ARTICLE IN PRESS

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Solid State Nuclear Magnetic Resonance 28 (2005) 13–21

www.elsevier.com/locate/ssnmr

Multiplex MQMAS NMR of quadrupolar nuclei

Nicolas Malickia, Luıs Mafraa,b, Anne-Agathe Quoineaudc, Joao Rochab,Frederic Thibault-Starzyka, Christian Fernandeza,�

aLaboratoire Catalyse et Spectrochimie, Unite Mixte de Recherche CNRS/ENSICAEN Universite de CAEN-Basse Normandie,

6 Bd. Marechal Juin, 14050 CAEN, FrancebDepartment of Chemistry, University of Aveiro, CICECO, 3810-193 Aveiro, Portugal

cLaboratoire RMN IR, Institut Franc-ais du Petrole, CEDI Rene Navarre, BP No. 3 69390 Vernaison, France

Received 23 January 2005; received in revised form 21 February 2005

Available online 25 March 2005

Abstract

A multiplex phase cycling method (N. Ivchenko et al., J. Magn. Reson. 160 (2003) 52–58) has been used to record two-

dimensional MQMAS spectra with a very short phase cycling. A straightforward procedure has been developed to easily process the

data. Combining this Multiplex approach and the new Soft-Pulse-Adding-Mixing (SPAM) method considerably increases the

signal-to-noise ratio of the conventional MQMAS experiment. The Multiplex acquisition procedure is much simpler than the echo/

anti-echo method recently proposed, and has been applied with success to record 87Rb spectra of RbNO3 and 27Al 3Q and 5Q

MQMAS NMR of microporous aluminophosphate AlPO4-14.

r 2005 Elsevier Inc. All rights reserved.

Keywords: Half-integer quadrupolar nuclei; High-resolution solid state NMR; SPAM; Pure-absorption 2D NMR; Sensitivity

1. Introduction

The power of NMR spectroscopy to probe thestructure of materials depends strongly on the avail-ability of high-resolution spectra. For nuclei with a spinI ¼ 1

2; a number of methods are now well established for

eliminating or significantly reducing the broadeningeffect of the anisotropic interactions. In contrast,narrowing the spectral lines of quadrupolar nucleiðI41=2Þ is a more challenging task and has attractedthe efforts of many NMR spectroscopists in the last 15years or so. The introduction in 1995, by Frydman andHarwood [1] of Multiple-Quantum Magic-Angle Spin-ning (MQMAS) NMR spectroscopy prompted a revolu-tion in this field, making possible to record high-resolution NMR spectra of important half-integerquadrupolar nuclei as 23Na [2–8], 27Al [9–15], 87Rb[16–20],17O [21–29] and 93Nb [21,30–32]. The advent of

e front matter r 2005 Elsevier Inc. All rights reserved.

nmr.2005.02.007

ing author. Fax: +332 31 45 28 22.

ess: christian.fernandez@ensicaen.fr (C. Fernandez).

MQMAS NMR also raised the possibility of studyingthe interaction of half-integer quadrupolar spins withthe neighbouring nuclei under high-resolution condi-tions. As a result, several double-resonance methodsinvolving quadrupolar nuclei have been reported astools for structural elucidation [33–37].A major problem of the original MQMAS NMR

experiment is its poor sensitivity. However, since itsdiscovery MQMAS NMR has evolved considerably,and several pulse sequences have been proposed toimprove the efficiency of the generation and/or conver-sion of MQ coherences [18,30,38–53].Another problem facing MQMAS NMR is the

acquisition of two-dimensional (2D) MQMAS spectrawith pure-adsorption lineshapes. The difficulty has beenovercome by designing new pulse sequences, like thenow widely used z-filtered method [54], in combinationwith the States–Ruben–Haberkorn (SRH) [55] or TPPIacquisition schemes [56].A solution to the efficiency and 2D-lineshape pro-

blems has been recently offered by Gan and Kwak [57]

ARTICLE IN PRESS

Fig. 1. (a) z-filtered MQMAS NMR pulse sequence. The first two

pulses are hard pulses while the last one is a soft, selective, 90� pulse on

the central transition. (b) Coherence transfer pathway for the z-filtered

3QMAS experiment. The number of phases is j2pj ¼ 6 for the first

pulse to select simultaneously (aliasing) the þp and �p coherences.

