2
H T
2q
relaxation dynamics and double-quantum filtered
NMR studies
Dennis W. Hwang
*, Wei-Jie Jhao, Lian-Pin Hwang
Department of Chemistry, National Taiwan University, Taipei, Taiwan, ROC Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan, ROC
Received 14 May 2004; revised 15 October 2004 Available online 21 November 2004
Abstract
In this study2H T2qDQF NMR spectra of water in MCM-41 were measured. The T2qdouble-quantum filtered (DQF) NMR
signal is generated by applying a radio frequency (RF) field for various durations and then observed after a monitor RF pulse. It was found that the transfer between different quantum coherences by the couplings during long-duration RF fields (i.e., soft pulses) and that residual quadrupolar interaction dominates the signal decay. Knowledge of coherence transfer during long-RF pulses has spe-cial significance for the development of sophisticated multi-quantum NMR experiments espespe-cially multi-quantum MRI applications.
2004 Elsevier Inc. All rights reserved.
Keywords: T2q; DQF NMR
1. Introduction
Knowledge of the dynamics of adsorbate molecules is very important for understanding mesoporous materials and catalysts. The dynamics of such molecules is generally slow on the NMR time scale. NMR rotating frame relax-ation rate measurements have been used to study the slow motional regime. In developing the theory needed to ana-lyze such experiments, Blicharski[1]considered the quad-rupolar relaxation for the spin I = 1 system in detail. In a later work, ignoring the effects of spin relaxation, the dynamics of a spin I = 1 nuclei system with a static resid-ual quadrupolar interaction under a short pulse irradia-tion of a radio frequency (RF) field were investigated by Vega and Pines [2]. Conventional double-quantum fil-tered (DQF) NMR spectroscopy probes residual quadru-polar interactions and it has been used as a diagnostic tool for detecting anisotropic adsorption interactions in
por-ous systems[3–5]. The effects of the residual quadrupolar interaction and the associated relaxation mechanisms on DQF NMR have been analyzed by Jacobsen et al.[6]and Van der Maarel[7].
The aim of the present study is to demonstrate a more sophisticated variant of conventional DQF NMR, the T2q double-quantum filtered (DQF) experiment. We
studied the evolution of the relevant spin tensor opera-tor describing the effects of long-duration RF fields (i.e., Ôsoft pulsesÕ) on the residual quadrupolar interac-tion resulting from adsorpinterac-tion. The theory developed in this work is useful for understanding the coherence-transfer pathway among different spin multi-poles, and in the development of sophisticated RF soft pulses for multi-quantum magnetic resonance imaging[8,9].
2. Theory
The spin system evolves under the simultaneous ac-tion of the Zeeman, residual quadrupolar interacac-tion,
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and RF Hamiltonians. Here the residual quadrupolar interaction is defined as a motionally averaged Hamilto-nian which is axially symmetric with respect to the prin-cipal axis of motion[5–8]
Hq¼ xq;hðI2z13IðI þ 1ÞÞ
xqð12Þð3cos2h 1ÞðI2z 1
3IðI þ 1ÞÞ; ð1Þ
where h is the angle between the z-axis of the molecular frame and the Zeeman field. xq,h and xq are the
(motionally averaged) residual quadrupolar interac-tions, defined in the laboratory and the molecular frames, respectively. An isotropic distribution of h is ap-plied to approximate the location of the adsorption sites under the random orientational distribution in our pow-der sample.
