Investigation of Slow Molecular Motions and Chemical Exchange in

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J. Phys. Chem. B 2002, 106, 2261-2268

2261

Investigation of Slow Molecular Motions and Chemical Exchange in the High Loaded Form of p-Xylene in ZSM-5 by Two-Dimensional 13C Solid-State NMR Exchange Experiments C. A. Fyfe* and A. C. Diaz† Department of Chemistry, UniVersity of British Columbia, 2036 Main Mall, VancouVer, B.C., Canada V6T 1Z1 ReceiVed: July 26, 2001; In Final Form: December 17, 2001

The slow molecular motions and exchange processes in the high loaded form of p-xylene in zeolite ZSM-5 have been investigated by a variety of solid-state NMR techniques. The 13C CP MAS NMR spectra of [13C, CH3] p-xylene show four resonances in the slow exchange limit, reflecting the four inequivalent methyl positions in the two organic molecules in the asymmetric unit. From the known assignment of the silicon resonances in the MAS NMR spectrum, the four carbon signals were assigned from the cross-correlations in a 1H/13C/ 29Si 2D CP TEDOR experiment. Using this information, the chemical exchange processes between the methyls was invesitgated by a series of 2D CP NOESY experiments with different mixing times at different temperatures. Two types of processes were identified: intramolecular exchanges with activation energies of 65 ( 2 kJ/m for the molecule in the zigzag channel and 56 ( 13 kJ/m for the molecule in the straight channel (the substantial error in the latter value reflecting the very limited temperature range over which measurements can be made). There is also intermolecular exchange between the two molecules with a much higher energy barrier. Possible mechanisms for the exchanges and the implications of slow motional processes for the use of solid-state NMR for the determination of sorbate/framework structures are discussed.

Introduction Among the many zeolites known to date, zeolite ZSM-5 occupies a unique place because of its high catalytic activity and the extreme size and shape selectivity it displays toward organic molecules.1 These properties have been applied in various important industrial processes such as the conversion of methanol to high-quality gasoline, the synthesis of ethylbenzene, and the catalytic production of p-xylene for the polymer industry.2 The high catalytic selectivity of ZSM-5 is attributed to the unique topology and the dimensions of the inner channels and cavities in the open zeolite framework, which makes the penetration and diffusion of molecules selective according to their molecular shapes and sizes.3,4 High-resolution solid-state NMR spectroscopy has emerged as a complementary technique to X-ray diffraction methods for the investigation of the structures of molecular sieve systems.5 In the case of low Si/Al ratio materials, the spectra give insight into the local silicon environments, the distribution of Al over the T-sites, and the effects of chemical treatment, information not directly obtainable from diffraction measurements.6 More recently, the link between the two techniques has been further developed by the demonstration that two-dimensional COSY and INADEQUATE experiments may be used to reliably delineate the three-dimensional bonding connectivities (SiAO-SiB) within the framework.7 In cases where the structure is known, these experiments may be used to assign the resonances in the 29Si MAS spectrum to silicons at specific T-sites where this cannot be done from the relative intensities. Even very complex cases can be solved, for example, the monoclinic form of ZSM-5 where there are 24 T-sites, all of which are of equal occupancy.8 * To whom correspondence should be addressed. [email protected]. † Present address: Department of Analysis and Evaluation, PDVSAINTEVEP, P.O. Box 76343, Caracas 1070A, Venezuela.

Much of the interest in the structures of these materials derives from a desire to understand their molecular sieving characteristics, which are critical to their use as catalysts and sorbents. We have followed the structural changes in zeolite ZSM-5 with the adsorption of p-xylene by high-resolution 29Si NMR spectroscopy9-11 and have recently investigated the potential of the cross-polarization (CP) MAS NMR technique to define the three-dimensional geometric relationship between sorbed organic molecules and the molecular sieve framework. For the system of zeolite ZSM-5 with eight molecules of p-xylene per u.c. (orthorhombic form, P212121 symmetry),12 the solid-state deuterium NMR spectra of partially deuterated p-xylenes showed no evidence of diffusion or of free rotation of the organic guest molecules within the channels, the p-xylene molecules having rigid rings and rotating methyl groups at room temperature at sorbate loadings between 6 and 8 molecules. However, it was found that the detailed cross-polarization behavior could not be fitted exactly to the theoretical equations, suggesting, perhaps, the presence of some very slow molecular motions not detected on the time scale of the deuterium NMR experiments (τc ) 10-5 s). Because of the small dipolar couplings involved and the corresponding long contact times of up to 60 ms, very slow motions could have an appreciable effect on the fits, particularly for the eight molecule per u.c. loading. To investigate this further, we have applied 2D 13C NMR exchange spectroscopy to demonstrate that slow motional/ exchange processes do in fact occur and present a detailed description of these experiments. Neutron and X-ray diffraction investigations can give information on long range order for sorbate configurations.13-15 However, the observation of discrete atomic positions in diffraction experiments does not necessarily indicate the absence of molecular reorientations, as these are often between equivalent positions. Even where disorder is detected, it could be either static or dynamic in nature. Information on the dynamics of

