129Xe and 13C PFG n.m.r. study of the intracrystalline self-diffusion of Xe, CO2, and CO

129Xeand 13C PFG n.m.r, study of the intracrystalline self-diffusion of Xe, COz, and CO j. I~rger, H. Pfeifer, and F. Stallmach Fachbereich Physik der Universitiit Leipzig, Leipzig, Germany N.N. Feoktistova and S.P. Zhdanov Academy of Sciences, Grebenshchicov Institute, Sankt Peterburg, Russia Using 129Xeand ~3C PFG n.m.r., the temperature dependence of the coefficients of self-diffusion of xenon, carbon monoxide, and carbon dioxide in zeolites X, NaCaA, and ZSM-5 (silicalite) are studied. In all cases, the measured diffusivities are found to follow an Arrhenius dependence. The determined activation energies and preexponential factors may be rationalized by relating specific properties of the sorbate gases (kinetic diameter, permanent electrostatic moments) to those of the considered zeolites (free diameter of the pores, cation content). Keywords: Pulsed-fieldgradient (PFG) n.m.r.; intracrystalline self-diffusion, NaX; NaCaA; ZSM-5

INTRODUCTION Pulsed-field gradient (PFG) n.m.r.>'4 proved to be a versatile tool for studying molecular mass transfer phenomena in zeolitic adsorbent-adsorbate systems. In particular, it allows the direct measurement of the translational molecular mobility in the interior of the crystallites represented by the self-diffusion coefficient D. So far, as a consequence of the favorable measuring conditions, such investigations have nearly exclusively been carried out using ~H n.m.r, with hydrocarbons as probe molecules. Recent progress in the experimental technique of PFG n.m.r, 2 has enabled PFG n.m.r, self-diffusion studies in zeolites using 129Xe5'6 and 13C,7 which as yet, however, were confined to room temperature. In the present contribution, first measurements of the temperature d e p e n d e n c e of the self-diffusion coefficients of xenon, carbon dioxide, and carbon monoxide in zeolites NaX, NaCaA, and silicalite are presented.

EXPERIMENTAL The self-diffusion measurements have been carried out by means of the home-built PFG n.m.r, spectrometer UDRIS, operating at resonance frequencies of 24.9 and 22.6 MHz for 129Xe and 1~C, respectively. Applying magnetic field gradient pulses after either of the two r.f. pulses of a Jt/2-x-~ pulse sequence, the Address reprint requests to Dr. K~rger at the Fachbereich Physik der UniversitSt Leipzig, D-0-7010 Leipzig, Germany. Received 16 March 1992; accepted 22 June 1992 © 1993 Butterworth-Heinemann

50

ZEOLITE& 1993, Vol 13, January

observed n.m.r, signal (the "spin echo"), appearing at t = 2z, is attenuated by3: (g6,A) = exp (-g282g ~
(1)

where 8 and g denote the duration and the amplitude of the magnetic field gradient pulses, respectively. is the mean-square displacement of particles sorbed, carrying the magnetic moment under consideration, during the time A between the two field gradient pulses. According to Einstein's equation: = 6DA can be easily transferred

(2)

to the selfdiffusion coefficient D. In the case of silicalite, as a consequence of diffusion anisotropy, 2,s the correct dependence of the spin-echo attenuation vs. the gradient intensity deviates from the pattern provided by Equation (1). However, this deviation only becomes apparent by following echo attenuations over more than one to two orders of magnitude, while less intense attenuations are sufficiently well approximated by Equations (1) and (2), with D = 1/a (Dx + Dy + Dz) denoting the mean of the diffusivities in the three principal directions. In the present case, such measurements were prevented by the limited signal-to-noise ratio. Due also to the same reason, a measurement with oriented zeolite crystallites as realized in Ref. 9 was excluded. Hence, in contrast to the most recent PFG n.m.r. measurements of methane self-diffusion, 9'1° it was

Intracrystalline self-diffusion of Xe, C02, and CO: J. K~rger et al. Table I Comparison of literature data for experimentally determined heats of adsorption for the investigated adsorbateadsorbent systems Heats of adsorption (kJ/mol) Adsorbent Adsorbate

