1 Introduction........................................................................................................................ 2 2 Basic theory of the solid-state NMR techniques................................................................... 3 3 Solid-state NMR studies of the structure............................................................................ 11
3.1 29Si NMR............................................................................................................. 11 3.2 27Al NMR............................................................................................................. 14 3.3 1H NMR............................................................................................................... 16 3.4 23Na NMR ........................................................................................................... 19 3.5 17O NMR............................................................................................................. 20 3.6 Some references to other nuclei............................................................................. 21
4 Conformation and conversion of molecules adsorbed in porous materials ............................ 22 5 Pulsed field gradient (PFG) NMR technique ...................................................................... 22 6 Magnetic resonance imaging (MRI) of porous materials...................................................... 25 7 129Xe NMR ...................................................................................................................... 26 List of symbols.......................................................................................................................... 27 List of abbreviations .................................................................................................................. 28 References................................................................................................................................ 29
__________________________________________________________________________________ * This review was written in summer 2001 as the base for Chapter 2.12 in the "Handbook of Porous Solids"
edited by Ferdi Schüth, Kenneth S.W. Sing and Jens Weitkamp. If someone likes to refer to this review, the following reference should be used:
D. Freude and J. Kärger: NMR techniques in F. Schüth, K.S.W. Sing and J. Weitkamp (eds.): Handbook of Porous Solids, Wiley-VCH, Weinheim, 2002, vol. 1, p. 465-504
2
1 Introduction
The applicability of nuclear magnetic resonance (NMR) techniques continues to expand in physics, chemistry, material science, geology, biology, and medicine for either spectroscopic studies, investigation of diffusivity or imaging purposes. Current Contents (Physical, Chemical and Earth Sciences) for the year 2000 refers to 2415 studies of porous materials, among them to 362 NMR studies in this field. This impressive number is the result of a remarkable development over the last 35 years with 6 NMR publications in the field in 1967, 17 in 1975, 72 in 1985 and 240 in 1995.
In view of their practical relevance for porous materials this review particularly emphasizes two branches of NMR techniques: Solid-state techniques for the investigation of the structure of the porous host material and pulsed field gradient techniques for the study of the dynamics of the guest molecules.
NMR techniques provide important new insights into the structure of porous materials and into the dynamics of the adsorbed molecules. Magic-angle spinning (MAS) NMR spectra of 29Si nuclei yield the Si/Al ratio of the zeolitic framework and monitor angles and connectivities of atoms. 27Al NMR quantitatively distinguishes between 3-, 4-, 5- and 6-coordinated aluminum sites. 1H NMR gives quantitative information about acid sites and framework defects. Also hydrogen exchange between acid sites and adsorbed molecules can be studied by 1H MAS NMR in fused glass ampoules rotating at 1-20 kHz. 23Na NMR studies show the location and mobility of cations. In situ 13C and 1H MAS NMR studies of catalytic reactions identify various species in the catalyst and monitor their fate as a function of time and temperature.
Among the methods of studying molecular diffusion in porous media, the pulsed field gradient (PFG) NMR technique has attained particular relevance as a non-invasive technique. PFG NMR is able to trace molecular displacements within the system under study over a space scale from about 100 nm up to 100 µm. Since NMR spectroscopy is sensitive to a particular nucleus and even to a particular chemical surrounding, PFG NMR is able simultaneously to determine the diffusivities of the individual species in multicomponent systems. From a historical point of view PFG NMR deserves particular interest. By revealing large discrepancies with the results of uptake measurements it was this technique that initiated a reconsideration of the conditions under which conventional adsorption-desorption measurements are able to provide unambiguous information about intracrystalline diffusion in zeolites [1]. This discrepancy between microscopic and macroscopic techniques still exists.
After describing the basic theory and the NMR techniques in Sect. 2, an overview about solid-state NMR studies of the structure of porous materials will be given in Sect. 3. The following Sect. 4 concerns NMR studies of the conformation and conversion of molecules adsorbed in porous materials. The diffusion techniques follow in Sect. 5 and we complete the survey in Sections 6 and 7 with magnetic resonance imaging and 129Xe NMR, respectively.
There exist many important reviews of NMR studies of porous materials and molecules adsorbed therein. A first summarizing account has been given by Harry Pfeifer [2] on "Nuclear magnetic resonance and relaxation of molecules adsorbed on solids". A complete text book of the subject is "High resolution solid-state NMR of silicates and zeolites" by Günter Engelhardt and Dieter Michel [3]. The book "NMR techniques in catalysis" edited by A.T. Bell and A. Pines [4] reviews in seven contributions the NMR techniques for porous materials in heterogeneous catalysis up to the year 1992: C.A. Fyfe, K.T. Mueller, G.T. Kokotailo: "Solid-state NMR studies of zeolites and related systems" [5]; J. Kärger, H. Pfeifer: "NMR studies of molecular diffusion" [6]; J.F. Haw: "In situ NMR" [7]; H. Eckert: "NMR spectroscopy of bulk oxide catalysts" [8]; G.E. Maciel, P.D. Ellis: "NMR characterization of silica and alumina surfaces" [9]; G.W. Haddix, M. Narayana: "NMR of layered materials for heterogeneous catalysis" [10]; W. Kolodziejski, J. Klinowski: "New NMR techniques for the study of catalysis" [11]. Since 1992 the following books or articles, given in the sequence of the year of publication, review applications of NMR techniques to study porous materials: "Diffusion in zeolites and
3
other microporous solids" by J. Kärger and D.M. Ruthven [12], "Applications of solid-state NMR for the studies of molecular sieves" by J. Klinowski [13], "NMR of solid surfaces" by H. Pfeifer [14], "NMR studies of zeolites" by H. Pfeifer, H. Ernst [15], "Solid state NMR - a powerful tool for the investigation of surface hydroxyl groups in zeolites and their interactions with adsorbed probe molecules" by E. Brunner [16], "Multinuclear solid-state NMR studies of acidic and non-acidic hydroxyl protons in zeolites" by M. Hunger [17], "Quantum-chemistry of zeolite acidity" by R.A. van Santen [18], "Bronsted acid sites in zeolites characterized by multinuclear solid-state NMR spectroscopy" by M. Hunger [19], "NMR Spectroscopy" by H. Pfeifer [20], "Solid-state NMR" by G. Engelhardt [21], "Design, synthesis, and in situ characterization of new solid catalysts" by J.M. Thomas [22], "Characterization of zeolites - infrared and NMR and X-ray diffraction" by H.G. Karge, M. Hunger, H.K. Beyer [23], "The dynamics of hydrogen bonds and proton transfer in zeolites" by H. Koller, G. Engelhardt, R.A van Santen [24], "Measurement of interatomic connectivities in molecular sieves using MQMAS-based methods" by M. Pruski, C. Fernandez, D.P.Lang, J.P. Amoureux [25], "High-resolution solid state NMR spectroscopy in the studies of hydrocarbons and alcohols conversions on zeolites" by A.G. Stepanov [26], "Methanol-to-hydrocarbons: catalytic materials and their behavior" by M. Stöcker [27] "Enhancement of surface and biological magnetic resonance using laser-polarized noble gases" by E. Brunner [28], "Characterization of Brønsted and Lewis acidity in zeolites by solid-state NMR" by A.L. Blumenfeld, J.J. Fripiat [29], E.G. Derouane, H.Y. He, S.B. Derouane-Abd Hamid, I. Ivanova: "In situ MAS NMR investigations of molecular sieves and zeolite-catalyzed reactions" [30] "Quadrupole nuclei in solid-state NMR" by D. Freude [31], "NMR spectroscopy applied to zeolite catalysis" by W.O. Parker [32]. For 129Xe NMR reviews see Sect. 7.
2 Basic theory of the solid-state NMR techniques
NMR experiments are performed in an external magnetic field, which points by convention into the z-direction, whereas the radio frequency (rf) coil is in x-direction of the laboratory system (LAB). The LAB (x, y, z) can be transferred into a system (ROT) rotating around the direction of the external magnetic field with the applied rf ν = ω /2π . The coordinates (x i, yi, zi) in this so-called interaction representation are x i = x cosωt, yi = ± y cosωt, zi = z. The microscopic properties of the material are described in the principal axis system (PAS). The principal axes (X, Y, Z) are related to the structure of the complex. For the dipolar interaction, for example, the Z-direction is parallel to the internuclear vector.
The various interactions of the nuclear spin I can be described by the corresponding Hamiltonians. In the following, we use I for the spin number and I for the spin angular momentum vector and for the corresponding vector operator with the components Ix, Iy and Iz as well. The component of the spin angular moment in the direction of the external magnetic field is denoted as the magnetic quantum number m instead of Iz. The interaction of a nuclear spin with an external magnetic field B gives the Hamiltonian
H = IZB (1)
Z = −γ h1 includes the unity matrix 1, the magnetogyric ratio γ of the nuclear spins and the Planck constant h = 2πh, as described by Abragam [33]. For the case of a static external magnetic field B0 pointing in z-direction and the application of a rf field Bx(t) = 2Brf cos(ωt) in x-direction we have for the external interactions
H0 + Hrf = hωLIz + 2hωrf cos(ωt)Ix, (2)
where ωL = 2πνL = −γ B0 denotes the Larmor frequency, and the nutation frequency ωrf is defined as ωrf = −γ Brf .
4
The transformation from the laboratory frame to the rotating frame gives, by neglecting the part that oscillates with the twice radio frequency
H0,i + Hrf,i = h∆ωIz + hωrf Ix, (3)
where ∆ω = ωL − ω denotes the resonance offset. In addition to the external interactions there are internal interactions of a nuclear spin, which can be efficiently expressed in the notation of irreducible tensor operators, as described by Weissbluth [34] or other text books. In this notation, the scalar product of two operators Tq
(k) and Vq(k) of rank k can be written in the
simple form
T V T Vqk
qk q
qk
q k
k
qk( ) ( ) ( ) ( )( )⋅ = −
=−
+
−∑ 1 . (4)
Fortunately, most internal interactions in the NMR can be written in this form [35]. In the following, the operators Tq
(k) and Vq(k) act on two non-interacting systems, the nuclear spin coordinates and the spatial
coordinates (lattice parameters), respectively.
