10162
J. Phys. Chem. B 2000, 104, 10162-10167
NMR Cross-Polarization when TIS>T1G; Examples from Silica Gel and Calcium Silicate Hydrates I. Klur,† J.-F. Jacquinot,§ F. Brunet, T. Charpentier, and J. Virlet* SerVice de Chimie Mole´ culaire, URA 331 CNRS and SerVice de Physique de l’Etat Condense´ , Direction des Sciences de la Matie` re, CEA Saclay, 91191 Gif sur YVette Cedex, France
C. Schneider and P. Tekely* Laboratoire de Me´ thodologie RMN, UPRESA CNRS 7042, UniVersite´ Henri Poincare´ , Nancy 1,54500 VandoeuVre-le` s-Nancy, France ReceiVed: April 7, 2000; In Final Form: August 3, 2000
NMR cross-polarization (CP) measurements are usually analyzed assuming that the cross-polarization time TIS of magnetization transfer from the abundant I spins to the rare S spins is shorter than the relaxation time T1F in the rotating frame of the I spins (fast CP regime). Here, it is shown that the reverse situation (TIS > T1FI, slow CP regime) may occur, for instance, for the 1Hf29Si transfer in commonly encountered inorganic materials and that analyzing the experimental data in this case under the usual fast CP assumption will, beside leading to erroneous dynamic parameters, underestimate the number of spins by a factor ∼TIS/T1F. Experimental ways to distinguish between the two situations are presented, the most efficient being to resort to the TORQUE experiment. Examples are given on silica gel and calcium silicate hydrate (CSH) samples for which the proper analysis allows a deeper insight into the nature of the protonated surfaces. This slow CP regime may be expected to occur also in some organic materials, for instance in 13C NMR of polyaromatic compounds.
Introduction In the course of 29Si NMR studies of silica gels and of hydrated calcium silicate hydrates (CSH), we found that the set of cross-polarization, T1F and equilibium magnetization measurements could not be interpreted without assuming that TIS > T1FI. That CP regime was apparently very unusual. From then a detailed examination was undertaken of the features of NMR cross-polarization in such a situation, as well as careful experimental studies on the CSH and silica gel samples. The simplest way to record NMR spectra is a direct excitation by a single pulse (SPE) applied close to the Larmor frequency of the nucleus under study. In this way, it is possible to get the line intensities proportional to the populations of chemically or crystallographically inequivalent sites, assuming that the waiting time Trecycle between the pulses is much longer than the longitudinal relaxation time T1 of those nuclei. Let F ) Trecycle/ T1. If the condition F >> 1 is not fulfilled, one can still obtain quantitative information by correcting the observed intensities for each site by a known function of the pulse angle θ and of the ratio F. For this, a rough estimation of the longest T1 in the first case or a more precise measurement of all the T1s in the second case are necessary. However, to increase the sensitivity and to reduce the measurement time, the NMR signal of nuclei with low gyro* To whom correspondence should be adressed: J.Virlet, Service de Chimie Mole´culaire, CEA Saclay, 91190 Gif-sur-Yvette Cedex, France. E-mail: . P. Tekely, Laboratoire de Me´thodologie RMN, UPRESA CNRS 7042, Universite´ Henri Poincare´, Nancy 1, 54500 Vandoeuvre-le`s-Nancy, France. E-mail: . † Present address: Rhodia Recherches, 52, Rue de la Haie Coq, 93308 Aubervilliers, France. § Service de Physique de l’Etat Condense ´.
