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H NMR Spectroscopy and Multiquantum Relaxometry as a Probe of the Magnetic-Field-Induced Ordering of Clay Nanoplatelets within Aqueous Dispersions
Patrice Porion,*,† Anne Marie Faugere,† Laurent J. Michot,‡ Erwan Paineau,‡ and Alfred Delville*,† †
Centre de Recherche sur la Matiere Divisee, CNRS—Universite d’Orleans, UMR6619, 1b rue de la Ferollerie, 45071 Orleans Cedex 02, France ‡ Laboratoire Environnement et Mineralurgie, Nancy Universite—CNRS, UMR7569, 15 avenue du Charmois, BP40, 54501 Vandoeuvre Cedex, France ABSTRACT: 2H NMR spectroscopy and relaxometry were used to investigate the orientation of nontronite clay nanoplatelets induced by the static magnetic field within dilute aqueous dispersions by exploiting the residual quadrupolar splitting resulting from the specific orientation of heavy water molecules physisorbed at the clay surface. A careful analysis of the variation of the residual 2H splitting as a function of clay concentration and magnetic field strength was required to extract the intrinsic clay ordering induced by the magnetic field. The variation of clay ordering as a function of clay concentration clearly indicated two concentration regimes, corresponding to free and collective orientations of the clay platelets, respectively. Multiquantum NMR relaxation measurements were further used to identify the main NMR relaxation mechanism whose temperature variation is compatible with a fast exchange, at the NMR time scale, between free and physisorbed water molecules.
I. INTRODUCTION For many decades, the structural, dynamical, and mechanical behaviors of aqueous dispersions of charged spherical colloids1,2 have been well understood and described on the basis of the overlap between their diffuse layers of condensed counterions. By contrast, dispersions of charged anisotropic colloids were recently the subject of numerous theoretical317 and experimental1831 investigations because the competition between antagonistic phenomena,11,15 such as long-range electrostatic coupling and short-range excluded volume effect, leads to more complex behavior including isotropic/nematic phase transition18,23 and some inversion of the influence of ionic strength on the sol/gel transition.18,27 Numerous studies were thus performed, by varying the parameters characterizing the interactions between these anisotropic charged colloids, such as shape,3235 aspect ratio,3638 and length of their ionic diffuse layer.18,21,26,27 Further investigations were recently devoted to the influence of external forces (shear,3943 gravity,44 electric30,45 and magnetic30,4649 fields) on the organization of these anisotropic particles. In that framework, we have analyzed the influence of magnetic field on the orientational ordering of nontronite, an iron-rich natural clay,50 within dilute aqueous dispersions. Such natural clays constitute a large class of well-characterized layered metallic oxides, with high specific surface and large size anisotropy. Because of some atomic substitutions within their atomic network, r 2011 American Chemical Society
swelling clays, like nontronite, bear a large amount of negative charges neutralized by exchangeable counterions. The swelling and mechanical behavior of these clay dispersions are modulated by the chemical nature (valence)5153 of their neutralizing counterions. As an example, sodium-exchanged nontronite is easily dispersed in water,26 leading to stable aqueous dispersions. For that reason, swelling clays are used in numerous industrial applications (drilling, cosmetic and food industries, waste storage) exploiting their physicochemical properties (high specific surface area, strong affinity for polar molecules, high ionic exchange capacity). Furthermore, because of the atomic roughness of the basal clay surface, clay/water interfaces were largely used to investigate the influence of confinement on the structural1,54,55 and dynamical5660 properties of complex liquids. Thanks to the residual quadrupolar coupling,61 the NMR spectroscopy of quadrupolar nuclei (I > 1/2) is a powerful tool to detect partial ordering within a large class of anisotropic materials including stretched hydrogels,6265 liquid crystals,6670 biopolymers,71 biological tissues,72 and colloidal dispersions.49,73,74 In that context, 2H NMR spectroscopy is used here as a probe of Received: April 12, 2011 Revised: June 16, 2011 Published: June 17, 2011 14253