The last pulse is cycled 4 times to retain only the transfer from zero to

N. Malicki et al. / Solid State Nuclear Magnetic Resonance 28 (2005) 13–2114

who introduced the Soft-Pulse-Added-Mixing (SPAM),which consists in adding several coherence transferpathways constructively. A complete description of thismethod has been given by Amoureux et al. [58].Although Gan and Kwak [57] alluded to the

possibility of using the multiplex phase cycling (asintroduced by Ivchenko et al. [59]) with the SPAMMQMAS experiment, no experimental 2D NMRspectra have been reported.In this article, we use the multiplex strategy to record

2D SPAM MQMAS spectra with much shorter phasecycling, and propose a simple method to process thedata. To illustrate its performance, we report 87Rb3QMAS NMR of RbNO3 and 27Al 3Q and 5QMASNMR of microporous aluminophosphate AlPO4-14.

�1:

2. Experimental

All NMR spectra have been recorded at 9.4T on aBruker Avance 400 spectrometer using a 4mm double-bearing probe. Larmor frequencies are 130.9 and104.3MHz for 87Rb and 27Al, respectively. The acquisi-tion of the 2D MQMAS data sets has been performed ina rotor-synchronized fashion by advancing the evolu-tion time t1 in increments equal to the rotor period [60].The shearing procedure was systematically applied toeach 2D spectra and the scaling of the spectra was donefollowing conventions of Ref. [61]. Specific experimentalconditions will be given in the figure captions.The model compounds rubidium nitrate (RbNO3;

Aldrich) and the aluminophosphate AlPO4-14 were usedto carry out the various MQMAS NMR experiments.The pulse sequences used in this work and the

processing programs (adapted to the BrukerXWinNMR software) will be available on the Internetas separate resources [62].

3. Results and discussion

3.1. Selection of coherence transfer pathways using a

multiplex acquisition scheme

A controlled selection of multiple-quantum coherencetransfer pathways is the basis of the acquisition ofMQMAS NMR spectra. Fig. 1a shows the z-filteredMQMAS sequence. As shown in Fig. 1b for a 3QMASexperiment, two different coherence transfer pathwayshave to be followed in such an experiment. This is anecessary condition to obtain pure-adsorption 2Dspectra. A second condition is that the amplitudes ofthe signals of both pathways are equal. These twopathways can be written as P�p;0 ¼ f0;�p; 0;�1g in-dicating the successive coherence orders selected duringdifferent time periods of the experiment. Note that for

spin 3/2 nuclei, the P�3;0 pathway corresponds to theformation of an echo signal in the t2 domain, and Pþ3;0

to the formation of an anti-echo. The situation is theopposite for higher spin numbers, Pþ3;0 correspondingto the echo and P�3;0 to the anti-echo. The mainadvantage of the z-filtered sequence over the two-pulsesequence is that the efficiencies of both P�p;0 coherencetransfer pathways are well balanced, leading to almostequal amplitudes of the corresponding signals. How-ever, the addition of the third rf pulse slightly decreasesthe overall efficiency of the experiment [61].Usually, a nested phase cycling of the rf pulses is used

to select the desired P�p;0 pathways. In this method, thereceiver phase frec is set to fulfil the condition:

Dp1:f1 þ Dp2:f2 þ Dp3:f3 þ frec ¼ 0, (1)

where Dpi represents the change in the coherence orderinduced by the ith pulse with phase fi: All coherencetransfer pathways that do not fulfil condition (1) will notcontribute to the final signal.As a coherence transfer pathway always starts at 0

(equilibrium) and finishes at �1 (observable single-quantum coherence), the Dpi sum is always equal to �1:Consequently, only two of the three rf pulses need to bephase cycled. For instance, keeping the phase f2 of thesecond rf pulse constant (e.g., f2 ¼ 0), the first rf pulsewith phase f1 is then cycled with m ¼ j2pj differentphases:

f1ðkÞ ¼2pk

mwith k ¼ 0; 1; . . . ;m � 1 (2)

and finally the last pulse is cycled 4 times:

f3ðlÞ ¼pl

2with l ¼ 0; 1; 2; 3. (3)

The overall number of signal transients to be acquiredis thus N ¼ 4 m, i.e., N ¼ 24 for 3QMAS and N ¼ 40for the 5QMAS experiments.