10.1021/jp0129028 CCC: $22.00 © 2002 American Chemical Society Published on Web 02/06/2002

2262 J. Phys. Chem. B, Vol. 106, No. 9, 2002 local guest species is difficult or impossible to obtain from these methods because of their very fast time scales; i.e., they detect where most of the atoms are most of the time. Although deuterium NMR has often been used as a probe of dynamic processes, the motional frequencies necessary to affect the deuterium spectra are much greater than those that could affect CP, TEDOR, and other experiments where evolution times of several tens of milliseconds are involved and different experimental probes are needed. Pulsed field gradient NMR methods have been applied to measure long time motions such as large scale molecular self-diffusion (ca. 1 µm)16,17 and solidstate 2D deuterium exchange NMR spectroscopy has been successfully used by Spiess and co-workers for studying the reorientation mechanisms and time scales of slow motional processes in polymers.18-20 Very few applications of 2D exchange spectroscopy to zeolite systems have been published: however, in recent studies, 2D 129Xe exchange NMR on static samples has been used to measure the slow intercage migration of xenon atoms physically adsorbed in NaA zeolite, relying on the high mobility of the xenon atoms within the cages to produce narrow isotropic NMR lines.21,22 In addition, Chmelka and co-workers have reported 2D exchange 13C NMR spectra of adsorbed benzene molecules in a static sample of powdered Ca-Y. The benzene molecules bind to Ca2+ adsorption sites, and since the observed 13C NMR spectra depend on the orientation of the benzene molecules with respect to the external magnetic field B0, it is possible to observe molecular exchange between different benzene sites.23 The application of the 2D CPMAS NOESY technique to study exchange in solid-state systems was first proposed by Maciel and co-workers.24 This method is completely analogous to the two-dimensional experiment introduced by Ernst and coworkers to study chemical exchange and spin diffusion processes in the liquid state.25 In the present work, we describe for the first time the application of high-resolution 13C CPMAS 2D NMR exchange spectroscopy to the investigation of the motions and exchange phenomena of guest molecules inside zeolite catalysts and obtain kinetic information on these processes. Particularly important in the broader context of the present work, the method detects very slow motions that do not affect the wide-line deuterium NMR spectra but that can have important effects on techniques such as CP, REDOR,26 and TEDOR27 when they are used to determine internuclear distances. The implications of these findings for sorbate-zeolite framework structure determinations by solid-state NMR techniques are discussed. Experimental Section The highly siliceous sample of ZSM-5 was similar to those used previously for 29Si MAS NMR investigations.5-8 The equilibrated samples were prepared by adding exactly measured amounts of [13C,CH3] p-xylene to weighed amounts of ZSM-5 in glass vials and then sealing and heating at 80 °C for 8 h. All 13C CPMAS NMR experiments were carried out using a Bruker MSL 400 spectrometer and standard CPMAS probe. Typical 90° pulse times were 5 µs for 1H and 13C, and the 13C spectra were referenced to TMS using adamantane as an intermediate external reference standard. The magic angle was set using the 79Br spectrum of KBr and samples were spun at 3.0-3.5 kHz. The experiments at low temperatures were carried out using cold nitrogen as the bearing gas. As most of the experiments required maintaining a sample spinning for long periods at low temperatures, liquid nitrogen was used as the source of the bearing gas.

Fyfe and Diaz

Figure 1. (a) Pulse sequence for 2D exchange spectroscopy (2D CP NOESY experiment). (b) Pulse sequence for the two-dimensional heteronuclear correlation TEDOR experiment with preliminary evolution of I spin magnetization during the t1 time period, and detection of S spin magnetization during the t2 time period. Cross-polarization from protons to carbons is to take advantage of the favorable magnetization and relaxation properties of the proton nuclei.