NaCaA

NaX

ZSM-5

Xenon Carbon dioxide Carbon monoxide

22.517 40.020

26.6TM 24.022

Methane

21.720

21.7TM 51.021 23.620 17.620

20.023

only possible to measure the mean diffusivity D = 1/3 (Dx + Dy + Dz) rather than the diffusivities in the different crystal directions. In comparison to XH n.m.r., the signal intensity in 13C and 129Xe n.m.r, is reduced by at least two orders of magnitude, 11 so that signal accumulation is inevitable. In the present study, for a single point in the In vs. 82 representation using 129Xe PFG n.m.r., up to 500 scans were necessary to achieve a sufficiently high signal-to-noise ratio. In the case of 13C PFG n.m.r., a smaller amount of scans (up to 200) was sufficient, since the sorbate gases CO2 and CO were enriched with lac by 50 and 90%, respectively, while the xenon was applied with natural abundance of 129Xe (26%). The necessary adjustment and the stability 7A2 of the field gradient pulses for all combinations of g, 8, and A used in the measurements have been ensured in a preparatory experiment with a sample of water using XH PFG n.m.r, at 24.9 MHz after a corresponding reduction of the intensity of the magnetic field. In c o n t r a s t to the first 12°Xe PFG n.m.r. measurements, 5 we have improved the accuracy of the adjustment of the two field gradient pulses by using a more sensitive matching potentiometer. 2 This turned out to be of special importance if pulsed-field gradients with extremely large intensities have to be applied in order to measure slow diffusivities. As a consequence, some of the values published in the former paper 5 (in particular, for xenon in NaCaA) have to be revised (see below, Figure 4). Since the intracrystalline self-diffusion coefficients D can only be determined if the mean displacement of the observed particles is less than the diameter d of the zeolite crystallites, large laboratory-synthesized crystallites of NaX (d = 50 ~tm), Na63%CaA (d = 15 l~m), and silicalite (100 x 30 x 30 ~tm3) have been u s e d . 13,14

The PFG n.m.r, sample tubes were prepared in the following way: For sample activation, the zeolite material (about 300 mg) was spread over the bottom of a small flask of about 50 mm diameter, whose upper part tapered off to a glass tube of 8 mm diameter. There, the zeolite material was heated at a rate of 10 K/h under continuous pumping (shallowbed conditions 15) up to a final temperature of 400°C. The system was kept for 20 h at this temperature. During this time, the pressure was less than 0.1 Pa. Subsequently, the sorbate gas was introduced into the zeolite by freezing from a fixed volume. The upper

end of the glass tube was sealed and the adsorption vessel (i.e., the flask with the glass tube at its upper end) was separated from the vacuum device. By turning the whole system, the zeolite material was run down from the flask into the glass tube to a final filling height of about 20 mm. Finally, the glass tube containing the a d s o r b a t e - a d s o r b e n t system was sealed at the other end and separated from the flask. In all cases, the sorbate concentration was chosen to be 3--4 atoms or molecules per 24 (Si + A1) atoms corresponding to one large cavity of the zeolites X and A and one channel intersection for silicalite. The achieved loading was checked both gravimetrically and by comparing the intensities of the n.m.r, signal following the first ~/2 pulse (free-induction decay). We had to confine ourselves to this single value for the sorbate concentration, since in view of the large accumulation numbers, a variation of the sorbate concentration (which meanwhile has become common practice in 1H PFG n.m.r.) would have led to an intolerable enlargement of the measuring time. During the PFG n.m.r, measurements, the samples were temperature-controlled by a stream of nitrogen issuing from a bath of liquid nitrogen for temperatures below room temperature (down to -120°C) and by a heated air stream for temperatures above room temperature (+200°C). The accuracy of the temperature adjustment was better than +2 K. However, in some cases, the temperature range of the measurements was reduced: at low temperatures, when the diffusivity dropped below the lower limit of measurability ( 1 0 - I 1 . • • 10 -1° m 2 s-l), and at high temperatures, as a consequence of the decrease of the n.m.r. signal intensity due to the Curie law. Desorption from the adsorbed phase into the gas phase within the sample volume, which would lead to the same effect (and, moreover, to a decrease of the zeolite loading; see, e.g., the considerations on this topic in Ref. 16 for methane in NaCaA), turned out to be of less importance. This may be explained by the small available gas volume (< 2 cm 3) within the sealed sample tubes as realized in these experiments and the larger values for the heats of adsorption (see Table 1).