magnetic ratio γ, such as 13C or 29Si (referred to below as spins S, or rare spins) is most often acquired in solids by using crosspolarization1 (CP) with nuclei having high γ, such as 1H or 19F (referred below as spins I or abundant spins). Here, quantitative analysis is not so easy to reach as with the direct single pulse excitation due to the fact that the signal intensities depend, in a complex way, upon the characteristics of the spin system and the experimental conditions. In the widely used simplified model,2-4 the signal intensities depend on the contact time tCP , the cross-polarization time constant TIS and the relaxation times in the rotating frame T1FI and TS1F of the spins I and S. These time constants are governed by the nature of the spins, the distances between involved nuclei, and the molecular mobility. The CP has first been used in 13C NMR spectroscopy of highly protonated and rigid organic solids5 where the condition TIS T1FI was shortly dismissed arguing more or less implicitly that it leads to a small unobservable signal. Such a point of view is still commonly found in the literature, although the slow CP regime has already been reported, for instance in polymer systems having the 19F rotating frame relaxation rate faster than the rate for 19F-1H or 19F-13C transfer6,7and for 1H-27Al in some clays and inorganic compounds.8 In this work, it is emphasized and analyzed in detail how in a case where TIS > T1FI, the erroneous assumption that TIS
T1FI situation, as compared to the usual one, it is shown that from a standard CP curve alone it is impossible to know which of these two situations rules the CP process. It will then be explained how these two situations can be distinguished experimentally. Two illustrative examples are presented in 29Si NMR of hydrated calcium silicate hydrates (CSH)10,11 and for a silica gel sample. In each case the unusual slow CP situation is shown to occur for some types of silicons. In CSH, the whole set of results may be interpreted as a biphase behavior due to different mobilities of protons within the internal layers and at the surface of the nanocrystals. Theoretical Considerations. The CP-MAS Experiment. We begin with a short theoretical discussion of the main CP features. It is now well established that the simplified thermodynamic model of cross-polarization dynamics2-4 may be used when the average I-I homonuclear dipolar interaction between the abundant I spins is larger than the I-S heteronuclear one between the abundant I spins and the rare S spins. As a rough rule, this may be expected when the I spins are more close together than they are to the S spins. We shall assume, as is most often done, that the heat capacity of the rare spins is much lower than that of abundant spins ( ) 0 with the notation of ref 3). The extension to the general case does not change the main features discussed below. We also assume that there is no relaxation of the S spins (1/TS1F ) 0), and that the initial S spin magnetization M (0) is equal to zero. With these assumptions, the signal of the S spins, as a function of the contact time takes the well-known form1
γI 1 I MCP (tCP) ) MeqR (exp(-tCP/T1F )γS 1 - TIS/TI 1F
exp(-tCP/TIS)) (1) where Meq is the equilibrium magnetization of spins S; R ) ω1I/ω1S ) (γIH1I)/(γSH1S) is the ratio of the radio frequency fields at the I and S frequencies (called the Hartman-Hahn mismatch parameter, usually R ) 1); 1/TIS is the crosspolarization rate, which increases with the strength of the heteronuclear I-S dipolar interaction but also depends in a more complex way on the strength of the homonuclear I-I dipolar interaction between the abundant spins, on the correlation time of molecular motions, and on the experimental parameters. Expression 1 is valid not only when λ 1 then TUP ) T1FI and TDOWN ) TIS. In fact, in this case, MCP (tCP) will as well begin to rise at a rate 1/TIS but this increase cannot proceed further when the I spin reservoir is rapidly depleted by the T1FI relaxation. Consequently,
the increase of MCP (tCP) is stopped at a time close to T1FI and there is a reverse flow from the S reservoir to the I reservoir which remains depleted by the faster T1FI relaxation. This reverse flow from the S to the I reservoir occurs (as does the forward one) at the cross-polarization rate 1/TIS. Thus, in a somewhat paradoxical way, the S magnetization rises with a time constant close to T1FI and decreases with a time constant close to TIS. For an arbitrary value of λ, it is known12 from eq 1 that at time tMAX ) TIS (ln(λ)/(λ - 1)) the CP signal reaches its maximum value
MCP MAX ) KMeq(RγI/γS)
(2)
where K is a function13 of λ
K)λ
( ) λ 1-λ
(3)
In the usual case(λ > 1. Thus, when λ increases, the achievable signal decreases, but may always be calculated, observed, and measured, even when λ >> 1. QuantitatiVe Reliability of the CP Experiment. For quantitative analysis based on the CP experiment, the usual recipe is: take TIS from the beginning of the cross-polarization curve MCP (tCP) and T1FI from the end of MCP (tCP); using eq 1, get Meq (which is proportional to the number of spins S) from MMAXCP. Although it is clear that this recipe is true in the usual assumption that is when λ < 1 (because then TUP ) TIS and TDOWN ) T1FI), it is definitely wrong when λ > 1. Thus if one assumes that as usual TUP ) TIS whereas the real situation is TUP ) T1FI, the quantitative analysis will be strongly in error. In fact, the value MeqCP deduced from the experimental MCP (tCP) will be TDOWN/TUP times lower than its real value (which would be calculated by letting TUP ) T1FI). In this way, the amount of S spins may be strongly underestimated. It is also obvious that it will be absolutely impossible to know from the cross-polarization curve MCP (tCP) alone, whether TUP ) TIS or TUP ) T1FI, that is whether λ ) Tup/TDOWN or λ ) TDOWN/TUP . This is due to the fact that apart from the intensity factor, eq 1, governing CP dynamics, is fully symmetrical with respect to the interchange of TIS and T1FI. Consequently, to distinguish between both cases, complementary information is required which may be available from different sources such as the following. (1) a knowledge of the nature of the sample: for instance, it is well-known that for CH2 in a rigid organic solid TIS = 15 µs T1FI. Note the change in the curvature of TORQUE curves and the CP value of the ratio of CP curves (MCP MAX)λ1 equal to TDOWN/ TUP according to eq 3.