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The Journal of Physical Chemistry C the clay ordering49,73,74 induced by the static magnetic field. Because of their specific orientation at contact with the clay surface,54,55 physisorbed heavy water molecules exhibit a residual splitting of their NMR resonance line easily detected by 2H NMR spectroscopy and relaxometry. The only difficulty is to separately quantify49,75 the contributions to the 2H residual splitting induced by the specific water organization at the clay surface from that induced by the orientation of the clay platelets into the static magnetic field. Such a separation is performed through a careful analysis of the influence of clay concentration and static magnetic field strength on the residual splitting of the 2H NMR resonance line. This analysis further exhibits a transition between two concentration regimes, corresponding to the free and collective orientation of these anisotropic clay platelets, respectively. Since that transition coincides with the sol/gel transition26 of the same clay dispersions, this result provides a particle picture of the influence of the mutual repulsions between the clay platelets on the mechanical behavior of these aqueous dispersions. Because of the large quadrupolar coupling felt by the deuterium atoms within heavy water (∼105 Hz),76 2H NMR spectroscopy77 is a sensitive probe able to detect the specific ordering of a small fraction (∼103) of physisorbed water molecules. We may reasonably assume that the same approach could be successfully applied to investigate the specific orientation of a large class of anisotropic materials,78 including biopolymers (such as DNA and membranes) and other metallic oxides (like cementitious materials). The only problem concerning the NMR spectroscopy applied to such heterogeneous materials originates from the fast relaxation of the magnetization induced by the presence of paramagnetic impurities.60 We thus performed the present study with an iron-rich clay50 (nontronite), in order to check the generality of our experimental procedure.
II. MATERIAL AND METHODS 1. Sample Preparation. The natural clay mineral used in that study is a nontronite from Southern Australia79 that was purchased from the Source Clays Minerals repository at Purdue University. Prior to use, the natural clay sample was purified according to classical procedures.26 Like montmorillonite, nontronite is a dioctahedral clay resulting from the sandwiching of one octahedral metallic oxide layer between two tetrahedral silica layers. By contrast with montmorillonite, almost all the aluminum atoms from the octahedral layer have been replaced by iron(III), leading to the following general formula:50 (Si7.55, Al0.16, Fe0.29)(Al0.34, Mg0.05, Fe3.54)O20(OH)4Na0.72). As illustrated by that formula, the excess negative charge of the clay particle, resulting from the atomic substitutions within the tetrahedral network, is neutralized by sodium counterions which may be hydrated within the interlamellar space between the clay platelets. In order to reduce size heterogeneity, the clay dispersions were successively centrifuged at gradually increasing speed (7000, 17 000, and 35 000 g) after recovering the supernatant.26 A histogram of the size distribution (Figure 1) of the clay sample used in that study (called “Size3” in ref 26) is obtained by an analysis of TEM observations.26 Figure 1 clearly exhibits the high anisotropy of these clay platelets whose thickness is 7 Å. Finally, the clay samples were prepared by dilution of dense clay dispersions with D2O, leading to clay samples with ionic strength varying between 8.8 104 and 103 M. 2. 2H NMR Measurements. 2H NMR spectra were recorded on DSX360 and DSX100 Bruker spectrometer operating at a
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Figure 1. Histogram illustrating the size distribution of the nontronite clay sample (cf. ref 26).