RESULTS Following Equations (1) and (2), the intracrystalline self-diffusion coefficients have been determined from the slope of the semilogarithmic plot of the attenuation • of the PFG n.m.r, signal intensity vs. the square of the width 8 of the magnetic field gradient pulses. In all cases, the obtained root mean square displacements were at least by a factor of two smaller than the crystallite diameters, so that any ambiguity in the obtained values for the intracrystalline diffusivities due to the influence of the crystallite boundary could be excluded. 1'a-6'24 Figures 1, 2, and 3 show the Arrhenius plots of the self-diffusion coefficients of Xe, CO2, and CO in NaX, silicalite, and Na63%CaA, respectively. As in previous PFG n.m.r, diffusion studies of n-paraffins and water adsorbed on the same zeolites, 16.'25--27 ' the

ZEOLITES, 1993, Vol 13, January 51

Intracrystalline self-diffusion of Xe, C02, and CO: J. K~rger et al.

tl 200

100

e r m o r e , it contains the values o f the kinetic diameters 2s of the adsorbed particles (as a measure of their geometrical size) and their permanent electrostatic moments 29 as well as the free diameters of the zeolite frameworks.

°C

0

-50

-100

I

I

NaX

16

,

DISCUSSION Activation energy In zeolite NaX (Figure i), the activation energy of CO and CO2 is found to be significantly above the corresponding value for xenon. The difference of about 3-4 kJ/mol between the inert xenon, on the one hand, and the carbon oxides, on the other hand, can be explained by the additional interaction of the permanent electrostatic dipole or quadrupole moment of the carbon oxides with the accessible Na + ions in the supercages of NaX. ~° The values for the activation energy of CO and CO2 coincide within the experimental error. This indicates that the interactions of the quadrupole moment of CO2 and of the dipole moment of CO with the Na + ions are of similar

Xe

"7

¢/)

04

E

"9

~10

co

\

a

-10

10

co

t/

2

200 I '

2

3

4

5

100

0

I

I

°C -50

I

6

Silicalite

-8

103K/T

-100

10 CO

Figure 1 Arrhenius plot of the intracrystalline self-diffusion coefficient D of (1") xenon, (11) carbon dioxide, and (O) carbon

monoxide in zeolite NaX.

diffusivities are found to follow the simple exponential dependence: D = Do exp (-R--F~T)

(3)

with Do and E denoting the preexponential factor and the activation energy of the self-diffusion, respectively. E is a measure of the energetic barriers that the molecules have to overcome on their diffusion path in the intracrystalline space. U n d e r the influence of extraframework cations, the electrostatic properties of the adsorbed particles will be of particular influence on the magnitude of the activation energy. Do is the self-diffusivity that would be attained at infinitely high temperatures, i.e., under conditions where energetical influences are of no influence any longer and the diffusivity is exclusively determined by the geometrical restriction of the adsorbed particles within the zeolite. Table 2 summarizes the experimental data for the activation energies and the preexponential factors for all investigated adsorbate-adsorbent systems. Furth-

52

ZEOLITES, 1993, Vol 13, January

E3

-10

10 I

2

,

I

3

l

I

4

,

I

5

,

I

6

103KIT Figure 2 Arrhenius plot of the intracrystalline self-diffusion coefficient D of (1") xenon, (11) carbon dioxide, and (0) carbon

monoxide in silicalite.

Intracrystalline self-diffusion of Xe, C02, and CO: J. KMger et al.

tloC -8 10

~0 I

1~

0

I

I

'

-~

5 kJ/mol is only slightly below the activation energy of Xe in NaX. The values of the activation energy of CO and CO2 in NaX and NaCaA are nearly equal and comparable with that of xenon in NaCaA, whereas for xenon in NaX, a smaller value results (Figure 3). Since the values of the diameter of xenon atoms are quite close to those for the supercages in zeolite NaCaA, it may be possible that a steric hindrance for xenon atoms on passing the windows between adjacent supercages leads to an enhancement of the activation energy, which (more or less incidentally) compensates the contribution due to the electrostatic interaction of the carbon oxides. It is remarkable that this interpretation of the activation energies is in agreement with the results of previous 1H PFG n.m.r, studies of methane, yielding values of E ~ 7 kJ/mol, 25 ~ 4 kJ/mol, 26 and ~ 8 kJ/mo116 for NaX, silicalite, and NaCaA, respectively. These activation energies coincide with those of xenon in the corresponding zeolites, indicating a similar behavior of both adsorbates within these frameworks. For xenon in silicalite, it was already noted in Ref. 5 that the 129Xe PFG n.m.r, and molecular dynamics (MD) calculationsal yield quite similar results with respect to both the absolute values of the selfdiffusion coefficients at room temperature and their concentration dependence. Now it turns out also that the activation energies (EMD = 4.7 . . . 6.2 kJ/mol, depending on the direction of the self-diffusion with respect to the orientation of the silicalite crystalal) for both methods agree quite well with each other. All values for the activation energy of the intracrystalline self-diffusion (Table 2) are found to be much smaller than the heats of adsorption (Table I). This is in agreement with previous experimental studies 16,25,32,33 and a simple consequence of the fact that the differences in the potential energies, which the molecules have to overcome during the process of intracrystalline diffusion, are, in general, considerably smaller than the difference between the intracrystalline space and the gas phase. Since the activation energy of intracrystalline self-diffusion and the heat of adsorption refer to differences in the potential energy between quite different states, there is also no necessi-

