13484
J. Phys. Chem. 1993,97, 13484-13495
Solid-state Double-Resonance NMR Experiments Involving Quadrupolar and Spin l / z Nuclei C. A. Fyfe,’ K. T. Mueller,’ H. Crondey, and K. C. Wong-Moon Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC V6T 121, Canada Received: Februory 16, 1993; In Final Form: July 13, 1993@
In this work we describe coherence-transfer and dipolar-dephasing doubleresonance N M R experiments that demonstrate spatial proximity of quadrupolar and spin ‘/znuclei (other than protons) in solids. These experiments exploit heteronuclear dipolar couplings, whose magnitudes are proportional to the inverse third power of the internuclear distance and are therefore extremely sensitive to the separation of the coupled spins. Coherence transfer through cross-polarization is observed in both directions between 27Al( I = 5/2) and (I = l/2) nuclei in the inorganic aluminophosphate framework systems VPI-5 and AlP04-8, and an experimental investigation of the parameters controlling the efficiencyof the transfer is presented. Dipolar-dephasing difference experiments, rotational-echo double-resonance (REDOR), and transferred-echo double-resonance (TEDOR) experiments under magic-angle spinning conditions are also demonstrated. Two-dimensional extensions of the crosspolarization and TEDOR experiments reveal the dipolar couplings between specific pairs of 27Aland 31Pnuclei in two-dimensional correlation spectra, directly mapping connectivities from distinct sites with resolved N M R resonances.
Introduction Nuclear magneticresonance (NMR) spectroscopy has become a powerful sourceof informationregarding nuclear environments in solid-state systems.1,2Whereas diffraction techniques are useful for the investigation of long-range periodicities in solids, NMR is an important tool for the investigation of local ordering and topology, as well as bonding g ~ m e t r i e s . ~ When studying amorphous solids, for example, diffraction experiments are unable to provide detailed information regarding local structure, while NMR remains sensitive to local bonding parameters? and resonances from inequivalent sites with different environments may be resolved. In the study of crystalline solids, the use of NMR and diffraction methodstogether provides a more complete understanding of structure and bonding. Magic-angle spinning (MAS) NMR5s6 is used routinely to average anisotropic interactionsthat broaden resonance lines from magnetically dilute nuclei in polycrystalline solids. Crosspolarization techniques7** or multiple-pulse decouplingschemea9Jo may be combined with MAS to increase the sensitivityi1 or resolutionI2 of the experiment. The major succcss of MAS techniques has been in the resolution of signals from crystallographically inequivalentspin l / z nuclei in solids, since in normal one-dimensional MAS NMR spectroscopy, the chemical shift and heteronuclear dipolar coupling tensors are averaged to their isotropicvalues (cis0and zero, respectively). Homonuclear dipolar interactions may also be averaged by spinning at a frequency greater than the coupling strength,I3 which has led to the development of ultrafast spinning devices.I4 Success from the application of solid-state NMR in a variety of fields has encouraged many advances in the experimental techniques.ls One particular recent gain has been in the ultimate resolution available in the spectra of quadrupolar nuclei. For half-odd integer spins greater than spin the central ( I / * -I/Z) transition is not affected to first order by the quadrupolar interaction, while the other Am = 1 transitions (the satellites) are broadened and spread over a wide frequency range. The central transition experiences a second-order quadrupolar broadening that is not averaged completely by MAS experiments.l6,l7 It was
-
* To whom correspondenceshould be addressed. t Present address: Department of Chemistry, The Pennsylvania State University, 152 Davey Laboratory, University Park, PA 16802. Abstract published in Aduonce ACS Absrracrs, October 1 , 1993. 0022-365419312097-13484$04.00/0
realized that more complete averagingcould be accomplished by spinning about more than one axis during the experiment,leading to the development of dynamic-angle spinningisJ9and doublerotation20*2i NMR. Using these new techniques, resonances from quadrupolar nuclei may now be resolved, with lines as narrow as those from spin ‘/znuclei under MAS. A second important recent advance in the NMR of solids is the ability to determine connectivities between nuclei which are coupled via scalar or dipolar interactions? Focusing specifically on heteronuclear dipolar interactions, distance information may be obtained directly from the NMR spectrum of a static sample if the spin interactions are simple enough to show a well-resolved multipletor a Pake pattern from a polycrystalline sample, through this is rarely the case. When a broad line shape is composed of contributions from some nuclei with no heteroatoms nearby and others with dipole-coupled spin partners, the technique of spinecho double-resonance (SEDOR) may be used to discern between the “connected” or Yunconnected”species.22v23In cases where there are many resonances in the spectrum which are broad and overlapping, MAS is conveniently used to narrow and resolve the resonances, at the expense of averaging the dipolar couplings to zero over each rotor period. Munowitz and Griffinz4discuss MAS experiments where the dipolar and chemical shift interactions are separated in a two-dimensional correlation plot, aimed specifically at larger dipolar interactions such as those found between I3Cand ‘H in organic solids. For weaker heteronuclear couplings, this method becomes impractical due to the need for slow MAS spinning which introduces the complication of many sidebands in the spectra. To study weaker I3CJ5N dipolar connections, Gullion and Schaefer introduced rotational-echo double-resonance (REDOR) exprimen@ and have applied them to determine distancesbetween pairs of spin l / 2 nuclei in complex biological The extension of the REDOR techniqueto eliminate complications arising from natural abundance background signals led to transferred-echo doubleresonance (TEDOR) spectroscopy,27where coherence transfer between dipole-coupled nuclei gives rise to NMR spectra from only dipolar coupled spins. Using a combination of the REDOR and TEDOR experiments, a fluorinGcarbon internuclear distance of 8 A has been measured.Z8 SEDOR and other double-resonanceexperiments have been used in inorganic systems where nuclei such as Z7Aland (or Z9Si)have been shown to be conne~ted,2~ and a triple-resonance 14N-I )C-IH experiment has been reported which allows the entire 0 1993 American Chemical Society
Quadrupolar and Spin
l/2
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13485
Nuclei Alp04 -8
(90)
SpinLock
S
(90)
Spin Lock
VPI-5 n
n
- t2-
S
V
Figure 1. Projections ([Ool]) of layers in the framework structures for the two aluminophosphates, AlP04-8 and VPI-5. The unit cells are shown as dashed boxes. Each framework vertex represents a phosphorus or aluminum site, and the lines connecting the vertices are oxygen linkages between the strictly alternating aluminum and phosphorus atoms. Octahedral aluminum sites are formed by coordination with two water molecules at some of the tetrahedral sites.
