanol [ 21. In this study we report results for benzene (diameter = 0.56 nm) which has molecular dimensions, close to those of the zeolite near circular (0.54 x 0.56 nm) and elliptical (0.51 x 0.55 nm) channels. Over the millisecond timescale of the NMR experiment sorbed molecules can exchange between the inter- and intra-crystalline environments and the calculation of characteristic diffusion coefficients requires a model [ 31. The diffusion in these systems var- ies from very fast 2 lo-’ m2 s-l in the case of water due to the hydrophobicity of the zeolite to very slow ( z lo-” m2 s-l) in the case of methanol which has very specific interactions with adsorption sites in the zeolite. The slow intra- crystalline diffusion of methanol has been confirmed using quasi-elastic neu- tron scattering (QUENS) [ 41 which probes diffusion on the nanosecond time-

*To whom correspondence should be addressed.

0166-6622/89/$03.50 0 1989 Elsevier Science Publishers B.V.

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scale such that there is very little or no exchange during the scattering event. Also, the molecules are restricted to one or more molecular jumps in this time hence only intra-crystalline diffusion in the unit cell is observed. The motion in the unit cell over this timescale cell may also be complex and may require a more complex analysis to extract the diffusion coefficients.

Several ZSM5 systems have been studied using adsorption uptake methods [ 51. In contrast to the PFGNMR and QUENS techniques, sorption studies do not determine the diffusion coefficients under equilibrium conditions. Hence a direct comparison of diffusion coefficients as described by Bulow et al. [6] requires the use of a thermodynamic approach in the limit when adsorption is considered an isothermal process.

EXPERIMENTAL

PFGNMR

The zeolite ZSM5 used was synthesized by ICI and had a crystallite diameter of 1.0 2 0.25 pm and a Si/Al ratio of 8OO:l. The NMR samples were prepared by outgassing the zeolite for 24 h at 550 K. The benzene was subsequently adsorbed from the gas phase at the appropriate pressure.

The PFGNMR experiments were carried out on a homemade spectrometer and pulse programmer [ 71 controlled by a PDP11/23 minicomputer. The probe was of single coil design incorporating quadrupolar field gradient coils [8], driven by a current stabilized pulse generator, delivering 100 A at 90 V. The standard Stejskal and Tanner spin-echo diffusion sequence [9 ] was used, but with very short diffusion times = 1 ms. Under these circumstances incomplete spin echoes are formed and in order to maximize sensitivity and also to avoid the necessity for phase correction, the partial echoes were reconstructed using an algorithm previously described [lo]. The resultant complete echo was Fourier transformed and integrated. The general form of the spin echo atten- uation function is as follows:

A(6) = A(G=O)exp( -y262G2D[d-d/3])exp( -2r/T,) (1)

where y is the nuclear magnetogyric ratio, G is the field gradient, d is the dif- fusion time, 6 is the gradient pulse duration, D is the diffusion coefficient, z is the 90,-180, pulse interval and T, is the spin-spin relaxation time.

In a multiphase system, the attenuation function is complex and various models have been proposed to extract diffusion coefficients from the experi- mental data. In the slow exchange limit, where there is no exchange between phases on the NMR timescale, the attenuation function may be represented by a sum of individual attenuations [ 111.

A(6) = ~A(G=O)iexp(--y2G2620id) (2) i

In the intermediate-fast exchange regime Karger et al. [ 31 have proposed a model in which it is assumed that one of the environments contains a relatively small quantity of diffusing material and has a very efficient diffusion mecha- nism, then the form of the attenuation is as follows:

A(6) = A(6=O)exp{--2G262d[Da+ (p,D,/(1+y2G26’~~p,D,))]} (3)

where D, is the intra-diffusion coefficient, D, is the inter-diffusion coefficient, ta is the average residence time in the intra-phase and pe is mole fraction of inter-phase material.

