Investigation of the Benzene Molecule Adsorbed on Faujasite Zeolite Using Double Quantum Filtered NMR Spectral Analysis

Transcription

1 5070 J. Phy. Chem. B 1999, 103, Invetigation o the Benzene Molecule Adorbed on Faujaite Zeolite Uing Double Quantum Filtered NMR Spectral Analyi Yu-Huei Chen and Lian-Pin Hwang* Department o Chemitry, National Taiwan UniVerity, P.O. Box 23-34, Taipei, Taiwan, R.O.C., and Intitute o Atomic and Molecular Science, Academia Sinica, Taipei, Taiwan, R.O.C. ReceiVed: Augut 11, 1998; In Final Form: March 24, 1999 Downloaded by NATIONAL TAIWAN UNIV on September 3, Deuteron NMR relaxation tudie including double quantum iltered (DQF) pectral analye, T 1, and line width are ued to probe the dynamic and exchange proce o variou-loading benzene molecule adorbed into NaY and dealuminated Y (DAY) including ultratable Y (USY) zeolite. DQF NMR i a very enitive method to determine the reidual quadrupolar interaction reulting rom the local order. In thi work, we modiied the cone model to decribe the in-plane rotation around the hexad axi and the retricted wobbling motion o the benzene ring on the urace o the interaction ite. The in-plane rotation and wobbling motion o adorbed benzene molecule relect a hot-guet eect on the iolated adorption ite and alo the mobility in the cage. In addition, the eect o a ite-to-ite hopping proce reult in a mall net reidual quadrupolar interaction. With increaed loading, the in-plane rotation o benzene i igniicantly hindered in all aujaite but the population o adorbed benzene dramatically reduce in DAY (including USY) ytem only. Thi indicate the nature o ite interaction on benzene molecule in a upercage. The population proile o adorbate thu determined provide ueul knowledge o loading eect, and the ite interaction and ditribution. Introduction A detailed knowledge o the interaction o adorbate in zeolite ytem i eential in undertanding the adorption and catalytic propertie. Molecule with appropriate ize and peciic interaction uch a benzene have been extenively ued a a probe or the tudy o adorption interaction and adorbate dynamic. 1-3 The benzene molecule in aujaite-type zeolite are preerentially adorbed at cation ite which in the cae o NaY are odium cation located at ite S II in the upercage. The le trong adorption ite are the oxygen atom o the 12-ring window. 4-6 In the cae o dealuminated Y (DAY) including ultratable Y (USY), benzene molecule are preerentially adorbed at the hydroxyl group. 6 Evidence i known that benzene perorm the rapid rotation about the ixold ymmetry axi and the hopping o benzene between the adorption ite i aociated with molecular reorientation The behavior i conitent with reult rom molecular dynamic imulation and kinetic Monte Carlo calculation A decription o the theoretical background o NMR analyi o adorption ytem ha been given by Peier. 7-9 Scharer et al. employed two-dimenional (2D) exchange 13 C NMR technique to the tudy o the reorientation dynamic o hydrocarbon molecule adorbed on Ca-LSX zeolite with variou loading. The tudy enabled the geometry and time cale o molecular hopping procee between adjacent adorption ite to be characterized. 14 Further, Iort et al. ued 2 H NMR exchange experiment to tudy the reorientational dynamic o benzene molecule at ull occupancy o the upercage o NaY. Experimental 2D pectra and 2D echo time-domain decay proile are obtained and the value o the relevant correlation unction can be meaured directly. Comparion with model calculation give evidence or tetrahedral-like jump aociated * Correponding author. Tel: Fax: nmra@po.iam.inica.edu.tw. with the mall-angle reorientation motion or benzene molecule in the neighborhood. 15 The mall-angle reorientation o C 6 D 6 are interpreted to be due to intantaneou relaxation ater the hopping o neighboring molecule in the upercage. Furthermore, the mall-angle jump are about 2 time ater than the interite jump. The advantage o the exchange technique and analye i that certain reult are unique and directly obtained without recoure to modeling. Mot NMR method or tudying adorption report on only the T 1 and the uual line-width analyi. It can be diicult to analyze the adorption eect due to ite ditribution in the upercage and the loading eect aociated with intra- and interupercage adorption. However, Pearon et al. 16 take advantage o intra- and intermolecular proton-proton dipolar interaction to generate multiple-quantum coherence in order to evaluate the pin cluter ize o benzene and their ditribution in variou loading o NaY ytem. Furthermore, the recent developed multiquantum (MQ) MAS techenique ha alo been employed to examine the loading eect on 23 Na iotropic chemical hit and the econd-order quadrupolar eect o odium ite. 17 The reult how that with an increae in bulk benzene loading rom 0 to 2 benzene molecule per upercage, there i an upield trend in iotropic chemical hit and a decreaing econd order quadrupolar eect or the S II odium ion. With the loading rom 2 to 5 benzene molecule per upercage, the variation o iotropic chemical hit and a econdorder quadrupolar eect are not igniicant. The ue o double quantum iltered (DQF) NMR pectrocopy 18,19 a a diagnotic tool or the detection o aniotropy in macrocopically diordered ytem ha recently been developed. It may be utilized a a enitive method or the determination o the reidual quadrupolar interaction reulting rom adorbate dynamic among interaction ite in zeolite cage. In particular, or the I ) 1 pin ytem, the double quantum coherence vanihe in the iotropic medium, and hence /jp983342o CCC: $ American Chemical Society Publihed on Web 06/02/1999

2 Benzene Molecule Adorbed on Faujaite Zeolite J. Phy. Chem. B, Vol. 103, No. 24, Figure 1. Schematic repreentation o benzene adorption with exchange proce in zeolite. The benzene molecule exchange between the at () and low () ite. For low ite, an adorption coordinate i aumed to repreent the variou trength o reidual adorption interaction (ω q) which i in turn related to the reidual quadrupolar interaction and alo to the order parameter (S) which decribe the degree o retriction in out-o-plane reorientation (the wobbling motion) or adorbed benzene. Downloaded by NATIONAL TAIWAN UNIV on September 3, obervation o the DQF ytem indicate the preence o the aniotropic motion o the pin-bearing molecule due to reidual quadrupolar interaction. 20 In the preliminary tudy on ultratable Y (USY) and other aujaite zeolite, the oberved uual deuteron pectra o benzene-d 6 retain the iotropic peak with no olid pattern over a broad temperature range However, when oberved in 2 H DQF pectra o C 6 D 6 in USY, an additional central line appeared. 23 Thi i evidence o the iotropic motion o the benzene through exchange with the benzene ituated at adorption ite with nonvanihing quadrupolar interaction. For the quadrupolar ytem o adorbate molecule, experiment how the collape o the olid tate pattern into a inglet at elevated temperature. Baed on thi act, it i aumed that the reidual interaction on adorption i averaged out by the iotropic motion among the variou adorption ite in the upercage. 