The RF field is assumed to be exactly on resonance along the x-axis with field strength B1 and frequency
x1. Thus the total Hamiltonian expressed in the rotating
frame reads:
Htotal¼ Hqþ H1 xq;hðI2z13IðI þ 1ÞÞ þ x1Ix
xqð12Þð3cos2h 1ÞðI2z 1
3IðI þ 1ÞÞ þ x1Ix: ð2Þ
In this study, the spin density operators and Hamilto-nian are expressed in terms of irreducible tensorial oper-ators. The mth component of a rank l irreducible tensorial component, Tlm, can be related to the elements
of a common density matrix. The symmetric and anti-symmetric combinations of spin irreducible tensor oper-ators[7,10]are defined by
TlmðsÞ 1= ffiffiffi 2 p ðTlmþ TlmÞ; TlmðaÞ 1= ffiffiffi 2 p ðTlm TlmÞ: ð3Þ The irreducible tensor operators in Eq. (3) can be ex-pressed in terms of conventional spin operators by
T10¼ I1; T11ðsÞ ¼ iIy; T11ðaÞ ¼ Ix; T20¼ 1 ffiffiffi 6 p ½3I2 z IðI þ 1Þ; T21ðsÞ ¼ i ffiffiffi 2 p ðIzIyþ IyIzÞ; T21ðaÞ ¼ 1 ffiffiffi 2 p ðIzIxþ IxIzÞ; T22ðsÞ ¼ 1 ffiffiffi 2 p ðI2 x I 2 yÞ; T22ðaÞ ¼ i ffiffiffi 2 p ðIxIyþ IyIxÞ: ð4Þ
T10, T11(a), and T11(s) denote the usual longitudinal
magnetization, and the components of transverse mag-netization along the x- and y-directions, respectively. Eq.(2)may be recast in terms of the tensorial operators
Htotal¼ Hqþ H1 ffiffiffi 2 3 r xq;hT20þ x1T11ðaÞ: ð5Þ
The time evolution of the density operator under Htotal
is given by the Liouville equation drðtÞ
dt ¼ i½Htotal;rðtÞ; ð6Þ where r (t) represents the density operator defined in terms of the set of irreducible tensor components [^T20,
^
T11ðaÞ, ^T21ðsÞ, ^T22ðsÞ, ^T10, ^T11ðsÞ, ^T21ðaÞ, and ^T22ðaÞ].
The evolution of the initial Zeeman order T10 evolves
through the coupling scheme to ^T11ðsÞ, ^T21ðaÞ, and
^
T22ðaÞ. Using the commutation relations [6,7], Eq. (6),
in terms of the irreducible tensor component, under the influences of residual quadrupolar interaction, RF field, and spin relaxation[4]becomes
d dt Ta 10 Ta11ðsÞ Ta21ðaÞ Ta 22ðaÞ 2 6 6 6 4 3 7 7 7 5¼ Ra 10 ix1 Rax1 0 ix1 Ra11s ixq;h 0 0 ixq;h Ra21a ix1 0 Ra x1 ix1 Ra22a 2 6 6 6 4 3 7 7 7 5 Ta 10 Ta11ðsÞ Ta21ðaÞ Ta 22ðaÞ 2 6 6 6 4 3 7 7 7 5 R ar a; ð7Þ where Ra x1 C a½3x 1xq;h½Ja0ð0Þ J a 0ðk1Þ=k21; Ra10 Ca½2Ja 1ðx0Þ þ 4Ja2ð2x0Þ; Ra 11s C a f3½x2 q;hJ a 0ð0Þ þ 2x 2 1ðJ a 0ð0Þ þ J a 0ðk1ÞÞ=k21 þ 5Ja 1ðx0Þ þ 2Ja2ð2x0Þg; Ra21a Caf3½x2 q;hJ a 0ð0Þ þ 2x 2 1ðJ a 0ð0Þ þ J a 0ðk1ÞÞ=k21 þ Ja 1ðx0Þ þ 2Ja2ð2x0Þg; Ra22a Ca½2Ja 1ðx0Þ þ 4Ja2ð2x0Þ: ð8Þ In this case, k1¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 q;hþ 4x 2 1 q , Ca 3 160v 2 a, R a is the cou-pling matrix, and rais the related irreducible tensorial
operator sets where the subscript a denotes a specific adsorption site, and va” (e2Qqa)/h are the associated
quadrupolar coupling constants. According to our pre-vious study [5], there are two major types of water adsorption sites on the inner surface of MCM-41: slow motion sites and fast motion sites. The water in the slow motion sites is mainly bound water on the inner surface of MCM-41 which can be observed directly by DQF NMR due to residual quadrupolar interaction. Accord-ing to Jacobsen et al.[6], the definitions of the spectral-density functions for slow motion site are given by