Only tensor elements with q = 0 contribute to the secular part of the internal Hamiltonians in a strong external magnetic field, if the system is described in the laboratory frame (LAB). However, the microscopic properties of the system are described in the principal axis system (PAS) and a rotation of the coordinates from the PAS to the LAB by means of the Wigner matrix elements [34] ( )D Rq
k'
( )0 must be performed. The element q = 0 of
the tensor V(k) is obtained by
( )( ) ( )( ) ( )( )V V D Rkq
k
q k
k
qk
0 0LAB PAS= ′′=−∑ ' . (5)
Operators of rank 0 are invariant with respect to rotations. For the chemical shift we have
( )T I Bz00
013
=−
, ( )V00 3= σ iso and H chemical shift
isotropiciso= −γ σh I Bz 0 . (6)
σiso is the isotropic part of the shielding tensor with σiso = (σXX + σYY + σZZ)/3. Rank 0 operators do not contribute to dipolar interactions or quadrupole interaction in first order. The contribution of the rank 1 operators can be neglected for all considered interactions. Therefore, anisotropy of the chemical shift, dipolar interactions and first-order quadrupole interactions can be described by rank 2 operators in the form
( ) ( ) ( )H = − −=−
+
∑C T Vqq q
q
1 2 2
2
2
. (7)
Several contributions as described in Table 1 can be superimposed. The elements of the shielding tensor σ (trace 3σiso) and of the traceless tensor of the electric field gradient V (which should not be confused with the operator V(k)) are given in the principal axis system. Parameters of the anisotropy are δ = σZZ − σiso for the chemical shift (CSA) and VZZ = eq for the electric field gradient, where e denotes the elementary charge. (The value q alone has no physical meaning.) Q is the quadrupole moment with the dimension m−2, eQ is often called the electric quadrupole moment. With the conventions |VZZ| ≥ |VYY| ≥ |VXX| and |σZZ − σiso| ≥ |σYY − σiso| ≥ |σXX − σiso| we obtain the asymmetry parameters η in the range 0 ≤ η ≤ 1 by the definitions
iso
and σσσσ
ηη−−
=−
=ZZ
YYXX
ZZ
YYXX
VVV
. (8)
5
Table 1: Some contributions to the Hamiltonian. The dipolar interaction is the homonuclear one. For heteronuclear dipolar interactions T0
(2) must be substituted by 1 6/ IziIzk.
Term Chemical shift Dipolar interaction between Ii and Ik
Quadrupole interaction
C h γ −24
2 0γ γµπi kh
( )eQ
I I2 2 1−
( )T02 2
3 0I Bz ( )16
3I Izi zk i k− I I ( )[ ]16
3 12I I Iz − +
( )T±12 1
2 1 0I B± ( )12 1 1I I I Ii zk zi k± ±+ ( )1
2 1 1I I I Iz z± − ±+
( )T±22 0 I Ii k± ±1 1 I±1
2
( )V02 PAS ( )3
232
σ σ δZZ − =iso 32
3rik−
32
32
V eqZZ =
( )V±12 PAS 0 0 0
( )V±22 PAS ( )1
212
σ σ ηδXX YY− = 0 ( )12
12
V V eqXX YY− = η
( )V02 LAB ( )3
2δ α β ηF , ,
32
1 3 123
2
rik
ikcos θ −
( )3
2eq F α β η, ,
I±1 = ( )m12
I Ix y± i and ( )F α β ηβ η
β α, ,cos
sin cos=−
+
3 12 2
22
2 are used in Table 1. The last row in
Table 1 gives components that were transformed from the PAS into the LAB by the Euler angles α and β [34] using Eq. (5) for rank 2. With Eq. (7) we obtain for the secular part of the Hamiltonian in the LAB for first-order quadrupole interaction
( ) ( )( )H Q =−
− +−
+
eQVI I
I I IZZz4 2 1
3 13 1
2 222
22cos
sin cosβ η
β α . (9)
The quadrupole coupling constant Cqcc is commonly defined as
Ce qQ
hqcc =2
. (10)
However, for the quadrupole frequency, νQ or ωQ, different definitions exist in the literature. We use the values
( ) ( )νQqcc
=−
=−
32 2 1
32 2 1
2e qQI I h
CI I
or ( )ω Q =−
32 2 1
2e qQI I h
, (11)
which were introduced for half-integer spin nuclei in the field of nuclear quadrupole resonance (NQR) by Das and Hahn, [36] and established by Abragam [33] also for NMR. By substituting VZZ = eq and using the angular-dependent quadrupole frequency
′ =−
+
ν ν
β ηβ αQ Q
3 12 2
22
2cossin cos (12)
one can write
( )( )H Qfirst -order Q=
′− +
hI I Iz
ν6
3 12 . (13)
6
Eq. (13) represents the first-order contribution of the quadrupole interaction in the strong external magnetic field. From the second-order contribution, the secular part with respect to Iz is
( )[ ] ( )[ ]{ }H Qsecond-order Q
2
LZ Z
2Z Z
2= − + + + − + +− −
hI I I I V V I I I I V V
ν
ν92 2 1 1 4 1 1 21 1 2 2 . (14)
The components V in Eq. (14) are divided by VZZ and correspond to the LAB. They can be obtained from the components in the PAS by means of Eq. (5).
The homonuclear dipolar interaction of a pair (i, k) of spins with the distance rik and an angle θ between the internuclear vector and the direction of the external magnetic field is described by the Hamiltonian
( )H D =−
−
µγ γ
θ0 22
343 1
23
π i kik
ikz i z k i kr
I Ihcos
, , I I . (15)
and it holds γi = γk. For heteronuclear dipolar interaction we have γi ≠ γk and (3Iz,iIz,k − IiIk) in Eq. (15) must be substituted by (Iz,iIz,k).
The Hamiltonian of the chemical shift is the sum of the isotropic and the anisotropic contributions:
H CS iso= +−
+
γ σ δ
β ηβ αh B I z0
223 1
2 22
cossin cos . (16)
For the excitation of NMR signals we discuss the size of the corresponding Hamiltonian ||H||. The usual sequence is ||H0|| » ||Hrf|| » ||HQ||, ||HD||, ||HCSA||. Expressed in frequencies: the Larmor frequency (||H0||), cf. Eq. (2), is of the order of 10-1000 MHz, the nutation frequency (||Hrf||), cf. Eq. (2), is of the order of 50-500 kHz, if the π/2-pulse duration is 5-0.5 µs, and the internal interactions are smaller than 50 kHz. However, the latter is sometimes not the case for quadrupole nuclei in solids. We can assume the relation ||H0|| » ||HQ|| » ||HD||, ||HCSA|| and have to distinguish the well-defined cases ||Hrf|| » ||HQ|| (*) or ||Hrf|| « ||HQ|| (**) and the ill-defined intermediate case (***). A so-called hard pulse can perform a nonselective excitation of the whole quadrupole broadened spectrum, if the radio frequency field strength meets (*). The soft-pulse (**) excitation is limited to any single transition (m = −I, −I+1, ..., I−1) in a single crystal or to the central transition (m = −1/2) for powdered materials. Here the transition m denotes the transition between the magnetic quantum numbers m ↔ m+1.
The excitation of quadrupole nuclei with half-integer spins is discussed in detail elsewhere [37]. Here we give only the result that the maximum intensity observed is reduced by ( ) ( )I I m m+ − +1 1 , but, the effective nutation frequency is enhanced by the same value. For the central transition, m = −1/2, we obtain
ν νrfeff
rf= +
I
12
. (17)
Thus, for the selective excitation of the central transition, the optimum pulse duration is equal to the duration of a nonselective π/2-pulse divided by I + 1/2.
Adiabatic passages are discussed by Kentgens et al. [38,39]. In the frequency-stepped adiabatic half-passage (FSAHP) the spin system is far off-resonance at the beginning of the irradiation. The frequency is then stepped through the region of resonance slowly enough, that the density operator can follow the Hamiltonian. Switching off the rf power at the resonance position of the central transition creates a single-quantum coherence like a π/2 pulse applied to a spin-1/2 system. A full passage would be comparable with a nonselective π pulse.
7
Another NMR technique that uses adiabatic passage in combination with rotational echo and double resonance was introduced by Gullion [40]. He combined the principles of rotational-echo double resonance (REDOR) [41] with the transfer-of-populations-double-resonance (TRAPDOR) developed by Grey, Veeman and A.J. Vega. [42] The so-called REAPDOR NMR technique allows first, like TRAPDOR, the indirect detection of signals that are too broad to be directly observable for the single-resonance observation of the quadrupole nucleus and second, like REDOR the measurement of distances between spin pairs [40].
Cross-polarization (CP) excites a spin system by polarization transfer from another spin system. CP was introduced by Hartmann and Hahn [43] and is described in detail in the textbook of Slichter [44]. S. Vega [45] firstly applied static CP to half-integer quadrupole nuclei and A.J. Vega [46,47] considered the spin dynamics of CP MAS NMR in dependence on the ratio νrf
2/νQνrot.
The following considerations concern the angular dependent quadrupole shift. Assuming the resonance offset to be zero, the quadrupole shift should be given as ν − νL. For simplicity, we omit −νL, the subtraction of the Larmor frequency. The conventions νm,m+1 and νm,−m for single-quantum transitions and symmetric transitions, respectively, are used here in agreement with the majority of the literature. In this notation, we have m = −1/2 for the central transition ν−1/2,+1/2. With ′ν Q from Eq. (12), the first-order quadrupole shift for single-quantum
transitions becomes
ν νm m m, + = ′ +
1
12Q , (18)
that means zero for the central transition m = −1/2. The first-order quadrupole contribution is zero for all symmetric transitions m ↔ −m as can be derived from Eq. (13). (Note that Iz ≡ m is a number in this case.)
The second-order quadrupole shift can be obtained by means of Eq. (14) as
( ) ( )[ ] ( ) ( )[ ]{ }νν
νm m m m I I V V m m I I V V, + − −= − + − + + + + − + +1 1 1 2 224 1 4 1 9 6 1 2 1 3Q2
L18 (19)
or
( )[ ] ( )[ ]{ }νννm m
mI I m V V I I m V V,− − −= − + − − + + − −Q
2
L184 1 8 1 2 1 2 12
1 12
2 2 (20)
for single or symmetric quantum transitions, respectively. The components Vj are given in the LAB and can be described, with the Wigner matrices of rank 2, as functions of corresponding values in the PAS, which are given in Table 1. The VjV−j terms in Eqs. (19) and (20), therefore, can be written also as Wigner matrices for which the rank goes up to 4. Amoureux [48] gave a corresponding equation with the coefficients for the transformation of Eq. (20) from the LAB into the PAS.