static magnetic field B0 of 8.465 and 2.351 T, respectively. Spectra were recorded with a time step of 500 μs, corresponding to a spectral width of 2 kHz. Figure 2 illustrates some 2H NMR spectra with a direct measurement of the residual quadrupolar splitting. A complete basis set, with eight independent operators, is required to describe the various quantum states available to spin 1 nuclei like deuterium. A possible basis is defined by the irreducible tensors operators80 (T10, T1(1, T20, T2(1, T2(2). The three first operators correspond to the longitudinal (T10) and transverse (T1(1) components of the spin magnetization, while the five residual components describe the five components of the magnetic quadrupole. The relaxation rate constant of the T1(1 coherence,81 also called transverse relaxation rate constant (R2), was measured by using a Hahn echo pulse sequence82 (see Figure 3b) allowing the additional determination of the residual quadrupolar splitting54 (νQ) (see Figure 4). MX ðτÞ ¼ MX ð0Þ cosð2πνQ τÞ expðτR2 Þ
ð1Þ
Although this latter experimental procedure is more timeconsuming (∼1 h), it is very appropriate in cases where the residual splitting remains smaller than the spectral resolution of our NMR spectrometers (typically a few hertz as displayed in Figure 2). The relaxation rate constant of the T10 coherence,81 also called longitudinal relaxation rate constant (R1), was measured according to the classical inversionrecovery pulse sequence (see Figure 3a). The relaxation rate constants of the T2(1 (Figure 3c), the T20 (Figure 3d), and T2(2 coherences (Figure 3e) were obtained by using double-quantum filtered pulses sequences63,83,84 modified in order to eliminate the effects of the static magnetic field B0 inhomogeneity. For all of the sequences, an adequate phase cycling85 is used to select the coherence pathway illustrated in Figure 3ae. For the measurement of the relaxation rate constants of the T20 and the T2(2 coherences, the maximum signal/noise ratio is obtained by optimizing the free delay δopt of these pulse sequences as a function of the residual quadrupolar coupling νQ. The delay ε is taken equal to 50 μs for all the experiments. The 2H pulse gradient spin echo (PGSE) attenuation measurements were performed on the DSX100 spectrometer to determine the water self-diffusion tensor D. More details on these PGSE experiments may be found elsewhere.75,8690 14254
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Figure 2. Variation of the 2H NMR spectra of the heavy water recorded at B0 = 8.465 T as a function of clay concentration c (g/L).
3. Numerical Modeling. A molecular model of the clay/water interface was used to determine the specific orientation of the water molecules at the clay surface (see Figure 5) by using grand canonical Monte Carlo (GCMC) simulations.89,91 As already shown, that specific orientation is at the basis of the quadrupolar splitting detected by 2H NMR spectroscopy.49,54 More details on these molecular simulations may be found in previous publications.55,56,89,91 Figure 5 illustrates a snapshot of 5216 water molecules confined between two nontronite sheets with a period of 30 Å. Each clay layer is composed of 84 unit cells, and the total surface of these clay fragments accessible to the water molecules is 1.56 104 Å2. These molecular configurations perfectly illustrate the specific water ordering within dense clay dispersions.54,92 This result is used to quantify the average water ordering within dilute clay dispersions by treating the additional water molecules as fully disordered. Such an assumption is justified since the specific orientation of the water molecules induced by the clay surface does not propagate at distances larger than 10 Å.
The residual quadrupolar splitting of the heavy water molecules detected by 2H NMR results from a double average54 νQ
ð2aÞ where the first Legendre polynomial is averaged over the orientations of the OD directors by reference with the normal to the clay surface and the second Legendre polynomial is averaged over all the orientations of these clay directors in the static magnetic field B0. The quadrupolar coupling constant of the deuterium atoms in heavy water76 is 210 kHz, and pS is the fraction of surface water molecules. From our GCMC simulations,54,56,89 we determine the average ordering of the confined water molecules (see Figures 5 and 7)
III. RESULTS AND DISCUSSION 1. Separation between Clay and Water Organization. The residual quadrupolar coupling νQ detected by 2H NMR spectroscopy and relaxometry (see Figure 6) is an equilibrium property of the water molecules. It is used here as an indirect probe of the ordering of the clay platelets induced by the static magnetic field B0. The key feature for these investigations is the specific orientation of the water molecules in contact with the clay surface (see Figure 5). The atomic concentration profiles of the confined water molecules (see Figure 7) better exhibit the water organization induced by the clay lamellae: three hydration layers are identified, and the water density at contact with the clay surface is twice its bulk value. Furthermore, the relative positions of the first layers of the hydrogen and the oxygen atoms pertaining to the water molecules of the first clay hydration layer clearly indicate that these water molecules point one hydrogen atom in the direction of the basal clay surface. Such configuration is favored by the hydrogen bond between the oxygen atoms of the silicate layers and the hydrogen atoms of the water molecules.