Js 0ð0Þ ¼ j0ð0Þ½1 þ107hD 2 00i þ 18 7hD 4 00i 5hD 2 00i 2 ; Js0ðk1Þ ¼ j0ðk1Þ½1 þ107hD200i þ187hD 4 00i 5hD 2 00i 2 ; Js1ðx0Þ ¼ j1ðx0Þ½1 þ57hD 2 00i 12 7hD 4 00i; Js 1ð2x0Þ ¼ j2ð2x0Þ½1 107hD200i þ 3 7hD 4 00i; ð9Þ
where jm(x) (m = 0, 1, and 2) is the spectral density for
adsor-bate dynamics in the slow motion sites modeled by the modified cone model of Brainard and Szabo[5,11]with two motion modes: the wobbling motion of the D2O
molecule along its C2 and internal rotation motion of
D2O. The motional correlation times are defined by sw
and si, respectively. Thus the spectral density, jm(x),
can be defined by jmðxÞ 4S 2ðd2 10ðbÞÞ 2 Di D2 iþ ðmxÞ 2þ 4S 2ðd2 20ðbÞÞ 2 4Di ð4DiÞ 2 þ ðmxÞ2 þ 2ðd2 00ðbÞÞ 2 ð1 S2Þ½6Dw=ð1 S2Þ ½6Dw=ð1 S2Þ 2 þ ðmxÞ2 þ 4ðd2 10ðbÞÞ 2 ð1 S2Þ½Diþ 5Dw=ð1 S2Þ ½Diþ 5Dw=ð1 S2Þ 2 þ ðmxÞ2 þ 4ðd2 20ðbÞÞ 2 ð1 S2Þ½4Diþ 2Dw=ð1 S2Þ ½4Diþ 2Dw=ð1 S2Þ 2 þ ðmxÞ2; ð10Þ
where Di= 1/(4si) and Dw= 1/(6sw). d2nmðbÞ are elements
of the reduced Wigner rotation matrix and b is the fixed angle between the C2axis of D2O molecule and principal
axis of the residual quadrupolar interaction, i.e., the O–D direction. The distribution of orientations in the cone in the molecular frame is characterized by an order param-eter, S (0 6 S 6 1). In the formulation, both S and xq
are both subject to the same averaging process, thus, for convenience we define S = xq/xqm. S characterizes the
strength of the residual interaction of the adsorbed water molecules. xqm is the maximum residual quadrupolar
interaction for a D2O molecule adsorbed on the
adsorp-tion site. For the D2O quadrupolar interaction,
xqm¼34vs, where vsis the quadrupolar coupling constant.
For the water molecules in the fast motion sites is mobile water in the pores of MCM-41 which the reori-entational Brownian motion of water molecules aver-ages the anisotropic quadrupole interaction experienced by the 2H nucleus to zero, i.e., xq,h= 0.
Thus no double-quantum coherence (DQC) is generated in fast motion sites. The spectral-density function for fast motion site is given by
Jf m¼
2sc
1þ ðmx0scÞ
2; ð11Þ
where scis the effective reorientational correlation time
of water molecules. Despite the signal from fast motion sites cannot be investigated directly, it still can be ob-served by DQF NMR indirectly due to the water being in exchange with water molecules in the slow motion site. Including the exchange process between the two sites, Eq.(7) becomes
d dt rs rf ¼ R s K sf Kfs Ksf Rf Kfs r s rf ; ð12Þ
where Kab” kabI and I is the 4· 4 identity matrix. The
definitions of rs and rf follow those in Eq. (7) kfs is
the microscopic rate constant for transfer from fast
mo-tion sites to slow momo-tion sites, and ksfis the microscopic
rate constant for transfer from slow motion sites to fast motion sites. The principle of detailed balance applied to the exchange process requires that Pfkfs= Psksfwhere Pf
and Psdenote the populations of spin-bearing molecules
in the fast and slow motion sites, respectively. To guar-antee the validity of Eq. (12), the condition sex sc
must hold, where sexis defined as sex” Ps/kfs= Pf/ksf.