An alternative and rather informative way to analyze these results is to cal- culate explicitly the time-space correlation function directly from the observed attenuation function. This so-called average propagator, P(r,d) [ 121, can be obtained from interpolation and Fourier transformation of the attenuation function. An estimate of an effective diffusion coefficient can be then calcu- lated as follows assuming an average distance travelled ( r”) :

(r2) = Ir’P(r,d)dr (4)

(r2) = 2Dt

QUENS

The same zeolite was used for both the PFGNMR and QUENS experiments. An aluminium sample cell was designed and built at the Rutherford Appleton Laboratory (RAL), and is shown in Fig. 1. The cell had a path length of 2 mm which optimized the neutron transmission of the sample. The cell was filled with ZSM5 and attached to a vacuum line and outgassed for 24 h at 550 K. Benzene was then adsorbed to the desired coverage from the vapour phase in a similar manner to the NMR samples. Two samples were prepared, one with benzene, at a coverage of 0.07 g/g and one without (background). The exper- iments were run on the IRIS high resolution inelastic spectrometer on ISIS at RAL. The spectrometer was set up in pyrolytic graphite mode with the chopper phased to utilize the 002 graphite planes. These planes reflect neutrons with the lowest energy bandwidth and highest energy thus giving the instrument its maximum resolution of 15 ,ueV [ 131.

Neutron time of flight spectra were collected for the background and the sample at various temperatures (213 to 343 K) from scattering angles 2$ = 40-130’. Seventy spectra were collected in all and summed.

The entire experiment was controlled by a VAX 730 minicomputer. The time of flight spectra incident neutron flux, detector efficiency and converted to energy transfer spectra for analysis, using standard analysis programs.

For isotropic diffusion, the Vineyard equation [ 141 predicts the form of the incoherent scattering broadening function.

NEUTRON SAMPLE CELL

G32

Fig. 1. Neutron scattering cell.

XrYs(Q,o) = (l/n) (DQ”)/W+ [D&T) (5)

where D is the translational diffusion coefficient, Q is the scattering vector, tiw is the energy transfer on scattering. The broadening is thus a simple Loren- tzian function for all values of Q. However in a complex system, such as the intra-crystalline motion in zeolites, a more detailed model may be required. Jobic and Renouprez have suggested the use of the following scattering func- tion due to Chudley and Elliott [ 1516 J.

%Y”(Q,~) = (l/n) [J’(Q) I/b”+J’~Q)“l (6)

where F(Q) has to be evaluated for different jump models. This model was not used as the resolution of the IRIS instrument was not good enough to warrant it.

The data was analyzed using a computer program which deconvoluted the broadening function from the data and background functions [ 171. For a fixed temperature the spectra have been analyzed individually to produce diffusion coefficients as a function of scattering vector and temperature, using Eqn (5). Alternatively, the complete Q data set can be analyzed simultaneously assum- ing that D is independent of Q. The ratio of the elastic intensity from the zeolite to the quasi-elastic intensity from benzene was independent of the scattering vector, confirming the model of translational diffusion for benzene [ 181.

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RESULTS AND DISCUSSION

The adsorption isotherm for benzene on ZSM5 is shown in Fig. 2. The iso- therm rises smoothly to the plateau level. The interaction of the benzene with the zeolite cage in this instance is dominated by the benzene-proton interac- tions and no evidence of heterogeneous adsorption sites is seen.

Figure 3 shows typical spin-echo attenuation plots for two coverages (0.04

g/g, % 1 molecule/unit cell; 0.11 g/g, = 4 molecules/unit cell) [ 191 and three different diffusion times (0.8,5.4 and 9.0 ms ) . The functions decay initially as in Eqn (l), i.e. single component isotropic diffusion. However, there are long tails observed in each set of data.

Figure 4 shows a standard ‘H-NMR spectrum for the low coverage sample revealing at least two discernible populations. It is reasonable to assume that the broad component arises from benzene moving slowly in a restricted envi- ronment, i.e. inside the zeolite. Hence, with respect to the data sets in Fig. 3, the initial decay could result from inter-crystalline motion and the long tail from intra-crystalline motion.

r . . . .

.

f

: 0. 0 4. 0 8.0

Relative Pressure (P/Peat) x10-1

Fig. 2. Adsorption isotherm for benzene on ZSM5 at 298 K.

(b) 0 c)

A.. (a) c: . . . . .

6 . 6 2 ;m

. .

2” Yd- (u . k .=- :: -= _. . . < _ n =

:: . . . < _ . -... .

0 0 a 4. . . . o Cl 0.0 4. 0 8. 0 0.0 0. 8 1. 6

Gradlent Duration (s) /10e4 Gradient Ourotlon (s) /10m4

Fig. 3. (a) Attenuation plot for A = 0.8 ms, coverage = 0.04 g/g at 298 K. (b) Attenuation plot for A = 5.4 ms (m), A = 9.0 ms (A), coverage = 0.11 g/pat 298 K.