14N spin reservoir to be perturbed under MAS conditions and monitored via the effect on the 13Cspin system.30 Many compounds of interest in solid-state chemistry contain quadrupolar nuclei such as B, 1 7 0 , 23Na,or 27Al,and it is clear that dipolar discrimination techniques could be of use in determining internuclear connectivities and obtaining distance information in these situations. In addition, it will often be advantageous with these systems to utilize the polarization of quickly relaxing quadrupolar spins to increase the sensitivity or speed of accumulation of signals from coupled spins with very long spin-lattice relaxation times. Difficulties, however, arise due to the increased complexity of the spin energy levels for nuclei with spin greater than l/2. For example, Vega31z2has shown that for quadrupolar nuclei the spin-locking of the central transition is a complex process due to the time dependence of the first-order quadrupolar splitting in rotating samples. In this work we expand upon earlier reports of crossp o l a r i z a t i ~ and n ~ ~REDOR and TEDOR experiments34on solidstate systems involving quadrupolar and spin l / 2 nuclei. In addition, other dipolar-dephasing experiments are considered in order to form a more complete picture of the available techniques. One main concern is the feasibility of using quadrupolar nuclei in all of these experiments,as well as the experimental advantages or disadvantageswhen consideringdifferentsequencesin inorganic systems. Techniques found applicable to systems of many spin l / 2 nuclei, such as an abundant proton bath coupled to isolated and dilute spin l / 2 species (e.g., 13Cor 29Si),must be carefully reconsidered in order to determinethe reliability of the information obtained when considering more general systems. Likewise, the dipolar-dephasing experiments are usually applied to isolated pairs of spin I/2 nuclei such as 13Cand 15N, and their general applicabilityto more complex geometriesand systemsof multiple nonisolated spins must be established. Experimental Section The samples chosen for study were the two aluminophosphate molecular sieves VPI-535 and A1P04-8.36 The latter was formed by thermal treatment of VPI-5,37which involved calcining the sample at 400 'C overnight and then rehydrating by stirring in water overnight. The structure of AlP04-8 as well as the mechanism of its formation from VPI-5 is still a matter of debate.37 Projectionsof the proposed structures for both aluminophosphates are reproduced in Figure 1. In both samples, the basic bonding
I
Figure 2. Pulse sequences for cross-polarizationexperiments: (a) spinlocking pulse sequence used for polarization-transferfrom Z spins to 5' spins; (b) two-dimensional heteronuclear correlation experiment with cross-polarization. The tl time period (Z spin evolution) is varied for a series of experiments with acquisition of the S spin free induction decay during the t2 period.
unit is an A1-O-P linkage joining tetrahedrally-coordinated P sites with octahedral or tetrahedral A1 sites. The arrangements of one aluminum or phosphorus atom and four shared (bridging) oxygens are strictly alternating in these aluminophosphates, leading to perfectly ordered structures whose isotropic average spectra show signalsfor the crystallographicallyinequivalent sites for each nucleus in the unit cell. As prepared, both aluminophosphates contain water of hydration with two water molecules completing an asymmetric octahedral coordination at certain aluminum sites. Average distances between nearest-neighbor A1 and P atoms are approximately 3.1 A in both samples. VPI-5 was chosen as a representative example of three-dimensional inorganic framework structures, and the unit cell is of sufficient complexity that a number of resonances are observed in the onedimensional MAS spectra of both 27Aland 31Pnuclei at 9.4 T (two for 27Aland three for 31P). The unit cell of the AlP04-8 is somewhat more complex, with at least five inequivalent T sites for both 27Aland 31Pin the dehydrated form, and its investigation here addresses the general applicability of these techniques. NMR experiments were performed on a Bruker MSL-400 spectrometer where the resonance frequencies for 27Aland 31P are 104.264 and 161.977 MHz, respectively. The 31Pchannel was the normal X channel on the spectrometer, while the 27Al channel was obtained by external modification (mixing, amplification, and remixing before detection) of the frequency from the lH channel. The probehead contained a home-built MAS system with a double-tuned solenoid coil. Internal trapping of the 31Pfrequencywas employed,complemented by external filters on both channels to prevent pulse breakthrough back to the amplifiers. The rotational frequency of the MAS spinner was kept constant during each of the experiments,monitored through the sidebands in the 31PMAS spectrum of VPI-5. The spinning speeds in different experiments ranged from 2.9 to 3.3 kHz. Nominal 90° pulse lengths for both channels were 11 ps, and these were set by a null 180' pulse on the 31Pchannel (22 ps) and a maximum signal intensity for 90' nutation of the 27Alspins ( 11 ps) in the solid samples themselves. The aluminum 90' pulse was found to be approximately one-third of the 90° time for 27Al spins in solution (saturated aqueous Al(NO&), confirming that only the central (+l/2 J/2) transition was being irradiated and d e t e ~ t e d . ~ *The - ~ ~power of the 31Ppulses was varied for certain experiments using an attenuator inserted before the highpower radio-frequency (rf') amplifier. The MAS experiments were one-pulse experimentswith signal averaging over a number of free induction decays. Crosspolarization MAS experiments were performed using the conventional spin-lock sequence* as shown in Figure 2a. The
-
Fyfe et al.
Figure 3. Dipolar-dephasing difference experiments under MAS conditions with a rotational period of rr: (a) Difference experiment where a signal from a spin echo is recorded first with no S spin irradiation. The experiment is immediately repeated with subtraction of the spin-echo signal obtained with irradiation of the S spins during the first half of the experiment. (b) Modification of (a) to take into account instrumental timing errors which occur when pulses are not applied during the first part of the experiment.
-
Hartmann-Hahn matching condition7 for Z and S spins (not necessarily spin l / 2 ) must be modified if only the + * / 2 -l/2 spin transitions are irradiated. This becomes
with yx the gyromagnetic ratio and B1.x the strength of the rf field for the X nuclei. For the spin 5 / 2 aluminum nuclei and spin l / 2 31Pnuclei, this becomes
Experimentally, this corresponds to setting the pulse power for both channels so that the 90’ times are equal, and this was determined experimentally as explained above. In separate experiments, both 27Aland 31Pnuclei were used as sources of the magnetization which was transferred by cross-polarizationto the other spin species. After the contact time where both rf fields are on, free induction decays were accumulated and alternately added and subtractedfrom memory following a reversal of rotating frame spin temperature in order to suppress experimental artifacts.40 Null experiments were also carried out where one pulse or a set of pulses from the sequence in Figure 2a were removed to determine that the observed signal arose from only the cross-polarization process. For the VPI-5 sample, variable contact time 27Alto 31Pcrosspolarization experiments were performed, as well as experiments where the magnitude of the 31PB1 field was varied. A further cross-polarization experiment of interest is the study of the disappearance of the source ( I ) magnetization in the crosspolarization p r ~ c e s s . ~ . Experiments *.~~ werecarried out both with and without spin-locking fields applied on the S channel, and the signal obtained from the Z spins rather than the S spins. We observe the difference signal which reflects the depletion of the Z spin signal due to polarization transfer to the S spins. Dipolar-dephasing difference MAS NMR experiments are extensionsof those introduced by van Eck and c o - ~ o r k e r which s~~ resemble earlier SEDOR experiments.22The dipolar-dephasing techniques allow detection of coupled heteronuclei through the dipolar interaction between them. The pulse sequence used here differs from that originally proposed42by performing a difference experiment as shown in Figure 3, rather than two separate onedimensional experimentswith subsequent subtraction. In a perfect experiment, a spin-echo from the I nuclei is acquired and stored in memory (denoted [acq]+ in Figure 3a) followed by a second acquisition where the S spins are also irradiated during part of the experiment, and this is subtracted from memory (shown as [acql- in Figure 3a). The difference signal then reflects the