P L 3 3cos2 θOD 1 3cos2 θP 1 ¼ 210 kHz pS 4 2 2
3cos2 θOD 1 2
P ¼ 0:016 ( 0:005
ð2bÞ
per water molecule. Because of the large anisotropy of the clay platelets, the specific orientation of the clay platelets induced by the static magnetic field is also detected by the measurement of the water selfdiffusion tensor93,94 exploiting pulsed gradient spin echo (PGSE). Figure 8 exhibits the water mobility within the three planes defined by the three principal axis of the water self-diffusion tensor.88,89 The average water self-diffusion constant ÆDæ (defined as ÆDæ = (1/3)tr D = 1.69 109 m2/s) is reduced by reference to that of bulk water D0, ÆDæ/D0 = 0.923 ( 0.005 (with D0 = 1.83 109 m2/s). The small anisotropy95 of the water self-diffusion tensor (Dz DF)/Dz = 0.110 ( 0.005 (see Figure 8) results from the average alignment of the clay platelets by the static magnetic field B0 (i.e., the OZ direction). Since the water mobility is larger in the direction parallel to the static magnetic field, one may conclude that the clay directors preferentially orient themselves perpendicular to the static magnetic field, in agreement with previously published data.47,49,96,97 14255
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Figure 4. Typical evolution of the T11 coherence (i.e., the transverse magnetization MX) measured during the Hahn echo attenuation NMR sequence and used to extract the residual quadrupolar splitting νQ and the transverse relaxation rate constant R2 (c = 31.10 g/L).
Figure 5. Snapshot illustrating one equilibrium configuration of the sodium counterions and water molecules confined between two fragments of nontronite clay platelets.
Figure 3. Schematic view of the pulse sequences used to measure the relaxation of the (a) T10, (b) T11, (c) T21, (d) T20, and (e) T22 coherences.
In dilute regime, the orientation of the clay directors is expected to be independent of clay concentration (c). In this regime, the residual splitting increases linearly as a function of clay concentration (see inset in Figure 6) due to the corresponding increase of the fraction of water molecules in contact with the clay surface.98 The detected quadrupolar splitting νQ indeed results from an average of the contributions from the free (νFQ) and surface (νSQ) water molecules νQ ¼ pF νFQ þ ps νSQ
ð3Þ
where the free water molecules are randomly oriented (νFQ = 0). As shown in Figure 6, such a linear behavior is detected for clay concentrations lower than around c = 10 g/L. Above this concentration, the detected residual splitting is significantly larger than the value expected from the linear variation. Such a behavior was shown recently to result from the mutual repulsions between the charged
Figure 6. Variation of the residual quadrupolar splittings νQ measured at B0= 2.351 T and B0 = 8.465 T as a function of clay concentration c. The inset helps to better visualize the linear variation of the residual quadrupolar coupling detected at low clay concentration.
clay platelets:49 the largest platelets, with a stronger magnetic coupling, increase the ordering in the static magnetic field of the 14256
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Figure 7. Atomic concentration profiles obtained by GCMC numerical simulations illustrating the specific orientation of water molecules in direct vicinity of the basal surface of the clay platelet.
Figure 9. Determination of the anisotropy of the volumetric magnetic susceptibility |Δχ|/μ0 of the nontronite clay particle from the ratio of the residual quadrupolar splitting νQ measured respectively at B0 = 2.351 T and B0 = 8.465 T under condition of infinite dilution (see text).
where pi is the size probability displayed by the histogram (see Figure 1), Si is the corresponding clay basal surface, and Oi is the order parameter characterizing the intrinsic degree of ordering induced by the static magnetic field for clay platelets with the same size. The anisotropy of the tensor describing the magnetic susceptibility (|Δχ|/μ0) of these clay platelets is at the basis of their ordering Z π 0:5ð3cos2 θ 1Þ expðEi ðθÞ=kTÞ sin θ dθ Z π Oi ¼ 0 ð4bÞ expðEi ðθÞ=kTÞ sin θ dθ 0
with Figure 8. Determination of the principal components of the water selfdiffusion tensor determined at B0= 2.351 T within nontronite aqueous dispersion (c = 31.10 g/L). The OZ director is parallel to the static magnetic field B0.