24,25 From a phyical point o view, the adorption ite in the upercage are not iotropically arranged in the upercage. Beide, it eem unreaonable to aume iotropic motion o the adorbate molecule i it remain attached to the adorption ite or a igniicant time. In thi paper, we report on the ue o deuteron NMR relaxation tudie to invetigate the dynamic and exchange proce o benzene molecule adorbed on aujaite-type zeolite, NaY, and dealuminated Y (DAY) including ultratable Y (USY). Low loading o zeolite with benzene are invoked to probe or ite ditribution and ite interaction, and high loading o zeolite with benzene or the orbate-orbate interaction in the ame upercage o variou aujaite. In addition to the uual invetigation by T 1 and line-width analyi, DQF NMR with dierent creation time wa alo employed in the analye. The order parameter pertinent to the model, the motional correlation time, and exchange parameter thu determined provide ueul inormation on the adorptive propertie o the zeolite ytem. Formulation o Theory Two-Site Exchange Model with Reidual Quadrupolar Interaction. The denity matrix approach ha been invoked in the tudy o exchange proce with coherence traner. The problem may be urther impliied by expreing the rate equation on the bai o an irreducible tenorial et 26,27 where the individual element o the denity matrix tranorm a component o the ull rotation group. The element o qth component o a rank K irreducible tenor, σ Kq, can be obtained rom the element o the uual denity matrix, F mn,by σ Kq (-1) m-1 2K + 1( I I K m -n -q) F mn (1) m,n where ( I I K m -n -q ) ia3-j ymbol 28 and I i the nuclear pin quantum number o the relevant nuclei. The baic relaxation theory o thee irreducible tenorial et i the ame a that ued in previou work. 29 Additionally, we have included adorption eect and exchange proce in the relaxation matrix R. The equation o motion or thi ytem deined in a rotating rame may be expreed by the ollowing Liouville equationr σ(t)/ t ) (-il + R)σ(t) (2) where σ(t) i the denity operator at time t. The component o σ(t) are related to the irreducible tenorial component o interet. In eq 2, we deine Lσ(t) [H,σ(t)], where L i the Liouville operator correponding to the Hamiltonian o the reidual quadrupolar interaction, H, which i given by H ω q,θ (I z 2 - I(I + 1)) 1 / 2 ω q (3 co 2 θ - 1)(I z 2 - I(I + 1)) (3) where I z i the z component o pin I. ω q,θ and ω q are the reidual quadrupolar interaction in the laboratory rame o reerence and in the molecular rame, repectively. θ i the angle between the principal axi o the reidual quadrupolar interaction in the molecular rame and the Zeeman ield. Without exchange and pin relaxation procee, the equation o motion or the related irreducible tenorial component under the inluence o reidual quadrupolar interaction in a rotating rame i given by 30 d dt[ σ 11 σ 21 ] [ ) 0 -iω q,θ -iω q,θ 0 ][ σ 11 σ 21 ] (4) where σ 11 I + /2 and σ 21 (I z I + + I + I z ). The trength o interaction o the benzene molecule with the adorption ite depend on the ditance between them and their relative orientation. For implicity, it i reaonable to aume that the magnitude o ω q increae with the adorption poition cloe to an adorption ite. Thu, the variation o ω q may be conidered a the adorption coordinate, and all poition o the adorption coordinate are treated a the low motion ite or benzene molecule. The decription o adorption and dynamic along the adorption coordinate i depicted in Figure 1. It hould be noted that dierent type o aujaite poe variou characteritic ω q. Beide, thermal and hopping averag-

3 Downloaded by NATIONAL TAIWAN UNIV on September 3, J. Phy. Chem. B, Vol. 103, No. 24, 1999 Chen and Hwang d σ 21 dt(σ11 (-R11 - k 0 k 0 0 -R )) 21 - k 0 k σ 11 k 0 -R 11 - k -iω q,θ - k ) Figure 2. Pule equence and coherence-traner pathway ued in DQF experiment. σ 1q repreent the irreducible tenorial component with rank l and coherence q. τ i the creation time or double quantum coherence and δ wa et at 10 µ. ing procee may render a maller characteritic ω q. At room temperature and down to below 100 K, the benzene molecule perorm rapid internal rotation about their hexad axi in aujaite ytem. 9,11-13 Particularly, in NaY the intra- and interupercage hopping between adorption ite i aociated with molecular reorientation In order to treat the reorientational dynamic o benzene in aujaite ytem, the relation among the motion, including internal rotation, wobbling motion, and ite-to-ite hopping motion, and the order parameter involved in a modiied Brainard and Szabo model 30,31 will be dicued below. In DQF NMR, the detectable ignal i generated rom the econd-rank tenor that i ormed during the creation time o the double quantum iltered pule equence. The pule equence o the double quantum iltered NMR i hown in Figure 2. Since we have retricted our problem to the cae o a pin 1 ytem a hown in eq 4, the only coherence-traner pathway to be conidered are between rank one and rank two alone. 20,30 The irt π/2 pule tranorm the Zeeman order σ 10 (σ 10 I z / 2) into ingle-quantum coherence σ 11 which then generate σ 21 in the creation time, τ, via the reidual quadrupolar interaction given in eq 3. The econd π/2 pule with DQF phae cycling tranorm σ 21 into double-quantum coherence σ 22 (σ 22 I + I + / 2) only. Since δ i et to be 10 µ, the relaxation o the σ 22 component may be neglected during time δ. The lat π/2 pule tranorm the double-quantum coherence into an obervable ignal. In the preent relaxation tudy, a repreentation o the molecular ituation with exchange between a at motion ite and a low motion ite, characterized with a reidual quadrupolar interaction, i needed to account or the adorption proce o benzene onto aujaite. The at motion ite repreent a dynamic tate o benzene experiencing at and highly ymmetric reorientation. The low motion ite in NaY aujaite tand or the dynamic tate o the benzene molecule in upercage aected by the Na S II (and W) ite interaction while or DAY and USY ample the dynamic tate o the benzene molecule i rather aected by the hydroxyl aluminum group. It hould be noted that ω q i obtained ater averaging over the coordinate o in-plane rotation, wobbling motion, and ite-to-ite hopping motion 11,12 o the adorbate molecule. Furthermore, the ite-to-ite hopping interaction i only conidered in the cae o multiple-ite ditribution uch a in the adorption cage o NaY aujaite. The benzene reorientation in low motion ite experience a reidual adorption interaction, ω q. Hence, the evolution o related tranvere component σ 11 and σ 21 during creation time may be augmented rom eq 2 and 4. It ollow the rate equation o denity operator: e.g. σ 21 0 k -iω q,θ -R 21 (σ11 σ 21 (5) σ 11 σ 21 where the reidual quadrupolar interaction exit in ite only, k i the microcopic rate contant or traner rom ite to ite, and k i the microcopic rate contant or traner rom ite to ite. In addition, the detailed balancing o the exchange proce demand that P k ) P k (6) where we deine P and P a the total population in ite and ite, repectively. The incluion o exchange proce ha placed not a limitation but rather a ditribution uitable or tudying the time cale o dynamic exchange proce with adorption conined inide the zeolite. In eq 5, the pin relaxation rate contant or ingle and double quantum coherence (expreed by the irt ubcript o R) with dierent ite (expreed by the upercript) are given by 30 R 11 C (3J 0 + 5J 1 + 2J 2 ) R 21 C (3J 0 + J 1 + 2J 2 ) R 11 C (3J 0 + 5J 1 + 2J 2 ) R 21 C (3J 0 + J 1 + 2J 2 ) (7) where we have C (3/160)χ 2 and C (3/160)χ 2 and where χ and χ are deined a the quadrupolar coupling contant χ / 2π (e 2 Qq /h) and χ /2π (e 2 Qq /h) or at and low motion ite, repectively. J n and J n are the pectral denity unction, deined below or reorientational relaxation o benzene molecule in and ite, repectively. Since the C-D bonding o the benzene molecule i conidered to be cylindrical, the contribution o the aymmetry parameter (η ) 0.06) o the electric ield gradient to the relaxation interaction i negligible. 