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Frequency (Hz) /lo5

Fig. 4. ‘H-NMR spectrum for benzene adsorbed on ZSMB, coverage = 0.04 g/g, at 298 K with double Lorentzian fit.

(a)

0 o o I 0.0 2. 4 4. 8 0.0 1. 0 2. 0

Gradxent Durot~onZ: W)/10-@ Gradient Duration2 (s2) /lo-'

Fig. 5. (a) d = 0.8 ms function with double exponential fit. (b) d = 5.4 ms function with double exponential fit.

TABLE 1

PFGNMR data

Coverage Diffusion time (ms)

Diffusion coefficients (m* s-r)

Slow model Fast model (10-9) (10-9)

Low” 0.8 (intra) 0.470 k 0.052 0.760 f 0.066 Low 0.8 (inter) 125.0? 15.5 151.0 + 25.0 Highb 5.4 (intra) 0.016 f 0.0022 0.033 k 0.0029 High 5.4 (inter) 5.090 + 0.530 6.930 + 0.623 High 9.0 (intra) 0.022 k 0.0028 0.044 f 0.0039 High 9.0 (inter) 2.600 k 0.310 5.400 + 0.590

“Coverage low = 0.04 g/g. “Coverage high = 0.11 g/g.

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Having established that there are two phases, the next question is one of the exchange rate between the two phases. As the two populations are separable on the NMR timescale ( z ms) the exchange of material may be regarded as slow.

There will of course be some material adsorbed on the outer surface of the crystallites, but this will be very small in comparison to the intra-phase ma- terial especially at low coverages.

The respective diffusion coefficients are extracted using a double exponen- tial fit [using Eqn (2) 1. The results are shown in Fig. 5.

The results for slow exchange are shown in Table 1 together with those ob- tained assuming intermediate-fast exchange [ Eqn (3) ] for comparison. Within experimental error it is difficult to distinguish between the two models though the slow exchange picture is favoured as discussed above.

Inter-diffusion

At low coverage the majority of the benzene molecules will be resident inside the zeolite crystallites. The remainder will therefore move in a low pressure regime, comprising the particle surface and the inter-crystalline voids, undergoing relatively few collisions. An estimate of the diffusion coefficient for the vapour phase can be made using Eqn (7) [ 201 for an ideal gas.

D,, = (2/3)(nd’p)-‘(k3T3/n~)“’ (7)

where d is the molecular diameter, m the molecular mass, k the Boltzmann’s constant, and T the absolute temperature.

For a pressure of z 10 Torr DgasN - 10e6 m2 s-l, hence the fast inter coeffi- cients obtained by PFGNMR would appear reasonable (Table 1) . However, it should be noted that systematic errors in the experiment may lead to a slight overestimate of the attenuation in this region. Figure 6 shows the propagator function (dotted line ) derived from Fig. 3a. The propagator decays rapidly at

k . ;o . y ci - a 0. 0 1. 0 “2.0

D~stonce travelled h,/lD -5

Fig. 6. Propagators for 0.04 g/g ( - * * * ) and 0.11 g/g (-).

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first and then rather slowly up to distances very much greater ( > 10 ym) than the average particle diameter. This is in line with the observed diffusion coefficients.

At higher coverage when the zeolite is full (over ~0.08 g/g) benzene will begin to fill the inter-crystalline voids. In this case a rather different propa- gator is seen, Fig. 6 (solid line). The function decays faster in this case indi- cating that material builds up at or near distances = 2 pm. In the inter-crys- talline voids one would expect the motion to be liquid-like with diffusion coefficients close to that for bulk liquid benzene (D = 1.33*10-’ m2 s-l). This is in fact the case as the diffusion coefficients obtained are only slightly larger than the bulk liquid value.

Intra-diffusion

At low coverage and slow exchange a simple restricted diffusion model has been employed to estimate diffusion coefficients in the NaX zeolite [ 211. This can be easily applied to the ZSM5 case as follows:

Dintra = (o/3 I( Vdm) “2ew ( - V,IkT) (8)

where a is the jump distance which in this case is given by an intersection- intersection jump ( = 1 nm), and V, is the diffusion potential energy barrier, 5.0 kJ mol-’ (obtained experimentally from QUENS, see later).