interaction of these heterospins via the dipolar interaction, though the mechanism for this behavior is complicated and will be addressed in the following section. The advantage of the direct difference experiment is that artifacts due to small variations in experimental conditions are minimized compared to running the experiments separately. Surprisingly, our attempts to acquire “null” signals in the dipolar-dephasing difference experiment by completely turning off or disconnecting the high-power amplifier for the S spins resulted in observationof a difference signal with nofield applied to theS spins. A simulation of small (microsecond) timing errors during spin-echo cancellation experiments provided the reason for such a strange observation. The “hidden” switching times within the spectrometer (Bruker MSL 400) do not allow perfect difference experiments to be performed with pulses on the S channel in one-half and not in the other. This may well Ire a general problem in performing these experiments and should always be taken into account. It was necessary to always turn on pulses on the S channel during the first half of each echo experiment, with switching of the resonance frequency between positive ([acq]+) and negative ([acql-) scans (Figure 3b). This was accomplishedwith a frequencyoffset list. Theusual resonance offset was 2-5 MHz to ensure that no rf power on the S channel was available during the accumulation of the normal spin echo, with reasonable attenuation provided by the Q of the probe and the band-pass tuning of the final stageof the high-power amplifier. Null experiments were then accomplished by having no pulses on the S spin channel, by having off-resonance pulses in both parts of the difference experiment, or by having on-resonance pulses in both parts of the experiment. The number of rotor cycles between the initial 90’ pulse and the refocusing pulse was five in each of these types of dipolar-dephasingdifference experiment. The modifications to a standard spin-echo pulse sequence (Figure 4a) necessary for the REDOR and TEDOR experiments are shown in Figure 4b,c. In the REDOR e ~ p e r i m e n ta, ~90’ ~ pulse is applied to the Z spins (either 27Alor 31P)to begin spin evolution. After an integral number of rotor cycles have passed (t = n7,/2, with n even), a 180’ refocusing pulse is applied to the Zspins and a spin echo is formed at time t = nrr. The amplitude of this spin echo is designated SO,the full signal with no dipolar dephasing. A second experiment (Figure 4b) is then carried out exactly as the first, but at half-integral multiples of the rotor cycles a 180’ pulse is applied to the S spins. The only exception is at time nr,/2 when the 180° pulse is applied to the Z spins in order to form the spin echo and no S spin pulse is applied. The outcome is a signal Sfthat differs from the SOsignal due to dephasing caused by the nonzero average dipolar coupling. Retention of the coupling is generated by a change of sign of the dipolar coupling every half rotor cycle (at each 180° pulse). When the signal Sfis subtracted from the full echo intensity SO,the difference signal (AS = So - Sf) is due solely to spins that have Z-S dipolar interactions. In the experimental pulse sequences actually used, a direct difference experiment was usually performed in order to obtain the AS signal, while a normal spin-echo experiment provided the So signal used for normalization. The A S signals were compared with those obtained from separate SO and Sfexperiments with results agreeing to within less than 1%. If n is the total number of dephasing rotor periods, then for an isolated pair of nuclei the dipolar dephasing of the REDOR signal is
A@,,n = n4&D7,
sin a! sin /3 cos /3
(3)
where D = ynsh/(27rr3) is the strength of the dipolar coupling, and the azimuthal and polar angles a and @ describethe orientation of the internuclear vector in the reference frame of the MAS spinner. The expected difference signal, normalized to the full echo intensity, is calculated by averaging over all possible
Quadrupolar and Spin
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13487
Nuclei
I/*
Now 180' pulses are necessary on both channels at t = nr,/2 in order to form the spin echo while also preserving the sign of the dipolar coupling. At the maximum of the spin echo the antiphase magnetization which has built up due to the retaining of dipolar interactions during n periods of dipolar dephasing is now transferred to the S spin system through a set of simultaneous 90° pulses on the Z and S channels. After a further m rotor cycles with continued dephasingpulses on the Sspins, the TEDOR signal (ST)may be acquired directly. The placement of the dephasing pulses on the S channel after the coherence transfer (differing from the scheme in ref 27) was chosen to minimize the number of pulses on the I nuclei (in our studies, exclusively the quadrupolar species). The dipolar dephasing in the first part of the TEDOR experiment evolves for n rotor periods as
A @ , , = n4&Dr,
-
Y
--mTr-
-
nTr ----mTr-
normal spin-echo sequence to retain dipolar coupling under MAS. The 180' pulses are applied to the S channel twice per rotor cycle, and the is recorded after this sequence. (c) For the TEDOR modified signal, Sf, experiment, 180' pulses are also applied for n rotor cycles to the S spins, shown here at sr/4 and 3rr/4 in each rotor cycle. Simultaneous 90' pulses then transfer the spin coherence from the I to the S spins, and further evolution for m rotor cycles under dipolar dephasing produces observable signal,ST.(d) The two-dimensionalheteronuclear correlation TEDOR experiment has a preliminary evolution of I spin magnetization during the 11 time period, with detection of S spin magnetization during the 12 time period. internuclear vector orientations: 2r
(5) with similar dephasing ( A ~ T ,during ~) the m rotor periods of evolution after the coherence transfer. Comparing eq 5 to eq 3, it can be seen that that the TEDOR dephasing now contains a cos a rather than the sin a dependence in the case of the REDOR signal. The complete TEDOR signal (ST)after n periods of preparativedephasing and m periods of evolution after the transfer is
(ST)n,m= ( 1 / 2 ? r ) ~ 0 2 r ~ ~ ~ ' 2 S i n ( ASin(A@T,,) @ ~ , n ) Sin j3 dj3 da (6)
Figure 4. Pulse sequences for REDOR and TEDOR experiments: (a) Conventional spin-echo under MAS conditions provides the reference signal, SO.No pulses are applied to the S channel. (b) Modification of
(AS/S0), = 1 - (1/2?r)s0
cos a sin j3 cos j3
rf2
cos(A@R,,) sin j3 dj3 d a (4)
The Fourier transform of the time-domain signal collected from the top of the echo separates the intensities from each of the resolved resonances in the Z spin spectrum. This was performed on a direct difference A S signal as well as on the full echo (SO) signal, and values of AS/& were calculated for each resonance by the ratio of the peak areas of the AS and SOspectra, including peak intensities in the spinning sidebands when present. Null experiments were performed by removing all of the S spin pulses during the experiments or, alternatively, moving them all offresonance by many megahertz. On the basis of our discussion of small timing errors in the dipolar-dephasing difference experiment, we also performed the REDOR difference (AS) experiment with S spin pulses on during both the SOand Sfspin echoes. Again, the resonance frequency was switched between the So and Sf spin echoes using a frequency offset list. For the TEDOR experiments (Figure 4c), the beginning of the experiment is much the same as in the REDOR experiment. The dephasing 180° pulses on the S channel are still one-half rotor cycle apart but are also now offset by rr/4; i.e., they occur at one-quarter and three-quarters of each cycle.27 Movement of the pulses by one-quarter of a rotor cycle makes certain versions of the TEDOR experiment possible (e.g.,single-point acquisition) and only affects the trigonometric function present in the evolution of the dipolar dephasing (see below). The desired goal of retaining terms with the dipolar coupling involved is still accomplished.