The TORQUE Experiment. In the TORQUE experiment one uses a spin lock period on spins I of duration tSL followed by the CP transfer of variable duration tCP , the total time TTORQUE ) tCP + tSL being kept constant. This experiment has been originally designed with the aim of quenching the I spin T1F dependence (T One Rho QUEnching) when studying crosspolarization dynamics in solids with TIS < T1FI. It has been demonstrated that by using this simple procedure, subtle details of CP dynamics, usually hidden by the T1FI decay, could be revealed in homogeneous and heterogeneous macromolecular materials.15 The TORQUE signal MSTORQUE (tCP) measured at time TTORQUE is given by eq 1 multiplied by exp(-tSL/T1FI). We shall assume here, as it is generally done, that the relaxation time T1FI is the same during the spin lock and CP periods.16 The signal grows now as a function of tCP according to
MTORQUE (tCP) ) exp(-TTORQUE/T1FI ) × S
(
)
1 - exp(-(1 - λ)(tCP/TIS)) (1 - λ)
(5)
The rise time constant of MSTORQUE (tCP) is (1 - λ)/TIS ) 1/TIS - 1/T1FI, that is the difference between the I-S crosspolarization rate and the I spin relaxation rate. MSTORQUE (tCP) grows with a negative curvature if λ < 1 (the usual case) and a positive one if λ > 1 and this allows an easy distinction between the two cases in a single experiment. In Figure 1 the results of simulations of these two different situations in a standard CP experiment and in the TORQUE experiment are shown. The curves labeled a and b differ only by the interchange of the values of T1FI and TIS. As expected, beside the differences in the absolute intensity in each case, identical temporal evolution of magnetization is observed in the
standard CP experiment. This is a direct consequence of a fully symmetric form of eq 1 with respect to the interchange of TIS and T1FI. Contrary to the standard CP experiment, dramatic differences in the curvature of TORQUE curves may be observed in corresponding situations. This allows a direct visualization of the λ ) TDOWN/TUP ratio encountered in different experimental situations and will be helpful in an appropriate analysis of TIS in terms of structural and/or motional features of a system under study. Results and Discussion Calcium Silicate Hydrates. The calcium silicate hydrates (CS-H), which are the major constituant of Portland cement, have a layered structure formed by a calcium sheet bordered by two silicate planes and separated by the interlayer space.17 These planes are composed of silicate tetrahedral chains with a specific three unit repetition (dreierketten).18,19 Two silicate tetrahedra (noted as Q2) share two of their oxygen atoms with the calcium of the plane, whereas the third silicate, called the bridging tetrahedron (noted as Q2p or Q2i) does not share oxygen atoms with the calcium. The end-chain tetrahedra are noted as Q1. The interlayer space contains water, hydroxyl groups, and some calcium ions showing larger mobility than those in the sheets. When the ratio Ca/Si increases from 0.66 to 1.5-2.0, that layered structure is conserved,20,21 whereas the length of the chains of silicate tetrahedra decreases.10,11 Figure 2 shows a typical 29Si high-resolution solid-state MAS NMR spectrum of C-S-H with Ca/Si ratio of 1.05, obtained by single pulse excitation. The main resonance lines at -78.90 ppm and -84.85 ppm are respectively due to the end-chain tetrahedra Q1 and nonbridging tetrahedra9,10 Q2. Small intensity lines at -81.48 ppm and at -83.20 ppm are assigned to the bridging tetrahedra.11 The resonance line at -81.48 ppm is attributed to bridging tetrahedra Q2p with only hydroxyl and water neighbors in the interlayer space, the other line at -83.20 ppm to bridging tetrahedra Q2i with hydroxyl, water, and a calcium ion neighbor in the interlayer space.11 The relative intensities of the four lines in the SPE spectrum are in the ratio 35:7:17:41. The experimental results obtained from CP, TORQUE, and T1F(1H) experiments are shown in Figure 3. The CP curves can be analyzed as usual according to eq 1, and each of them is characterized by two time constants TUP and TDOWN for their rising and decreasing parts (see Table 1).