33 It i worth noting that all the parameter ued or a low ite have the characteritic o adorption interaction. To guarantee the validity o thi equation, the condition τ ex. τ c mut hold. Here τ c repreent the microcopic motional correlation time related to the adorbed benzene molecule and τ ex i deined a τ ex P /k ) P /k. It i noted that eq 5 i invoked in the calculation o SQ and DQF pectra. In addition to the contribution rom uual tranvere pin relaxation, the reidual quadrupolar interaction may alo aect the line hape o SQ and DQF pectra. The crucial eature o DQF pectra lie in the pectral line with phae modulation reulting rom the reidual quadrupolar interaction. Furthermore, the trong reidual quadrupolar interaction may aect dominantly in the houlder o the pectral line. For SQ pectra, it give broadened houlder while in DQF pectra it give wiggling. The eect may be een obviouly in the DQF pectra o the ytem with lower ymmetric arranged adorption ite, epecially in the cae o benzene in USY ytem. )

4 Benzene Molecule Adorbed on Faujaite Zeolite J. Phy. Chem. B, Vol. 103, No. 24, Downloaded by NATIONAL TAIWAN UNIV on September 3, For the calculation o T 1 the time evolution o the longitudinal component ollow the rate equation. 29 d dt( σ 10 σ 10 ) ( ) -R 10 - k k k -R 10 - k )( σ 10 σ 10 ) (8) where R 10 and R 10 are the longitudinal relaxation matrix element or ite and ite, a deined by R 10 C (J 1 + 4J 2 ) R 10 C (J 1 + 4J 2 ) (9) The calculation o T 1 value and the ingle quantum (SQ) line width were alo employed in the determination o imulation parameter. The detail o imulation are decribed in a later ection on imulation. Spectral Denity or Benzene in Fat Motion Site. For a at motion ite, the reorientational Brownian motion o benzene molecule average to zero the aniotropic quadrupole interaction experienced by the 2 H nucleu. The pectral denity unction expreed in eq 7 and 9 or at ite i given by 34 J n ) 3 4 J i n J o n (10) i where J n and J o n are the pectral denity unction related to in-plane and out-o-plane rotation, repectively, and are given by 2τ i J i n ) (11) 1 + (nω 0 τ i ) 2 2τ o J o n ) (12) 1 + (nω 0 τ o ) 2 where ω o i the Larmor requency o deuteron nuclei and τ i and τ o are the correlation time or in-plane rotation about the hexad axi and out-o-plane reorientational correlation time o the aromatic ring, repectively. For implicity, in the preent calculation, we ue only one reorientational correlation time or benzene in a at motion ite; i.e., we let τ ) τ i ) τ o in eq 11 and 12. Spectral Denity or Benzene in Slow Motion Site. The pectral denity unction or ite with conideration o reidual quadrupolar interaction are deined by 30 J 0 j 0 ( D (2) D (4) 00 - D (2) 00 ) 2 J 1 j 1 ( D (2) D (4) 00 ) J 2 j 0 ( D (2) D (4) 00 ) (13) where j n i the pectral denity, deined below, or the dynamic part o the motion at ite, D (n) 00 are the Wigner rotation matrix element 28 with the orientation relative to the laboratory rame, and mean taking the average over pace o motion not retricted by the adorptive interaction, i.e., averaging over the coordinate o in-plane and wobbling motion. For multiple adorption ite, additional averaging over the motion o iteto-ite hopping i perormed. In eq 13 the igniicance o the nonvanihing D (n) 00 repreent the plateu term or orientation relaxation in the preence o reidual quadrupolar interaction. The model-ree nonexponential unction, uch a Kohlrauch-William-Watt tretched exponential decay unction, 15 may be involved to evaluate the pectral denity j n or orientational relaxation. However, the dynamic behavior o the benzene molecule under the inluence o adorption i taken into account in the ormulation o the time-correlation unction. To decribe the intererence between the variou mode o molecular motion in low motion ite, we include in-plane rotation about the hexad axi o benzene, and wobbling motion o the ring normal uniormly in a cone. Thereore, it i convenient to modiy the cone model o Brainard and Szabo 31 to acilitate the calculation o the time-correlation unction o the adorbed benzene molecule. Note that the dynamic characteritic o variou motional mode mentioned are preumably lower than the hopping proce in order to introduce the coare coure graining-in-time approximation by mean o averaging over the motion due to ite-to-ite hopping. Thereore, we leave out the overall reorientation o the whole molecule rom the cone model due to adorption onto zeolite. The pectral denity unction i deined by 31,32 j n ) 2{ 3 4 S2 4D i (4D i ) 2 + (nω 0 ) (1 - S 2 )[4D i + 2D w /(1 - S 2 )] 4 [4D i + 2D w /(1 - S 2 )] 2 + (nω 0 ) (1 - S 2 )[6D w /(1 - S 2 ) 2 ] (14) 4 [6D w /(1 - S 2 ) 2 ] 2 + (nω 0 ) 2} It i aumed that the internal rotation and the wobbling motion o the adorbed benzene ring have correlation time τ i 1/(4D i ) and τ w 1/(6D w ), repectively. Here the wobbling motion i preumably lower than the in-plane rotation. Thee two motional correlation time are preumably larger than the reorientational correlation time τ i and τ o. The wobbling motion i aumed to be within a cone with the director normal to the adorption ite. The ditribution o the cone may be expreed by an order parameter S given by S D (2) 00 where the average i over the in-plane rotation and wobbling motion deined in the rame o an adorptive ite. Here we have S ) 0 or completely random wobbling motion. For S ) 1, there i inplane rotation only and no wobbling motion. With thi deinition the econd term in eq 13 may be readily evaluated a D (2) 00 ) SD (2) 00 (θ) where axial ymmetry o the adorption interaction and ite ditribution are aumed, while the third term in eq 13 give D (4) 00 ) D (4) 00 D (4) 00 (θ). To evaluate the D (4) 00 term in term o S, a peciic ditribution o the cone model i needed. For iotropic ditribution within a cone angle o β with the director, Brainard and Szabo obtained S ) 1 / 2 co β(1 + co β). 30 We then obtain D (4) 00 ) (S/8)(28S - 7(1+8S) 1/2 + 1). The above ormulation i or a imple adorption in the upercage. For multiple ite in a upercage, need the additional average over the motion due to ite-to-ite hopping motion. Then θ, a deined in eq 3, may repreent the angle between the principal axi o the averaged reidual quadrupolar interaction in the molecular rame and the Zeeman ield. Hence with the model given, one may evaluate the pectral denity unction or ite. Furthermore, it hould be noted that τ i and τ w are ued in an averaged ene; i.e., their magnitude remain