The NOESY solid-state sequence is identical to that used in solution except that the first 90° pulse applied to the 13C spins in the liquid-state experiment is replaced by a CP sequence to make use of the favorable relaxation and sensitivity properties of the abundant nuclei (1H in this case) to generate observable magnetization in the less abundant spin system (13C in this case), as shown in Figure 1. The 2D NOESY experiments were carried out with proton decoupling during the mixing time to quench possible 13C13C spin diffusion via the proton nuclei. Because of the use of proton decoupling during the mixing times, the longest mixing time used was 120 ms. The TEDOR experiments were carried out at a temperature of 273 K using the pulse sequence illustrated in Figure 2 with TPPI,28 using a standard Bruker triple-tuned probe. The number of cycles before the transfer of coherence was n ) 22 and after the transfer was m ) 22, which were the optimal values (determined from previous one-dimensional CP TEDOR experiments) to obtain maximum signal intensity in the spectra. The sample was kept to a constant spinning speed of 2600 ( 5 Hz, and 1200 scans were accumulated for each experiment with a repetition delay of 6 s. Typical 90° pulses were 9.5 µs for 1H, 7.8 µs for 29Si (F1 channel) and 11.5 µs for 13C (F3 channel). A CP pulse sequence using a contact time of 3 ms was used for the magnetization transfer from protons to carbon. Results and Discussion 13C NMR spectroscopy was first used to study the motional behavior of the high loaded complex of zeolite ZSM-5 with p-xylene. The p-xylene was specifically labeled in 13C (98%) in one methyl group to increase the sensitivity of all of the experiments and correspondingly shorten the experimental times

Molecular Motions and Exchange in p-Xylene in ZSM-5

J. Phys. Chem. B, Vol. 106, No. 9, 2002 2263 S2 in structure 1. The p-xylene in the sinusoidal or zigzag channel is identified as XYL2, and in structure 2, the two distinct methyl carbons are labeled as Z1 and Z2. The numbering of the atoms in 1 and 2 is the same as used in the published X-ray

Figure 2. 13C CP MAS NMR spectra, at the temperature indicated, of the complex of eight molecules of p-xylene [methyl, 13C] in ZSM-5.

Figure 3. Representation of a view down a straight channel of the ZSM-5 lattice showing the locations of the p-xylene molecules in the sinusoidal channel (XYL2), and in the intersection of the channels (XYL1) (From the data in ref 29).

required. This was also essential to make the coherence transfer experiments from carbon to silicon possible. Figure 2 shows the 13C CPMAS NMR spectra of the complex of eight molecules of 13C[C-1] p-xylene in ZSM-5 as a function of temperature. The line widths of the peaks change with temperature, and they tend to broaden and coalesce at higher temperatures. At 273 K, four well-resolved peaks can be distinguished in the spectrum, corresponding to four different environments for the methyl groups of the p-xylene molecules within the zeolite framework and no further changes in the spectrum are observed at lower temperatures. Figure 3 shows a representation of the structure of this complex based on the single-crystal X-ray diffraction by van Koningsveld and co-workers.29 The p-xylene molecule labeled as XYL1, located in the intersection of the channels has two chemically different carbons indicated, for simplicity, as S1 and

structure. The changes in the line shapes of the 13C NMR signals with temperature indicate slow motion(s) of the p-xylene molecules within the channels (correlation time τc e 10 ms). The separation of the lines is on the order of ∼100 Hz, and any exchange processes of this frequency will be expected to affect the spectra. Although there is a clear evidence for chemical exchange, it is unclear which sites the exchange(s) is (are) between and it is not possible to unambiguously interpret the spectral changes. To investigate these motions in detail by 2D NOESY spectroscopy, it is first necessary to assign the 13C NMR signals observed in the spectrum to the four different methyl groups of the p-xylene molecules the zeolite channels. The unambiguous assignment of these resonances was done using 2D TEDOR (Transferred Echo Double Resonance),27 where the 13C spins are correlated to the 29Si spins through the dipolar interactions between them. Because the dipolar interaction has a very strong dependence on the internuclear distance (1/r3), only those pairs of nuclei with relatively large dipolar couplings will show crosspeaks in the spectrum and correlations will not be observed for carbons that are too far away from the 29Si nuclei. The intensity of a cross-peak is a measure of the strength of the dipolar interaction; and thus, for a given silicon atom a more intense cross-peak indicates that a carbon is closer to that silicon in the zeolite lattice. Therefore in the 2D TEDOR spectrum shown in Figure 4 only those carbons relatively close to framework silicon atoms will show cross-peaks. Since the silicon resonances have been assigned to specific T-sites by previous INADEQUATE experiments, the carbon resonances can therefore also be assigned. Table 1 shows the shortest Si-C distances calculated from the XRD data within a cutoff distance of 7 Å, the corresponding dipolar couplings and the cross-peaks expected for each of the resolved silicon signals in the spectrum according to the magnitude of the individual dipolar couplings. The S, M, and W nomenclature is used in Table 1 to indicate strong, medium and weak dipolar couplings and gives an approximate indication of the expected cross-peak intensities. Thus, for example, for Si 10, Table 1 indicates only two 13C-29Si interactions that are relatively strong (78.8 and 78.3 Hz) involving the methyl carbons Z1 and Z2 in the p-xylene in the zigzag channel. The 2D TEDOR spectrum in Figure 4 shows only two strong cross-peaks to that silicon, which must correspond to these Z1 and Z2 interactions assigning Z1 and Z2 as the two outermost signals in the 13C spectrum. The individual assignments of Z1 and Z2 are obtained from the expected crosspeaks to Si 16. From Table 1, a very strong interaction between Si 16 and Z1 is predicted, and this is observed in the 2D TEDOR