-1~ I

Na63%CaA

"7,(/}

169

E E3

1l~1°

I

I

2

I

3

I

I

I

4

I

5

,

I

6

103KIT Figure 3 Arrhenius plot of the intracrystalline self-diffusion coefficient D of (f) xenon, (B) carbon dioxide, and (0) carbon monoxide in zeolite N a 6 3 % C a A .

influence upon the energetic barriers controlling the intracrystalline diffusion. In the cation-free zeolite framework of silicalite, the electrostatic moments of the adsorbed particles should be of minor influence. The experimental results show, in fact, for xenon and both CO2 and CO (Figure 2) no significant differences in the values of the activation energy. Its mean value of about

Table 2 Values for the activation energy and preexponential factor of the intracrystalline self-diffusion of xenon, CO2, and CO in zeolites NaX, silicalite, and NaCaA Adsorbent: Limiting free diameter: Accessible cations: Adsorbate

Kinetic diameter (nm)

C02

0.49 0.46

CO

0.38

Xe

Permanent electrostatic moment

Quadrupole Q/e = - 4 . 3 x 10 -30 m 2 Dipole 1 ~ = 3 . 6 × 10 - 3 1 c m

NaX 0.75 nm Na*

Silicalite 0.55 nm None

Na63%CaA 0.4-0.5 nm Na+/Ca 2÷

Do x 10 e

E

Do x 10 e

E

Do x 108

E

(m 2 s -1)

(kJ mo1-1)

(m 2 s -1)

(kJ mo1-1)

(m 2 s -1)

(kJ mo1-1)

8_+3 15 -+ 4

6_+ 1.5 10 _+ 2

0.9_+0.2 1.7 _+ 0.7

5-+ 1 4.5 _+ 1

0.9-+0.3 1.5 -+ 0.8

8-+3 9 _+ 3

25_+8

9+__2

8_+3

8_+3

9-+2

5+

1

ZEOLITES, 1993, Vol 13, January

53

Intracrystalline self-diffusion of Xe, C02, and CO: J. K~rger et al. 2

between zeolite X and silicalite, which may indicate that the differences in the free diameters of the pores as "seen" by the diffusing particles are less pronounced. Again, as with the activation energies, the preexponential factors for xenon in the three adsorbents may be as well correlated with those of methane (Do 35 x 10-8m2/s [Ref. 25] in NaX, Do ~- 6 x 10 -s m2/s [Ref. 26] in silicalite, and Do = 2 x 10 -8 m2/s [Ref. 16] in NaCaA). The decrease of these values for xenon in comparison with methane may be considered as a consequence of the larger kinetic diameter of the xenon atoms.

b

10 -e 4 2

10 .9 4

.~

10

=L

4

=

oo

E

2

10 "~1 2

a"

•

, <>

z

o~,\

\

4

10"12

o~,\

4 2

Comparison with literature data Figure 4 provides a comparison of the diffusivity

16 TM 4 2

10"1. 4 2-

10-15 2

\ I

I

3

4

I

5

I

I

I

I

I

6

3

4

5

6

7

3

10 K / T Figure 4 Comparison of the presented PFG n.m.r, diffusivities for xenon in NaCaA (a, solid symbols) and silicalite (b, empty symbols) with literature data: (B) PFG n.m.r. (present study, 3-4 atoms per cavity); ( 0 ) PFG n.m.r. (preliminary value, communicated in Ref. 5, 3 atoms per large cavity); (0) uptake measurements (Ref. 34, about 1 atom per large cavity); ( I ) Monte Carlo calculations (Ref. 35, about 1 atom per large cavity) (x) uptake measurements (Ref. 17, about 4 atoms per large cavity; these low values are most likely due to the finite rate of heat dissipation, see Ref. 36); (r-i) PFG n.m.r. (present study, 3-4 atoms per intersection); (~1) molecular dynamics calculations (Ref. 31, 1 atom per intersection); ( A , O ) frequency response measurements (Ref. 37, at 0°C about 0.2-0.5 atoms and at -80°C about 2.5 atoms per intersection); (©) uptake measurements (Ref. 19, about 0.1-1.5 atoms per intersection).

ty of a close correlation between these values. This may be illustrated, e.g., by a comparison between the carbon oxides in NaX, where the activation energies of self-diffusion are nearly the same, while the heats of adsorption differ by a factor of about two.