Samoson [49] has shown that the second-order quadrupole shift of the m ↔ m + 1 transition, cf. Eq. (19), can be split into an isotropic part describing the center of gravity of the quadrupole shift and an angular dependent part:
( ) ( )[ ]
( ) ( ) [ ]
νν
νη
νν
β β
m m I I m m
I I m m A B C
,
cos cos
+ = − + − + − +
− + − + −
+ +
1
2
4 2
301 9 1 3 1
3
301
173
1136
Q2
L
Q2
L
(21)
8
with
A = − +10516
358
23548
22 2η α η αcos cos , B = − + + −458
512
5 23524
22 2 2η η α η αcos cos and
C = + + − +9
1613
58
23548
22 2 2η η α η αcos cos . The upper part in Eq. (21) represents the isotropic
quadrupole shift. For the central transition, m = −1/2, Eq. (21) gives the isotropic quadrupole shift as
νiso Q −1/2,+1/2 ( )[ ]( )3143130
2
L
2Q ην
ν+−+−= II . The true value of the isotropic chemical shift can be
determined from the experimentally obtained isotropic shift (center of gravity of the signal), if the isotropic quadrupole shift can be determined as shown below, cf. [49-51]. For nonselective excitation, or at least partially selective excitation, MAS sidebands can be observed, which are just outside of the spectral range of the static spectrum of the central transition. Their main intensity results from the ±1/2 ↔ ±3/2 transitions, whereas the center band results mainly from the +1/2 ↔ −1/2 transition. The average resonance position of two equal-order-sidebands can be experimentally obtained as the center of gravity of the corresponding sidebands. Thus, the difference ∆ = νiso Q ±1/2,±3/2 − νiso Q −1/2,+1/2 of the average resonance position of two first satellite sidebands to the center of gravity of the center band (central transition) can be measured and compared with the corresponding difference derived from Eq. (21):
∆ = − +
νν
ηQ2
L309 1
3
2
. (22)
Finally, the combination of Eq. ( 22) with the isotropic part of Eq. (21) gives the isotropic quadrupole shift of the center band, which isequal to νiso Q −1/2,+1/2 = ∆ × 8/9 for I = 5/2 .
This procedure for the determination of the quadrupole shift or other quadrupole parameters was introduced by Samoson [49]. It is convenient for I = 5/2 nuclei, because the linewidth of their ±1/2 ↔ ±3/2 satellites is decreased (factor 0.3) with respect to the central line. Jäger [51] used this sideband analysis for the study of various inorganic compounds and denoted it as SATRAS (satellite-transition spectroscopy).
Another satellite technique was proposed by Z. Gan [52]. The key idea is a coherence transfer between inner satellites and central transition. Coherences develop in the inner satellites and were detected in the central transition. The two-dimensional satellite transition magic-angle spinning (STMAS) experiment consists also of single-quantum transitions but requires a very accurate setting of the magic-angle [53]. Isotropic spectra with a relatively good signal-to-noise ratio (compared to MQMAS or DOR, see below) can be obtained.
Now we go back to Eq. (20) and use the representation of Amoureux [48] for the shift of a symmetric transition in the case of very fast sample rotation around the magic-angle θ = 3/1arccos ≈ 54.74°. Then, the contributions from the rank 2 components disappear and we obtain [54]
( ) ( )( )
( )
( ) ( ) ( ) ( ){ }
( ){ } ( )
ν ν νν η
ν
νν
η η α η α
θ θ
p p p p
pI I p
pd d d
I I p
/ , /
, , ,cos cos
cos cos ,
2 2
22
20 0
42 0
4 24 0
4
2 4 2
390
134
1296018 360 2 70 4
36 1 17 10928
35 30 3
− = + =+
+ −
− + + +
× + − − −
− +
iso Q anisoQ
Q2
L
Q2
L
(23)
where p denotes the quantum level pQ and symmetric coherences with the notation p/2 ↔ −p/2 instead of m ↔ −m are considered. The Euler angles (α, β) describe the spinner axis with respect to the PAS.
9
The elements d of the reduced Wigner matrices are related to β by ( ) ( )d0 04 4 21
835 30 3, cos cos= − +β β ,
( ) ( )d2 04 2 210
87 1, cos sin= −β β and ( )d4 0
4 47016, sin= β .
Equation (23) appears as a unique equation for multiple-quantum magic-angle spinning (MQMAS) and double rotation (DOR) as well, which will be described below. It contains a function of the rotor angle θ in the last brace. If we insert the magic-angle with cos2θ = 1/3, then the value of the last brace equals to one and the equation can be used as the basic formula for the MQMAS NMR. If we consider a double rotation and
the second rotor angle is fixed to ( )arccos / /6 96 5 14± ≈ 30.56° or 70.12°, then the value of the last
brace equals to zero and the total anisotropic part of Eq. (23) disappears. For the central transition, p = −1, only the isotropic quadrupole shift remains, which can be directly observed by DOR NMR. The isotropic contribution in Eq. (23) (right hand side of the first line of the equation) is identical with the isotropic part of Eq. (21), if the central transition is considered (p = −1 and m = −1/2).
An important parameter of the powder lineshape f (ν) is the second moment defined by ( )M f2
2= −∫ ( )ν ν ν νiso d with ( )f ν νd∫ = 1 . The dimension Hz2 of M2 changes to s−2 or T2, if the
lineshape is given as f (ω) or f (B), respectively. The square root of M2 characterizes the second-order broadening of the signal. Equation (24) gives the second moments as a function of νiso for the static and for the MAS spectrum and in addition the narrowing factor, which can be achieved by the application of MAS to the second-order quadrupole broadening of the central transition:
M MMM2 2
2
2
237
14
927
36staticiso2 MAS
iso2
static
MAS= = = ≈ν ν, , . . (24)
Equation (24) in combination with the relation νiso ( )[ ]( )3143130
2
L
2Q ην
ν+−+−= II from. Eq. (23) allows
the determination of ν ηQ 1 32+ / from the second moment of the central transition lineshape, if the latter is
exclusively broadened by second-order quadrupole interaction. But also other contributions to the second moment of the static lineshape should be considered. The anisotropy of the chemical shift gives
( )
M 2
224
9 51
3csa L= +
∆σ ν η, (25)
where ∆σ = σZZ − (σXX − σYY)/2 denotes the total anisotropy and η is the asymmetry parameter, cf. Eq. (8),
and νiso in the relation ( )M f22= −∫ ( )ν ν ν νiso d must be taken as the isotropic value of the chemical shift.
If the dipolar interaction is small compared with the quadrupole interaction, the spin flipping between different transitions is prohibited, and the second moment due to the dipolar interaction is modified [33,37]. We will give here only the equations for dominating dipolar interaction. The dipolar second moment of a spin system consisting of N resonant spins of type I (homonuclear interaction of spins with the distance rI) and M non-resonant spins of type S (heteronuclear interaction of spins with the distance rS) can be determined by the dimensionless equation
M z M
MC
rC
r2
2
22
2
2 22
6 6 6 6
/ //
/ /H
2
sT
m mI I
I
I
S
Sγ γπ
= = = +−
(26)
10
with
( )C I II I= +
35
14
02
2 2µπ
γ h , ( )C S SS S= +
415
14
02
2 2µπ
γ h , 1 1 16 6
1r N rikk i
N
i
N
I
=≠=
∑∑ , 1 1 16 6
11r N rikk
M
i
N
S
===
∑∑ .
The value CS of a non-resonant nucleus can be easily calculated from the value of the same resonant nucleus CI by CS = CI × 4/9. If in Eq. (26) the unit T of the magnetic flux density is substituted by 10−4 T (this corresponds to the old cgs unit Gauss) and the unit m is substituted by the old unit Å, then the values CI can be taken from Table 2.
Table 2: Values of CI in the equation MC
rC
r28 2
6 6 6 610// /
− = +TÅ ÅI
I
S
S
. Values of CS are given by
CS = CI × 4/9.The distances rI and rS denote in a simple model the internuclear distances of one resonant spin to another resonant spin and to a non-resonant spin, respectively. For the general case, see the definitions of rI and rS after Eq. (26).
Another dimensionless equation is very helpful, in order to correlate the second moment of a line, which is broadened by any interaction, to the line width, which is commonly described by the full width at half maximum (fwhm ≡ δν1/2). Under the assumption of a Gaussian lineshape, we obtain for M2/s−2 = γI
2 M2/T2 = (γI/2π)2 M2/Hz2, cf. Eq. (26), with T2 as the transverse relaxation time and the line width δν given in Hz:
( )
( ) ( )MT
22
2
2 1 2
22
1 2
224
712//
/ln
. // /ss
Hz Hz− = = ≈ ×δπ
δν ν . (27)
Samoson, Lippmaa and Pines [55] succeeded in 1988 in building a double-rotor probe. The outer rotor is inclined by β2 = 54.74° with respect to the external field and has a diameter of about 20 mm. The angle between inner rotor (of about 5 mm diameter) and outer rotor axes is β1 = 30.56°. The rotation frequencies of the inner and outer rotor presently do not exceed νinner = 12 kHz and νouter = 2 kHz, respectively. A pneumatic unit, which is controlled by a computer, simplifies the experimental setup and makes it safer. However, compared to the MAS technique, a more complicated setup and stronger wear of the rotors must still be accepted for DOR experiments.
DOR NMR gives accurate values of the isotropic shift, δ iso, of the nuclear magnetic resonance of a quadrupole nucleus. Two shift effects are superimposed: the isotropic quadrupole shift, which is described below Eq. (23), and the isotropic value of the chemical shift, which was introduced in Eq. (6). We substitute σiso, the isotropic part of the shielding tensor, by the value of the chemical shift δCS iso = σref − σiso (with respect to a given isotropic chemical shift of a reference compound).
11
Then we substitute the second-order quadrupole shift νiso Q by the dimensionless value δQ iso = (νiso Q)/νL. In this notation we obtain for the observed isotropic shift in the DOR experiment
( )δ δ δ δνν
ηDOR CS iso Q iso CS iso
Q2
L230
= + = − + −
+
I I 1
34
13
2
. (28)
For the common use, the shifts can be expressed in parts per million (ppm) by multiplying the right hand side of Eq. (28) by 106. Equation (28) reflects the fact that the value of the isotropic chemical shift cannot be obtained from one DOR experiment, if the quadrupole shift is unknown. But two DOR experiments at different external field strengths, that means at different Larmor frequencies, give the value of the chemical shift
δCS iso and the quadrupole parameterν ηQ 1 32+ / as well. Important applications of the DOR technique to
microporous materials were reviewed previously [31].
In 1995 Frydman and Harwood [56] proved the feasibility of a two-dimensional NMR experiment that makes use of invisible multiple-quantum transitions combined with MAS to remove the anisotropy of the quadrupole interaction. Symmetric p/2 ↔ −p/2 coherences with the quantum level pQ were selected, since the corresponding powder resonances are not influenced by first-order quadrupole effects.
The phase development ϕ (t) of the single- or multiple-quantum coherence can be written as
( ) ( ) ( )[ ]
( ){ } ( ) ( ) ( ) ( ){ },4cos702cos3601812960
1017136
360
3143
2
40,4
240,2
40,0
2
L
22Q
L
222Q
2/,2/
αηαηην
ν
ν
ηνννν
ϕ
dddpIIp
pIIppp
tt
pp
+++−−+
−
−+++=+= −
(29)
with νp/2,−p/2 from Eq. (23), which is reduced under MAS condition. The contributions from the chemical shift and from the resonance offset are included in ∆ν = σisoνL − νoffset. Equation (29) shows that by going from the multiple-quantum level pQ to the −1Q level of observation, the sign of the phase development can be inverted. Thus, the influence of the anisotropy of the second-order quadrupole interaction is averaged out, if the times t1 and t2 spent on the quantum levels pQ and −1Q, respectively, fulfill the condition:
( )
( ) ( )t pI I p
I It R I p t2
2
1 1
36 1 17 1036 1 27
=+ − −
+ −= , . (30)
This relation describes the appearance of the isotropic echo, and thus gives the slope R(I, p) of the anisotropic axis in the two-dimensional spectrum, which is obtained after the 2D Fourier transform with respect to t2 and t1. Further details and MQMAS applications are discussed in Refs. [31,57-59].