NMR CP Study of 1H29Si Transfer
J. Phys. Chem. B, Vol. 104, No. 44, 2000 10165
Figure 3. Time dependence of 29Si magnetization for Q1, Q2p, Q2i, and Q2 sites of a C-S-H sample (Ca/Si ) 1.05) in (b) CrossPolarization 1H-29Si standard sequence; (9) TORQUE sequence with total constant time ) 4 ms; (2) indirect T1F (1H) measurements. Solid lines correspond to the fitted curves from eqs 1, 4, 5, and 6. Fitted parameters are given in Table 2. Experimental conditions: 29Si frequency: 59.595 MHz; MAS rate νr ) 4 kHz; 1H decoupling; RF field: ω1s ) ω1I ) 50 kHz; recycle time: 2 s; number of scans: 1544.
The results bring forth following comments: (1) Two very different (λ < 1 and λ > 1) equilibrium magnetization values MeqCP can be calculated from the CP data values (Table 1). The MCPeq values calculated assuming TIS>T1F are found, especially for the Q2, to be in better but not perfect agreement with the directly measured MeqSPE. However, neither of two MeqCP values is equal to the directly measured MeqSPE SPE CP value and (MCP eq )λ1. (2) At first glance, no striking departure from a single-exponential relaxation can be seen on the T1F relaxation curves for protons for each Qn site which leads to a uniform value T1F (1H) ≈ 1.1 ms. This relaxation time is equal neither to TDOWN nor to TUP . In fact, it is shorter than TDOWN and longer than TUP . (3) The observed curvature in TORQUE temporal dependence makes it immediately evident that the TIS > T1FI situation holds for the Q2. For Q1, Q2p, and Q2i species, the TORQUE curves exhibit a more or less pronounced S-shaped character. This means that neither the usual nor the unusual condition holds for these sites. A simple model for which each Q1, Q2p, and Q2i is characterized by a single set of values of TIS and T1F (1H) is thus found to be inadequate. Such a model is clearly oversimplified. A more realistic model should assume two (or more) different proton environments, some silicons being coupled to one species of protons under TIS < T1FI, the others to a second type of protons under TIS > T1FI. This hypothesis could correspond to a two phase sample or to two different environments within the same phase, reflecting for instance some disorder inside the layers of the CSH (chain length distribution, substitution sites for Ca2+, etc.)10-11,17-22 These different environments may also represent the surface and core layers of the nanocrystals. In such a model, for each Qn species, the CP, TORQUE, and T1F signal intensities are each the weighted sums
M ) W Ma + (1 - W) Mb
(6)
of several contributions Ma and Mb, each one given by eqs 1, 4, and 5 for CP, T1F, and TORQUE, respectively. Figure 3 and Table 2 present the results of fitting procedure of the respective temporal dependences according to such a model. The polarizations are obtained by dividing the corresponding experimental magnetizations by the equilibrium magnetizations measured directly by SPE. The data have been fitted assuming that in the whole sample there are protons in two different environments, with respectively two different relaxation times T1F. Among the silicons of a Qn species, some interact with one kind of protons, some with another kind. It has been found that the rate of I-S cross-polarization does depend on the Qn silicon species involved, but not on the proton species. Despite the roughness of different assumptions, a good agreement between experimental and calculated temporal dependencies is observed. The possible departure