Once again, null experiments are performed by removing the 180° pulses on the S channel which are necessary for the dipolar dephasing. A two-dimensionalheteronuclear correlation experimentusing cross-polarizationcan be performed by preparing the I spins with a 90° pulse and then encoding their evolution frequencies in an initial (21) time period (see Figure 2b). The Z spin polarization is subsequently transferred to the S spins with a spin lock, and a free induction decay (the t 2 time domain) is accumulated from the S spins after each of a set of I spin evolution times. Twodimensional Fourier transformation then provides a correlation spectrum. Note that the spin lock, due to its direction along one well-defined axis in the rotating frame, may only select one orthogonal component of the Zspin magnetization in a particular experiment. This can be advantageous as the phase of the first pulse can be cycled using time proportional phase incrementation (TPPI)43v44 in order to obtain pure-absorption-phase line shapes in both spectral dimensions. A two-dimensional TEDOR experiment also involves an extra periodof encodingoftheZspinmagnetization(Figure4d). During t l , the magnetization of the Z spins evolves under the full MAS Hamiltonian. At the end of t l , a second 90' pulse removes one orthogonal component of the magnetization by returning it to the z axis, effectively selecting only one component for the rest of the experiment and again facilitating the use of TPPI. A TEDOR experiment is then begun for the magnetization that remains in the xy plane. The S spin signal is acquired for each of a set of t l values, and the data array is subjected to a two-dimensional Fourier transform. The result is again a two-dimensional correlation spectrum of the dipolar connected spins in the sample. These two-dimensional experiments were carried out with magnetization transfer from 27Alto 31P,as the short TIrelaxation times for the aluminum spins aid in rapid signal averaging of the data. Reasonable experimental times could not be obtained with transfer in the other direction, that is, from 3lP to Z7Al, due to the much longer T I relaxation times. Results and Discussion
27Aland 31PMAS NMR Experiments. Conventional onedimensional MAS experiments were performed on both samples investigated, yielding the 3IP and 27AlMAS spectra shown in
13488 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
I
100
.
,
7s
.
l
M
.
l
25
.
,
.
I
.
l
.
-25 -M Frequency (ppm from AI(NOJ)~) 0
Figure 5. One-dimensional MAS spectra for AIPOd-8 and VPI-5. Spinning sidebands in the spectra are labeled with an asterisk. (a) IIP signalfromAlPO4-8after 64scanswitha recycledelayof 30s. Lorentzian broadening of 25 Hz was applied. (b) I I P signal from VPI-5 after 16 scans with a recycle delay of 30 s. Lorentzian broadening of 25 Hz was applied. (c) 27Alsignal from AIP04-8 after 2048 scans with a recycle delay of 0.5 s. Lorentzian broadening of 50 Hz was applied. (d) 27Al signalfromVP1-5after128 scanswitha recycledelayof0.5s. Lorentzian broadening of 50 Hz was applied. Figure 5. For the spin IIP,M A S ideally averages the chemical shift anisotropy to zero for each of the magnetically inequivalent sets of nuclei. The resonances then appear at their isotropic shift values. Since the frequency of rotation is not larger than the frequency spread of the anisotropy, sets of spinning sidebands are also observed at multiples of the rotation frequency. The sidebands contain information regarding the anisotropic interaction that may be recovered from an analysis of the moments of the sideband pattem13or from a comparison of relative sideband For VPI-5, the 31Pspectra reveal three crystallographicallydistinct phosphorus sites. For AlPO4-8, three distinct resonances are also observed in an approximate ratio of 1:2:6. This indicatesthat thereareat least threedistinct 31Penvironments in the hydrated form of AIP04-8, most probably due to the water coordinated to neighboring (octahedral) aluminum sites.
Fyfe et al. The 27Al MAS spectra, acquired after short excitation pulses (tpulsc< 1 M, corresponding to magnetization tip angles of less than loo), show resonances from both tetrahedrally- and octahedrally-coordinated aluminum atoms, the latter appearing at lower frequency in both cases (less than 0 ppm). For quadrupolar nuclei such as 27Al,MAS does not completelyaverage the anisotropicsecond-orderquadrupolar interactionin the central transition. For tetrahedrally-coordinated aluminum atoms in VPI-5 and AlPO4-8, the strength of the local field gradients is such that, at 9.4 T, the resonance lines are broadened and shifted from their isotropic chemical shifts, but the broadened lines do not show dhthctsingularities. Therwnance for thecctahedrallycoordinated sites in VPI-5 shows a distinct powder pattern due to the enhanced second-order effects. Since the resonance from the octahedral site in VPI-5 is much broader than that from the tetrahedral site, the quadrupolar interaction must be stronger. In AlPO4-8, on the other hand, nutation NMR and proton-decoupled MAS NMR mea~urements~~ have been interpreted with the quadrupolar coupling at the tetrahedral site being larger than that at the octahedral site, and neither resonance shows a distinct second-order powder pattern. The second-order effects may be further averaged using the techniques of dynamic-anglespinning or double rotation NMR, but these were not used in the present work due to the additional experimental complexity involved. It is important to note that the tetrahedral and octahedral sites can still be resolved from each other at high field without the use of DAS or DOR. The DOR technique has been applied previously to VPI-5,47*48 and splitting of the tetrahedral resonance into two lines of equal intensity has been observed. One-Dimemsioml Cross-PolarizationExperiments. One-dimensional cross-polarization experiments were carried out with polarization transfer in both directions between phosphorus and aluminum nuclei, that is, from 27Alto 31Pand from SIP to 27Al. Representativeresults are shown in Figure 6for VPI-5 and AlPO48. Null experiments are also shown, confirming that each signal arises from the cross-polarization process and not as the result of direct irradiation of the observed nuclei with the spin-locking field. The repeat time between acquisitions in these experiments is dictated by the TI relaxation time of the source nucleus for the polarization transfer. In the case of 27Al/31P crass polarization, the TI of the 27Al(less than 100 ms) is much shorter than that of 31P.This is a common feature of quadrupolar/spin l / 2 doubleresonance experiments in general. The use of quadrupolar spins as a source of magnetization for slowly relaxing spin 1/2 species may therefore allow observation of the spin l / 2 nuclei in condensed solids such as minerals and ceramics, where their very long T I relaxation times could otherwisepreclude their direct observation. The growth of the magnetization as a function of contact time is governed by the cross-polarization time constant (TcP), while the decay of the total signal is affected by the efficiency of the spin-lock process (characterized by values for TIP). For theVPI-5 sample, the growth of the 31Psignal obtained from crosspolarization was studied as a function of contact time, and maxima were observed at approximately 1.5 ms for all three resonances. Using this contact time, the 31Pirradiation field was then varied and the jlP signal intensities measured as a function of field strength. The results are shown in Figure 7a. The maxima do not occur at the Hartmann-Hahn match condition (eq 1) derived for nonspinning samples but are offset by one rotor frequency in each direction. For these experiments,thisverifies the theoretical assertion that, in the limit of weak rf field and fast spinning, the Hartmann-Hahn match condition is shifted by once or twice the rotor frequency32or in the present case: Using the lower value of the jlP field where the signal is a maximum (Y] = 18.8 kHz, h0 = 13.3 ps), the variable contact time experiment was again repeated, and the results in Figure 7b were obtained. Once again, the maxima in all three curves occur
I
at approximately 1.5 ms. Notably, the signal maximum from the third 31Ppeak (that at lowest frequency)did not reach as high a value as the signal maxima from the other two 31Presonances. As stated earlier, certain complicationsmay arise when studying
where TIPH is the time constant for spin-lattice relaxation of the protons in the rotating frame and TCPis the cross-polarization time constant which is proportional to the second moment of the dipolar line shapes, and hence has a distance dependence of 1/lb. This model includes assumptionsthat the TI, for the dilute nuclei is very long and that the number of protons is much greater than the number of dilute spins. Without these assumptions, which cannot necessarily be made for the study of 27Al and 31P in aluminophosphates,the equations for the dynamics of the crosspolarization process are more complicated and involve the TIP values of both sets of nuclei. For cross-polarization from I spins to S spins, a spin thermodynamic treatment
where u* = c [ 1 f (1 - b / C 2 ) " 2 ]
I i ,
a
75
100
50
25
c=
h
0
-25
-
-
(1 + €CY2
+ TCP/TlpI+ TCP/TlpS)
(12)
-50
Frequency @pm from Al(N03)3) Figure 6. One-dimensional cross-polarization spectra for AlP04-8 and VPI-5: (a) 27Al 3lP cross-polarization signal from AlP04-8, with the null experiment shown below (seetext),. Contact time was 1.6 ms,and 12 800 scans were acquired with a recycle delay of 0.5 s, resulting in a total experimental time of 1.8 h. Jmentzian broadening of 50 Hz was applied. (b) 27A1-c 3lP cross-polarization signal from VPI-5, with the null experiment shown below. Contact time was 0.8 ms, and 16 732 scans were acquired with a recycle delay of 0.5 s, resulting in a total experimentaltime of 2.3 h. Lorentzianbroadening of 50 Hz was applied. (c) 31P 27Al cross-polarization signal from AlP04-8, with the null experiment shown below. Contact time was 1.5 ma, and 512 scans were acquired with a recycle delay of 30 s, resulting in a total experimental time of 4.3 h. Lorentzian broadening of 250 Hz was applied. (d) 31P *'AI cross-polarization signal from VPI-5, with the null experiment shown below. Contact time was 1.5 ms,and 512 scans were acquired with a recycle delay of 30 s, resulting in a total experimental time of 4.3 h. Lorentzian broadening of 250 Hz was applied.