ARTICLE IN PRESS

Fig. 2. Schematic representation of the DFT that allows transforming

the data acquired in a phase domain to data in the coherence domain.

Depending on the number of phases m, aliasing can occur in the

coherence domain. To select all p individually in a 3/2-spin system, m

must be greater or equal to 7.

N. Malicki et al. / Solid State Nuclear Magnetic Resonance 28 (2005) 13–21 15

For the z-filtered MQMAS experiment, the conditionto select desired P�p;0 pathways is simply

�p:f1ðkÞ � f3ðlÞ þ frecðk; lÞ ¼ 0. (4)

In this method, for each t1 increment, the N acquiredsignal transients sklðt1; t2Þ are readily summed up in theacquisition device to generate the final 2D time domainsignal.

Sðt1; t2Þ ¼1

N

X3l¼0

Xm�1

k¼0

sklðt1; t2Þ. (5)

As mentioned above, the overall signal arises from theaddition of the signals corresponding to the Pþp;0 andP�p;0 coherence transfer pathways. Because these twosignals are complex conjugates, Sðt1; t2Þ is cosine-modulated in the t1 dimension and, therefore, it is notpossible to determine the sign of the corresponding þp

and �p precession frequency. To solve this problem, weresort to the hypercomplex (SRH) [55] method, whichconsists of using a complementary set of data where theMQ coherence is phase shifted by p=2 and, thus, sine-modulated in t1: These two data sets are combined togenerate the pure-adsorption 2D MQMAS spectrawhere the signs of the frequencies are discriminated[17]. The p=2 phase shift is obtained by applying to thefirst (preparation) pulse a phase change of p=j2pj: Notethat using the hypercomplex method multiplies, by afactor of 2, the number of transients N to be acquired,i.e., N ¼ 48 for 3QMAS and N ¼ 80 for the5QMAS.The TPPI acquisition scheme may also be usedbut, in this case, it is not possible to perform rotorsynchronization, [60] which increases the signal intensityby aliasing the t1 spinning sidebands into the maincentral band.Ivchenko et al. [59] have shown that the length of the

phase cycling may be reduced considerably by storing inthe computer the individual signals of each acquiredtransient, instead of immediately adding them togetherin the acquisition device. Applying the concept to the z-filtered MQMAS experiment, it is clear that instead ofapplying a receiver phase shift to fulfil condition (4), it isnow possible to compute the phase change at the end, onseparated data sets sklðt1; t2Þ:For example, to select a given Pp;0 coherence transfer

pathway in the z-filtered MQMAS experiment, beingDp1 ¼ p the change in coherence for the first pulse, the rfpulse phases have to fulfil the condition:

p:f1ðkÞ � f3ðlÞ þ frecðk; lÞ þ fnumðk; lÞ ¼ 0, (6)

where fnumðk; lÞ is the numerically computed phasechange. Obviously, from Eq. (6), it is shown that thisnumerical phase is a function of the choice of thereceiver phase and of the p value.Now, for each t1 increment, the N signal transients

sklðt1; t2Þ acquired and stored individually can besummed up to produce Sp; the final 2D time domain

signal corresponding to the Pp;0 coherence transferpathway:

Spðt1; t2Þ ¼1

N

X3l¼0

Xm�1

k¼0

sklðt1; t2Þe�ifnumðk;lÞ. (7)

If the receiver phase follows the phase f3 of the thirdrf pulse, the condition (6) becomes

fnumðkÞ ¼ �p:f1ðkÞ ¼ �2ppk

m(8)

and the Eq. (7) is now,

Spðt1; t2Þ ¼1

m

Xm�1

k¼0

skðt1; t2Þe2pi k

m:p, (9)

where sk is the sum of the transients acquired for the 4phases of the third pulse:

skðt1; t2Þ ¼1

4

X3l¼0

sklðt1; t2Þ. (10)