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Figure 4. Contour plot of a 2D CP TEDOR experiment on the complex of eight molecules per u.c. of p-xylene [methyl, 13C] in ZSM-5 at 273 K with the 1D CP MAS NMR spectra shown above and at the side. A total of 32 experiments were acquired with a contact time of 3 ms and 1568 scans in each experiment with 5 s delay between pulses, for a total experimental time of approximately 70 h. Sine bell apodization was used in the data processing.

TABLE 1: Calculated Si-C Distances, Dipolar Coupling, and Expected Cross-Peak Intensities in the 2D TEDOR NMR Spectrum for the Complex of Eight Molecules of p-Xylene in ZSM-5a

29Si T-site

Si 1

Si 3

Si 4 Si 10 Si 12 Si 16 Si 17

Si 18

carbon atoms

rSi-X (Å) from XRD

dipolar coupling (Hz)

S2 Z2 Z1 S1 S2 S1 Z2 Z1 Z1 Z2 Z1 Z2 S2 Z2 Z1 Z2 Z1 S2 S1 Z2 S2 Z2 Z1 S1

4.459 4.491 4.972 5.950 4.685 5.296 5.380 6.139 4.537 6.954 4.240 4.248 5.207 5.428 4.179 6.314 4.598 4.696 5.893 6.595 4.481 5.650 5.652 5.988

67.73 66.30 48.87 28.51 58.41 40.43 38.56 25.96 64.31 17.86 78.77 78.32 42.5 37.56 82.28 23.85 61.79 58.00 29.35 20.93 66.75 33.29 33.26 27.97

expected cross-peak intensities in the 2D TEDOR NMR spectrumb S S M W M M W W S W S S W W S W S M W W S W W W

a Calculated from the XRD data from ref 29, up to a distance of 7 Å. b S ) strong dipolar coupling (between 60 and 85 Hz). M ) medium dipolar coupling (between 40 and 59 Hz). W ) weak dipolar coupling (between 20 and 39 Hz).

spectrum assigning Z1 as the lower field signal in the pair. The assignments of the methyl signals from the p-xylene in the straight channel are more difficult because these signals are very close in frequency. However for Si 17, the dipolar coupling for the interaction between Si17 and S2 is almost twice that for Si

Figure 5. Contour plots of 2D CP NOESY experiments on the complex of eight molecules of p-xylene [methyl, 13C] in ZSM-5 carried out at 297 K at mixing times of (a) 20 ms, (b) 40 ms, and (c) 100 ms. The 1D CPMAS NMR spectrum is shown above. Each plot is the result of 32 experiments, 80 scans in each experiment, with a 5 s delay between pulses, spectral width of 800 Hz, and 128 data points collected during acquisition. The spectra show the three regimes of exchange observed in this system at the different mixing times: (a) no exchange, (b) intramolecular exchange, and (c) intermolecular and intramolecular exchange.