Since we focus on the effects of the water adsorption dynamics on the T2q DQF spectrum, most parameters
for simulating the T2q DQF spectral lineshapes were
derived from conventional DQF and T1
inversion-re-covery spectral lineshape analysis [5]. Conventional and T2q DQF spectra were measured using the pulse
sequences shown in Figs. 1A and B, respectively. The coherence-transfer pathways are described in Eq. (7). The applied spin-lock field transforms the Zeeman or-der T10 into double-quantum coherence T22(a) and
then the p/2 pulse followed transfers double-quantum coherence into an observable signal. The other unde-sired coherences are canceled by the phase cycling.
Fig. 1. The pulse sequence and coherence-transfer pathway for (A) DQF NMR. The phase cycles for the various components of the pulse sequence are as follows: / = (X, Y,X, Y, X, Y, X, Y, X, Y, X, Y, X, Y, X, Y) and /0= (X, X, X, X Y, Y, Y, Y,X, X, X, X,
Y, Y, Y, Y), and receiver phase, /R= (X,X, X, X, Y, Y,
Y, Y, X, X, X, X, Y, Y, Y, Y). (B) T2qDQF NMR. / = (X, Y,
X, Y, X, Y, X, Y, X, Y, X, Y, X, Y, X, Y) and /0= (X, X,
X, X, Y, Y, Y, Y,X, X, X, X, Y, Y, Y, Y), and receiver phase, /R= (X,X, X, X, Y, Y, Y, Y, X, X, X, X, Y, Y,
As noted above, the T2qDQF NMR sequence mainly
reports on the water signal from slow motion sites. Whereas the single quantum (SQ) signals observed in the inversion-recovery experiment report on the water signal from both the slow and fast motion sites [5]. Hence the motional parameters determined from both T2q DQF NMR and inversion-recovery experiments
must be self-consistent.
3. Experimental 3.1. Sample preparation
Cetyltrimethylammonium bromide (CTAB) (99%; Acros) was dissolved in deionized water at 308 K while stirring. A solution of sodium silicate (Aldrich, 14% NaOH and 27% SiO2), was added and the resulting gel
was stirred for 20 min. The pH of the gel was adjusted to 10 with 1.2 M sulfuric acid (Acros). The molar com-position of the gel was 1.00 SiO2:0.35 CTAB:0.28
H2SO4:100 H2O. The gel was then stirred for a further
1 h before being transferred to a Teflon-lined autoclave where it was heated at 373 K for 48 h. The final solid product obtained after filtration, was washed with deionized water, dried in air at room temperature, and calcined at 833 K for 6 h.
X-ray powder diffraction data of the MCM-41 was collected on a Scientag XI diffractometer using CuKa
radiation. The average pore diameter was estimated from the d100-spacing of the X-ray diffractograms. The
surface-area and pore-size measurements were per-formed on a homemade high vacuum system. The sam-ple was degassed at 590 K and 1 mPa for 16 h. Assuming the thickness of the walls to be 1 nm, the esti-mated average pore diameter was 3.38 ± 0.17 nm. The sample has BET surface areas of 900 ± 45 m2g1, which is characteristic of mesoporous materials.