3 Solid-state NMR studies of the structure
3.1 29Si NMR 29Si MAS NMR spectra can be found in about one quarter of all recently published NMR studies of porous inorganic materials. Silicon is number one in spite of the fact that the 29Si nucleus has a natural abundance of 4.7 % and possesses a rather bad sensitivity due to the low sensitivity in natural abundance of 3.69 × 10−4 (relative to 1H) and also due to large relaxation times T1. The spin-½-nucleus has a Ξ-value of 19.867187 MHz (resonance frequency of TMS, 1 vol.-% in CDCl3, in that external field, for which the 1H NMR of TMS resonates at exactly 100 MHz). But the high resolution of the MAS spectra of well-crystalline materials and the central importance of silicon networks in porous solids outweigh the disadvantages of the 29Si MAS NMR.
12
The values of the 29Si NMR chemical shift of silicates cover a range from −60 ppm to −120 ppm, referring to TMS, cf. Fig. 1. The silicon atom is surrounded by four oxygen atoms, which build the corners of a SiO4-tetrahedron. This tetrahedron is connected to n tetrahedra (Qn, n = 0, 1, 2, 3, 4) via oxygen. The framework of porous materials consists mainly of the so-called Q4 coordination. A Q3 coordination appears at structural defects (for example at the surface) of porous materials, wherein one hydroxyl group (silanol group) and three other tetrahedra are attached to a silicon atom. The Si/Al ratio varies from one to more than one hundred in aluminosilicates.
−130 −110 −90 −70 −60 −80 δ / ppm
−100 −120
Si(1 Zn)
Si(2 Zn) zincosilicate-type zeolites
VP-7, VPI-9 Q4
alkali and alkaline earth silicates
Q0
Q2
Q1
Q4
Si(1 Al)
Si(0 Al)
Si(2 Al)
Si(3 Al)
Si(4 Al)
Si(3Si, 1OH)
aluminosilicate-type zeolites
Q3
Q4
Q3
Fig. 1: 29Si NMR isotropic chemical shift of silicates and zeolites [23,60,61,164] For Si/Al = 1 the Q4 coordination represents a SiO 4 tetrahedron that is surrounded by four AlO4-tetrahedra, whereas for a very high Si/Al ratio the SiO4 tetrahedron is surrounded mainly by SiO4-tetrahedra. For zeolites of faujasite type the Si/Al-ratio goes from one (low silica X type) to very high values for the siliceous faujasite. Referred to the siliceous faujasite, the replacement of a silicon atom by an aluminum atom in the next coordination sphere causes an additional chemical shift of about 5 ppm, compared with the change from Si(0Al) with n = 0 to Si(4Al) with n = 4 in Fig. 1. This gives the opportunity to determine the Si/Al ratio of the framework of crystalline aluminosilicate materials directly from the relative intensities In (in %) of the (up to five) 29Si MAS NMR signals by means of the equation [3]
∑=
= 4
0
400Al
Si
nnnI
. (31)
Considering the Q4 coordination alone, we find a spread of 37 ppm for zeolites in Fig. 1. The isotropic chemical shift of the 29Si NMR signal depends in addition on the four Si-O bonding lengths (see [62], [3] p. 132 and [63]) or on the four Si-O-Si angles α i, which occur between neighboring tetrahedra.
13
Correlations between the chemical shift and the arithmetical mean of the four bonding angles α using sin(α /2), αsec , ( )1coscos −αα and ( )1coscos −αα were proposed, cf. [3], page 130 and [63]. The correlation coefficients obtained in the range from 0.90 to 0.98 do not clearly favor one of the above mentioned functions. The dependence is best described in terms of ρ = cosα/(cosα − 1) or the mean value ρ = ( )1coscos −αα . The parameter ρ describes the s-character of the oxygen bond, which is considered to be an s-p hybrid orbital. For sp3-, sp2- and sp-hybridization with their respective bonding angles α = arccos(−1/3) ≈ 109.47°, α= 120°, α = 180°, the values ρ = 1/4, 1/3 and 1/2 are obtained, respectively. Radeglia and Engelhardt [64] proposed an equation depending on the number n of Al atoms in the second coordination sphere
δ /ppm = −223.9 ρ + 5n −7.2. (32)
The equation was obtained with a correlation coefficient of 0.90 from experimental data of various zeolites and silicates thath were measured by Ramdas and Klinowski [62], in order to establish a dependence of the chemical shift on the bonding distance. The most exact experimental data were published by Fyfe et al. [63] for an aluminum-free zeolite ZSM-5. The spectrum of the low temperature phase consisting of signals due to the 24 averaged Si-O-Si angles α between 147.0° and 158.8° (29Si NMR linewidths of 5 kHz) yielded the equation
δ /ppm = −287.6 ρ + 21.44 (33)
with a correlation coefficient of 0.969 [63]. By adding the data of the high temperature phase and the data of the p-xylene loaded zeolite, the best fit was δ /ppm = −267.9 ρ + 11.90 and the correlation coefficient decreased dramatically to 0.793.
Fyfe et al. [63] stated: "It is felt that the main limitation in these structure-chemical shift correlations is the accuracy of the X-ray derived parameters, particularly where refinements of powder diffraction data are involved."
Solid state 29Si NMR spectra are usually acquired after single-pulse excitation. A moderate MAS frequency of a few kilohertz is sufficient. Cross-polarization from the 1H to the 29Si nuclei is applied to characterize proton-silicon connectivities rather than to enhance the sensitivity. For example, {1H}29Si CP MAS NMR shows whether a signal at −104 ppm is caused by a Si(3Si,1Al) or by a Si(3Si,1OH) site. In contrast to the Si(3Si,1Al) signal, the Si(3Si,1OH) signal is enhanced in the {1H}29Si CP MAS NMR spectrum compared with an ordinary 29Si MAS NMR spectrum. 29Si MAS NMR is a good example for demonstrating that the attainment of high resolution for solid-state spectra is a problem of the solid-state chemistry rather than a technical problem of the NMR. Very narrow lines are observed only in spectra of porous materials with a very high degree of short-range order, such as highly crystalline cation-free zeolites (aluminum-free silicates or aluminophosphates) without structural defects. The resolution of the spectra published by Fyfe et al. [65] featuring line widths of about 5 Hz has not improved in the last 15 years. A similar resolution (about 7.5 Hz) was obtained only by Ganapathy and coworkers [66] in the 29Si MAS NMR spectra of silicalite-1. Highly resolved spectra enable the application of two-dimensional NMR experiments known from liquid-state NMR. The most famous, yet unsurpassed, example is already 10 years old: Fyfe et al. [67] used the scalar 29Si-O-29Si couplings (9-15 Hz) to detect connectivities of the SiO4 tetrahedra in the zeolite ZSM-11 by INADEQUATE (Incredible Natural Abundance Double Quantum Transfer Experiment), thus allowing the assignment of the low temperature phase to the spatial group 4I by evaluation of the 29Si NMR data in connection with the X-ray data.
14
3.2 27Al NMR
The framework aluminum atoms of the crystalline aluminosilicates are tetrahedrally coordinated by four oxygen atoms. Brønsted sites in dehydrated hydrogen forms of zeolites are an exception. The aluminum bonding to the OH is broken. Therefore, the tetrahedral symmetry is superimposed by a threefold symmetry. Extra-framework aluminum species occur in different coordinations. All aluminum atoms can be observed by 27Al NMR, if modern solid-state NMR technique is applied and the experiment is properly done. 27Al has the nuclear spin I = 5/2, a nuclear quadrupole moment of Q = 0.15 × 10−28m−2, 100% natural abundance, a fairly large magnetogyric ratio that gives Ξ = 26.056890 MHz for Al(NO3)3 diluted 1.1 m in D2O and short relaxation times T1 in mesoporous materials. Thus, 27Al NMR spectra with high signal-to-noise ratios can be obtained within a short time. The disadvantage of the solid-state 27Al NMR spectroscopy is the broadening of the signals by the quadrupole interaction of the nuclear quadrupole moment with the electric field gradient at the position of the nucleus. Four satellites appear in addition to the signal of the central transition (m = −1/2 ↔ m = +1/2). In powder samples the signals of these satellites are strongly broadened by first-order quadrupole interaction due to the anisotropy of the electric field gradient. This broadening can be described by a second-rank tensor and eliminated by means of the MAS technique. Nevertheless, satellites are rarely investigated in polycrystalline materials. Two exceptions are the SATRAS technique and the STMAS technique, see Sect. 2).
Second-order quadrupole interaction broadens the 27Al NMR signals in powder spectra also in case of the common practice that only the central transition is observed. This broadening can be described by a four-rank tensor and can be reduced (factor of about 1/4) but not eliminated by means of the MAS technique. Some techniques (DOR, MQMAS, STMAS described in Sect. 2) were developed and applied in the last decade, in order to remove the second-order anisotropic broadening and to obtain highly resolved 27Al NMR spectra of the central transition.
Even the four-fold coordination of the aluminum atoms to oxygen atoms in the zeolite framework yields a deviation from the ideal tetrahedral symmetry of the electronic charge distribution. This deviation creates an electric field gradient, which gives rise to a quadrupole coupling constant of the order of 1-10 MHz. Nevertheless, 27Al NMR follows after 29Si NMR in the sequence of the spectroscopic methods most frequently applied to structural investigations of zeolites, since the first 27Al MAS NMR study of zeolites was published [68].
The isotropic chemical shift of 27Al atoms in solids depends on their coordination number (three-, four-, five- or six-fold coordinated to oxygen atoms). Also the species of atoms in the next coordination sphere (following oxygen) and the bonding angle via oxygen atoms between linked tetrahedra influence the chemical shift.
Figure 2 shows values of the isotropic chemical shift depending on the coordination number taken from Table 5 in Ref. [31]. Aluminum signals of porous inorganic materials were found in the range −20 ppm to 120 ppm referring to Al(H2O)6
3+. The influence of the second coordination sphere is illustrated for tetrahedrally coordinated aluminum atoms: In hydrated samples the isotropic chemical shift of the 27Al resonance occurs at 75- 80 ppm for aluminum sodalite (four aluminum atoms in the second coordination sphere) [69], at 60 ppm for faujasite (four silicon atoms in the second coordination sphere) [70] and at 40 ppm for AlPO4-5 (four phosphorous atoms in the second coordination sphere).