17 and S1 (which is very small), and thus, an intense crosspeak between Si17-S2 and a weak correlation or no cross-peak at all for Si17-S1 are expected. This is observed in the 2D TEDOR spectrum (Figure 4), indicating that S2 is the lower field resonance of the central pair. All these assignments are self-consistent with the other 29Si-13C interactions observed in the 2D spectrum, as indicated in Figure 4. This assignment of the 13C NMR signals for the molecule in the zigzag channel agrees with that previously presented by Olson and co-workers30 on the basis of the known structure and the anticipated ring current effect of the molecule in the intersection (see Figure 4). However, they only detected three signals in the 13C spectrum and a completely unambiguous assignment of all four resonances is only possible using the 2D TEDOR experiment as described above. Most importantly, in the present study, the two outer resonances are due to the two methyls on the molecule in the zigzag channel and the two inner resonances to those on the molecule in the straight channel. Figure 5 presents a series of 2D CP NOESY experiments carried out at 297 K with different mixing times that illustrate

Molecular Motions and Exchange in p-Xylene in ZSM-5

J. Phys. Chem. B, Vol. 106, No. 9, 2002 2265

the three different exchange regimens observed. At short mixing times (20 ms) no exchange is detected in the 2D spectrum at this temperature, at intermediate times (40 ms) there is considerable intramolecular exchange between the two methyl groups of the molecule in the zigzag channel (Z1 and Z2) and between the two methyl groups of the molecule in the straight channel (S1 and S2). At long mixing times (90 ms) an additional very slow exchange process is detected that interchanges methyl group environments between molecules in the zigzag channel and molecules in the straight channels, S1,S2 to Z1,Z2, (intermolecular exchange). As expected, all of these exchange processes are slowed by reducing the temperature, confirming the chemical nature of the exchange process. 2D CP NOESY experiments carried out at 273 K and below showed that no appreciable exchange is observed between the p-xylene molecules even at very long mixing times (90 ms), indicating that it is possible to quench the observed motions of these molecules by decreasing the temperature. 2D CP NOESY experiments at different temperatures (313, 297, 283, and 273 K) were carried out as a function of the mixing time to determine the rate constants for the chemical exchanges and the activation energies of these processes. The intramolecular exchanges observed between carbons Z1 and Z2 of the p-xylene in the zigzag channel, and between carbons S1 and S2 of the p-xylene in the straight channels can be described quantitatively in terms of a two site chemical exchange model whose mathematical treatment has been presented,25,31 because the intermolecular exchange is very much slower and the error in not taking the intensities of these crosspeaks into account is negligible (see later). Any cross-relaxation effects can be neglected in this analysis, because the 2D NOESY experiments were taken using proton decoupling during the mixing time to quench 13C-13C spin diffusion through the proton nuclei. Direct 13C-13C spin diffusion effects are expected to be negligible because of the large internuclear distances between them and their (relative) spin dilution, but this was verified experimentally by investigating the behavior of a sample where the 13C was diluted 2-fold (50% p-xylene and 50% [13C,CH3] p-xylene): This showed similar exchange kinetics. For the intramolecular exchange of the methyl carbons from the p-xylene molecules in the zigzag channel: kZ

1Z2

Z1 {\ } Z2 k Z2Z1

Since kZ1Z2 ) kZ2Z1 ) kZ, the intensities of the diagonal peaks are given by

1 IZ1Z1(τm) ) IZ2Z2(τm) ) e-R1τm[1 + e-kZτm]M0 4

(1)

The intensities of the cross-peaks are given by

1 IZ1Z2(τm) ) IZ2Z1(τm) ) e-R1τm[1 - e-kZτm]M0 4

(2)

As can be seen from the cross-peaks in Figure 6 where no symmetrization has been applied, the relaxation rate R1 was the same for both methyl sites, as expected. The intramolecular chemical exchange rate can be determined by the ratio of the peak intensities given by eqs 1 and 2, according to

IZ1Z2(τm) IZ1Z2(τm) + IZ2Z2(τm)

1 ) [1 - e-kZτm] 2

(3)

Figure 6. Plots of the ratio of intensities for the intramolecular exchange of the molecules located in the zigzag channels obtained from the 2D CP NOESY spectra of the complex of eight molecules of p-xylene [methyl, 13C] in ZSM-5 as a function of the mixing time τm at the different temperatures indicated. The linear correlations yield the rate constants for this exchange.

which simplifies to

ln

[

]

IZ1Z2(τm) + IZ2Z2(τm)

IZ2Z2(τm) - IZ1Z2(τm)

) kZτm

(4)

These intensities can be measured directly by integration of the spectra obtained from the cross-section plots of the 2D NOESY spectrum, which was taken in magnitude mode and thus the measured intensities can be used directly in a quantitative evaluation.