It is easily recognized that in Eq. (9), the expression ofSp corresponds in the ‘‘coherence domain’’ to thediscrete Fourier transform (DFT) of the m sk dataacquired in the ‘‘phase domain’’ (Fig. 2). Therefore,applying Eq. (9) is equivalent to perform a DFT,allowing the separation of the signals coming fromall coherence orders p that were created by the firstpulse.As mentioned by Ivchenko et al. [59], it is not

necessary to acquire the data in the SRH or TPPI mode,in contrast with what is done in the usual nested phasecycling. This is because, as shown in Figs. 2 and 3, both�p coherences are separated provided the number ofdifferent phases is larger than j2pj: Therefore, a pureadsorption 2D MQMAS NMR spectrum may beconstructed by combining the S�p and Sp signals, whichare extracted by the DFT process.Formally, the process consists of directly computing

the cosine and sine-modulated signals evolving in t1

ARTICLE IN PRESS

Fig. 3. (a) Multiplex z-filtered MQMAS NMR pulse sequence. The first two pulses are hard rf pulses while the last one is a soft, selective, 90� pulse

on the central transition, exactly as in the conventional z-filtered experiment. (b) Coherence transfer pathway for the Multiplex z-filtered 3QMAS

experiment. The last pulse is cycled 4 times to retain only the zero to �1 transfer. For the first pulse, the number of phases m is 7 in order to separate

all p coherence.

Fig. 4. 87Rb 2D Multiplex 3QMAS spectrum of RbNO3: The

conventional 2D 3QMAS is almost the same and thus is not shown.

On the right side the cross sections are represented (dotted line) and

compared to the corresponding cross sections of the conventional z-

filtered MQMAS spectra (continuous line). The Multiplex spectrum

was acquired at a spinning rate of nR ¼ 5 kHz and a 0.3 s recycle delay.

Rotor synchronization was used in the t1 domain. The initial excitation

and conversion hard pulse lengths were 3.3 and 1:2ms; respectively,using a B1 field of ca. 130 kHz. The soft pulse length was 12:5ms; usinga B1 field of ca. 10 kHz.

N. Malicki et al. / Solid State Nuclear Magnetic Resonance 28 (2005) 13–2116

using the expression of Eq. (9):

Scosðt1; t2Þ ¼1

2ðSþpðt1; t2Þ þ S�pðt1; t2ÞÞ

¼1

2m

Xm�1

k¼0

skðt1; t2Þ e2pi km:p þ e�2pi k

m:p

� �

¼1

2m

Xm�1

k¼0

skðt1; t2Þ cos 2pk

m:p

� �ð11Þ

and

Ssinðt1; t2Þ ¼1

2iðSþpðt1; t2Þ � S�pðt1; t2ÞÞ

¼1

2m

Xm�1

k¼0

skðt1; t2Þ sin 2pk

m:p

� �. ð12Þ

A Fourier transformation with respect to t2 of theScosðt1; t2Þ and Ssinðt1; t2Þ signals is applied, givingScosðt1;o2Þ and Ssinðt1;o2Þ:Using the SRH method, the last step is to build a new

2D signal from the real parts of these Fourier trans-forms:

Sðt1;o2Þ ¼ ReðScosðt1;o2ÞÞ þ iReðSsinðt1;o2ÞÞ (13)

and to apply a Fourier transform in the t1 domain to getSðo1;o2Þ:Clearly, the Multiplex approach has the advantage of

reducing the length of the phase cycling, albeit with anincreased data storage space. However, this is not reallya problem for modern computers.The conventional and corresponding 87Rb ðI ¼ 3=2Þ

Multiplex z-filtered MQMAS NMR spectra of RbNO3

are shown in Fig. 4. The pulse sequence used to recordthe conventional z-filtered MQMAS spectrum is de-picted in Fig. 1. In this experiment the radiofrequencypower of the first two pulses is high ðB1 � 130 kHzÞ;while the last pulse is a soft 90� pulse ðB1 � 10 kHzÞselective on the central transition. To complete thenested phase cycling, 24 transients per t1 increment (6for the first pulse and 4 for the last pulse) were acquired.