The isotropic chemical shift of the AlO4 tetrahedra is a function of the mean of the four Al-O-T angles α (T = Al, Si, P). Their correlation is usually given as δ /ppm = −c1 °/α + c2. (34) c1 was found to be 0.61 for the Al-O-P angles in AlPO4 by Müller et al. [71] and 0.50 for the Si-O-Al angles in crystalline aluminosilicates by Lippmaa et al. [72]; Weller et al. determined c1-values of 0.22 for Al-O-Al angles in pure aluminate-sodalites and of 0.72 for Si-O-Al angles in sodalites with a Si/Al ratio of one [69].
Fig. 2: Isotropic values of the chemical shift δ for the 27Al NMR signals of polycrystalline material at ambient temperature [164] Ghose and Tsang [73] were the first to point out a linear correlation between the 27Al NMR quadrupole coupling constant of feldspars and a so-called shear strain parameter Ψ. The correlation and the parameter Ψ are defined by
Cqcc = c Ψ = c Σi |tan(α i – αT)| (35)
from the deviation of the six O-Al-O bonding angles αι of an AlO4 tetrahedron from the ideal angle of a tetrahedron αT = arccos (−1/3) ≈ 109.47°. The study of Engelhardt and Veemann [74] revealed c ≈ 10.5 MHz for feldspars, aluminate sodalites and the aluminophosphate molecular sieve VPI-5, whereas the study of Weller et al. [69] yields c ≈ 8.6 for aluminate sodalites.
High-resolution 27Al NMR spectra can also support the structure determination of porous materials as was shown for a few examples, such as the application of the 27Al MQ MAS technique to the investigation of AlPO4 molecular sieves [75]. Many 27Al MAS NMR studies of porous materials focus on the determination of the signal intensity of aluminum atoms on tetrahedral positions in the framework, in order to determine the Si/Al ratio of silicon-rich aluminosilicates. Also the quantity and nature of aluminum species on extra-framework positions (mostly generated by modification of the as-synthesized form) is the subject of many studies. About one hundred 27Al NMR studies on the dealumination of zeolites have already been published. The isotropic chemical shift for the remaining four-fold coordinated framework aluminum in a strongly dealuminated faujasite type zeolite USY occurs at 60 ppm, the respective values for five-fold and six-fold coordinated extra-framework species are 34 ppm and 4 ppm [70]. But this general assignment of the signals should be taken with care. Signals in the range of 30 to 50 ppm might be generated by an isotropic chemical shift of 60 ppm and a superimposed quadrupole shift by strongly distorted four-fold coordination. Tetrahedrally coordinated extra-framework aluminum can also be found at about 60 ppm. In such cases fast MAS in high magnetic fields, MQ MAS and DOR techniques allow the assignment of these signals to the species [76-80].
16
Another complication of the 27Al NMR spectroscopy is related to the appearance of strongly broadened signals that are caused by three-fold coordinated aluminum atoms of structural OH-groups in dehydrated porous samples and by extra-framework species of low symmetry. Such species are often wrongly denoted as "NMR-invisible". However, the observation of lines featuring a quadrupole coupling constant of about 16 MHz has been reported in the literature several times [31]. For example, the quadrupole coupling constant of aluminum atoms at Brønsted sites (≡SiO
HAl≡) of dehydrated H-ZSM-5 zeolite amounts to 16 MHz. This result
was obtained from the central transition signal with a spectrum width of about 800 ppm measured in a 11.7 T external magnetic field [81]. Signals with quadrupole coupling constants up to 20 MHz can be observed in a magnetic field of 17.6 T by using static echo techniques, whereas the application of MAS with a maximal rotation frequency of 40 kHz is not useful at a spectrum width of 100 kHz. Larger quadrupole coupling constants of the 27Al nuclei in inorganic materials are not known. Thus, NMR-invisible aluminum does not exist, if up-to-date solid-state NMR technique is applied in a high external magnetic field.
Acid properties of porous materials are connected to the structural OH-groups (≡SiOH
Al≡), which act as a proton donators (Brønsted acid) or as a electron pair acceptors (Lewis acid). Extra-framework aluminum is assumed to be the source of the Lewis acidity. 27Al NMR investigations should be performed with dehydrated samples, which are then (after activation by dehydration) loaded with basic molecules. Corresponding studies [17,19,81,82] confirmed the known structure of Brønsted sites. However, very little progress could be made by means of the 27Al NMR, in order to clarify the unknown nature of the Lewis sites in zeolites.
3.3 1H NMR 1H NMR techniques play a very important role in NMR spectroscopy of adsorbed molecules, especially for in situ-studies of the heterogeneous catalysis and for the NMR-diffusiometry. But concerning the structural investigation of porous materials, after 29Si NMR and 27Al NMR¸ 1H NMR is only the third frequent application, being mainly limited to the investigation of hydroxyl groups. NH4
+ as the only cation that is detectable by 1H NMR gives rise to a signal with a chemical shift of 7-7.5 ppm, referring to TMS. Deammoniation takes place by heating the ammonium form of zeolites above 100 °C. Further calcination up to 400 °C leads to a total conversion into the H-form. The hydrogen form can as well be obtained by acid treatment of silicon-rich zeolites. Protonation can also proceed by the Plank mechanism in zeolites containing multivalent cations, cf. [19] p. 358.
Sites ≡SiOH
Al≡ in the H-forms of zeolites contain the so-called structural hydroxyl groups or bridging hydroxyl groups. The hydrogen atoms of these sites belong to the framework of the zeolite, whereas other hydroxyl groups belong to framework defects. Exceptions are for example the hydroxyl groups in hydroxyl sodalite [83], which like the zeolitic cations belong to the zeolite lattice rather than to the zeolite framework. With respect to the adsorbed basic molecules, the structural OH groups in the hydrogen form of zeolites act as proton donors like a Brønsted acid site. They cause the catalytic properties of the zeolites. SiOH and MeOH groups in zeolites, which are usually generated by structural defects during synthesis or an after-treatment-procedure are less acidic. The determination of the concentration of acid sites and of different defects in zeolites are the main motivations for solid-state 1H NMR studies of porous materials. However, the 1H MAS NMR measurements have to be performed on dehydrated samples, which should be encapsulated in a glass tube to prevent rehydration of the strongly hygroscopic porous materials. Fused glass ampoules containing the dehydrated material can be rotated in 4 mm rotors up to 16 kHz ( with lower risk up to 12 kHz). But this technique is applied in only few laboratories, since the first 1H MAS NMR study of zeolitic hydroxyl groups in a fused sample was performed at a rotation frequency of 2.7 kHz [68]. It should be noted that 1H NMR measurements of dehydrated samples filled into the rotor within a glove box do not provide unambiguous results quite generally, and particularly not in 1H NMR.
17
−4 −2 0 2 4 6 7 5 δ / ppm 3 1 −1 −3
Bridging OH groups in small channels and cages of zeolites
SiOHAl
Disturbed bridging OH groups in zeolite H-ZSM-5 and H-Beta
SiOH
Bridging OH groups in large channels and cages of zeolites SiOHAl
Cation OH groups located in sodalite cages of zeolite Y and in channels of ZSM-5 involved in hydrogen bonds
CaOH, AlOH, LaOH OH groups bonded to extra-framework aluminium species located in cavities or channels involved in hydrogen bonds AlOH
Silanol group at the externel surface or at lattice defects
SiOH
Metal or cation OH groups in large cavities or at the outer surface of particles MeOH
Fig. 3: Isotropic chemical shift of 1H NMR signals of hydroxyl groups in dehydrated zeolites [19, 164].
Figure 3 is based on Table 1 in Ref. [19] and references therein. The range of values for the cation OH groups (MeOH) was extended to −3.5 ppm, since the signal of NaOH groups of the dehydrated hydroxyl sodalite was found at this position, cf. [83]. Thus, the chemical shift of hydroxyl protons covers a range of more than 10 ppm from −3.5 ppm up to 7 ppm. Bridging hydroxyl groups in the layer silicate ilerite were even found at 16 ppm [84] due to the small oxygen-oxygen distance (2.4 Å) of the OHO bridge.
The chemical shift of the hydroxyl protons can be influenced by adsorbed molecules (pyridine causes a shift of about 10 ppm) and by an additional electrostatic interaction in the oxygen framework of the zeolite. The latter can be seen from the two top bars in Fig. 3. The next bar in the figure concerns AlOHSi sites for which the hydrogen atom has no additional interaction with another oxygen atom of the framework. The chemical shifts are limited to the range 3.8 - 4.3 ppm and increase if the portion of aluminum atoms in the framework decreases [19]. It is wellknown that the acidity of the zeolite decreases with increasing aluminum content. We can consider the chemical shift of hydroxyl protons as a measure for the zeolite acidity, if we exclude additional electrostatic or adsorption interactions. Brunner extended the corresponding studies to silanol groups in zeolite, cf. [16] p.72, and obtained by using results of ab initio calculations of Fleischer et al. [85] a correspondence between the deprotonation energy EDP of the hydroxyl group and their shift of the 1H NMR signal δH:
EDP/kJ mol−1 = 1570 −84 δH/ppm. (36)
Equation (36) neglects additional electrostatic interactions with other oxygen atoms of the framework and any interaction with adsorbed molecules, which leads to increase of the chemical shift of the hydroxyl protons by a value of ∆δ. In analogy to the frequency shift in the infra red spectroscopy, cf. [86], this increase would depend not only on the basicity of the adsorbed molecule, but also on the acidity of the hydroxyl group. In order to characterize the acidity of bridging hydroxyl groups in zeolites, Sachsenröder et al. [87] used the following equation (originally introduced by Paukshtis et al. [86] for infrared shifts) for the determination of the change ∆EDP of the deprotonation energy between acidic ≡SiO
HAl≡ groups and non-acidic ≡SiOH groups from
the chemical shift changes upon adsorption of molecules:
The local structure of bridging OH groups is the topic of numerous quantum-chemical studies, cf. [18]. Very few experimental data exist, in order to verify the results of the quantum chemical calculations. The proton-aluminum distance in the Brønsted sites can be obtained from the heteronuclear (aluminum-to-proton) dipolar broadening of the 1H NMR signal. The analysis of the spinning sideband patterns at moderate MAS frequencies allows the determination of the 1H-27Al distances for several ≡SiO
HAl≡ sites in one zeolite, cf. [19]
p. 372. 1H NMR investigations of the proton mobility of hydroxyl protons in zeolites were already carried out in the past by continuous wave broad line NMR. Proton mobility is a permanent topic of NMR studies of zeolites for more than 30 years, since the elementary step of a Brønsted acid-catalyzed reaction is the proton transfer from a surface hydroxyl group to the adsorbed molecule. Results have been presented in several reviews [15,19]. Recent studies concern the proton transfer between Brønsted sites and benzene molecules up to 300 °C [88] and the proton mobility in the dehydrated and unloaded hydrogen zeolites up to 450 °C [89] by means of laser heating of the sample during the 1H MAS NMR measurement.