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Figure 8. Arrhenius plot of the log of the rate constant vs the inverse of the temperature to obtain the activation energy for the intramolecular exchange of the molecules located in the zigzag channels.

TABLE 2: Kinetic Constants at Different Temperatures for the Intramolecular Exchange of the p-Xylene Molecules in the Straight and Zigzag Channels in the System of Eight Molecules of p-Xylene per u.c. in ZSM-5

Figure 7. Plots of the ratio of intensities for the intramolecular exchange of the molecules located in the straight channels obtained from the 2D CP NOESY spectra of the complex of eight molecules of p-xylene [methyl, 13C] in ZSM-5 as a function of the mixing time τm at the different temperatures indicated. The linear correlations yield the rate constants for this exchange.

The plot of ln[IZ1Z2(τm) + IZ2Z2(τm)/IZ2Z2(τm) - IZ1Z2(τm)] versus τm should be a straight line with slope kZ and intercept zero. These plots are shown in Figure 6, for the different NOESY experiments at the various temperatures indicated. Similar expressions can be obtained for the intramolecular exchange of the methyl sites S1 and S2 for the p-xylene molecules in the straight channels: kS

1S2

S1 {\ } S2 k S2S1

Again, plots of ln[IS1S2(τm) + IS2S2(τm)/IS2S2(τm) - IS1S2(τm)] as a function of τm for the 2D CP NOESY experiments at different temperatures should yield straight lines with slopes equal to the intramolecular exchange rate constants of the p-xylene molecules in the intersection of the channels at those temperatures and should have intercepts of zero. The linear correlations shown in Figure 7 are not as good as those obtained for the intramolecular exchange in the zigzag channels, mainly because the signals corresponding to S1 and S2 in the 13C NMR spectrum are very close, resulting in some peak overlap. This results in overstimates of the cross-peak areas, which are more important at very short mixing times, because the very small intensities of the cross-peaks for the exchange between S1 and S2 are somewhat enhanced by the tails of the larger diagonal peaks. As a consequence of this, the initial points in the plots shown in Figure 7 are higher than the general trends. The calculated rate constants for the intramolecular exchange of the methyl groups inside the channels are listed in Table 2 together with their experimental errors. These were calculated by differentiating the expression in eq 4 with respect to intensity, with the errors in measuring the intensities determined to be approximately 4-5% of the integral values. The errors in the

temp (K)

intramolecular exchange zigzag channel kZ (s-1)

intramolecular exchange straight channel kS (s-1)

313 297 283 273

75 ( 2 19.7 ( 0.4 7.2 ( 0.8 1.8 ( 0.3

21.6 ( 0.2 7.0 ( 0.6

rate constants were determined from the maximum and minimum slopes obtained using the intensity based error bars shown in Figures 6 and 7. The intramolecular exchange rate constants between the methyl groups on the molecules in the straight channel could not be obtained from 2D CP NOESY experiments at 313 K and above because the signals corresponding to S1 and S2 collapsed into a single peak at this temperature. Further, as noted above, there are substantial errors introduced at shorter diffusion times from the contributions from the wings of the larger diagonal peaks, which make the data at 273 K less reliable. The motion is quenched at lower temperatures, resulting in only two reliable data points. However, from Table 2, it is clear that the rates are very similar to the corresponding values for the Z1Z2 exchange at these temperatures, implying that there could perhaps be a single rate-limiting process common to both molecules. The activation energies for the intramolecular exchanges can be calculated from the data shown in Table 2 according to the Arrhenius equation k ) Ae-Ea/RT (Figure 8), yielding a value of 65 ( 2 kJ/mol (15.4 kcal/mol) for the intramolecular exchange in the zigzag channels. The error in the activation energy for the intramolecular exchange in the zigzag channels was determined from the maximum and minimum slopes obtained with the errors calculated for the rate constants. Using only the two kS values in Table 2 yields an activation energy of 56 ( 13 kJ/mol for the exchange in the straight channel. However, since this value comes from only two data points, the real error is difficult to estimate. To investigate the effect of sample loading, 2D CP NOESY experiments were carried out at 297 K on the complex of six molecules of p-xylene [methyl, 13C] in ZSM-5. The rate constant obtained from the slope of the plot of the ratio of intensities as a function of the mixing time for the chemical exchange of the methyl sites in the zigzag channel is 89.5 ( 0.5 s-1, which is