In addition, the acquisition of a second data set with thesame number of transients was necessary in order toapply the SRH method in the 2D Fourier transforms.The overall number of acquired transients was thus 48.The Multiplex z-filtered MQMAS spectrum was

recorded using the pulse sequence in Fig. 3. Theradiofrequency power and lengths used for the threepulses are exactly the same as in the conventional z-filtered experiment. To perform this experiment, the f1

phase of the first pulse was cycled as follows:

f1ðkÞ ¼ k2p7

with k ¼ 0; 1; . . . ; 6. (14)

For each f1 phase, the receiver and the last rf pulsewere synchronously cycled 4 times and the 4 transientswere added for averaging, following Eq. (10). The

ARTICLE IN PRESSN. Malicki et al. / Solid State Nuclear Magnetic Resonance 28 (2005) 13–21 17

resulting 7 transients were stored separately for furtherprocessing.The numerical phase used to process the data was

computed from Eq. (8):

fnumðkÞ ¼ �pk2p7. (15)

Using Eqs. (9), (11) and (12), it was possible, withoutacquiring any additional data, to obtain the cosine- andsine-modulated 2D signals necessary to perform theSRH procedure. The overall number of acquiredtransient was, thus, 28.The cross sections in Fig. 4 show that the conven-

tional and multiplex MQMAS spectra are almostidentical. The signal-to-noise ratio of both spectra isalso very similar. It is interesting to note that we haveobserved that the quality of the Multiplex spectrum inthe high-resolution dimension (n1) was slightly betterthan in the conventional z-filtered MQMAS spectrum.Indeed, less residual dispersive components were presentin the 2D spectrum using the Multiplex method. Thisseems to indicate that the compensation between theecho and anti-echo signal required to get a pure-adsorption spectrum is slightly better with this newapproach. This may be related to the fact that the sine-and cosine-modulated signals are computed from thesame set of data in the Multiplex procedure, instead ofbeing acquired independently in the conventionalmethod, reducing the possibilities of adding experimen-tal phase errors.In conclusion, the experimental realization of the

Multiplex z-filtered MQMAS experiment confirms thevalidity of the approach. Applying the multiplexprocedure to the acquisition of triple-quantumMQMAS spectra of spin 3/2 nuclei reduces the numberof acquired transients to N ¼ 7 4 ¼ 28; instead of 48in the conventional phase cycling. As expected andshown experimentally, there are no particular advan-tages, in terms of signal-to-noise ratio, of using the

Fig. 5. (a) Pulse sequence for the Multiplex SPAMMQMAS NMR sequence

pulse on the central transition, exactly like in the conventional z-filtered exp

short as possible, typically of the order of the phase-shifting time. (b) Co

experiment. In order to separate all p coherences, the number of phases for th

form zero to �1 and from �1 to �1:

multiplex procedure to simply acquire the z-filteredMQMAS.However, the Multiplex method may be very useful

when combined with the SPAM procedure. This will bediscussed in the following.

3.2. Selection of multiple-coherence transfer pathways

(SPAM) using a multiplex acquisition scheme

Recently, Gan and Kwak have shown that theefficiency of the MQMAS experiment can be enhancedby using the signals from multiple-coherence pathways[57]. Indeed, in this experiment the Pp;0 ¼ f0; p; 0;�1gand Pp;�1 ¼ f0; p;�1;�1g coherence transfer pathwaysyield signals which may be easily added together(Fig. 5). Two methods have been proposed to processthe data.Firstly, Gan and Kwak showed that, in principle,

multiplex acquisition may be applied using a 2-phasecycling of the third pulse, although no actual 2D spectrahave been reported in the paper [57]. Secondly, theseparation of the echo and anti-echo in two differentexperiments has been proposed. This alternative method,named Soft-Pulse-Added-Mixing (SPAM), has beenrecently demonstrated experimentally by recording 2DMQMAS of several samples [58]. Here, we show that it ismuch simpler to use the multiplex phase cyclingprocedure, instead of the echo/anti-echo SPAMmethods.Due to the use of a soft pulse (SP), it is assumed that