between the equilibrium magnetization calculated from CP and that directly measured by SPE is indicated by the value of the parameter R in eq 1, which was left free, but common to the four Qn species. It is found to be 0.83. This departure from 1, its optimum value, may reflect either an experimental Hartmann-Hahn mismatch (the meaning of R in eq 1), either the global inaccuracy of the NMR amplitude measurements in the SPE or in the CP experiments, which could in turn be due either to instrumental imperfections or to some imperfection of the model. For Q1, Q2i, and Q2p species, the cross-polarization times TIS are longer than one of two proton T1F values. For Q2 site, the TIS is longer than both proton T1F relaxation times. The proportion of silicons that see the protons with longer T1F is found to be similar (∼10%), within experimental error, for all Qn species. This result may be interpreted as follows. The fact that there is a single value for the cross-polarization time TIS of the silicons of a given Qn species to the protons in two different environments suggests that the structure and dynamics of the close proton neighboring of the silicons are the same in these two cases. On the other hand, the difference in the relaxation rates of the protons neighboring the silicons may be induced by different mobilities of protons more remote from the silicons. The two different environments of remote protons may be interpreted as being the internal interlayer space and the external surface of the nanocrystalline CSH crystals. Short range forces between silicons and protons are likely to be the same in these two environments, whereas the mobility of the protons in the second proton layer is expected to be less restricted at the surface of the crystals in contact with the pore water than in the more constrained internal interlayer space of the CSH crystals. These results agree well with the size of the CSH nanocrystals. In a CSH cell19 there are two calcium layers, each one bordered by two silicon layers. Measurements of the thickness of the CSH nanocrystals by Atomic Force Microscopy are under way. That thickness is found to be 5 nm for C/S ) 1.7,23 and 9 to 10 nm,24 that is about four crystalline cells, for C/S ) 1.05. In such a CSH nanocrystal with C/S ) 1.05 there are therefore about sixteen silicon layers, of which two (that is 12.5%) are at the surface of the crystal. This is in good agreement with the results given in Table 2 and suggests that one is thus able to distinguish between core and surface of the CSH cristallites. On the other hand, the values of the cross-polarization time TIS reflect the expected decreasing number of hydroxyl neighbors of the bridging Q2p, end chain Q1, bridging Q2i close to a calcium ion, and Q2 silicons, in that order. We have found this two environments behavior in several CSH, pure or substituted. It has yet to be determined if this is
10166 J. Phys. Chem. B, Vol. 104, No. 44, 2000
Klur et al.
TABLE 1: Analysis of Cross-Polarization Curves for C-S-H (Ca/Si ) 1.05) Samplea CP analysis TIST1F
δ (ppm)
T1F (ms)
TUP (ms)
TDOWN (ms)
λ ) TUP/TDOWN
MeqCP/MeqSPE
λ ) TDOWN/TUP
MeqCP/MeqSPE
-78.90 -81.48 -83.20 -84.85
1.2 1.2 1.0 1.3
0.57 0.52 0.45 0.71
4.24 4.03 4.76 11.5
0.134 0.13 0.095 0.06
0.22 0.29 0.20 0.085
7.44 7.75 10.6 16.2
1.61 2.27 2.15 1.36
a The data have been fitted according to eq 1 assuming two opposite situations: TIS < T1F and TIS > T1F. The Hartmann-Hahn match (R ) 1) was assumed to hold.