5 5074 J. Phy. Chem. B, Vol. 103, No. 24, 1999 Chen and Hwang Downloaded by NATIONAL TAIWAN UNIV on September 3, the ame irrepective o the variation o S along the adorption coordinate at a given temperature. Reidual Quadrupolar Interaction and Order Parameter in Adorptive Proce. The trength o adorption interaction depend on the relative poition o the adorbate and the adorption ite. The poition with maximum ω q, denoted by ω qm, may be deined a the benzene molecule adorbed on the adorption ite with maximum trength o interaction. At low temperature, the motion aociated with ω qm involve in-plane motion around the hexad axi only, while there i neither wobbling motion o the ring normal nor ite-to-ite hopping motion. Thu, rom both the experimental evidence and the ymmetry argument reulting rom the at internal motion around the hexad axi, the quadrupolar interaction o perdeuterobenzene molecule in thi cae reduce to hal o the value obtained or rigid tationary benzene. Hence we take ω qm ) 0.5ω q0 where ω q0 3 / 4 χ. 9 Since both the S and ω q parameter hare the ame degree o randomne by the ame average over the motion aociated with benzene, one may relate S linearly with the reidual quadrupolar aniotropy ω q with S ) ω q /ω qm. The pictorial decription o the order parameter and molecular motion along the adorption coordinate i depicted in Figure 1. It hould be noted that the adorption proce i o thermal kinetic origin and hence there exit a dierence in adorbate population along the adorption coordinate a a conequence o exchange between at and low motion ite, and migration o adorbate rom dierent adorption coordinate. Since exchange and migration are diuive procee (ee Appendix), a probability ditribution o adorbate along the adorption coordinate may be repreented approximately in an exponential orm by exp(-ω q /ω c ) (ω q ) ) ω c (1 - exp(-ω qm /ω c )) (15) where ω c characterize a correlation trength o reidual quadrupolar interaction. Beyond thi value the population o adorbate molecule with ω q > ω c drop o igniicantly. Equation 15 i normalized in the range rom 0 to ω qm. The adorbate ditribution unction given in eq 15 may be expreed in term o the correlated order parameter S c ω c /ω qm. For aujaite, with merely a ingle ite in the upercage, the average over the adorption coordinate with the help o eq 15 repreent the thermal kinetic origin o adorption proce mentioned previouly. Since ω q i the reult ater averaging over all the motion concerned, the eective ω q repreent an average over ite-to-ite hopping and the accompanying mall-angle reorientation or multiple-ite adorption ,15 Thereore, with the hopping proce, one may thu expect a mall eective reidual quadrupolar interaction and thu a mall ω c (or S c ) value, in particular in the ytem o ymmetrical averaged adorption ite uch a Na S II ite and W ite in NaY ytem. The ue o eq 15 to decribe the eect o multiple-ite ditribution in a upercage i only valid within the limit o at ite-to-ite hopping; i.e., we have τ -1 hop. ω c, where τ hop i the correlation time o the ite-to-ite hopping proce. Calculation o T 1. Here we decribe the ue o the above theory in imulating the ree-induction decay ignal ater the inverion recovery pule equence (i.e., π-τ -π/2-acq.). The total equilibrium tate multipole can be calculated rom the correponding denity matrix element a σ 10,eq γpb 0 I(I + 1)/3 2kT, where γ i gyromagnetic ratio, k i the Boltzmann contant, and B 0 i the Zeeman ield. Since we have exchanging pecie, the individual multipole mut be appropriately population weighted. The eect o the π pule are then calculated, and thu immediately ater the π pule and including population weighting tate multipole a the initial condition beore evolution o τ we have σ 10 (0) ) -p σ 10,eq and σ 10 (0) )-p σ 10,eq. For the calculation o T 1, eq 8 i ued to ollow the evolution o the longitudinal magnetization and the motional behavior o the pin during the delay time τ. Ineq8,R 10 i calculated rom eq 9 with the help o eq 13 and 14 according to the ditribution o ω q and θ or the low motion ite, and R 10 i calculated rom eq 9 with the help o eq or the at motion ite. The probability ditribution in term o ω q i decribed in eq 15. An iotropic ditribution o θ i applied to imulate the ituation o the random orientational ditribution o zeolite crytal in the powder ample. Then the ignal o longitudinal magnetization ater the delay time τ can be evaluated a ω M z (τ ) qm π (ωq 0 )dω q 0 in θ dθ (σ10 (τ ) + σ 10 (τ )) (16) The calculation i perormed by numerical integration 29 and the T 1 value can then be evaluated rom M z at variou τ. Simulation o Double Quantum Spectra. We imulate the double quantum pectra in accordance with the DQF pule equence hown in Figure 2. The irt π/2 pule tranorm the Zeeman order σ 10,eq into ingle-quantum coherence σ 11 which then generate σ 21 in the creation time τ via the reidual quadrupolar interaction given in eq 3. Equation 5 i ued to calculate the evolution o σ 11, σ 21, σ 11, and σ 21 during the creation time τ with the initial condition σ 11 (0) ) (1/ 2)P σ 10,eq, σ 11 (0) ) (1/ 2)P σ 10,eq, and σ 21 (0) ) σ 21 (0) ) 0. In eq 5, R 11 and R 21 are calculated rom eq 7 with the help o eq 13 and 14 according to the ditribution o ω q and θ or the low motion ite, and R 11 and R 21 are calculated rom eq 7 with the help o eq or the at motion ite. In Figure 2, the ignal immediately ater the third π/2 pule with DQF phae cycling i proportional to the quantity o double quantum coherence σ 21 (τ) and σ 21 (τ). Thu with the initial condition σ 21 ) σ 21 (τ), σ 21 ) σ 21 (τ), and σ 11 ) σ 11 ) 0 (ee Figure 2), eq (5) i ued again to calculate the the ree induction decay (FID) during the acquiition time t. In analogy to eq 16, the FID ignal or the tranvere relaxation i proportional to ω qm(ωq π 0 )dω q 0 in θ dθ(σ11 (τ + t) + σ 11 (τ + t)) (17) The DQF pectra may be obtained by the previouly decribed Fourier tranorm procedure. 28 Calculation o Line Width. Since the uual pectra were obtained by one-pule experiment, the π/2 pule tranorm the Zeeman order σ 10,eq into ingle-quantum coherence σ 11 with the ame initial condition σ 11 (0), σ 11 (0), σ 21 (0), and σ 21 (0) deined in the previou ection. Equation 5 i ued to calculate the evolution o σ 11 and σ 11 during the acquiition time t. In analogy to eq 17, the uual pectrum may be obtained rom the FID ignal expreed by (σ 11 (t) + σ 11 (t)). Then the ull width at hal-height υ 1/2 and one-third height were calculated. Experimental Section The NaY (LZY-52, Si/Al ) 2.4) ued wa upplied and characterized by Union Carbide Co., USA. Two dealuminated Y ample (CBV720, Si/Al ) 15 and CBV780, Si/Al ) 40) ued were upplied and characterized by PQ Zeolite, Holland.