even-order multiple quantum, Pp;�2; and triple-quantumcoherences, Pp;�3; do not contribute significantly to thespectrum. The time between the second and last pulses iskept as short as possible in order to avoid dephasing ofthe �1 coherences.To separate the Pp;0 from Pp;�1 coherence transfer

pathways, two phases (0,p) are sufficient for the thirdpulse. As both Pp;�1 pathways yield signals with thesame sign, they are constructively aliased using thissimple phase cycling.

. The first two rf pulses are hard and the last one is a soft, selective, 90�

eriment. The delay between the second and the last pulses must be as

herence transfer pathway for the Multiplex z-filtered 3QMAS NMR

e first pulse is 7. The last pulse is cycled 2 times to separate the transfers

ARTICLE IN PRESSN. Malicki et al. / Solid State Nuclear Magnetic Resonance 28 (2005) 13–2118

Eq. (6) may be rewritten as follows:

p:f1ðkÞ þ frecðk; 0Þ þ fnumðk; 0Þ ¼ 0, (16)

when

f3 ¼ 0 ðl ¼ 0Þ

and

p:f1ðkÞ þ Dp3:pþ frecðk; 1Þ þ fnumðk; 1Þ ¼ 0 (17)

when f3 ¼ pðl ¼ 1Þ:Dp3; the change of the coherence order after the third

pulse is equal to �1 and 0 (or �2) for the Pp;0 and Pp;�1

pathways, respectively.Setting the phase of the receiver to 0, the numerical

phase fnumðk; lÞ may then be written as

fnumðk; 0Þ ¼ �p:f1ðkÞ ¼ �2ppk

m(18)

and

fnumðk; 1Þ ¼ �p:f1ðkÞ � Dp3:p ¼ �2ppk

m� Dp3:p.

(19)

Applying this numerical phase to the differenttransients and adding them together, one obtains Sp;0;the signal coming from the Pp;0 pathway (Dp3 ¼ �1):

Sp;0ðt1; t2Þ ¼1

2m

Xm�1

k¼0

Xl¼0;1

sklðt1; t2Þe�ifnumðk;lÞ

¼1

2m

Xm�1

k¼0

sk0ðt1; t2Þe�ifnumðk;0Þ

þsk1ðt1; t2Þe�ifnumðk;1Þ

!. ð20Þ

After replacing fnum by the expression in Eqs. (18)and (19), it may be written

Sp;0ðt1; t2Þ ¼1

2m

Xm�1

k¼0

sk0ðt1; t2Þ

þsk1ðt1; t2ÞeiDp3:p

!e2pip k

m

¼1

2m

Xm�1

k¼0

ðsk0ðt1; t2Þ � sk1ðt1; t2ÞÞe2pip k

m. ð21Þ

The cosine-modulated 2D signal is obtained aspreviously by adding the complex conjugate signalsfrom the symmetric Pp;0 and P�p;0 pathways

Scos0 ðt1; t2Þ ¼

1

2ðSp;0ðt1; t2Þ þ S�p;0ðt1; t2ÞÞ

¼1

2m

Xm�1

k¼0

sk0ðt1; t2Þ

�sk1ðt1; t2Þ

!cos 2pp

k

m

� �ð22Þ

while the sine-modulated signal is obtained by subtract-ing these signals

Ssin0 ðt1; t2Þ ¼

1

2iðSp;0ðt1; t2Þ � S�p;0ðt1; t2ÞÞ

¼1

2m

Xm�1

k¼0

sk0ðt1; t2Þ

�sk1ðt1; t2Þ

!sin 2pp

k

m

� �. ð23Þ

Finally, the 2D spectrum S0ðo1;o2Þ is obtained by the2D Fourier transform of these two signals, following theSRH procedure. We note that this spectrum isequivalent to a z-filtered MQMAS spectrum.Similarly, the signal coming from both the Pp;�1

aliased pathways (Dp3 ¼ 0 or �2) is

Sp;�1ðt1; t2Þ ¼1

2m

Xm�1

k¼0

sk0ðt1; t2Þ

þsk1ðt1; t2ÞeiDp3:p

!e2pip k

m

¼1

2m

Xm�1

k¼0

ðsk0ðt1; t2Þ þ sk1ðt1; t2ÞÞe2pipk

m. ð24Þ

Because the signal from the Pp;�1 and P�p;�1 pathwaysare complex conjugates with opposite sign [17], thecosine-modulated 2D signal is obtained by subtractingof these two signals:

Scos�1ðt1; t2Þ ¼

1

2iðSp;�1ðt1; t2Þ � S�p;�1ðt1; t2ÞÞ

¼1

2m

Xm�1

k¼0

sk0ðt1; t2Þ

þsk1ðt1; t2Þ

!sin 2pp

k

m

� �

ð25Þ

and the sine-modulated signal by adding them

Ssin�1ðt1; t2Þ ¼

1

2ðSp;�1ðt1; t2Þ þ S�p;�1ðt1; t2ÞÞ

¼1

2m

Xm�1

k¼0

sk0ðt1; t2Þ

þsk1ðt1; t2Þ

!cos 2pp

k

m

� �.

ð26Þ

A 2D Fourier transform using the SRH procedureyields a second MQMAS spectrum: S�1ðo1;o2Þ:Both S0ðo1;o2Þ and S�1ðo1;o2Þ spectra can now be

added to produce the final Multiplex SPAM MQMASNMR spectrum.One remark can be made at this stage: indeed,

following the Gan and Kwak statement, in the abovedemonstration it has been assumed that using a softpulse only signals coming from Pp;0 and Pp;�1 areretained. However, it is worth noting that in a moregeneral situation, where the third pulse is not entirelyselective, some signal will also come from the Pp;�2 andPp;�3 additional pathways, as only two phases are usedfor this pulse. This is not a problem because thesesignals will also be aliased constructively to the signalcoming from the Pp;0 and Pp;�1 pathways, respectively.The choice of the power of the last pulse is, thus, acompromise between the efficiency of the SPAMexperiment and the need for a good excitation of thefull MAS spectrum. This may depend on the spread ofchemical shifts.Fig. 6 shows the 87Rb Multiplex SPAM MQMAS

spectrum of RbNO3 acquired using the sequencedepicted in Fig. 5. The optimization of the rf pulses in

ARTICLE IN PRESS

Fig. 6. 87Rb 2DMultiplex SPAM 3QMAS spectrum of RbNO3: On the right side, the cross sections are represented (dotted line) and compared withthe corresponding cross sections of the conventional z-filtered MQMAS spectrum (continuous line).The amplitudes and lengths of the pulses are the

same as in Fig. 4.

Fig. 7. 27Al 2D Multiplex SPAM 3QMAS (left) and 5QMAS NMR

(right) spectra of microporous aluminophosphate AlPO4-14 in the

tetrahedral-Al region. On the top, the projections are represented for

both SPAM (dotted line) and the conventional z-filtered MQMAS

spectra (continuous line). The Multiplex spectrum was acquired at a

spinning rate of nR ¼ 14kHz and a 0.5 s recycle delay. Rotor

synchronization was used in the t1 domain. For the 3QMAS/5QMAS

spectra, the initial excitation and conversion hard pulse lengths were

2.4/4.0 and 0:8=2:0ms; respectively, using a B1 field of ca. 130 kHz. The

soft pulse length was 8:3ms; using a B1 field of ca. 10 kHz.