TABLE 2: Best Fit Parameters of CP, TORQUE, and T1G (1H) Polarization Curves for the CSH Samplea sites
δ (ppm)
-78.90 -81.48 -83.20 -84.85 T1F (ms) MeqCP/MeqSPE
Q1
Q2p Q2i Q2
TIS (ms)
Ma weight
Mb weight
2.3 ( 0.05 1.6 ( 0.04 2.25 ( 0.05 6.75 ( 0.2
90 ( 1% 87 ( 1% 91 ( 1% 92 ( 1% 0.65 ( 0.02 ms 0.83 ( 0.02
10 ( 1% 13 ( 1% 9 ( 1% 8 ( 1% 6.3 ( 0.9ms
a Three curves for each silicon Q1, Q2p, Q2i, and Q2 site were fitted simultaneously according to eqs 1, 4, 5, and 6.
a general property of the CSH, and if the present interpretation may be used more generally. Relaxing the simplified constraints used here, i.e., ) 0 and 1/T1FS ) 0, may improve the quality of the fit, but will not change the general features of the present analysis. As may be expected, the apparent quality of the fit, especially that of the S-shaped TORQUE curves, is also improved when both proton relaxation times are allowed to be unequal for different Qn species, or when the cross-polarization times to the two proton environments are allowed to be different. A greater number of different proton or silicon species (with discrete or continuous distribution of TISs and T1Fs) might also be assumed. However, in any case, a model with too many parameters will lead to a fit close to underdetermined and to a loss of physical significance of the relevant parameters. In quantitative terms, the results show that when a dominant population of silicons is in a slow CP regime (TIS > T1FI), even a small fraction of silicons within a fast CP regime (TIS < T1FI) may increase to a significant extent (here a factor 2 to 3) the maximum CP signal. Finally, the results presented in Table 1 show how a standard CP analysis may lead, when inappropriate, to equilibrium magnetization values strongly erroneous. Silica Gels. Silica gels are highly porous materials which play an important role in numerous applications such as catalysis or chromatographic separation25 and have been the subject of much NMR investigations for several years.26-29 The highresolution solid state 29Si CP/MAS NMR spectra of silica gel show three peaks at -91.5 ppm, -101 ppm and -110 ppm assigned respectively to three Q2, Q3, and Q4 types of silicon environments.26-29 The results from the delayed-CP T1F (1H), CP, and TORQUE experiments on a Fisher S-157 silica gel sample are presented in Figure 4. Assuming a simple monoexponential polarization transfer, the results of a fit of three CP curves using eq 1 are TUP ) [2.3, 2.6, 10.3] ms and TDOWN ) [10.3, 13.4, 30] ms, for [Q2, Q3, Q4] silicons, respectively. It is also observed that the T1F (1H) relaxation curves are identical for protons involved in the cross-polarization process of Q2, Q3, and Q4 silicons and give the unique value T1F (1H) ) 10.3 ( 0.5 ms. This clearly indicates that the differences observed in the decreasing part of the CP curves do not correspond to different T1F of protons involved in the CP transfer on different sites. The value of 10.3 ms is equal to TDOWN for Q2, close to TDOWN for Q3, and equal to TUP for Q4. This suggests that TIS
Figure 4. Time dependence of 29Si magnetization for Q2 ([), Q3 (9), and Q4 (2) sites of silica gel (Fisher S-157) in the (a) indirect T1F (1H) measurements; (b) TORQUE experiment with a total constant time of 20 ms; (c) standard cross-polarization 1H-29Si experiment. Full lines: fitted curves from eqs 1, 4, 5, and 6. Insert: 29Si CP/MAS spectrum of a silica gel sample (Fisher S-157) showing three peaks assigned to three types of silicon environment. Experimental conditions: 29Si frequency: 59.59 MHz; MAS rate νr ) 2.0 kHz; 1H decoupling; RF field: ω1s ) ω1I ) 70 kHz; recycle time: 10 s; number of scans: 64.