Some hints should be given for the determination of the concentration of the hydroxyl groups by 1H MAS NMR. It is wellknown that the integral of the NMR line is proportional to the number of the resonant nuclei in the sample coil. Using a reference sample with a known number of resonant nuclei, one can determine the absolute number of resonant nuclei in the sample under study. In such experiments an echo pulse sequence with a pulse delay of one ore more rotation periods between the π/2 and π pulses and a 16-phase cycle (π/2 steps of the first pulse and π/2 steps of the second pulse with respect to the first one in addition) should be applied, in order to decrease an undesirable signal from the NMR probe. The following conditions should be met too: The time interval between two rf pulses must be longer than 5T1, where T1 is the longitudinal relaxation time. Note that T1 of hydroxyl groups can attain some 10 seconds. The MAS frequency should be above 8 kHz, or the spinning sidebands must be added to the center band. The shape of the reference sample and the actual sample should be identical and the quality factor of the NMR coil containing the actual sample must be the same as the quality factor of the coil with the reference sample. Thus, the best reference sample is a dehydrated hydrogen form of a zeolite with known residual Na concentration and known silicon-to-aluminum ratio. For such a sample the number of bridging hydroxyl groups in the sample can be determined from the mass of dehydrated zeolite in the glass tube. The dehydration of the sample under study and of the reference sample should be performed under high vacuum increasing the temperature at a rate of 10 K h−1. The samples should be kept at the final activation temperature of 400 °C under a pressure below 10−2 Pa for 24 h, and then be sealed.
The determination of the concentration of hydroxyl groups by 1H MAS NMR can be supplemented by two NMR experiments, one with a physical and one with a chemical background. The first one is based on the adsorbate-induced chemical shift of the 1H NMR signal of the hydroxyl groups [19]. An often applied procedure is the loading of the porous material with fully deuterated pyridine. It causes a quenching or strong shift of the signals of those hydroxyl groups, which are accessible for pyridine. The NMR experiment with physical background is based on the dipolar 1H-27Al interaction (Sect. 2). The experiment, which is often denoted as TRAPDOR [42], includes a strong 27Al irradiation in the time between the two 1H pulses of a Hahn echo pulse sequence. This allows the separation of the 1H MAS NMR spectrum into two spectra: The spectrum with 27Al irradiation includes only those signals of hydroxyl species, which are far from aluminum nuclei. The difference spectrum consists of the signal of hydroxyl species, which are in the neighborhood of 27Al nuclei. The combination of all techniques enhances the resolution of the 1H MAS NMR spectra [90].
C. Doremieux-Morin [91] introduced a low-temperature 1H NMR approach for measuring the Brønsted acidity of porous materials based on their interaction with water molecules. Continuous wave 1H NMR measurements at 4 K give broad signals, which reflect hydrogen bonding or formation of H3O+ ions dependent on the acidity of the hydroxyl group [91].
19
3.4 23Na NMR
The sodium ion is the most important cation that compensates the negative charge of a aluminum-oxygen tetrahedron in zeolites. 23Na nuclei have a natural abundance of 100 %, a nuclear spin of I = 3/2, a nuclear quadrupole moment of 0.18 × 10−28 m2, a Ξ-value of 26.451921 MHz (resonance frequency of the reference NaBr, diluted 9.9 M in D2O, which is almost identical with a 1.0 M NaCl solution) in that external field, for which the 1H NMR frequency of TMS equals to exactly 100 MHz) and a relative sensitivity of 0.0925 compared with 1H. (Note that in some studies the solid-state 23Na NMR shifts refer to solid NaCl as standard. The equation for the conversion is δ (1M NaCl) = δ (solid NaCl) + 7.2 ppm.) The above parameters yield a good NMR sensitivity for the investigation of location and mobility of zeolitic cations.
Hydrated porous materials show very few signals, since a fast exchange takes place between some positions. The 23Na MAS NMR spectra of several hydrated zeolites Y consist of two lines at −1.8 and −5.8 ppm. The first line is caused by the signal of the hydrated sodium cations in the supercages, and the second signal is a superposition of two components due to the sodium on position SI in the hexagonal prism and hydrated sodium cations in the sodalite cages [92]. The sodium cations become strongly coordinated with the oxygen framework upon dehydration of the zeolite. Then, the lineshapes in 23Na MAS NMR spectra are determined by second-order quadrupole broadening, and the usual techniques to overcome this broadening (DOR, 3QMAS, STMAS, Sect. 2) have to be applied in order to get well-resolved spectra. The isotropic values of the chemical shift and the quadrupole parameters for zeolitic cations on various sites are presented in Table 3. Table 3. Quadrupole coupling constant Cqcc = e2qQ/h, the asymmetry parameter η, and the isotropic value of the chemical shift δ (relative to 1.0 M NaCl) for the 23Na NMR of porous dehydrated aluminosilicates at ambient temperature. This table is part of a Table 6 in ref. [31] compound site Cqcc/MHz η δ /ppm reference NaX (Si/Al=1.0) I 1.1 0.5 5.2 [93] I’ 5.8 0.0 −12.8 [93] II 5.0 0.0 −8.8 [93] III’(1,2) 2.2 0.7 −10.8 [93] III’(3) 1.2 0.9 −22.8 [93] NaX (Si/Al=1.23) I 0.0 0.0 1.2 [94] I’ 5.2 0.0 −11.8 [94] II 4.6 0.0 −7.8 [94] III’(1,2) 2.6 0.7 −5.8 [94] III’(3) 1.6 0.9 −21.8 [94] NaY (Si/Al=2.5) I 1.2 0assumed 2.2 [95] I’ 4.8 0.0 3.2 [94] II 3.9 0.0 −4.8 [94] EMT (Si/Al=3.7) I 1.0 0assumed 0.7 [95] I’+II 4.1 0.3 0.2 [95] NaMOR (Si/Al=7.1) 12-ring 2.0 0assumed −6.8 [95] sidepockets 3.1 0assumed −16.8 [95] NaZSM-5 (Si/Al=18) 2.0 0assumed −10.8 [95] NaCl-sodalite 0-0.5 - −8.8 [96] ∼0 0.67assumed 6.3 [97] NaBr-sodalite 0.72 0.12 −9.9 [96] 1 0.67assumed 8.5 [97] NaI-sodalite, 1.73 0.06 −20.6 [96] 1.9 0.67assumed 9.3 [97] Na-hydroxosodalite 2.00 0.10 3.2 [98] Na-nitride sodalite 1.00 0.18 0.4 [98]
20
3.5 17O NMR
The abundance of elements in porous materials is certainly not far from that in the earth's crust: 50% oxygen, 28% silicon and 8% aluminum. But until now, the number of solid-state 17O NMR applications cannot be compared with those of 29Si or 27Al NMR spectroscopy. Whereas the spectroscopy of the quadrupole nuclei 27Al and 23Na is already well established. 17O NMR (nuclear spin I = 5/2, nuclear quadrupole moment Q = −0.026·10−28 m2, Ξ = 13.556430 MHz for neat D2O) suffers from the disadvantage of a smaller magnetic moment and the very low natural abundance of 0.037% or the high costs of enrichment. Relatively few solid-state 17O NMR studies have been published since the first investigation on MnO2 was performed by J.A. Jackson [99] in 1963. The fact that the nuclear quadrupole moment of 17O is much smaller than that of the 27Al nuclei might lead one to assume that the quadrupole broadening of the NMR signal is relatively small. However, the very anisotropic bonding of the oxygen atoms in many solids produces strong electric field gradients at the oxygen nuclei and quadrupole coupling constants Cqcc of several MHz. The mean values and the standard deviations for about 300 references to values of Cqcc in inorganic materials [31] are 4.2±1.5 MHz and 4.8±3.5 MHz for 17O and 27Al, respectively.
New NMR techniques such bas dynamic angle spinning (DAS) [100,101], double rotation (DOR) [55] and multiple-quantum excitation in combination with fast spinning (MQMAS) [56], have been recently developed for quadrupole nuclei with half-integer spins, and, in addition, the perturbing effect of the electric quadrupole interaction is reduced at the higher magnetic fields that are now available. Some 17O NMR investigations applying these techniques have been performed, in order to correlate the obtained NMR parameters of resolved oxygen signals with structure data obtained by diffraction methods: Grandinetti et al. [102] investigated the SiO2 polymorph coesite, Mueller et al. [103] measured the 17O signals of diopside, forsterite, clinoenstatite, wollastonite and larnite by DAS NMR, Bull et al. [104,105] investigated the silicon-rich forms of zeolite Y and ferrierite by 17O DOR NMR. Investigations with several hydrated zeolites by 17O 3Q MAS and DOR NMR demonstrated the reasonably good resolution in the field of 17.6 T, whereas in the lower field of 11.7 T insufficient resolution was obtained [54,106]. Pingel et al. [106] proposed a correlation between Si-O-Al angles and the 17O chemical shift, whereas Bull et al. [104,105] claimed that no simple correlation like Eq. (33) exists between the zeolite bond angles and the 17O NMR parameters.
17O DAS NMR studies of the SiO2 polymorph coesite by Grandinetti et al. [102] yielded the correlations
η = 1 + cosα (38)
and
Cqcc = Cqcc(180°) 2ρ (39)
for the asymmetry parameter η and the quadrupole coupling constant Cqcc, respectively. Some functions η(α), which are less simple than Eq. (38), are discussed by Sternberg [107]. The question of whether a correlation between T-O-T angles and 17O NMR parameters does [102,106] or does not exist [104,105], could be answered for zeolites by a study of low silica zeolites of X and A type [108].
Figure 4 plots the seven isotropic chemical shift values (calculated from the 17O DOR NMR spectra) of the zeolites Na-A and Na,K-LSX against the values of the s-character of the oxygen bonds in the various Si-O-Al sites. The solid line in Figure 4 corresponds to the correlation
δ (17O) /ppm = −214ρ + 136. (40)
21
Fig. 4. Correlation between the isotropic chemical shift of the 17O DOR NMR and the s-character of the oxygen hybrid orbitals for the oxygen sites of the zeolites Na-A (circles) and Na,K-LSX (rectangles). The straight line represents the best linear fit.
This result approves the existence of a correlation between chemical shift and bond angle in the samples under study. In contrast, Grandinetti et al. [102] did not find a monotonic correlation between 17O NMR shift and bond angle for the SiO2 polymorph coesite. But the linear fit of the data [102] gives δ /ppm = −0.61α/° + 139, which is similar to the corresponding α-equation δ /ppm = −0.71α/° + 143.7 for the low silica zeolites [108]. This emphasizes the tendency that the chemical shift decreases with increasing bond angle. But it does not prove the existence of a simple correlation in general. Two facts argue against a general correlation [108]: (i) The dehydration of the zeolites causes changes of the 17O NMR chemical shift by the superposition of two effects: the wellknown changes of the Si-O-Al bond angles and the polarization of the framework by the adsorbed water molecules. The total effect is about 8 ppm, whereas the angular-corrected effect amounts to about 4 ppm. The low field shift due to the adsorption interaction is relatively small (about 2.2 ppm) for formic acid. (ii) A downfield shift of about 10 ppm from the lithium to the cesium form of zeolite LSX and a shift of about 34 ppm for the O3 signal after the substitution of sodium by thallium cations in zeolite A reflect the increase of the basicity of the oxygen framework of the zeolite by ion exchange with larger cations.