Preexponential factor The effect of steric restriction in the process of molecular migration is reflected by the preexponential factor. Correspondingly, in all considered adsorbents, the highest Do values have been observed with carbon monoxide, which is the smallest molecule used in these investigations (Table 1). With increasing values for the kinetic diameter of the adsorbed particles, the preexponential factors decrease in all cases, indicating an increasing geometrical restriction of the self-diffusion. Following this concept, for a given sorbate gas, one may likewise rationalize the decreasing Do values with decreasing values of the free diameter of the pores (zeolite X > silicalite > zeolite A). The differences in the preexponential factors between silicalite and zeolite A are smaller than

54

ZEOLITES, 1993, Vol 13, January

data for xenon in silicalite and. NaCaA of the present study with the literature data, where the transport diffusivities Dt as determined in nonequilibrium measurements (uptake, frequency response) have been transferred into "corrected" transport diffusivities Dt.... by the relation: Dt.... = Dt d ln______~c

dlnp

(4)

with c(p) denoting the sorbate concentration in equilibrium with the sorbate pressure p. For a variety of microdynamic models, the "corrected" transport diffusivity may be expected to coincide with the self-diffusion coefficient.38 It becomes apparent that there is an excellent agreement for silicalite with the MD calculations by Pickett et al. 31 and with frequency response measurements (data at 0°C) by Rees and Shen. 37 The frequency response data at -80°C as well as uptake measurements by Billow et al., 30 however, yield substantially lower values. Moreover, the activation energy of the diffusivities as obtained in Ref. 19 (15 kJ/mol) are much larger than the corresponding n.m.r, data (see Table 2). These uptake measurements have been carried out at lower sorbate concentration covering a range from about 0.1 to 1.5 atoms per intersection. In this concentration range, the diffusivities were found to be essentially independent of concentration. In agreement with previous studies of methane in silicalite,26 for further increasing concentrations, the diffusivities were found to decrease. Considering such a concentration dependence, the difference between the quoted uptake data z9 and the PFG n.m.r. data would become even larger. It is obvious that this discrepancy cannot be simply explained by the difference between equilibrium and n o n e q u i l i b r i u m m e a s u r e m e n t s , since besides c o n t r a d i c t o r y results ~2'3~ (e.g., for the larger n-paraffins in zeolite NaX and silicalite and for benzene in NaX), there are also several examples of satisfactory agreement between PFG n.m.r. (i.e., equilibrium) and sorption (i.e., nonequilibrium) measurements (as in the present case on comparing the PFG n.m.r, and frequency r e s p o n s e data ~7 at O°C or for n - p a r a f f i n s in -16 32 NaCaA ' and neopentane in NaX 3 9 ).- - Another ex-

Intracrystalline self-diffusion of Xe, COz, and CO: J. K~rger et al.

ample for contradictory results o f PFG n.m.r, and uptake m e a s u r e m e n t s is f o u n d in this study for CO2 a d s o r b e d on zeolite NaCaA, for which the uptake m e a s u r e m e n t s (preexponential factor o f 1.8 × 10 l° m2/s, 40 to be c o m p a r e d with 1.5 × 10 -8 m2/s o f this study, see Table 2) yielded diffusivities o f 1-2 o r d e r s o f m a g n i t u d e below the n.m.r, data. T h e origin o f these differences is still unclear, and its clarification is one o f the c u r r e n t problems in zeolite research. 38 I n c l u d e d as well in Figure 4 are the results o f earlier u p t a k e m e a s u r e m e n t s and o f calculations o f the intracrystalline self-diffusion o f x e n o n in NaCaA. With respect to the very first uptake m e a s u r e m e n t s 36 with small commercial crystallites, which exhibited a difference u p to 5 o r d e r s o f m a g n i t u d e to the n.m.r. data, the differences o f these m e a s u r e m e n t s are not so dramatic. It has been f o u n d , however, that in these cases the differences are probably d u e to the influence o f the finite rate o f sorption heat dissipation, which leads to e r r o n e o u s l y low diffusivities and which is most stringent for high diffusivities and small zeolite crystallites. ~6 It is probably also this influence that explains the lower diffusivities d e t e r m i n e d in Ref. 34. However, in m o r e recent u p t a k e measurements, this source o f e r r o r has generally been excluded.

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