smallest platelets that otherwise would be much less ordered because of their weaker magnetic coupling. As displayed in Figure 6, this phenomenon appears to have a larger impact on clay ordering induced by the weaker magnetic field. By comparing the ratio of the initial slopes reported in Figure 6 for the two magnetic fields, it is possible to extract the order of magnitude of the anisotropy of the tensor describing the volumetric magnetic coupling (|Δχ|/μ0) of nontronite clay particles. Since contributions from water organization by the clay surface (eq 2a) are the same for both systems, the ratio of the two limiting slopes is equal to the ratio of the order parameters quantifying the specific organization of the clay platelets induced by these magnetic fields. In the lack of mutual repulsion between the platelets, their average ordering in the static magnetic field becomes
L 3cos2 θP 1 ¼ 2
∑i pi Si Oi ∑i pi Si
ð4aÞ
Ei ðθÞ ¼ 0:5Si HjΔχj=μ0 B20 cos2 ðθÞ
ð4cÞ
where H is the clay thickness (7 Å). By numerically integrating eqs 4a4c, we evaluate the ratio of the average clay ordering measurable at 8.465 and 2.351 T for this nontronite clay sample as a function of the a priori unknown magnetic susceptibility (see Figure 9). For both magnetic fields, maximal sensitivity is obtained in the range 101000 J/(T2 m3). Below that range, the average clay ordering increases linearly with magnetic coupling (i.e., |B0|2, see eq 4c), and their ratio at the two magnetic fields (8.465 and 2.351 T) becomes equal to 12.94. Above that range, the order parameter becomes equal to 0.5, corresponding to a fully ordered system, and their ratio at the two magnetic fields becomes equal to 1. The ratio of the two limiting slopes measured at 8.465 and 2.351 T (i.e., 9 ( 0.5 in Figure 6) fits within the optimum range leading to a good estimate of the volumetric magnetic coupling: |Δχ|/μ0 = 33 ( 3 J/(T2 m3). That value is 1 order of magnitude larger than the value previously reported for montmorillonite.49 This result is not surprising since the iron content of nontronite is also 10 times larger than that of montmorillonite. Once |Δχ|/μ0 is known, it is possible to evaluate the intrinsic order parameter induced by the magnetic field B0 and corresponding to the limiting ordering measurable in dilute nontronite dispersions (see inset in Figure 6). As displayed in Figure 10, these intrinsic clay orderings induced at 8.465 and 2.351 T are 14257
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Figure 10. Determination of the limiting order parameters detected at B0 = 2.351 T and B0 = 8.465 T for noninteracting nontronite clay platelets under infinite dilution.
0.21 and 0.024, respectively. By considering eqs 2a and 3, we divide the limiting slope reported in Figure 6 at 8.465 T (i.e., 0.71 Hz 3 L/g) by the absolute value of that limiting order parameter of the clay platelets (i.e., 0.21) induced by the same magnetic field. This ratio (3.4 Hz 3 L/g) contains the contribution from the specific ordering of the water molecules at contact with the clay surface. By assuming that such water contribution remains unchanged in the whole range of clay concentrations c, the simple relationship 3cos2 θ 1L νQ P ð5Þ ¼ 2 3:4Cclay can be used to evaluate the clay ordering induced by the magnetic field B0 at any clay concentration. Figure 11 clearly exhibits the transition between two different regimes: at low clay concentration (below c = 10 g/L), the clay platelets orient themselves independently in the static magnetic field, leading to the smallest absolute value of the order parameter; at higher concentration, the orientation of the clay platelets is a collective phenomenon due to mutual repulsion,49 enhancing the absolute value of the order parameter. As displayed in Figure 11, the same global enhancement of the absolute value of the order parameter induced by the mutual repulsions between the clay platelets (i.e., roughly 0.15) is detected for both magnetic fields. Such transition between independent and collective ordering of the clay platelets occurs well before the isotropic/biphasic/nematic phase transitions26,27 (c = 20.1 ( 0.1 g/L and c = 24.6 ( 0.1 g/L, respectively) and the sol/gel transition26,27 (c = 27.6 ( 0.05 g/L) in these aqueous dispersions of nontronite at the same ionic strength. As a consequence, NMR detection of the 2H quadrupolar coupling as a function of clay concentration provides a sensitive probe of the mutual interactions responsible for the mechanical behavior26,27 of these clay dispersions. This result is based on a single assumption: the specific orientation of the water molecules physisorbed on the basal surface of the clay platelets remains unaltered upon increasing clay concentration. Such an assumption appears reasonable, since the average separation between the clay platelets at the highest investigated concentration (c = 40 g/L) is
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Figure 11. Comparison between the influence of clay concentration c on the order parameter P2 quantifying the platelet orientation induced by the two static magnetic fields (i.e., B0 = 2.351 T and B0 = 8.465 T). The isotropic/biphasic/nematic and sol/gel transition lines are taken from the Figure 1 in ref 27.