The MCM-41 was initially dried under a vacuum of 105torr at 650 K for more than 16 h and then trans-ferred to an 8 mm ID tube approximately 40 mm long. Two samples with deuterated water loadings of 11.1 and 4.8% (w/w%) were prepared. From our previous DQF NMR and inversion-recovery measurements [5], the water distributions in MCM-41 in these two samples were known to be different. Water is distributed in both the slow and fast motion sites in the 11.1% D2O loaded
sample and, as expected, it gives a better S/N ratio than the 4.8% D2O loaded sample and this sample was mainly
utilized in the investigation of trend of intensity varia-tion for saving time. Since the 4.8% D2O loaded sample
has only water in the slow motion site, its DQ signals are much simpler. Then, the sample tubes were sealed and kept at 373 K for at least 24 h to ensure a homogeneous distribution of adsorbate in the sample before the NMR measurement.
3.2. NMR measurement
The2H NMR measurements were performed on Bru-ker MSL-500 spectrometer operating at 76.78 MHz (11.75 T) with a 90 pulse of 16 ls. The receiver recovery time is less than 10 ls, and the probe dead time is 10 ls. Typical acquisition parameters were a spectral width of 125 kHz digitized into 8K data points. Each spectrum was the result of averaging 10,000 scans. A delay of at least 5 T1was allowed between scans for the T1, DQF,
and T2qDQF NMR spectra. The temperature was
con-trolled to a precision of ±0.1K and was calibrated using methanol. The magnetic inhomogeneity was estimated by comparing Hahn spin-echo and linewidth measure-ments and was found to account for less than 5 Hz of the observed linewidth at half height. The longitudinal relaxation measurements were obtained using the inver-sion-recovery pulse sequence. For the T2qDQF NMR,
the RF pulse profile was monitored and recorded by a Tektronix TDS 3032B oscilloscope. InFig. 2, the long-RF pulse profile is distorted due to the duty cycling lim-itation of the RF transmitter. All NMR measurements reported here were performed within 1 month of sample preparation. However the longitudinal relaxation behavior was observed to be constant over a period of 2 months—indicating that equilibrium had been reached in the pore systems prior to the initiation of the NMR measurements.
4. Results and discussion
To investigate the characteristic features of the T2q
DQF NMR spectra, the T2q DQF NMR spectra of
the 11.1% D2O loaded sample at 273 K are exhibited
in Fig. 3A and for comparison the conventional DQF NMR spectra are presented in Fig. 3B. The T2q DQF
NMR spectral intensity oscillates with the double
Fig. 2. The RF profile of the T2qDQF NMR pulse sequence (seeFig.
1B) monitored using an oscilloscope. The RF pulse profile is distorted due to the duty cycling limitation of the RF transmitter.
quantum evolution time, s, while the conventional DQF NMR spectra show monotonic decay with s. To clarify the origin of the oscillation in the T2qDQF NMR
spec-trum, the experimental spectrum of the 11.1% loaded sample at 273 K was compared with a theoretical simu-lation (see Fig. 4). And inFig. 5, the oscillation of the T2q DQF NMR spectral intensity of the 11.1% sample
at 295 K with 10 ls increments of the DQ evolution time is presented together with the simulated results. Excel-lent agreement was obtained between the experimental and simulated results and the parameters used in the theoretical calculations are tabulated inTable 1.
T21(a) and T22(a) are coupled to each other by the
RF field via the x1 term as shown in Eq. (7). The
DQC, T22(a), oscillates approximately following
sin (x1t), that is, the period of oscillation of the T2q
DQF NMR signals is proportional to the amplitude of the RF field. As can be understood fromFig. 2, as s in-creases, the RF field strength decreases. And as shown in Fig. 5 the oscillation period increases from 60 to 70 ls with increasing s. The B1-dependence of the
oscil-lation frequency provides a means for determining the RF strength, including the effects of the amplitude de-crease with increasing RF duty cycle, for use in the simulations.
In addition to the effect of RF field, the residual quadrupolar interaction also has unique influences on the T2q DQF NMR spectra. To investigate the effect
of residual quadrupolar interaction, the 4.8% loaded sample was so as to minimize the effect of water ex-change. The DQF NMR and T2q DQF NMR spectra
of the 4.8% D2O loaded sample in the temperature range
from 220 to 273 K is shown in Fig. 6. The T2q DQF
NMR intensity profile shows temperature-dependent damped oscillations and phase variation. The T2q
DQF NMR spectral intensity profiles is clearly more sensitive to temperature than that of conventional DQF NMR.