6 Benzene Molecule Adorbed on Faujaite Zeolite J. Phy. Chem. B, Vol. 103, No. 24, Downloaded by NATIONAL TAIWAN UNIV on September 3, Hereater we denote the ormer a DAY and the latter a USY. N 2 adorption-deorption iotherm or USY at 77 K wa meaured with Micrometric ASAP The adorbate material, C 6 D 6, wa purchaed rom Merck. With a minimum purity o 99.5%, no urther puriication proce wa ued. One mall gla ball containing the required amount o C 6 D 6 ample wa ealed and then admitted to the upper part o the ample tube with gla wool eparating it rom the zeolite in the lower part o the tube. The ample wa dehydrated under a 10-5 Torr vacuum at 673 K or at leat 12 h. Ater cooling, the tube wa ealed, leaving the dried zeolite and the C 6 D 6 -carrying ball in the tube. The C 6 D 6 -carrying ball wa then broken by haking the tube. The lower part o the ample tube wa chilled in liquid N 2. The ection o the NMR tube containing the loaded zeolite powder wa ealed and eparated rom the upper part containing the ret o the gla capillary ball. Aterward, the ample wa then kept at 353K or 12 h to enure a homogeneou ditribution o adorbate onto the zeolite. Reproducibility o relaxation data wa checked to examine whether equilibrium i reached in all upercage over a period o 4 month. The loading o C 6 D 6 (molecule per upercage) in variou ample are a ollow: or low-loading ample NaY 0.5, DAY 0.8; and or high-loading ample NaY 3.0, DAY 3.9, USY 3.2. The 2 H NMR meaurement were perormed on Bruker MSL- 500 and MSL-300 pectrometer operating at MHz (11.75 T) and MHz (7.05 T), repectively. In a quadrupolar echo meaurement, a π/2 pule o 7 µ and a delay o 10 µ wa ued to obtain the olid pectrum o adorbed benzene at 130 K. For tranvere relaxation tudie, the line width υ 1/2 were meaured a the ull width at hal-height rom the one-pule experiment. The magnetic inhomogeneity wa etimated by comparing the Hahn pin-echo and line-width meaurement o C 6 D 6 liquid. The magnetic inhomogeneity wa ound to account or le than 5 Hz o the oberved line width at hal-height in the pectra. The longitudinal relaxation meaurement were obtained uing the inverion-recovery pule equence. The 2 H T 1 and line-width meaurement were perormed on Bruker MSL-500 and MSL-300 pectrometer operating at MHz (11.75 T) and MHz (7.05 T), repectively, with π/2 pule length o about 15 µ. A delay o at leat 5 T 1 wa allowed between can or the T 1 and DQF pectra with proper phae cycling. DQF pectra are conventionally meaured uing the pule equence π/2-τ -π/2-δ-π/2-(acq.). Since there i no ield-dependent eect, the DQF pectra were diplayed at MHz only. The temperature wa controlled to within (0.1 C and wa calibrated uing a methanol reerence. There are error o approximately 10% aociated with T 1 and line-width meaurement, repectively. Reult To undertand any poible change o tructure ater dealumination, the tetrahedral/octahedral Al ratio o DAY and USY, a determined by 27 Al MAS NMR, are obtained a 4.8 and 5.2, repectively. IR tudie o dealuminated Y how that hydroxyl aluminum group on extraramework Al atom are inacceible to benzene molecule. 6 Furthermore, in accordance with N 2 adorption-deorption iotherm experiment, the microporou/ meoporou adorption urace ratio or USY i 5.6 i pherical pore are aumed. Thu, one may expect a higher microporou/ meoporou adorption urace ratio or DAY ytem. Thereore, benzene molecule can be conidered a being dominantly adorbed on upercage but not on meopore ite ormed in DAY and USY. In the preent work, DQF pectra, line width, and T 1 meaured at and MHz are obtained or ample TABLE 1: Experimental and Calculated 2 D T 1 and Line Width in Low-Loading Sample Meaured at Variou Temperature and Two Reonance Field a T 1 (m) υ 1/2 (Hz) temp MHz MHz MHz MHz zeolite (K) calc exp calc exp calc exp calc exp NaY DAY USY b a 10% error i expected in all value. b Thi reult ha been hown in re 16. TABLE 2: Experimental and Calculated 2 D T 1 and Line Width in High-Loading Sample Meaured at Variou Temperature and Two Reonance Field a T 1 (m) υ 1/2 (Hz) temp MHz MHz MHz MHz zeolite (K) calc exp calc exp calc exp calc exp NaY DAY USY a 10% error i expected in all value. decribed in the Experimental Section. For the purpoe o comparion, data or the low-loading (0.5 benzene/upercage) USY ample preented previouly are lited again in Table The Value o ω qm. We oberve a powder pattern in the 2 H NMR pectrum or low-loading zeolite NaY at 130 K. The edge plitting ν o the NaY ample i 69 khz which implie a quadrupolar coupling contant χ/2π o 184 khz. Thi reult agree with that o Peier 9 and Soua Goncalve et al. 22 and ugget that immobile benzene i undergoing only in-plane rotation. However, a olid pattern with a central peak appeared in 2 H NMR pectra or the USY ample meaured at 135 and 150 K. 23 The appearance o a central peak may ugget that a low exchange proce till exit at thee temperature. From thee two meaurement the ame 67 khz edge plitting in USY ample are obtained. According to the above reult, we may take an average value ω qm ) 68 khz or χ /2π ) 181 khz a the maximum value ω qm in our calculation or all o the aujaite ample. Moreover, the quadrupolar coupling contant at the at ite may be etimated or C 6 D 6 in liquid crytal phae. χ /2π i etimated to be 183 khz. Thereore, one may take χ / 2π χ /2π ) 181 khz in our calculation. Parameter and the Simulated DQF Spectrum. It i ound that the imulated DQF pectrum i not enitive to the variation τ i provided τ i < τ w. P, S c, τ w, and k may be etimated rom the line-width analyi and DQF pectrum with variou DQ creation time τ. In Figure 3, the eect o variou parameter on pectral line are demontrated. Figure 3a how the typical DQF pectra with the eect o the preence o at motion ite which reult in a central peak with P dependent intenity

7 5076 J. Phy. Chem. B, Vol. 103, No. 24, 1999 Chen and Hwang Downloaded by NATIONAL TAIWAN UNIV on September 3, Figure 3. Eect o P, S c, k, and τ w parameter on the imulated DQF pectra. The DQF pectra are not enitive to τ i and τ parameter provided that τ i < τ w and τ < In (a) the parameter ued are P ) 0.5, S c ) 0.7, k ) , and τ w ) 50 n. In (b), the ame parameter are ued except P ) 1.0. In (c)-(), one o the parameter ued in (a) i altered and denoted in the buttom o the pectra. (Figure 3c). However, it vanihe in the DQF pectra with no at motion ite conidered (Figure 3b, P ) 1). A diplayed in Figure 3, d and e, the wiggling wing in the DQF pectra diappear in the cae o S c, 1 and k τ g 1(τ ) 40 µ), repectively. A mall S c indicate that the eective reidual quadrupolar interaction i inigniicant. A large k value repreent a at exchange proce which account or the vanih o the wiggling wing due to the contribution rom the at motion ite. Moreover, in Figure 3e a the creation time increae, the two pattern o negative intenity line correponding to k τ < 1(k ) ) and k τ >1 (k ) ), repectively, diplay oppoite trend a depicted in Figure 3e. Alo in the cae o k τ >1, an intene negative peak i oberved with increaing k τ. Thereore, thee eect may be ued to ditinguih the ource or the vanihing o the wiggling wing. The eect o wobbling motion may be revealed rom the pattern o the central peak with increae o creation time. A hown in Figure 3a,, or long τ w it diplay monotonically decreaing central peak while or hort τ w it how a revere trend with increaing creation time. Figure 4. Experimental (let) and imulated (right) 2 H double quantum iltered pectra o (a) NaY and (b) DAY low-loading ample at the variou cited temperature. For a given temperature, the our DQF pectra rom let to right are obtained with DQ creation time t given by 40, 160, 280, and 400 µ, repectively. Etimation o τ rom DQF Spectra. Under the exchange proce, the contribution o the at motion ite reult in the central peak which appear in Figure 4 and 5 or USY and DAY ample. For NaY ample, the central peak i not o obviou epecially or a mall population o the at motion ite (P 0.1). Thu, all the imulated reult are inenitive to τ a long a the magnitude are kept below The motional narrowing condition are required or τ in order to match the narrow width o the central peak. Parameter Fitting Algorithm. Except the one oberved at 350 K in NaY ytem howing almot equally negative intenity with increaing creation time τ (Figure 4a), all the intenity o negative peak o experimental DQF pectra decreae a the creation time increae rom τ ) 160 µ. Following the imulated DQF pectra with variou k, P, and S c, the upper bound o k may be et to be ince a large k yield a DQF pectra imilar to the pectra hown in Figure 3e with k ) Neverthele, the appropriate k value or the DQF pectra at 350 K in NaY ytem hould be about the maximum value we et.