A comparison of the DOR and MQMAS techniques gave the following results [108]: 17O DOR NMR spectra are superior to 17O 3QMAS NMR spectra with respect to the resolution by a factor of two. The signal-to-noise ratio of DOR and 3QMAS NMR spectra is comparable, whereas that of 5Q MAS NMR spectra is lower by more than one order of magnitude, and the spectral window is lower by a factor of five. This limits the application of the 5QMAS technique to 17O NMR. The residual linewidths of the signals in the 17O DOR and 17O 5QMAS NMR are caused by a distribution of the Si-O-Al angles in the zeolites.
3.6 Some references to other nuclei
Sections 3.1 - 4 concerned the most frequent NMR applications (29Si, 27Al, 1H, 23Na) to the structure of porous materials. The previous Sect. 3.5 is devoted to a field (17O NMR) of substantial current activities. Concerning MAS NMR studies of other nuclei in the framework or lattice of the host systems, only one reference to the most recent studies will be given for each nucleus: hydrogen-2 [81] lithium-6 and lithium-7 [109], beryllium-9 [110], boron-11 [111], nitrogen-14 [112], nitrogen-15 [113], fluorine-19 [114], phosphorus-31 [115], potassium-39 [116], titanium-47/49 [117,118], vanadium-51 [119], cobalt-59 [120], copper-65 [121], gallium-69/71 [122,123], rubidium-85/87 [124], cesium-133 [23,125], lanthanum-139 [126], thallium-205 [127], lead-207 [128].
0.38 0.40 0.42 0.44 0.46 0.48 0.50
30
35
40
45
50
Na-A (O2)
Na-A (O3) Na-A (O1)
LSX (O4)
LSX (O2)
LSX (O3)
LSX (O1) δ
/ ppm
hybridisation parameter ρ
22
4 Conformation and conversion of molecules adsorbed in porous materials
The NMR spectroscopy of molecules adsorbed in porous materials was initiated by J.R. Zimmerman et al. [129] in 1956. Their nuclear magnetic relaxation studies of water adsorbed on silica gel were followed by H. Winkler [130] in Leipzig, who studied water on aluminum oxide. Modern applications of high-resolution MAS NMR to study the structure of adsorbed molecules and the in situ MAS NMR studies of chemical reactions on porous catalysts are subject of several reviews. A summarizing account of the literature up to 1987 has been given by by G. Engelhardt and D. Michel [3]. More recent reviews were given by J.F. Haw [7] in 1993 (and in 1999 [131]), H. Pfeifer and H. Ernst [15] in 1994, E. Derouane et al. [30] in 1999 (and in 2000 [132]), and by W.O. Parker [32] in 2000.
Recent studies of the conformation and conversion of adsorbed molecules benefit from two developments, the application of double resonance and NMR exchange techniques from one side and the use of probes for in situ NMR experiments from the other side. In situ NMR techniques are important tools for the elucidation of interactions between surface sites and adsorbates, as well as catalytic conversion of organic molecules. For modeling of catalysis in technical gas flow reactors, spectroscopists are faced with the combined problems of duplicating flow conditions, high reaction temperatures and matching the density of reactants (feed). The first open gas-flow MAS rotor was presented by M. Hunger and T. J. Horvath [133] in 1995. This complicated technique, which is now available in several laboratories, allows replication of flow conditions, but the feed in the NMR experiments is higher than in technical gas flow reactors. The relatively high loading with molecules is also the crucial point of the NMR batch reactor, which became available by the laser-supported heating of sealed samples under MAS conditions [134]. But the laser heating causes quick temperature jumps, which allows the measurement of time-resolved (steps of 2 s) 13C MAS NMR spectra of chemical reactions in situ [135] and the measurement of rate constants over five orders of magnitude for the hydrogen exchange between Brønsted sites and adsorbed molecules [88].
However, traditional NMR techniques in a moderate temperature region up to 300 °C and the use of labeled molecules give still very important information about the mechanism of heterogeneous catalysis in porous materials [26,136,137].
5 Pulsed field gradient (PFG) NMR technique
The application of NMR to studying molecular transport is based on the Larmor condition ωL = 2πνL = −γ B0, cf. Eq. (2). We omit the minus sign and superimpose the constant magnetic field B0 by an inhomogeneous field Badd = g z (the "field gradients"). Then the Larmor frequency becomes space dependent:
( ) ( ) ,00 gzgzBz γωγωω +=+== (41)
where the z coordinate is assumed to be aligned along the direction of the applied field gradient. In the pulsed field gradient (PFG) NMR technique (see. for example[12,138-141]), the inhomogeneous field is applied over two short time intervals of duration δ separated by the "observation time" ∆. These two field gradient pulses are applied either with opposite signs (i.e. the amplitudes +g and −g) or with an rf pulse of suitable duration (a "π pulse") in between. In both cases, the effect of the second field gradient pulse has to be subtracted from that of the first one. The phase shift ϕ of a nuclear spin, which during the observation time ∆ has been displaced over a distance z2 − z1 in z-direction, in comparison with a spin, which has remained at the same position, is therefore
( )21 zzg −= δγϕ . (42)
23
Since the intensity of the NMR signal (the "spin echo" as generated, for example, in the π/2-τ-π-τ-echo sequence, see Fig. 5) is proportional to the total magnetization, that is to the vector sum of the contributions of the individual spins, the application of field gradient pulses thus leads to a signal attenuation
( ) ( )( )
( ) ( ) zzgzP
zzzzg,zzP
dcos,
ddcos, 121212
δγ∆
δγ∆ψ
∫∫∫
=
−= (43)
with
( ) ( ) ( ) 1111 d,,, zzzzPzpzP ∆∆ += ∫ . (44)
p(z1) is the a priori probability (density) of finding a spin at position z1 for t = 0 and P(z2, z1, ∆) the probability (density) that the spin has moved from z1 to z2 in the time interval t = ∆. P(z, ∆) is the so-called mean propagator: the propagator averaged over all starting positions z1. It is the probability density that an arbitrarily selected particle in the sample is shifted over a distance z in z-direction (which is the direction of the magnetic field gradient) during the time interval between the two field gradient pulses. Since in a heterogeneous sample the probability function of molecular displacement may depend on the starting point, in this case the propagator as used in Eq. (44) is understood as a mean value all over the sample.
Fig. 5. rf pulses, pulsed field gradients and time intervals in the PFG and SFG NMR experiment with the Hahn echo.
By Fourier inversion of Eq. (43) the mean propagator may be directly deduced from the primary data of the PFG NMR experiment, yielding
( ) ( ) ( ) ( )ggzgzP γδγδ∆δψ∆ dcos,21
, ∫π= (45)
As an example, Fig. 6 displays the first application of this possibility showing the propagation patterns of ethane in beds of zeolite NaCaA with two different crystallite sizes [140]. Being symmetric in z, for simplicity the propagator is only represented for z ≥ 0. For the lowest temperature (153 K), the distribution widths of molecular displacement during the considered time intervals (5-45 ms) are found to be small in comparison with the mean radius of the larger crystallites (8 µm). In this case, the observed mean square displacement increases in proportion with the observation time as to be required for normal diffusion so that PFG NMR is able to monitor genuine intracrystalline self-diffusion.
rf pulses t
π /2 π
gradient pulses t
magnetization ψ in the homogeneous field t
free induction echo
fringe field gradient
t
magnetization ψ in the fringe field
t
free induction echo
δ δ ∆
24
In the smaller crystallites, obviously, molecular propagation is terminated by the surface of the crystallites so that PFG NMR provides information on the size of the crystallites rather than the intrinsic mobility. This way of tracing the extension of microscopic regions has become popular under the name "dynamic imaging" [139]. With increasing temperature, however, the thermal energy of the diffusing molecules becomes large enough so that a substantial fraction of the ethane molecules are able to surpass the step in the potential energy from the intracrystalline space into the surrounding gas phase (intercrystalline space). Consequently, distribution widths of molecular propagation much larger than the crystallite radii become possible. Eventually, the conditions for the application of the central limit theorem are again obeyed and molecular propagation is described by a Gaussian with an effective long-range diffusivity Dlr, which is the product of the diffusivity of the molecules in the intercrystalline space and their relative amount.
The measurement of the spin-echo attenuation ψ as a function of the field gradient pulse program clearly implies the existence of a measurable NMR signal. Therefore, the molecules under study must contain "NMR active" atoms, that is nuclei with a non-vanishing magnetogyric ratio, which have to occur with a sufficiently large density. For hydrogen, which offers the best measuring conditions with respect to both the minimum number of diffusants and minimum displacements, typical minimum concentrations are of the order of one hydrogen nucleus per 10 nm3 which corresponds to about 0.1 moles per liter. Hence, PFG NMR is not very appropriate for studying the diffusivities of species that are only present in minor concentration. In principle, clearly, with a sufficiently large number of acquisitions, even at much smaller concentrations NMR signals may be generated. For the measurement of small diffusivities, however, such a procedure is far more subjected to the risk that signal attenuation is due to a mismatch between the field gradient pulses or mechanical instabilities rather than to diffusion. Diffusivity data determined under such conditions may dramatically exceed the real values. We shall return to this point at the end of this section.
The measuring conditions are furthermore determined by the nuclear magnetic relaxation times. In the above introduced primary or Hahn-echo experiment (π/2-τ-π-τ-echo), the observation time is essentially limited by the transverse relaxation time T2. If the longitudinal relaxation time T1 is notably larger than T2, the observation time may be further enhanced by applying the stimulated echo (π/2-τ1- π/2-τ2- π/2-τ1-echo), where the field gradient pulses are applied during the two time intervals of duration τ1. As in the case of the primary echo, signal attenuation during these two time intervals occurs with the time constant T2, while during the time
20 40 60 80
z /µm
P ( z,∆ )
∆ /ms 100 200 300 400
200
10 20 40 60 80
z /µm
P ( z,∆ )
∆ /ms 100 200 300 400
200
10
z /µm 1 2 3 4
P ( z,∆ )
∆ /ms
5
45
0.5 1.0 1.5 2.0 z /µm
P ( z,∆ )
∆ /ms
5
45
10 20 30 40 z /µm
P ( z,∆ )
∆ /ms
4 10
21
20 40 60 80 z /µm
P ( z,∆ )
∆ /ms
20 40
60 80
100 120
140
153 K a b
233 K
293 K
Fig. 6. Propagator representation of the self-diffusion of ethane in zeolite NaCaA: (a) left hand side. loading 40 mg ethane per g zeolite, mean crystallite radius rc = 8 µm; (b), right hand side, 58 mg g−1, rc = 0.4 µm, after ref. [140].