Experimental and simulated T2qDQF spectral
inten-sity profiles of the 4.8% loaded sample in the tempera-ture range of 220–273 K are shown in Fig. 7. The simulation parameters are tabulated in Table 2. From the lineshape analysis of the conventional DQF NMR and inversion-recovery experiments for the 4.8% D2O
loaded sample, it was inferred that only slow-site water molecules exist. Hence, the effects of exchange were ne-glected when simulating the results from this sample. The agreement between experimental and theoretical simulation shows that the variation of intensity profiles
Fig. 4. (A) T2qDQF spectra and (B) simulations of the 11.1% D2O
loaded sample for various DQ evolution times at 273 K. The parameters used in the simulations are tabulated inTable 1.
Fig. 5. The change in intensity of the T2qDQF NMR spectra with DQ
evolution time of the 11.1% D2O loaded sample at 295 K. Solid circles
(d) represent the T2qDQF NMR peak intensity data and the solid
curve is the theoretical calculation.
Fig. 3. (A) T2qDQF and (B) conventional DQF NMR spectra of the
11.1% D2O loaded sample for various DQ evolution times at 273 K.
Table 1
Parameters used in simulation for 11.1% D2O contained sample
Temperature (K) Pf/Ps sfc1 (s) sw(s) si(s) sfex1s(s) S
295 0.3 1.0 ± 0.5· 1011 6.0 ± 0.2· 105 3.0 ± 0.1· 1011 4.0 ± 0.1· 104 0.023 ± 0.001
with temperature mainly results from the wobbling mo-tion and the distribumo-tion of the adsorbate which is characterized by the order parameter [5]. The values of the order parameters tabulated inTable 2show that the water molecules become more ordered at lower temperatures, and as a consequence there is a stronger residual quadrupolar interaction as well. The rugged features that appear around s = 500 ls in the calcu-lated curves inFig. 7provide direct evidence of the var-iation of the residual quadrupolar interaction with temperature. As mentioned above, the residual quadru-polar interaction coupling may account for an extra oscillation of the form of sin (xq,ht) in addition to the
effect of the RF field. Using Eq. (7) and the time at which the rugosity appeared it was possible to estimate the residual quadrupolar interaction (i.e., xq,h) to be
around 4 kHz. This value roughly equals the splitting of the SQ spectra found in the temperature range 220–273 K. To verify the periodic behavior of the rug-osity, Fig. 8 demonstrates the theoretical calculations of the spectral intensity profiles for the 11.1 and 4.8% D2O loaded samples. The result in Fig. 8B obviously
shows the rugosity with a period of500 ls. Therefore, the s value at which rugosity appears is thus an indica-tor of the strength of the residual quadrupolar interac-tion of the water in MCM-41. Since the strength of the
Fig. 8. The theoretical simulations of the spectral intensity profiles for (A) the 11.1% and (B) 4.8% D2O loaded samples at 273 K. The solid
curves are simulations including the effects of the RF field, residual interaction, and electric quadrupolar relaxation. The simulations represented by the dashed curves neglect relaxation effects during DQ evolution period.
Fig. 7. T2qDQF NMR spectral intensity profile for the 4.8% D2O
loaded sample at: (a) 220 K, (b) 230 K, (c) 240 K, (d) 250 K, (e) 260 K, and (f) 273 K. Solid rectangles (j) represent the peak intensity of the T2q DQF NMR spectra. The solid curves are the theoretical
simulation.
Fig. 6. (A) Conventional DQF NMR and (B) T2qDQF NMR spectra
for the 4.8% D2O loaded sample at various values of the DQ evolution
time in the temperature range from 220 to 273 K.