8 Benzene Molecule Adorbed on Faujaite Zeolite J. Phy. Chem. B, Vol. 103, No. 24, Downloaded by NATIONAL TAIWAN UNIV on September 3, Figure 5. Experimental (let) and imulated (right) 2 H double quantum iltered pectra o (a) NaY, (b) DAY, and (c) USY high-loading ample at the variou cited temperature. For a given temperature, the our DQF pectra rom let to right are obtained with DQ creation time t given by 40, 160, 280, and 400 µ, repectively. A we examine the DQF pectra o NaY ytem at 290 K, the eective S c i inigniicant and the contribution to the pectra i dominantly rom the low motion ite. The upper limit o τ w may be etimated rom the line width obtained in NaY ytem at thi temperature; i.e., in accordance with eq 5 and 7 the upper bound o τ w may be etimated rom the line width ν 1/2 ) (1/π)R 11 (3/2π)C τ w. It yield τ w 500 n. The lower bound o τ w may be determined rom the ω 0 τ w. 1 in accordance with ield-independent ingle quantum and DQF pectra. It yield τ w 3 n. Taking advantage o the contraint impoed on k and τ w, we may obtain everal et o parameter (P, S c, k, and τ w ) which have good it to the SQ Lorentzian line width within the experimental error. The contrained nonlinear optimization package o MATLAB 5.1 (The Math Work Inc., MA), which i baed on the equential quadratic programming algorithm, wa ued to it the ull width at hal-height and one-third height o SQ pectra at two ield. Further creening or the good et may be done by comparing the DQF pectra at creation time τ ) 400 µ with regard to the three criteria decribed below or comparing DAY and USY ytem: (1) The intenity ratio o central peak to the larget wiggling peak. The reult i P enitive. (2) The intenity ratio o the larget wiggling peak to the econd larget wiggling peak. The reult i S c enitive. (3) The intenity ratio o central peak to the larget negative peak. The reult i k enitive. A compared to the NaY yem, the experimental DQF pectra how a imple tructure. The ollowing itting criteria are ued intead: (1) Separation o the negative doublet and the line width at hal-height o DQF pectra with τ ) 40 µ are invoked to evaluate P and S c. (2) The intenity ratio o the central peak to the negative peak at τ ) 400 µ i invoked to evaluate k. Following the above comparion, we may exclude mot o the inappropriate et o parameter. Then we ue the remaining et o parameter to imulate the DQF pectra with other creation time and make urther creening o P, S c, and k et. According to the relative intenity o the central peak in the DQF pectra at variou creation time, we may then chooe the bet parameter et with the reined τ w. It i ound that there exit no other ditinct et o parameter to it the DQF pectra equally well. It wa ound that the T 1 i not enitive to the etimated value o P, S c, and k (or k ), but very enitive to the choice o τ i, which i 1-2 order maller than τ w. Finally, we ue the parameter et to calculate the T 1 value at and MHz in order to obtain an unambiguou τ i value. Reult o DQF Spectra and T 1 Value. Figure 4 and 5 how the experimental DQF pectra together with their correponding imulation, or low-loading and high-loading ample, repectively, over a range o temperature at MHz. 2 H longitudinal relaxation time meaurement were conducted over the ame temperature range a or the DQF and line-width meaurement. The experimental and calculated T 1 reult obtained at the two reonance requencie or both low- and high-loading ample are lited in Table 1 and 2, repectively. Except or the T 1 data or the DAY ample at MHz and 210 K, the conitency between experimental and calculated reult in thee two ield i excellent. Dicuion The aujaite zeolite poe dierent adorption ite in the upercage. Adorption o benzene ha been tudied by inrared pectrocopy over NaY, DAY, and USY. 3,5 In NaY, it i wellknown that two pair o band correpond to the υ 5 + υ 17 and υ 10 + υ 17 vibration o liquid benzene at 1960 and 1815 cm -1, and the conequent hit to higher wavenumber and plit into two pair o band i related to benzene adorption on S II ite and on oxygen atom o 12 ring window (or W ite), repectively. 4 The high-wavenumber peak aigned to benzene adorbed on the W ite grow with a benzene loading higher than 2-3 molecule per upercage. For lower-loading ample, benzene give only one pair o CH band aigned to benzene interacting with the Na cation at S II ite. Thi agree with the reult o X-ray powder diraction 35 and MQMAS evaluation o 23 Na iotropic hit and econd-order quadrupolar eect. 17 Molecular mechanic imulation alo conirm uch benzene ite on dierent poition in NaY. 35 Both o the above reult how that adorption at W ite i weaker than that occurring with benzene at I S ite. A or benzene adorbed on DAY and USY, the interaction o the benzene π-electron cloud with the hydroxyl aluminum ite reult in adorption in uch a ytem, while no igniicant adorption interaction o benzene on the

9 5078 J. Phy. Chem. B, Vol. 103, No. 24, 1999 Chen and Hwang Downloaded by NATIONAL TAIWAN UNIV on September 3, TABLE 3: Parameter Ued in the Fitting o T 1, Line Width, and Double Quantum Filtered Spectra or Low-Loading Sample a zeolite temp (K) P S c τ i (n) τ w (n) k 10-2 ( -1 ) NaY ( ( ( ( ( ( ( 2 60( DAY ( ( ( ( ( ( ( ( USY b ( ( ( ( ( ( ( ( a 10% error i expected in k, 5% error in P, and 20% error in S c. b Thi reult ha been hown in re 16. W ite ha been detected. Auerbach et al. ued a kinetic Monte Carlo method to calculate ite-to-ite hopping activation energie and ound everal kind o ite-to-ite hopping motion between 200 and 300 K, e.g., S II T S II,S II T W, W T S II, and W T W within the rate ranging rom 10 4 to or benzene in NaY. Thi may et a time cale or ite hopping and alo or the concomitant mall-angle reorientation. 15 It allow an eicient average or the procee or NaY ytem. The ame condition i aumed to be available in DAY ytem. Furthermore, the application o modiied cone model with ite-to-ite hopping proce in the preent work i qualitatively imilar to the model o benzene orientation randomization (BOR) ued by Auerbach and Meitu. 