< T1FI for Q2 and presumably for Q3, whereas TIS > T1FI holds for Q4. For Q2 and Q4 silicons, these two diametrically opposite situations are apparent immediately from the opposite curvatures of the TORQUE temporal dependence. For the Q3 site, the shape
NMR CP Study of 1H29Si Transfer
J. Phys. Chem. B, Vol. 104, No. 44, 2000 10167
TABLE 3: CP Dynamics Parameters for Fisher S-157 Silica Gel Sample sites
δ (ppm)
T1F (ms)
TIS (ms)
MCPeq (u.a)
sites (%)
Q2 Q3a Q3b Q4
-91.5 -101 -101 -110
10.3 10.3 10.3 10.3
2.3 1.7 7.7 30
7.1 30 40 125
3.5 15 20 62
of the TORQUE curve indicates the existence of at least two different Q3 species, the first one having TIS , T1FI, the second one with TIS ∼ T1FI. The corresponding best fit parameters are given in Table 3. Two Q3 species are found to have a relative abundance ∼43% and ∼57%, each of them showing different rate of crosspolarization transfer. These results suggest strongly the presence of at least two Q3 sites with a different mobility of hydroxyl groups. Such a difference can be expected between external hydroxyl groups located at the surface and those embedded more deeply in the silica structure or between isolated and hydrogenbonded silanols on a silica surface.28,29 As expected, the longest TIS value is observed for Q4 silicons that do not bear any hydroxyl group. It must be quoted that, here, the usual analysis of the data would have lead to an underestimation of the abundance of those Q4 silicons. However, although it was shown above in the case of CSH that the analysis of the T1F (1H), CP, and TORQUE may lead to a MeqCP magnetization equilibrium value close to its true value MeqSPE, it is not yet clear in the present case whether the Q4 proportion is or is not underestimated. To reveal the presence of Q4 much more distant from the surface protons, a careful analysis of the shape of the CP curve decay at longer times than those used in the present measurements would be necessary. Work along these lines is in progress. Conclusions We have presented the analysis of the cross-polarization dynamics occurring in the unusual, slow CP regime i.e., for the cross-polarization time TIS longer than the relaxation time T1FI of the abundant nuclei. A novel experimental approach is proposed in order to avoid important errors in structural and dynamic conclusions, when making wrong assumptions about the time scale of the relevant dynamic processes. The efficiency of TORQUE experiment in visualizing the real CP regime or its possible mixed character has been underlined. It has been also pointed out that the equilibrium magnetization values MeqCP recalculated from the CP data showing complex character have to be analyzed with the utmost possible caution. Although the slow CP regime has seldom been reported so far (as already mentioned, we are aware of only three such cases6-8), it is likely (and most probably has already been observed without being recognized) commonly encountered in typical inorganic solids where protons are more remote from rare nuclei than in organic systems. This is directly connected with the cross-polarization time constant TIS strong dependence on the distance between rare and abundant nuclei and on the molecular mobility. In fact, this is clearly the situation for Q4 silicons located far from the surface of silica gels. In a more subtle way, this may also occur in layered or nanoporous hydrated silicates where the molecular motions may reduce the 29Si-1H dipolar interactions and modify considerably the proton relaxation rate. The present examples prove that the refined analysis of the NMR data can be used to distinguish between internal and external surface of nanocrystals, or to get a deeper insight into the structure and dynamics of protonated surfaces.