Molecular Motions and Exchange in p-Xylene in ZSM-5

J. Phys. Chem. B, Vol. 106, No. 9, 2002 2267

TABLE 3: Pore Opening (O‚‚‚O Distances, Å) for the Double 10-Rings in the Straight and Sinusoidal Channels of the Complex of Eight Molecules of p-Xylene Per u.c. in ZSM-5 (from Ref 29a) 10-rings

1f 6 7.774c

straight channel 7.503c sinusoidal 9.071d channel 8.846d

2f7 3f8

4f9

7.949 7.968 8.606 8.533

8.755d

8.615 8.489 7.578 7.447

8.882d 7.456c 7.278c

5 f 10 max.b min.b 8.099 8.071 8.302 5.891

6.06 6.18 6.37 6.15

5.07 4.80 4.76 4.58

a The O numbering is for use in this table only and is defined as given in the diagram below.

b

Max. and min. pore sizes are calculated using 1.35 Å for the O-atom radius. c Minimal O‚‚‚O distances. d Maximal O‚‚‚O distances.

much larger than that calculated for the eight molecules per u.c. complex at the same temperature (19.7 s-1). This suggests a mechanism dependent on the number of available unoccupied sites in the system. The rate constant for the intramolecular exchange of the p-xylene molecule in the straight channels was not calculated because of the much larger errors involved. The rate constant of the much slower intermolecular exchange cannot be calculated using the simple two-site exchange and the initial rate approximation approach for multiple site exchange has to be used.31 Because this exchange is very slow, the only rate constant that could be calculated was for the intermolecular exchange at high temperature (313 K). At lower temperatures and shorter mixing times, the intensities of the cross-peaks due to the intermolecular exchange are negligible. At 313 K, the rate constant kinter ) 15.5 ( 0.3 s-1 for the intermolecular exchange was calculated using the data from the experiments taken with mixing times of 20 and 40 ms. The error was calculated by assuming the error in the measured intensities to be 5% and the value compares with 75 s-1 for the intramolecular exchange. Possible Exchange Mechanisms Although the exchange experiments yield quantitative information on the rates and activation barriers involved in the exchange processes, they provide no information on the mechanism. The elliptical cross-section of p-xylene has main axis lengths of ∼6.1 and 4.0 Å, calculated from the van der Waals radii15 of the atoms. The reported kinetic diameter is 5.85 Å.32 Table 3 lists the sizes of pore openings (O‚‚‚O distances) for the double 10-rings in the straight and sinusoidal channels, obtained from the XRD structure.29 The p-xylene molecules in the straight channels (XYL1) can be involved in two different motions. The first and most obvious one, which would be expected to be of relatively low energy, is where the p-xylene in the channel intersection (XYL1) jumps (diffuses) along the straight channel to the next intersection site (assuming that the molecule at the channel intersection has diffused to another position, e.g., defect, so the intersection is empty). However, this motion does not interchange the crystallographic positions of S1 and S2 since the two sites are equivalent. Therefore, even although this motion could well occur, it would not show up as cross-peaks in the NOESY experiment. It is possible that the observed intramolecular methyl exchange could occur by molecules leaving the framework and then reentering in a different orientation. However, in this