Table 2
Parameters used in simulation for 4.8% D2O contained sample
Temperature (K) sw(s) ssi (s) S 220 8.0 ± 0.5· 105 9.5 ± 0.5· 1011 0.030 ± 0.001 230 4.5 ± 0.6· 105 7.0 ± 0.4· 1011 0.030 ± 0.001 240 2.5 ± 0.1· 105 6.5 ± 0.3· 1011 0.030 ± 0.001 250 2.3 ± 0.1· 105 6.5 ± 0.2· 1011 0.030 ± 0.001 260 2.3 ± 0.1· 105 5.0 ± 0.1· 1011 0.026 ± 0.001 273 2.3 ± 0.2· 105 2.0 ± 0.1· 1011 0.026 ± 0.001
residual quadrupolar interaction increases with decreas-ing temperature the rugosity appears at progressively shorter s values as shown inFig. 7.
To clarify the effect of the exchange process on T2q
DQF NMR, the experimental spectral intensity profiles for the 11.1 and 4.8% D2O loaded samples at 273 K
and the corresponding theoretical simulations (both with and without the effects of relaxation; see Eq. (7)
are compared in Fig. 8. The simulation parameters are tabulated inTables 1 and 2. Clearly the T22(a) term
remains constant in the absence of RF irradiation. Comparison of Figs. 8A and B reveals that the ex-change between the slow and fast motion sites en-hances the signal decay, but the RF field and residual quadrupolar interactions are nevertheless the dominant factors in determining the intensity decay during the DQ evolution period. The node that appears around 500–600 ls in Fig. 8B is due to the interference of T11(s) and T21(a) via the residual quadrupolar
interac-tion. Vega and Pines [2] demonstrated a similar effect by using different combinations of RF fields and quad-rupolar interaction strengths. However, as they used a short RF field duration (60 ls) they did not demon-strate the decay of the coherences.
To clarify the detailed time evolution of the coher-ence transfer more precisely, the effects of the coupling of the terms were investigated with the 4.8% D2O
loaded sample. As shown in Fig. 9, T10 and T11(s)
are dominant initially due to their coupling by the RF field. The effects of T21(a) and T22(a) start to
ap-pear around s = 200 ls and have their maximum value at around 300–400 ls. T21(a) is generated mainly due
to the residual quadrupolar interaction and later the coupling of the RF field with T22(a). In the present
studies, the RF field strength is much stronger than the other coupling interactions.
By examining the evolution of each component, as shown in Fig. 9, it is observed that the decreasing of the SQ coherences is correlated with an increase of the T21(a) and T22(a) coherences during the periods
s= 200–400 ls and 800–1000 ls. By judicious choice of DQ evolution time, DQC or SQC can be selectively enhanced. Further, the coupling RF field can lead to de-cays of individual coherences. The decay pathway can be considered as a re-distribution process even in the ab-sence of the influence of spin relaxation—an entropic ef-fect for magnetization within a given coupling scheme.
In addition to the present application, the effect of long-duration RF irradiation is especially important in MRI due to the prevalence of soft pulses in MRI se-quences. During such long-RF pulses, coupling through other interactions, such as the residual dipolar interac-tion, may create the multi-quantum coherences as ob-served in this study. Specially designed soft RF pulses may provide an alternative means for generating mul-ti-quantum coherences in intermolecular and intramo-lecular dipolar interaction systems. This work may lead to the design of simple pulse sequences for MQ imaging. We are presently developing sophisticated T2q
DQF NMR-based MRI techniques in our laboratory.
5. Conclusions
We have experimentally and theoretically demon-strated the creation of multi-quantum coherences in spin systems coupled with the residual dipolar interaction during long-duration RF pulses. The results have special significance for the development of multi-quantum MRI techniques.
Acknowledgments
This work was supported by the National Science Council of the Republic of China under Grant No. NSC 92-2113-M-001-038 and Ministry of Education of the Republic of China under Grant No. A-91-N-FA01-2-4-3.
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