From this data a Dintra of 10-l’ m* s-l is found which is in reasonable agree- ment with the data in Table 1 obtained by PFGNMR. It should be noted, how- ever, that over the timescale of the PFGNMR experiment (d = 0.8 ms) the adsorbed molecules will undergo many such jumps. With increasing coverage the molecular jump distance should decrease and the potential barrier decrease effectively lowering Dintra. In the case of methanol in ZSM5 [ 21, Dintra varies by an order of magnitude between high and low coverage, and similar behav- iour with benzene is expected.

With regard to the high coverage sample, it can also been seen that there is little difference between diffusion coefficients measured at 5.4 and 9.0 ms (Ta- ble 1).

On the NMR diffusion timescale any intra-crystalline directional depen- dence of the diffusion coefficient is averaged out. However, Eckman and Vega [ 221 have probed benzene in ZSM5 at high coverage using 2H-NMR and have discovered two types of benzene intra-motion. (i ) Near isotropic motion of the benzene molecules involving reorientation of the molecule about its C, and C, axes in the intersections in order to travel down the different channels. (ii) A hindered “Cartwheel-like” motion in the channels involving rotation about the C, axis. This type of behaviour has been confirmed by the molecular simula- tions of Ramdas et al. [ 231.

This detailed intra-crystalline motion can be investigated with neutron scat- tering. The results of this investigation are shown in Tables 2 and 3 and Fig.

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TABLE 2

QUENS data single angle fits (coverage = 0.07 g/g)

Q (A-‘) Diffusion coefficient/ (lo-” m* s-‘)

0.848 20.02 +z 2.823 0.965 11.94k2.433 8.075 11.25 + 2.993 1.310 7.432 2 1.268 1.401 7.352 f 1.430 1.487 5.983 zb 1.135 1.565 2.238 + 0.355 1.630 2.970?0.311

298 K 253 K

12.87? 1.807 -

5.506 ?z 0.434 4.457 k 3.567 4.388 + 3.951 3.351+ 0.238 3.613 kO.412 2.378+ 0.138

233 K

11.432 1.590 8.214 50.610 4.646 + 0.322 4.220? 0.352 3.824 IO.263 2.953 2 0.164 2.057 k 0.103 2.196 kO.104

TABLE 3

Multiple angle fit

Temperature (K) Diffusion coefficient/ (lo-” m* s-l)

213 2.60 ? 0.33 233 2.77 + 0.41 253 3.18kO.54 298 3.95 i- 0.48 343 4.14*0.51 Activation energy = 5.0 + 0.4 kJ mol- ’

Fig. 7. Diffusion coefficient as a function of Q (A-‘) and T (K). (m) 298 K, (A ) 253 K, (0 ) 233 K.

7. The diffusion coefficients have been obtained from the linewidth of the quasi- elastic broadening function, shown in Fig. 8. The observed diffusion coeffi-

218

-1. 5 -0.15 1. 2

Fig. 8. (...I Raw data, (---) fitted function, (-_) scaled backgroundzeolite and (-.-) deconvoluted Lorenztian broadening function.

cients decrease with increasing scattering vector, and decreasing temperature by an order of magnitude. At low Q, the D values are of the order of bulk benzene. Using the Arrhenius equation a value of 5.OkO.4 kJ mol-’ can be obtained for the diffusion activation energy. The value is rather small suggest- ing that the barrier to diffusion is very low.

At a low Q (0.8 A-’ ), which corresponds to distance = 0.8 nm (i.e. approx- imately the intersection dimension) the molecule is moving in a relatively un- perturbed environment leading to a relatively high diffusion coefficient. At a higher Q of (1.63 A-‘), corresponding distance ~0.4 nm, the diffusion coef- ficients are smaller presumably due to hindered motion in the channels. These findings are consistent with the 2H-NMR data and the Ramdas model.

CONCLUSIONS

PFGNMR results for benzene in ZSM5 indicate that two different dynamic environments exist, with the possibility of exchanging populations. The ob- served diffusion coefficients are strongly dependent on coverage/partial pres- sure. QUENS data on the same system indicates a spatial dependence of dif- fusion with a small activation energy.

ACKNOWLEDGMENTS

M. Morgan acknowledges a CASE award provided by SERC and I.C.I. Pe- trochemicals. The authors wish to thank Dr Angus Hearmon and Dr David Johnson for their continued support and interest in this project.

Special thanks Laboratories.

REFERENCES

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go to Dr Colin Carlile and his team at the Rutherford

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