-
I/2
(10)
and NX is the number of X nuclei present in the sample. The parameter a is a measure of the modified Hartmann-Hahn matching condition, and for strictly alternatingaluminophosphate systems, ea2is equal to 3 (27Al 31P)or l / 3 (3lP Z7Al) when the modified matching condition is satisfied. It is possible to fit the behavior of the curves in Figure 7b using eq 9. The parameters S,,,, Tcp, TlPA1, and TlPPwere fit with a nonlinear least-squaresroutine in the Mathematica programming environment running on a Macintosh IIci computer. Initial estimatesforthe T1,valueswereprovidedbeforethefitbyaverages of the measured TI, values for the aluminum and phosphorus spins in VPI-5. The results for all of the relevant time constants in the direct cross-polarization experiment appear in Table I. The closeness of the fits may be judged by simulating the curves of Figure 7b with the parameters obtained, and these are shown
-
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Fyfe et al.
13490 The Journal of Physical Chemistry, Vol. 97, No. 51. 1993
t1 25
35
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55
--.
1 0
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r
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L
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power setting
5
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20
0
5
IO
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20
31Ppeak 3
0
65
0
5
10
15
contact time (msec)
20
contact time (msec)
Figure 7. Variation of experimental parameters in the Z7Al 31Pcross-polarizationexperiment on VPI-5: (a) The magnitude of the ,IP spin-locking field was varied by attenuating the power of the rf amplifier. The B I field was linear over a range around the theoretical Hartmann-Hahn match for a static sample (power setting of 43), including the first maxima on either side. The horizontal bar showing a range of 6.1 kHz comes from a true
measurement of 90° pulse widths at those power settings. The maxima are observed in the cross-polarizationsignal at integer multiples of the rotor frequency for all three IlP peaks (numbered from high to low frequency). (b) Variation of the 3'P cross-polarizationsignal as a function of contact time. The maxima occur at approximately 1.5 ms, and the dashed lines are from a nonlinear least-squares fit to eq 9. (c) Cross-polarizationdifference experiments as a function of contact time measure the draining of the 31Psignal by contact with 27AIspins in VPI-5. The dashed lines are from fits to eq 15.
TABLE I: Experimentally Determined Parameters (in ms) for the Cross-Polarization between Z7Al and 31PNuclei in VPI-5 direct CP difference CP 31Psite spinlock Cp Cp $ * TCP Cp TCP 1 2 3
31 28 21
12 13 13
0.45 0.40 0.40
55 55 92
29 27 23
57 55 96
values were 0.20 ms for the tetrahedral Direct measurementsof sites and 0.37 ms for the octahedral. (1
as dashed lines on thegraphs. In addition, the parameters obtained may be compared to the measured T I ,values. It is observed that the jlP T1,values are considerably lower from the fits, while the (average) 27AlTI, values are higher. The T I ,values calculated from the fits are similar for the three 31Presonances, but they differ in the calculated values for Tcp. The third (lowest frequency) 31Ppeak has a much larger value for TCPcompared to the other two peaks which have equal values for this parameter. S,,, values for these peaks are found to be in a 1.O: 1.0:1.2 ratio, and therefore we attribute the difference in the dynamics of the low-frequency peak in the cross-polarization process to be mainly due to the difference in TCP.This cross-polarization time constant is related to the strength of the dipolar coupling and hence the rate at which the cross-polarization signal is obtained. A longer time constant describes less efficient polarization transfer due to a weaker dipolar coupling between the nearby aluminum spins and the phosphorus spins contributing to this resonance. On this basis, we make a preliminary assignment of this 3lP peak to the phosphorus site in VPI-5 that lies between two four-membered rings (P1 of ref 50), since the other two phosphorus sites are more alike (shared between four- and six-membered rings) and may be expected to show similar behavior under cross-polarization compared to the other site. This assignment agrees with that of other auth0rs.~~-~3 Although calculated values of the second moments could be obtained from the X-ray structure parameter^,^^ we do not feel
that the quantitative reliability of the Tcp data justifies more than a qualitative interpretation. Cross-PolarizationMereace Experiments. These experiments were carried out to understand further the numerical values and relative importance of the TI, and Tcp parameters in the crosspolarization process. In this case the magnetization is observed from the source (I)nuclei after the coherence transfer, and this signal is subtracted from the signal obtained from a similar spinlock on the Z spins alone with no S spin irradiation. For the experiment with cross-polarizationfrom 31Pto *'Al, the magnitude of the 31Pdifference signal from VPI-5 was studied as a function of contact time, and the behavior of the signal for all three resonances is shown in Figure 7c. It has been demonstrated that oscillations in cross-polarization signals between pairs of spins may be observed due to heteronuclear dipolar couplings, with reverse polarization transfer occurring as the magnetization is shuttled between the coupled nuclei. This has been reported for static single-crystal samples,54as well as for polycrystalline samples under MAS conditions.55 Rapid phase modulation of the spinlocking field of the unobserved nucleus can quench reverse polarization transfer, effectively forcing a short T I , on the unobserved nucleus. The reverse transfer of polarization is quenched by rapid dephasing of the magnetization, and the direct difference signal does not show oscillations but continues to grow to a higher value than if reverse transfer were a dominant mechanism. Under these conditions, thedifference magnetization, &iff(?), should grow as a function of the cross-polarization time constant, Tcp, while decaying due to the loss of Z magnetization from the spin-lock (governed by TI,^), so thats6
Stejskal and co-workers have also shown that the dependence of the signal on the TI, of the observed nucleus may also be removed by normalization of the difference signal by the signal with no draining by the unobserved nucleus,56but we did not perform this
The Journal of Physical Chemistry. Vol. 97, No. 51, 1993 13491
Quadrupolar and Spin I/z Nuclei
l
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100
.