process, it is unclear why the intramolecular rates should be similar for the two sites or why the intermolecular exchange should be so much slower. A further possible motion that interchanges the two methyl sites on a p-xylene is when the molecule turns around by 180° around the C2 axis, thus interchanging S1 and S2. Although this motion is precluded as a simple in-place rotation with no translation due to the channel dimensions, it could occur at the channel intersection by a series of small steps involving both translation and rotation but would be expected to have a high activation barrier, as observed. Although the maximum pore size in the straight channel (6.18 Å) is about the same value as the long molecular axis length of the p-xylene molecule (6.1 Å), it is still possible that this turning motion could occur because the channel intersections produce a “cage” with a larger volume. Derouane and Vedrine have observed that the channel intersections afford a free volume of somewhat larger size.33 In the case of the molecules in the zigzag channels, translational diffusion (jumping) of the p-xylene molecules within the sinusoidal channel (assuming that the molecule at the channel intersection has diffused to another position, e.g., defect, so the intersection is empty), will again locate the molecule in an equivalent crystallographic position in the zigzag channel. Although this diffusion process very likely occurs, again, due to the lack of associated chemical exchange, it will not show up as cross-peaks in the 2D CP NOESY experiment. The remaining possibility by which the intramolecular exchange of the methyl groups can occur is again by rotating the molecule by 180° around the C2 axis. Comparing the effective maximum size of the pore openings for the sinusoidal channel listed in Table 3 (6.37 Å) with the long molecular axis calculated for the p-xylene molecule (∼6.1 Å), it is not possible for the rotation of the molecule around the C2 axis to occur at the position of minimum potential energy in the zigzag channels. However, if the molecule (XYL2) diffuses to the (empty) larger cage formed by the intersection of the channels (possible only when the molecule XYL1 has diffused to a “vacancy”), the molecule can rotate around the C2 axis exactly as described for XYL1, so the carbon atom Z2 exchanges with Z1. After the rotation, the molecule can reenter the zigzag channel and reoccupy its original site. If the 180° rotation, which is common to both exchanges, is the rate-limiting step, as expected, then both intramolecular exchanges would have similar rates, as is observed. The fact that the exchange process is highly accelerated when the loading is lowered to six molecules per u.c. (kZ ) 89.5 ( 0.5 s-1) is consistent with this mechanism for the exchange, because it is necessary to have void spaces (vacancies) in order for the intramolecular exchange to occur. The framework must contain volumes with less than eight molecules per u.c. because of the loading, although the whole framework has adopted a structure with P212121 symmetry. Although it is not clear from NMR how large these volumes are, there is obviously a large reservoir of empty lattice sites to promote the exchange processes described here. In other reported studies of the dynamics of the p-xylene molecules in ZSM-5, the activation energy for rotation about the long axis of p-xylene in ZSM-5 (not detected in the present experiment) has been found to be approximately 20 kJ/mol.16,34 Activation energies for jumps between the two sites have been estimated at around 30-70 kJ/mol.19 There are no previous data relevant to the intramolecular exchange studied here. It is difficult to compare the results from the present work directly with those from diffusion studies35 due to the large

2268 J. Phys. Chem. B, Vol. 106, No. 9, 2002 differences in rates that are involved and also because the present experiments sample only a subset of motions, those that involve chemical exchange. However, just from the observation of intermolecular exchange between the two sites, it is clear that the diffusion processes in the two channels are not completely independent although the very large barrier to exchange probably indicates that this could be a reasonable assumption in most circumstances. Conclusions The results presented in this work demonstrate that very slow chemical exchanges are occurring involving the p-xylene guest molecules in ZSM-5. These exchanges could not be detected using 2H NMR spectroscopy because they occur on a much slower time scale (correlation time τc e 10 ms). However, these motions will undoubtedly affect experiments such as CP, REDOR, or TEDOR because they occur on a time scale significant for these experiments due to their long evolution times. The exchange is slowed when the temperature is lowered, and it was shown that at 273 K and below, no observable chemical exchange was detected even at long mixing times (90 ms). The effects of these slow motions on solid-state NMR structure determinations have not been recognized to date. In future studies of other sorbate-zeolite framework structures, it will be critical to anticipate their presence and to work at low enough temperatures to quench them effectively on the time scale of the experiments being used. In some cases, very low temperatures may be needed: for example, in the case of the low-loaded form of p-xylene in ZSM 5 reliable data can only be obtained at temperatures of 213 K and below.36 Acknowledgment. C.A.F. acknowledges the support of the Natural Sciences and Engineering Research Council (NSERC) of Canada in the form of operating and equipment grants. A.C.D. thanks INTEVEP, Venezuela, for a Postgraduate Scholarship. References and Notes (1) (a) Breck, D. W. Zeolite Molecular SieVes; John Wiley: New York, 1974. (b) Meier, W. N. In Molecular SieVes; Barrer, R. M., Ed.; Soc. Chem. Ind.: London, 1968. (2) Chen, N. Y.; Degnan, T. F., Jr.; Smith, C. M. Molecular Transport and Reaction in Zeolites. Design and Application of Shape SelectiVe Catalysis; VCH: New York, 1994; p 33. (3) Smith, J. V. In Zeolites Chemistry and Catalysis; Rabo, J. A., Ed.; ACS Monograph 171; American Chemican Society: Washington, DC, 1976. (4) Barrer, R. M. Zeolites and Clay Minerals as Sorbents and Molecular SieVes; Academic Press: London, 1978. (5) A description of the range of applications of these experiments in chemical systems is given in (a) Fyfe, C. A. Solid State NMR for Chemists; CFC Press: Guelph, ON, 1984. (b) Engelhardt G.; Michel, D. HighResolution Solid State NMR of Silicates and Zeolites; John Wiley and Sons: New York, 1987.

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