13 In the early time o orientation correlation unction, the orientation randomization in their model i aociated with the ite-to-ite hopping proce. The long-time behavior o orientational correlation unction may be correlated to the τ w proce o preent model ince the wobbling motion i induced by the benzene mobility in the cage. The long-time BOR rate give a correlation time 500 n at 300 K. It agree well with τ w 300 n or our NaY ytem at thi temperature. The long-time BOR rate i controlled by the rate o cage-to-cage motion. Thi ugget a new approach rom NMR relaxation to etimate el diuion coeicient in zeolite. Although the wobbling motion decribed here and the mall-angle reorientation ound by Iort et al. both reult in mall-angle reorientation or benzene molecule on adorption ite, the ormer i related to S II -W hopping while the later i aociated with S II -S II hopping. Since there are dierence in time cale and the phyical origin o the above two procee, one may decouple thee two procee. Even without intracage tetrahedral jump between adjacent ite, e.g. in the USY ample, the wobbling motion till exit and it i aociated with intercage diuion. Low-Loading Sample. In accordance with the reult o the itting hown in Table 3, maller magnitude o S c may be expected in the NaY or DAY ytem that contrat with the S c value oberved in the USY ytem. Thereore, one may expect a mall correlated order parameter S c (or reidual interaction ω c ) or a aujaite with more ymmetrically arranged multiadorption ite in the ame upercage. Owing to thee dierence, the DQF pectra recorded in Figure 4 or benzene adorbed in DAY ramework how le wiggling in the houlder o the pectral peak than in that or USY publihed previouly. 23 It i alo ditinctly dierent rom thoe acquired or the benzene/ NaY ytem which give the mallet S c value. According to the line width lited in Table 1, due to a higher Si/Al ratio, TABLE 4: Parameter Ued in the Fitting o T 1, Line Width, and Double Quantum Filtered Spectra or High-Loading Sample a zeolite temp (K) P S c τ i (n) τ w (n) k 10-2 ( -1 ) NaY ( ( ( ( ( ( DAY ( ( ( ( ( ( USY ( ( ( ( ( ( a 10% error i expected in k, 5% error in P, and 20% error in S c. which ha ewer cation, and weaker hydroxyl aluminum ite are expected in the DAY and USY ytem, benzene become more mobile within thee ytem. 22 The temperature dependence o the imulation parameter i hown in Table 3 or lowloading ample. A expected or a thermally activated proce, P and k decreae with the increae o temperature. From the Arrheniu analyi or the data hown in Table 3, the activation energy o wobbling motion and in-plane rotation or the NaY ample are much larger than thoe or the DAY and USY ample. Furthermore, the magnitude o both τ w and τ i are in the order NaY > DAY > USY. They all indicate that the mobility o benzene i trongly correlated with the number o adorption ite and the trength o adorption. The reult agree well with the act that the enthalpy o adorption or a benzene- NaY ytem i about 5 kcal/mol cation per unit cell larger than that or a benzene-dealuminated Y ytem. 36 It i expected that only NaY and DAY may poe multiple adorption ite available or benzene. The proce o ite-toite hopping may reduce the net trength o reidual quadrupolar interaction and thereore the decreae o S c in NaY and DAY ytem with increaing temperature. However, in contrat, the S c value in the USY ytem increae with increaing temperature. From the phyical igniicance o τ j and D in the jump model decribed in the Appendix, their temperature dependency i in the oppoite direction. In multiple ite adorption uch a in NaY, a the temperature rie, the decreae o τ j dominating the eect o increaing D give a decreae in S c, a hown in Table 3 (alo ee Table 4). For the USY ytem, ince there i a lack o ite-to-ite hopping, the diuion proce i the dominant contributor to the increae o S c. High-Loading Sample. It i ound that benzene adorbed at S II ite within NaY zeolite give an average diplacement rom the Na + ion o about 3Å From 23 Na MQMAS tudy, more ymmetrical urrounding o quadrupolar interaction i ound in NaY with a increaing o benzene loading. 17 Beide, or a loading o three benzene molecule per upercage, tudied by 1 H MQ-NMR, a much horter MQ coherence time or a much ater pin network growth rate i oberved in the NaY ytem. 16 Thu, in high-loading ample, occupation o dierent Na + S II ite by benzene molecule in the ame upercage would generate barrier or benzene rotation. Thi upport our obervation that a lower internal rotation rate wa ound. For benzene adorbed on hydroxyl aluminum ite o DAY and USY, there are about 12 and 4.8 hydroxyl aluminum ite per unit cell o aujaite. However, one cannot be ure whether the location o the hydroxyl are in the upercage or in the odalite cage. There are le than 1.5 and 0.6 hydroxyl aluminum ite per upercage in DAY and USY, repectively. Due to a mall number o benzene ite and a weaker adorption interaction in thee ytem, the intermolecular ditance between benzene

10 Benzene Molecule Adorbed on Faujaite Zeolite J. Phy. Chem. B, Vol. 103, No. 24, Downloaded by NATIONAL TAIWAN UNIV on September 3, molecule may not be a cloe a in NaY ytem. Alo, a compared with thoe in low-loading ytem (c. Table 3 and 4), one may iner that the rotation barrier reulted rom high benzene loading low down the in-plane rotation appreciably in all thee aujaite ytem. However, in DAY and USY ytem the wobbling motion correlation time τ w o high-loading ample i igniicantly maller than that o low-loading ample, wherea negligible dierence are ound between low- and highloading NaY ample. Thi may be due to a tronger trength o adorption and more Na + ite in the latter ytem. With increaing loading in DAY and USY, additional benzene molecule are hardly aected by the interaction with weak adorption ite. Thu the loading eect account or the maller value o τ w and k ound in thee ytem. In Table 3 and 4, except or the τ i and k procee, no loading eect i ound or the other itting parameter in the NaY ytem. The tudy o powder neutron diraction or NaY indicate the diplacement, by about 0.09 Å, o Na in S II ite along the cube diagonal toward the center o the upercage. Thi relect the adorption o benzene on S II ite becoming a little more diordered with the increaing loading. 