.
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.
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.
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.
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.
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.
0 -25 -50 Frequency (ppm from Al(N03)3) 50
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Figure 8. Dipolar-dephasing difference experiments on VPI-5. (a) ,'P dipolar-dephasingdifference signal showing those resonancesconnected to the 27Alspins. The null experiment is shown below (see text). Thirtytwo scans were acquired with a recycle delay of 30 s, and 25 Hz of Lorentzian broadening was applied. (b) 27Aldipolar-dephasingdifference signal showing both the resonancesfrom tetrahedrally-and octahedrallycoordinated aluminum sites. The null experiment is shown below. A total of 4096 scans were acquired with a recycle delay of 0.3 s, and 100 Hz of Lorentzian broadening was applied.
normalization in order to obtain another experimental estimate of the TIPpvalues under cross-polarization conditions. The observation in Figure 7c that the signals continue to grow and do not show any oscillations is not unexpected due to the short TI, values for the aluminum nuclei. The cross-polarization time constants and TlPPvalues were again estimated with a nonlinear least-squares analysis, fitting eq 15 to the data in Figure 7c. The calculated results appear in Table I, and these values were used for the simulations in Figure 7c (dashed lines). Here, the values for TipPare very close to the directly-measured values, while the cross-polarization time constants are almost identical to those from the fits of the full cross-polarization dynamics. The TlPPdata are consistent with the anticipated behavior arising from the differences in the three experimental methods used for T I P determination. Thus, the results from the difference experiments are the same as those from the spin-lock measurements since the role of the aluminum nuclei in the difference experiments is only to remove 31Pmagnetization via the modified Hartmann-Hahn match. In the direct CP experiments, the total efficiency is determined by the effectiveness of both individual spin-locking processes, and therefore we obtain reduced TlPP values. Dipolar-Dephasing Difference Experiments. The results of dipolar-dephasing difference experiments applied to VPI-5 and performed in both directions between the Z7Al and 31Pnuclei are shown in Figure 8. Here, the null experiments were carried out by moving all pulses applied to the S nuclei far off resonance, as described in the Experimental Section. The appearance of signals in these experiments again establishes 27Al/31Pinternuclear connectivities in the VPI-5 aluminophosphate system, and this
is the first time that these experiments have been used to show clear connectivities within 27Al/31Psystems with more than one site. The mechanism of the effect leading to the observation of differencesignalsin these MAS spin-echoexperimentsis described by van Eck et al.42to be different from the mechanism operating in static SEDOR experiments. Through an array of experiments, they determinedthat theeffectwas not due toa changein evolution frequency with and without S spin irradiation, nor could it be described by a change in T2 during the irradiation. They suggest a mechanism whereby some of the Z spin order is transferred to another spin reservoir and regained after the refocusing pulse. The irradiation on the S spins partly or fully destroys the transferred magnetization, which cannot then be regained. In light of the discussionsby Vega3'q32on passage through resonance of quadrupolar satellite transitions, this is a distinct possibility for irreversible loss of magnetization during one or both halves of the spin-echo experiments. These experimentsmight also bedescribed in terms of adiabatic rapid passage between eigenstates through the time dependence of the 27Alfirst-order or second-order quadrupolar interaction or the 31Pchemical shift anisotropy. As the spinner completes one rotor cycle, the effective field for some of the S spins during the long pulses passes from negative to positive and back again either two or four times depending upon the orientation of the crystallite within the spinner. If this occurs on a time scale such that the S spin magnetization can adiabatically follow the effective field, the result is an adiabatic passage through resonance and an effective inversion of the magnetization either two or four times per rotor cycle. This modulates the sign of the dipolar coupling during a rotor cycle so that the coupling does not average to zero, similar in action to the dephasing pulses of a REDOR or TEDOR experiment. The reason that adiabatic rapid passage can be accomplished in both directions in these experiments is due to the relatively weak rf fields used. Independent confirmation of this mechanism could be accomplished with variable rf field experiments or experiments on single crystals under MAS conditions. REDOR Experiments. In a REDOR experiment, dipolar dephasing from 180° pulses during a spin-echo experiment is used todetermine internuclear connectivitiesor, in ideal situations, internuclear distances. In aluminophosphatesystemswith strictly alternating aluminum and phosphorus tetrahedra, the average distance between neighboring tetrahedral sites is 3.1 A. The second-nearest tetrahedral sites are populated only by the same nuclear species in a strictly alternating arrangement, and since the dipolar coupling drops off very steeply with interatomic distance (magnitude proportional to 1/ r 3 ) ,these sites would provide less dipolar coupling than the nearest neighbors. The appearance of a difference signal in a REDOR spectrum is therefore assumed to arise only from nearest-neighbortetrahedral sites, although a more exact calculation could be made in a specific case by taking into account the complete crystal structure. For the aluminophosphates, REDOR spectra (hs experiments) are shown in Figure 9. Null experiments (not shown) were also performed and gave the expected null results. The strong AS signals from both samples, with both types of nuclei being clearly observed, demonstrate the utility of these experiments for determining dipolar connectivities in solids. Variation of the number of rotor cycles in the REDOR experimentleads to a different amount of dipolar dephasingwhich will accumulate in time as shown in eqs 3 and 4. For individual pairs of dipolar coupled nuclei, these equations may be used to generate the universal curve of Figure loa, which indicates the amount of REDOR signal scaled by the full (uncoupled) echo intensity. However, this curve is valid only for an isolated pair of spins. In the aluminophosphate systems studied here, there are four nearby heterospins contributing dipolar dephasing to the signal of the observed spins, and the theoretical analysis must therefore be altered to take this into account. Figure lOb,c shows the evolution of the REDOR signals for
Fyfe et al.
13492 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
*'AI (tetrahedral)
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5
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Figure 10. Evolution of REDOR (AS/&)signals: (a) Ideal evolution assuming an isolated of the REDOR signal for M rotor cycles of period if, spin pair with dipolar coupling D. (b) Evolution of the REDOR signal for the tetrahedral aluminum sites in VPI-5. Here, if = 322 ps, and the number of rotor cycles was varied from 2 to 30. (c) Evolution of the REDOR signal for the octahedral aluminum sites in VPI-5.
l.Ol
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25 0 -25 -50 F q W M y (ppm from AI(NOj)j) Figure 9. REDOR experiments in both directions for AIP04-8 and VPI5. (a) ,IP AS REDOR signal from AlF'04-8 showing those resonances connected to 27Alspins; 48 scans were acquired with a recycle delay of 90s,and25HzofLorentzianbroade~ngwasapplied. (b)3LPASREDOR signal from VPI-5 showing those rcSOnanccS connected to Z7Al spins; 1536 scans were acquired with a recycle delay of 30 s, and 25 Hz of Lorentzian broadening was applied. (c) 27AlA S REDOR signal from AIPO4-8 showing both resonances connected to 31Pspins; 4096 scans were acquired with a recycle delay of 0.5 s, and 100 Hz of Lorentzian broadening was applied. (d) 27AIAS REDOR signal from VPIJ showing both resonances connected to 31Pspins; 4096 scans were acquired with a recycledelay of 0.5 s, and 75 Hz of Lorentzian broadening was applied. 100
75
50
both the tetrahedral and octahedral 27Alnuclei in VPI-5. As anticipated, thecurvesdonot show anoscillationasin theuniversal curveof Figure loa; rather, they show a smooth approach toward unity. Computer modeling of the REDOR behavior for a tetrahedron of 31Pspins surrounding a central 27Alnucleus at an average internuclear distance of 3.1 A also shows this behavior, but the curves do not give a quantitative measure of the average bond distance. A fuller account of this calculation a n d the corrections needed will be given elsewhere. The behavior as a function of rotor cycle of the 31PREDOR intensities for t h e three remnancesfrom VPI-5areshownin Figure 11, and once again these curves show no oscillations as they
AS SO 0.2 0.0 0
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.