25
interval τ2 signal attenuation is governed by T1. Typical values of T2 and T1 and hence of the observation times in diffusion studies by PFG NMR are of the order of milliseconds to seconds.
In deriving Eqs. (42) and (43) we have assumed that during the field gradient pulses the spins assume well-defined positions. Such an assumption is clearly only acceptable if molecular displacements during the field gradient pulses are negligibly small in comparison with those between the pulses. In the case of normal diffusion it may be shown [138,139,141] that these relations may be maintained also for field gradient pulses of finite duration by simply replacing the quantity ∆ by an "effective" observation time ∆ − δ /3.
The PFG NMR method works under the supposition that the values of δg for the first and second field gradient pulses are identical. Any difference had the same effect as a translational motion of the molecules under study, leading to a signal attenuation. The correct application of PFG NMR therefore necessitates extremely stable gradient currents, which generate the field gradient pulses within suitably structured field gradient coils, see [139, 138]. Likewise high mechanical stability of both the field gradient coils and the sample must be ensured, since any movement of the sample with respect to the coils would also lead to differences in the local field at the instants of the first and second field gradient pulses.
Methodical development in PFG NMR is focussed on the generation of extremely large field gradient pulses [139,142]. The difficulties due to the requirement of perfect matching between the two field gradient pulses may be circumvented by applying the stimulated spin echo under the influence of a strong constant field gradient [138,143], which is provided by the stray field of the superconducting magnet ("stray field gradient" (SFG) or "supercon fringe field" (SFF) NMR). The intensity of the stimulated echo is only influenced by the field gradient applied during the two time intervals of duration τ1. These are exactly those time intervals during which (as we have seen above) also the pulsed field gradients are applied. Therefore, signal attenuation is described by the same equations as in the case of PFG NMR with the pulse width δ replaced by τ1 and the observation time ∆ being equal to τ1 + τ2. By this technique, presently the largest field gradient "amplitudes" (up to 180 T/m) may be achieved [144]. In comparison with PFG NMR, however, the signal-to-noise ratio is dramatically reduced, so that much larger acquisition times are inevitable. These are, however, much easier to be accomplished since the requirement of identical field gradient "pulses" is automatically fulfilled in this technique. A severe disadvantage of SFG NMR is the fact that the large constant magnetic field gradient excludes the possibility of Fourier transform PFG NMR for multi-component diffusion studies [143]. SFG NMR measurements are additionally complicated by the fact that by varying the "width" of the field gradient "pulses" the signal is affected by both diffusion and transverse nuclear magnetic relaxation.
6 Magnetic resonance imaging (MRI) of porous materials
The application of NMR imaging techniques to porous materials like zeolites [145] and wetted porous cement, lime or sand mortar [146] appeared with a delay of very few years after the discovery of the zeugmatography [147] in 1973, which is wellknown now as magnetic resonance imaging (MRI) mainly in medicine. About five applications to porous materials were published now per year in this field.
S.P. Rigby and L.F. Gladden [148] simulated the diffusion process in catalyst support pellets by MRI. S.P. Roberts et al. [149] used a broad-line gradient-echo technique for the spatial resolution of the vapor-percolation threshold of sandstone rock plugs. A single point ramped imaging of water in zeolite pellets was presented by P.J. Prado et al. [150]. J.L. Bonardet et al. [151] studied the diffusion of benzene in coked zeolites. I.V. Koptyug et al. [152] employed NMR microimaging to study several porous materials, including catalyst support pellets and beds comprised of porous grains (building-materials). S.T. Beyea et al. [153] introduced a new technique for MRI of heterogeneous broad linewidth materials. Their turbo spin-echo single-point imaging uses hard pulses (small flip angle of the excitation pulse) and refocussing π pulses, which are combined with bipolar phase encoding gradients [153].
26
Imaging by hyperpolarized xenon is limited to materials, in which the large steady-state nonequilibrium 129Xe or 131Xe spin polarizations can be maintained over sufficiently long times. This favors highly siliceous inorganic porous materials, in which the xenon is not fast relaxing by interaction with quadrupole nuclei like aluminum or even paramagnetic impurities in natural materials. But even a picture of the aluminum-rich zeolite A could be presented [154]. The application of laser-polarized noble gases for MRI is impressive in medicine and in porous materials as well. The latter was reviewed by E. Brunner [28], who described also the hyperpolarization technique. Most recent studies of porous glass and zeolites were published by I.L. Moudrakovski et al. [154,155].
G. Pavlovskaya et al. [156] used the quadrupole nucleus 131Xe, in order to benefit from specific contrast for imaging by dephasing of the coherence due to quadrupolar interactions. 131Xe cannot be hyperpolarized, since a fast quadrupole relaxation takes place. The high spin density of liquid xenon close to the critical point (289 K) was used to overcome the sensitivity problems with 131Xe [156].
7 129Xe NMR
Hyperpolarized xenon is used for the enhancement of surface NMR signals since the pioneering work of D. Raftery et al. [157]. The technique was applied for imaging, see above, and for the enhancement of surface NMR spectra as well [28]. But 129Xe has been a well-established NMR probe for a long time and was introduced into the investigation of zeolites and other porous materials by T. Ito and J. Fraissard in 1980 [158] and references therein. The key idea is the use of a chemically inert probe with a high sensitivity to physical interactions, which can be easily monitored by NMR. A time-consuming disadvantage of the 129Xe technique is that the chemical shift is influenced by collisions with the wall of the porous material and with other xenon atoms as well. Thus, measurements have to be performed in dependence on the xenon concentration, in order to subtract the contribution of the xenon-xenon interaction.
Owing to its large chemical shift range and relatively high NMR sensitivity 129Xe became a frequently used NMR probe. Many successful applications as a probe in porous materials caused a drastic increase of the number of 129Xe NMR references in Current Contents, which passed through a maximum of 38 references in the year 1995. Reviews were published (in the sequence of the year of publication) by C. Dybowski, N. Bansal, T.M. Cuncan: "NMR spectroscopy of xenon in confined spaces: Clathrates, intercalates, and zeolites" [159], P. Barrie, J. Klinowski: "129Xe NMR as a probe for the study of microporous solids" [160], D. Raftery, B. Chmelka: "Xenon NMR spectroscopy" [161], C.I. Ratcliff: "Xenon NMR" [162], M.A. Springuel-Huet, J. L. Bonardet, A. Gedeon, J. Fraissard: "Xe-129 NMR overview of xenon physisorbed in porous solids" [158], J. L. Bonardet, J. Fraissard, A. Gedeon, M.A. Springuel-Huet,: "NMR of physisorbed Xe-129 used as a probe to investigate porous solids" [163].
27
List of symbols
α, β Euler angles γ magnetogyric ratio of the nuclear spins δ duration of a field gradient pulse, cf. Fig. 5 δ /ppm resonance shift in ppm δ = σZZ − σiso anisotropy of the chemical shift, cf. above Eq. (8) δν1/2 full width at half maximum δCS iso = σref − σiso isotropic chemical shift with respect to a reference compound δQ iso = (νiso Q)/νL dimensionless value of the second-order quadrupole shift
∆ time between the two gradient pulses, cf. Fig. 5 ∆ω = ωL − ω resonance offset, cf. below Eq. (3) ∆σ = σZZ − (σXX − σYY)/2 total anisotropy of the shielding tensor η asymmetry parameter, cf. Eq. (8) θ angle between the internuclear vector and B ν = ω /2π radio frequency, cf. above Eq. (1) ν' angular-dependent quadrupole frequency, cf. Eq. (12) νiso Q frequency of the second-order quadrupole shift νQ or ωQ quadrupole frequency, cf. Eq. (11)
νrot MAS frequency Ξ-value resonance frequency of a nucleus in that external field, for which the 1H NMR
of TMS resonates at exactly 100 MHz ρ s-character of the oxygen bond σ shielding tensor (trace 3σiso) σiso = (σXX + σYY + σZZ)/3 isotropic part of the shielding tensor ϕ phase shift of a nuclear spin ψ spin-echo attenuation, cf. Fig. 5 Ψ shear strain parameter, cf. Eq. (35) ωL = 2πνL = −γ B0 Larmor frequency ωrf = −γ Brf nutation frequency B or B0 external magnetic field Bx(t) = 2Brf cos(ωt) radio frequency field CI constants for calculation of M2, cf. Eq. (26) and Tab. 2 Cqcc quadrupole coupling constant, cf. Eq. (10)
CS = CI·4/9 constants for calculation of M2, cf. Eq. (26) and Tab. 2 d reduced Wigner matrix elements, cf. below Eq. (23) D Wigner matrix elements, cf. Eq. (5) EDP deprotonation energy
g magnetic field gradient h = 2πh Planck constant H Hamiltonian I spin angular momentum vector or vector operator I spin number Ix, Iy , Iz components of the spin vector or vector operator k rank of a tensor operator, cf. Eq. (4) m spin angular moment in the direction of B, cf. above Eq. (1) M2 second moment, cf. Eqs. (24-25) p quantum level of a pQ transition, cf. Eq. (23)
28
P(z, ∆) mean propagator p(z1) a priori probability to find a spin at position z1 for t = 0 Q quadrupole moment, cf. above Eq. (8) Qn, n = 0, 1, 2, 3, 4 tetrahedron which is connected to n tetrahedra via oxygen rI distance of homonuclear spins, cf. Eq. (26) and Tab. 2
rS distance of heteronuclear spins, cf. Eq. (26) and Tab. 2
t1 evolution time T1 longitudinal relaxation time t2 detection time T2 transverse relaxation time Tq
(k) tensor operators acting on the nuclear spins, cf. Eq. (4) Vq
(k) tensor operators acting on the spatial coordinates, cf. Eq. (4) VZZ = eq electric field gradient, cf. above Eq. (8) x, y, z coordinates in the laboratory system, cf. above Eq. (1) X, Y, Z coordinates in the principal axis system, cf. above Eq. (1) x i, yi, zi coordinates in the interaction representation, cf. above Eq. (1) z coordinate along the applied external field or field gradient
List of abbreviations
CP cross-polarization CSA anisotropy of the chemical shift DAS dynamic angle spinning DOR double rotation FSAHP frequency-stepped adiabatic half-passage fwhm full width at half maximum INADEQUATE incredible natural abundance double quantum transfer experiment LAB laboratory system MAS magic-angle spinning MQMAS multiple-quantum magic-angle spinning MRI magnetic resonance imaging NMR nuclear magnetic resonance NQR nuclear quadrupole resonance PAS principal axis system PFG pulsed field gradient REAPDOR combination of TRAPDOR and REDOR REDOR rotational-echo double resonance rf radio frequency ROT rotating system SATRAS satellite-transition spectroscopy SFF supercon fringe field SFG stray field gradient STMAS satellite transition magic-angle spinning TRAPDOR transfer-of-populations-double-resonance
29
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