17,37 Thereore, only negligible eect on S c are ound in high-loading ample. However, in DAY and USY the magnitude o P i dramatically reduced with loading. Unlike the cae o NaY, there are le adorption ite per upercage in DAY and USY. Thereore, the chance to ind appropriate ite ituated in the ame upercage imultaneouly to accommodate additional benzene molecule i relatively rare in DAY and USY ytem. The loading eect lead to a mall P ound in thee ytem. Concluion Thi work preent more detailed reult regarding the comparion between dierent aujaite and the loading eect o the benzene molecule in the upercage. For all ample, the magnitude o τ w and τ i are trongly correlated with the trength o adorption and the ree volume available or reorientation. S c value can be ued to dierentiate the nature o reidual quadrupole interaction remaining, ater averaging over the ditribution o adorption ite, rom the proce o ite-to-ite hopping. A lower internal rotation i ound in NaY with increaing loading. It i conitent with the act that the diplacement o benzene rom S II ite i toward the center o upercage, and then a cloer eperation o benzene molecule in NaY upercage i expected. DQF pectral analyi in conjunction with the uual relaxation tudie may be a better combination o NMR relaxation method or characterizing the dynamic and adorption interaction in the zeolite ytem. Thi tudy orm part o a continuing erie o tudie o NMR method or the invetigation o diuion and adorption in porou material. Acknowledgment. Thi work wa upported by the National Science Council o the Republic o China under Grant No. NSC M and No. NSC M We alo thank Dr. Hong-Ping Lin or hi aitance in N 2 adorptiondeorption iotherm meaurement. Appendix In our approach to the exchange adorption proce, it may be unneceary to peciy the ite interaction preciely. Conidering the exchange proce to be o diuive origin may be uicient. The motion o adorbate may be decribed by the diuion equation in the pace peciied by the adorption coordinate S, e.g. P(S,t) ) D 2 P(S,t) t S 2 where D i the diuion coeicient in unit o -1. Here, the probability ater time t that it will be at ite S in ds relative to the initial ite at S ) 0 i given by the olution o eq A1. P(S,t) ) 1 πdt exp(-s2 /(4Dt)) (A1) (A2) The adorbate molecule are conidered to pend mot o the time, characterized by τ j, reiding in a given ite with S * 0 beore moving to the ubequent ite. Similar to the treatment in Torrey theory 41 or jump diuion, the time interval t will not be contant, but will be governed by a probability ditribution o an exponential orm. Thu, in the preent cae, the probability denity (S) along the adorption coordinate may be obtained by multiplying eq A1 by exp(-t/τ j )dt/τ j and then integrating the reulting expreion over t. Hence (S) ) 0 P(,t) exp(-t/τj ) dt τ j ) 1 Dτ j exp(-s/ Dτ j ) (A3) The probability denity ollow the exponential ditribution which ha been adopted in eq 15, although the normalization actor i modiied or the preent cae with boundary condition et at S ) 0 and S ) 1. One may readily identiy the actor S c in the exponent o eq 15 a (Dτ j ) 1/2.(Dτ j ) 1/2 may be conidered to be a characteritic jump ditance in S pace. Beyond thi ditance the probability (S) drop o. Reerence and Note (1) Lechert, H. Catal. ReV. Sci. Eng. 1976, 14, 1. (2) Eckman, R.; Vega, A. J. J. Am. Chem. Soc. 1983, 105, (3) Barthomeu, D. Catal. ReV. 1996, 38, 521, and pertinent reerence therein. (4) de Mallmann, A.; Barthomeu, D. J. Chem. Soc., Chem. Commun. 1989, 129. (5) Su, B.-L. Stud. Sur. Sci. Catal. 1995, 97, 303. (6) Datka, J.; Sulikowki, B.; Gil, B. J. Phy. Chem. 1996, 100, (7) Peier, H. NMR-Baic Principle and Progre; Springer; Berlin, 1972; Vol. 7. (8) Peier, H. Phy. Rep. 1976, 26, 293 (Phy. Lett., Sect. C). (9) Zibrowiu, B.; Caro, J.; Peier, H. J. Chem. Soc., Faraday Tran , 84, (10) Demonti, P.; Yahonath, S.; Klein, M. C. J. Phy. Chem. 1989, 93, (11) Auerbach, S. M.; Henon, N. J.; Cheetham, A. K.; Metiu, H. I. J. Phy. Chem. 1995, 99, (12) Auerbach, S. M.; Metiu, H. I. J. Chem. Phy. 1996, 105, (13) Auerbach, S. M.; Meitu, H. I. J. Chem. Phy. 1997, 106, (14) Schaeer, D. J.; Favre, D. E.; Wilhelm, M.; Weigel, S. J.; Chmelka, B. F. J. Am. Chem. Soc. 1997, 119, (15) Iort, O.; Boddenberg, B.; Fujara, F.; Groe, R. Chem. Phy. Lett. 1998, 288, 71. (16) Pearon, J. F.; Chmelka, B. F.; Shykind, D. N.; Pine, A. J. Phy. Chem. 1992, 96, (17) Hu, K.-N.; Hwang, L.-P. Solid State Nucl. Magn. Reon. 1998, 12, 211. (18) Eliav, U.; Navon, G. J. Magn. Reon. 1994, B 103, 19. (19) Eliav, U.; Shinar, H.; Navon, G. J. Magn. Reon. 1992, 98, 223. (20) Shar, Y.; Eliav, U.; Shinar, H.; Navon, G. J. Magn. Reon. 1995, B107, 60. (21) Bull, L. M.; Henon, N. J.; Cheetham, A. K.; Newam, J. M.; Heye, S. J. J. Phy. Chem. 1993, 97, (22) Soua Goncalve, J. A.; Portmouth, R. L.; Alexander, P.; Gladden L. F. J. Phy. Chem. 1995, 99, (23) Chen, Y.-H.; Chang, W.-T.; Jiang, P.-C.; Hwang, L.-P. Microporou Meoporou Mater. 1998, 21, 651. There are miprint in the exchange

11 Downloaded by NATIONAL TAIWAN UNIV on September 3, J. Phy. Chem. B, Vol. 103, No. 24, 1999 Chen and Hwang rate term. The correct one i hown in eq 5 in the preent work. Alo the expreion o S and D (4) 00 hould be corrected a obtained S ) 1 / 2 co β(1 + co β) and D (4) 00 ) (S/8)(28S - 7(1 + 8S) 1/2 + 1), repectively. (24) Boddenberg, B.; Burmeiter, R. Zeolite 1988, 8, 488. (25) Boddenberg, B.; Beerwerth B. J. Phy. Chem. 1989, 93, (26) Blum, K. Denity Matrix Theory and Application Plenum: New York, The component o the irreducible tenor et (tate multiple) preented in thi reerence i denoted by T Kq which i the ame a σ Kq deined in thi work. (27) Ernt, R. R.; Bodenhauen, G.; Wokan, A. Principle o Nuclear Magnetic Reonance in One and Two Dimenion; Clarendon: Oxord, UK, (28) Brink, D. M.; Satchler, G. R. Angular Momentum; Oxord Univerity Pre: London, (29) Price, W. S.; Ge, N.-H.; Hong, L.-Z.; Hwang, L.-P. J. Am. Chem. Soc. 1993, 115, (30) Jacoben, J. P.; Bildoe, H. K.; Schaumburg, K. J. Magn. Reon. 1976, 23, 153. There i a miprint in eq 32. Intead o 5 2/7 a printed, the coeicient o D (2) 00 in J 2(2ω r) hould be corrected a 10/7. (31) Brainard, J. R.; Szabo, A. Biochemitry 1981, 20, (32) Wong, T. C.; Wang, P.-L., Duh, D.-M.; Hwang, L.-P. J. Phy. Chem. 1989, 93, (33) Millett, F. S.; Dailey, B. P. J. Chem. Phy. 1972, 56, (34) Lambert, J. B.; Niehui R. J.; Keeper J. W. Angew. Chem., Int. Ed. Engl. 1981, 20, 487. (35) Klein, H.; Kirchhock, C.; Fue, H. J. Phy. Chem. 1994, 98, (36) Barthomeau, D.; Ha, B.-H. J. Chem. Soc., Faraday Tran. I 1973, 69, (37) Fitch, A. N.; Jobic, H.; Renouprez, A. J. Phy. Chem. 1986, 90, (38) Lechert, H.; Wittern, K.-P. Ber. Bunen-Ge. Phy. Chem. 1978, 82, (39) Germanu, A.; Koager, J.; Peier, H.; Samulevic, N. N.; Zdanov, S. P. Zeolite 1985, 5, 91. (40) Homann, W.-D. Z. Phy. Chem. 1976, 257, 315. (41) Torrey, H. C. Phy. ReV. 1953, 92, 962.