N. Malicki et al. / Solid State Nuclear Magnetic Resonance 28 (2005) 13–21 19

this sequence is very simple because the settings areexactly the same as in the conventional (or Multiplex) z-filtered MQMAS sequence. The first pulse was phasecycled using 7 steps as previously. Only 2 phases wereused for the last pulse and the receiver was not cycled.The resulting 14 transients were all stored separately andprocessed using Eqs. (20) and (26). The comparison ofthis spectrum and the conventional z-filtered MQMASNMR spectrum shows an increase of the signal-to-noiseratio by a factor of ca. 1.7 for all sites. Using theMultiplex and SPAM, it is thus demonstrated that, withonly 14 transients, a pure-adsorption 2D spectrum of aspin-3/2 nucleus with enhanced intensity may beobtained.A second example concerns the application of the

Multiplex SPAM MQMAS NMR experiment to spin 5/2 nucleus. 3Q and 5QMAS spectra of an AlPO4-14aluminophosphate sample have been recorded, whichdisplays several Al sites with very different quadrupolarcoupling constants [11].The conventional z-filtered 3QMAS was obtained

using 6 phases for the first pulse (in order to select theþ3 and �3 coherences in t1). Similarly, the conventionalz-filtered 5QMAS was obtained using 10 phases for thefirst pulse (in order to select the þ5 and �5 coherencesin t1). The last pulse was cycled 4 times.Figs. 7a and b show the corresponding Multiplex

SPAM 3QMAS and 5QMAS spectra, obtained using 11phases for the first pulse and 2 for the third. It is worthnoting that 11 phases are necessary for spin 5/2 to avoidany undesired aliasing of the MQ coherence. Moregenerally, the number of different phases must begreater than 4*I for a nucleus with spin I.The signal-to-noise ratio improves by a factor of 1.7

and 2.7 for the Multiplex SPAM 3Q and 5QMASspectra, respectively. As observed for the Multiplexexperiment on 3/2 nuclei, the quality of the spectra isbetter than for the corresponding conventional z-filtered

MQMAS NMR spectra, as they show less dispersivecomponents.In principle, the 3Q and 5QMAS spectra may be

reconstructed using the Multiplex method from only asingle experimental data set, because it is only necessaryto change the numerical phase fnum; in Eqs. (18) and(19) according to the value of the desired p coherenceselection.

ARTICLE IN PRESSN. Malicki et al. / Solid State Nuclear Magnetic Resonance 28 (2005) 13–2120

Although this is working in practice, unfortunately agood signal-to-noise ratio cannot be obtained for the3QMAS and 5QMAS simultaneously, because the pulsesettings are rather different for the two MQ selections.This is especially true for the second pulse whichconverts MQ to zero or single quantum. Indeed, inorder to record the spectra of Fig. 7, the length of theconversion (second) pulse was 0.8 and 2:0ms for the 3Qand the 5QMAS spectra, respectively. If the pulselengths are optimized for recording a 3QMAS spectrum,it is very difficult to observe a signal in the 5QMASspectrum created from the 3QMAS. In contrast, if thesetting is optimized to record the 5QMAS, then the3QMAS spectrum may be created from the sameexperimental data set but the signal-to-noise ratio isvery poor (spectrum not shown).

4. Conclusions

It has been shown that MQMAS and SPAMMQMAS spectra are easily recorded using the Multiplexconcept introduced by Ivchenko et al. The reduction ofthe phase cycling is significant but probably not crucialin the conventional z-filtered experiment. How-ever, combination with SPAM allows performing theexperiment using only 14 scans for 3Q and 22 for5QMAS.Less dispersive contributions have been observed in

the Multiplex or Multiplex SPAM 2D MQMAS spectrathan in the conventional z-filtered MQMAS, which usesa nested phase cycling procedure. Hence, it is mandatoryto use this method to get pure-absorption MQMASNMR spectra.The possibility of simultaneously recording 3Q and

5QMAS experiments using a single set of experimentaldata has been demonstrated experimentally. Because itssignal-to-noise ratio is very poor, it is not possible to usethis method for real application of MQMAS. However,for some other pulse sequences, this concept presentsconsiderable potential.The sensitivity gain which is obtained, especially in 5Q

experiments, offers some interesting perspectives for arange of applications, for example in cross polarizationor J-coupling-based experiments. This will be the subjectof a future paper.

Acknowledgements

The authors thank Region Basse-Normandie forfinancial support. L.M. and J.R. are also grateful toFEDER, POCTI, and FCT for funding. L.M. thanksFCT for a Ph.D. research grant. N.M. thanks theANRT and IFP for a Ph.D. research grant.

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