, 5
.
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rotor cycles (n)
Figure 11. IlP REDOR evolution: (a) Evolution of the REDOR signal for the first (high frequency) IIP peak in VPI-5. Here, if = 322 p, and the number of rotor cycles was varied from 2 to 24. (b) Evolution of the REDOR signal for the second IIP peak in VPI-5. (c) Evolution of the REDOR signal for the third IIP peak in VPI-5.
approach unity. The study of these resonances is much more complex than the 27Al,however, as each aluminum spin near to a phosphorus nucleus is not necessarily perturbed by the 180°
Quadrupolar and Spin
Nuclei
I/2
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13493
I
I 1
25
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1
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1
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1
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1
.
-25
-50 -15 pnsuuVr (ppn fraa 85% HsPO,) F i 12. TEDORsignals from 27Al-, 31Pcoherencetransfer in AlP04-8 and VPI-5, with n = 2 and m = 1. (a) Signal from AlP04-8 after 14 400 scans with a recycle delay of 0.25 s, with a total experimental time of 1 h. Lorentzian broadening of 100 Hz was applied. (b) Signal from VPI-5 after 9000 scans with a recycle delay of 1 s, with a total experimental time of 2.5 h. Lorentzian broadening of 100 Hz was applied. 0
31Ppeak 2
pulses on the 27Alchannel. Only a certain percentage of the nuclei have a spin energy level characterized as in the central transition (either in the +'/2 or -l/2 level), and only these (to a first approximation)will be flipped by the 180' pulse. A complete analysiswould have to take into account all spin levels of the 27Al nuclei and the effect of an on-resonance 180' pulse for the central transition. Qualitatively, though, the behavior is as expected. At this point, we wish to emphasize the connectivity information obtained rather than quantitative bond distance measurements in these systems as their complexity precludes a more detailed analysis. TEDOR Experiments. The TEDOR experiment was initially introduced to overcome the contributions of uncoupled natural abundance spins to the echo signal measured in a REDOR experiment. In the systems studied here there should be no uncoupled spins measured, but such contributions will be important when other spin l / 2 and quadrupolar systems are considered. The use of coherence transfer also changes the experimental conditionsin that the repeat time is determined by the T Irelaxation times of the Ispins which are not detected after the coherence transfer, and this will be an important advantage when considering aluminophosphates. The 27Al spin-lattice relaxation times are often of the order of hundreds of milliseconds or less, while the 31Pspins have relaxation times of many seconds. Therefore, the experiments may be repeated much faster if the relaxation time governing the experimental repetition is that of the 27Al. This will generally be true when other quadrupolar species are involved. Figure 12 demonstrates the 31PTEDOR signals from experiments performed on VPI-5 and AlPO4-8. Initial aluminum antiphase magnetization was formed after two periods of preparative dephasing, with subsequent detection of 31Psignal after coherence transfer and one additional period of dipolar dephasing. The antiphase magnetization transfer (initially unobservable) has evolved during this additional period into the in-phase magnetization which is detected. The evolution of the sidebands, however, is different from that of the isotropic peaks, and therefore they are of different phase in the final spectra. Also important is proper cycling of the rf phases to remove any signal
rotor cycles (m)
Figure 13. Evolution of TEDOR signals: (a) Ideal evolution of the TEDOR signal for MDT,= 1 and assuming an isolated spin pair with dipolar coupling D. (b-d) Evolution of the TEDOR signal for the three 31Psites in VPI-5 after preparative dephasing for n = 2 rotor cycles. Here, T , = 319 w ,and the number of rotor cyclca after transfer (m)was varied from 0 to 8. Since there is no SOexperiment for reference, the peak heights are scaled in arbitrary units.
arisingjust from the 31P900pulse. Null experiments (not shown) were also performed and gave the expected null results. Variation of the number of rotor cycles after the coherence transfer in the TEDOR experiments leads to differing amounts of dipolar dephasing which will accumulate in time as shown in eqs 5 and 6. For individual pairs of dipolar coupled nuclei, these equations may again be used to generate a universal curve, shown in Figure 13a,which indicates the total amount of TEDOR signal obtained. As before, this curve is only strictlyvalid for an isolated pair of spins, and theoretical analysis is complicated by the tetrahedral geometry of the 27Alatoms surroundingthe 31Pnuclei. The TEDOR curves obtained with transfer from aluminum to phosphorus nuclei for the three different 31Psites in VPI-5 are shown in Figure 13b-d, where the intensities plotted are those of the isotropic resonances alone, Le., excluding the sidebands. Qualitatively, the expected rise in the early rotor cycles is seen, with very quick damping of the signal as the number of rotor cycles is increased. As in the REDOR experiments,we wish to emphasize the qualitative information regarding connectivities which can be obtained. The extension of this experiment into a second spectral dimension, discussed below, depends on observing qualitotive connectivities as cross-peaks in the two-dimensional correlation plots. Two-Dimensional NMR Experiments. Resolving an NMR spectrum into two or more dimensions is helpful when onedimensional spectra confirm that connectivities do exist between nuclei, yet direct connectivity relations between particular sites are still unknown or in question. For example, in the hydrated form of VPI-5, there are three phosphorus sites and three aluminum sites as deduced from MAS and DOR NMR results. Any proposed structures must contain three crystallographically inequivalent sites for both species to be consistent with these
Fyfe et al.
13494 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
0 ''
9 I
50
I
I
25
,
I
0
I
I
,
v
t 1 I
-25
-
Frequency (ppm from AI(N03)3) Figure 14. Two-dimensional 27Al 31Pcross-polarization experiment on AIP04-8, with a contact time of 1.6 ms; 800 scans were acquired for each of 128 experiments in t l . The recycle delay of 0.5 s resulted in a total experimental time of 14 h. Line broadenings of 200 and 150 Hz were applied in the first and second dimension, respectively.