Finally, the situation with TIS > T1FI might also be expected in organic solids, for instance in some polyaromatic compounds, where it may be one of possible explanations for frequently quoted discrepancies between the aromaticity factors determined by CP NMR and by other methods.30-31 Acknowledgment. The authors greatly thank A. Nonat for many helpful and fruitful discussions on the structural chemistry of the CSH. References and Notes (1) Pines, A.; Gibby, M. G.; Waugh, J. S. J. Chem. Phys. 1973, 59, 369. (2) McArthur, D.; Hahn, E. L.; Waldstaet, R. E. Phys. ReV. 1969, 188, 609. (3) Mehring, M. High-Resolution NMR in Solids, NMR Basic Principles and Progress; Springer: New York; 1983. (4) Michel, D.; Engelke, F. Solid State NMR III, Organic Matter, NMR Basic Principles and Progress; Springer: New York, 1994; pp 32, 69. (5) Schaefer, J.; Stejskal, E. O.; Buchdahl, R. Macromolecules 1977, 10, 384. (6) Klein Douwel C. H.; Maas W. E. J. R,; Veeman V. S.; Weremeus Buning G. H.; Vankan J. M. J., Macromolecules 1990, 23, 406; Maas, W. E. J. R.; Van der Heijden, W. A. C.; Veeman, W. S.; Vankan, J. M.; Werumeus Buring, G. H. J. Chem. Phys. 1991, 95, 4698; Veeman, W. S.; Maas, W. E. J. R., Solid State NMR III, Organic Matter, NMR Basic Principles and Progress; Springer: New York, 1994; pp 32, 127. (7) Monti, G. A.; Harris, R. K. Magn. Reson. Chem. 1998, 36, 892; Ando, S.; Harris, R. K.; Monti, G. A.; Reinsberg, S. A. J. Magn. Reson. 1999, 141, 91. (8) Mortuza, M. G.; Dupree, R.; Kohn, S. C. Appl. Magn. Reson. 1993, 4, 89. (9) Lipmaa, E.; Ma¨gi, M.; Samoson A.; Engelhardt, G.; Grimmer, A. R. J. Am. Chem. Soc. 1980, 102, 4889. (10) Klur, I. Thesis, Paris VI, 1996. (11) Klur, I.; Pollet, B.; Virlet, J.; Nonat, A. Nuclear Magnetic Resonance Spectroscopy of Cement-Based Materials; Colombet, P., Grimmer, A. R., Zanni, H., Sozzani, P., Eds.; Springer-Verlag: Berlin, 1998; p 119. (12) For λ ) 1, tMAX ) TUP; tMAX/TUP goes to infinity when λ > 1. More revealing are for instance the times t50% needed to reach 0.5 × MCPMAX (which goes from 0.69 TUP when λ > 1 to 0.23 TUP for λ ) 1) or t95% (which goes from 2.99 TUP when λ > 1 to 0.73 TUP for λ ) 1). (13) This expression is more condensed but strictly equal to that of Mehring (ref 3). (14) Note that very often the I spin T1FI is measured as the decay time of the MCP (tCP) curve: assuming that T1FI >> TIS, one finds invariably T1FI >> TIS, whatever the real situation. (15) Tekely, P.; Ge´rardy, V.; Palmas, P.; Canet, D.; Retournard, A. Solid State NMR 1995, 4, 361. (16) This may be questioned if there are slow motions, in which case the spectral density functions are expected to be different in the presence of one or two RF fields at the Hartmann-Hahn condition. (17) Taylor, H. F. W. J. Am. Ceram. Soc. 1986, 6, 69. (18) Taylor, H. F. W. Cement Chemistry, 2nd ed.; Thomas Telford Publishing: London; 1997. (19) Hamid, S. A. Zeitschrift fu¨ r Kristallographie 1981, 154, 189. (20) Nonat, A. Mater. Struct. 1994, 168, 27. (21) Nonat, A.; Lecoq, X. Nuclear Magnetic Resonance Spectroscopy of Cement-Based Materials; Colombet, P., Grimmer, A. R., Zanni, H., Sozzani, P., Eds.; Springer-Verlag: Berlin, 1998; p 197. (22) Cong, X.; Kirkpatrick, R. J. AdV. Cem. Res. 1995, 7, 103. (23) Gauffinet, S.; Finot, E.; Lesniewska, E.; Nonat, A. C. R. Acad. Sc. Paris, Sciences de la Terre et des plane` tes 1998, 327, 231. (24) A. Nonat, priVate communication. (25) Leyden, D. E.; Collins, W. T.; Silylated Surfaces; Gordon and Breach Science Publishers: New York; 1980. (26) Maciel, G. E. Encyclopedia of Nuclear Magnetic Resonance; Grant, D. M., Harris, R. K., Eds.; John Wiley and Sons: Chichester, U.K., 1996; p 4370. (27) Maciel, G. E.; Sindorf, D. W. J. Am. Chem. Soc. 1980, 102, 7607. (28) Chuang, I. S.; Kinney, D. R.; Maciel, G. E. J. Am. Chem. Chem. 1993, 115, 8695. (29) Chuang, I. S.; Maciel, G. E. J. Am. Chem. Chem. 1996, 118, 401. (30) Wind, R. A.; Maciel, G.; Botto, R. E. AdV. Chem. Ser. 1993, 229, 3. (31) Snape, C. E.; Axelson, D. E.; Botto, R. E.; Delpuech, J. J.; Tekely, P.; Gerstein, B. C.; Pruski, M.; Maciel, G. E.; Wilson M. A. Fuel 1989, 68, 547-560.