data. All of these sites are connected to each other (with only one oxygen atom between them) according to the proposed structure of McCusker and c o - w o r k e r ~ . ~ ~ Two-dimensional heteronuclear correlation experiments using cross-polarization were performed on both samples, with initial evolution of aluminum magnetization followed by polarization transfer to the 31Pnuclei. One of the resulting two-dimensional spectra is shown in Figure 14 for AlP04-8. The similar spectrum for VPI-5 was presented previously in ref 33, where connectivities were seen between all three 3IP sites and both of the resolved 27Al sites (tetrahedral and octahedral) in VPI-5. This is consistent with the proposed structure of ref 50, as all connectivities are observed. For AlP04-8, it can be seen that again both the tetrahedral and the octahedral aluminum resonances are connected via dipolar couplings to each of the three resolved 31Psites in the second dimension. The TEDOR experiment is also amenable to extension into a second spectral dimension as it involves coherence transfer to a heteronucleus, rather than spin-echo detection of dipolar decoupling in a difference experiment (as in the dipolar-dephasing or REDOR experiments). The two-dimensional TEDOR spectrum of VPI-5 is shown in Figure 15, with the first spin evolution again occurring for the 27Alspins before transfer to the 31Psystem with the TEDOR experiment. The experimentally optimized conditions of two periods of preparative dephasing and one period of antiphase to in-phase evolution after the transfer (or n = 2, m = 1) were used. As explained above, the sidebands in the onedimensional 31PTEDOR spectrum were negative or of mixed phase (see Figure 12b), and this is also true in the pure-absorptionphase two-dimensional version. Figure 15 shows both positive and negative contours, however, and the projections are absolute value mode due to the processing software of the spectrometer. All expectedconnectivitieswere again present between all observed resonances, in agreement with the proposed structure.50 The full assignment of peaks in these systems is not possible from qualitative connectivity data alone. However, as we begin to understand the dynamicsof coherencetransfer in these systems, further extensions of these experiments may aid the exact assignment of resonances. A study of cross-peak intensities in cross-polarizationheteronuclear correlation spectra as a function of contact time would provide further information, as would a two-dimensional TEDOR experiment as a function of number of
50
I
I
25
I
I
0
-
I
O
-25
Frequency (PPm from Al(N03)3) Figure 15. Two-dimensional 27Al TEDOR experiment on VPI-5, withn= 2andm= 1;3600scanswereacquiredforeachof128experiments in 11. The recycle delay of 0.5 s resulted in a total experimental time of 64 h. Line broadenings of 200 and 50 Hz were applied in the first and
second dimensions,respectively. The connected resonances are indicated by the dashed box.
rotor cycles after the transfer. Still, it is anticipated that there are many systems where the qualitative information alone will confirm, dispute, or suggest proposed structures or topologies in these three-dimensional inorganic frameworks. Spin-Diffusion NMR Measurements. An additional complicating factor arises in the analysis of all of these one- or twodimensionalexperiments: spin diffusions7could cause a widening of the connectivity networks, making such an analysis worthless for even qualitative information regarding molecular topology. To study this effect, a number of 31P spin-diffusion NMR experimentsSEwere undertaken with various conditions during the mixing period (continuous rf irradiation on one or both nuclei as in the cross-polarizationexperimentsor application of properly timed 27Al180° rf pulses as in REDOR/TEDOR experiments) to determine whether spin diffusion could occur. No significant cross-peak intensity was observed in the two-dimensional spin diffusion spectra with mixing times equal to or greater than the time scales of our one- and two-dimensional experiments, and therefore this effect has been discounted in the analysis. It is felt that these conclusions are valid for all AlP04's and other related systems, but once again a warning must be issued when new systems are being studied.
Conclwions In the application of polarization transfer techniques to less common pairs of nuclei (including quadrupolar), it is clear that a great number of experimentalvariations and permutationsexist. Cross-polarization and dipolar-dephasing experimentshave been demonstrated here for a system involving quadrupolar spins (27Al) connected via bridging oxygen atoms to 31P nuclei. However, these experiments should be more generally applicable to quadrupolar/spin systems such as 170/31P, 27A1/29Si,or 11B/29Si. In the systems studied here, the cross-polarization experiments involve a heightened degreeof selectivityrather than gains in signal-to-noise ratio. However, if the quickly relaxing quadrupolar spins are used as a polarization source, it will be possible to observe slowly relaxing spin '12 species in a much shorter time period, which will be important in condensed inorganic TI values may be as high as 1000 s. solids where spin In the case of cross-polarization involving less common spin pairs, many of the conventional ideas from IH/l3C CPMAS
Quadrupolar and Spin
l/2
Nuclei
experimentsare still useful, but they must be carefully reevaluated. More general equations are needed for the cross-polarization dynamics, and an important role may often be played by quickly relaxing nuclei or those with T I ,values shorter than the crosspolarization time constants. Measurement of all TI, values in the systems studied is necessary for a complete understanding of the cross-polarization dynamics. We have found internal consistencies among time constants gathered in these experiments for the behavior of the spin-locked systems using conventional T I ,measurements and a nonlinear least-squares analysis of direct cross-polarizationand cross-polarization difference experiments. Although not directly analogous to the cross-polarization experiments,the REDOR and TEDOR experiments also delineate connectivitiesvia the dipolar interactions and, very importantly, distance information may be obtained from a careful analysis of the data. The spins considered could be selectively enriched in combination (such as the 13C/1SN spin pairs in biomolecules), or they might occur naturally (as in the 27Al/31Pspin systems in aluminophosphates). The time developmentof the magnetization as a function of dipolar dephasing must be carefully examined in these systems, and a fuller theoretical treatment is currently under way for the more complex situation encountered in this work. Due to the selectivity of the dipolar interactions exploited in these experiments, it is useful to design two-dimensional NMR correlation experiments based on these methods. Both crosspolarization and TEDOR versions of heteronuclear correlation experiments are possible and corroborate the proposed structure of VPI-5 obtained from crystallographic measurements and refinement. The extension of this work to other pairs of nuclei will be useful in defining the local structure in other inorganic phosphates, as well as zeolites or borosilicate minerals and glasses. These ideas should also be extendable to pairs of quadrupolar nuclei (e.g., 170/27Alor llB/170)also occurring in many inorganic compounds. Especially useful would be heteronuclear correlation experiments with high-resolutionquadrupolar NMR (Le,,DAS or DOR) used in the first dimension to resolve resonances from inequivalent sites such as the tetrahedral aluminum sites in VPI-5. Subsequent transfer of the magnetization to another spin species with acrosspolarization or TEDOR step will then provide connectivity maps with a heightened degree of resolution, and experiments along these lines are currently under way in our laboratory.
Acknowledgment. C.A.F. acknowledges the financialassistance of the NSERC of Canada in the form of operating and equipment grants. K.T.M. thanks both the NSERC and National Science Foundation NATO Program for Postdoctoral Fellowships, and K.C.W.-M. thanks the NSERC for the award of a Postgraduate Fellowship. The authors acknowledge very helpful discussions with Dr. J. Schaefer and thank Dr. P. J. Grobet and Dr. M. E. Davis for kindly providing samples of VPI-5. They are indebted to Mr. T. Markus for assistance with probe electronics and spectrometer modification for these experiments. References and Notes (1) Mehring, M. Principles of High-Resolution NMR inSolids, 2nd ed.; Springer-Verlag: Berlin, 1983. (2) Ernst, R. R.; Bodenshausen, G.; Wokaun, A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions; Clarendon Press: Oxford, 1987. (3) Fyfe, C. A.; Feng, Y.; Grondey, H.; Kokotailo, G. T.; Gies, H. Chem. Rev. 1991, 91, 1525-1543. (4) Eckert, H. Prog. N M R Spectrosc. 1992, 24, 159-293. ( 5 ) Andrew, E. R.; Bradbury, A.; Eades, R. G. Nature (London) 1958, 182, 1659. (6) Lowe, 1. J. Phys. Rev. Lett. 1959, 2, 285-287. (7) Hartmann, S. R.; Hahn, E. Phys. Rev. 1962, 128, 2042-2053. (8) Pines, A.; Gibby, M. G.; Waugh, J. S.J. Chem. Phys. 1973, 59, 569-590. (9) Waugh, J. S.;Huber, L. M.; Haeberlen, U. Phys. Rev. Lett. 1968, 20. 180-182.
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