around 380 Å, i.e., one order of magnitude larger than the clay separation at which specific water ordering is expected to occur (see Figures 5 and 7). Predictions from the GCMC simulations may also be used to evaluate the limiting slope displayed in Figure 6. Starting from eq 2a, we determine the fraction of water molecules at contact with the clay surface and contributing to the detected 2H NMR splitting. By taking into account the mass of the nontronite unit cell (845 g/mol), the total number of unit cells implied in the GCMC simulations (168, see section II.3), the number of confined water molecules predicted by the GCMC simulations (5216, see section II.3), and the concentration of bulk water, we obtain pS ¼
Cclay ðg=LÞ 5216 845 ðg=molÞ 168 55:5 ðmol=LÞ
¼ Cclay ðg=LÞ 6:62 104 ðL=gÞ
ð6Þ
By using eqs 2a2b and the absolute value of the order parameter describing the clay ordering induced in dilute conditions (i.e., 0.21, see above), we obtain a limiting slope (0.35 Hz 3 L/g) in qualitative agreement with the value detected in Figure 6 (0.71 Hz 3 L/g, see above). Additional information can be obtained by analyzing the influence of temperature on the residual splitting detected by 2 H NMR and thus the ordering of the clay platelets induced by the static magnetic field. For that purpose, the residual splitting is measured in the dilute regime (c = 4.52 g/L) at both magnetic fields (Figure 12a, b) in order to determine the influence of temperature on the intrinsic ordering of noninteracting platelets (see inset in Figure 6). From the ratio of these residual quadrupolar splittings, the influence of temperature on the volumetric anisotropy of the magnetic susceptibility of the nontronite clay can be extracted (cf. eqs 4a4c). As displayed in Table 1, the anisotropy of the magnetic susceptibility remains constant within the whole range of investigated temperatures (i.e., between 285 and 333 K). Table 1 also shows the influence of temperature on the order parameter characterizing the alignment of 14258
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Figure 13. Variation of the longitudinal R1 and transverse R2 relaxation rate constants as a function of clay concentration c for two different values of the static magnetic field B0.
Figure 12. Variation of the residual quadrupolar splitting νQ as a function of temperature detected at the two magnetic fields (i.e., B0 = 2.351 T (a) and B0 = 8.465 T (b)) within dilute clay dispersion (c = 4.52 g/L) corresponding to noninteracting clay platelets.
Table 1. Variations of the Anisotropy of the Magnetic Susceptibility |Δχ|/μ0 and of the Order Parameter |P2| for the Two Static Magnetic Fields B0 as a Function of the Temperature temperature
|Δχ|/μ0
(K)
(J 3 T2 3 m3)
|P2| (at 2.351 T)
|P2| (at 8.465 T)
285
37 ( 4
0.028 ( 0.003
0.23 ( 0.01
298
33 ( 3
0.024 ( 0.002
0.21 ( 0.01
333
34 ( 3
0.022 ( 0.002
0.20 ( 0.01
noninteracting platelets by the static magnetic field: a slight decrease (∼10%) is detected in the same temperature range. 2. Exchange between Free and Physisorbed Water Molecules. Finally, our analysis of clay ordering deduced from the 2H residual splitting (eqs 2a and 3) implicitly assumes a fast exchange, at the NMR times scale, between the populations of free and physisorbed water molecules. Measurements of the NMR relaxation relaxation times is the only way to settle that question since the characteristic relaxation times of free and physisorbed water molecules are the reference times to decide if the exchange between these two environments occurs fast at the NMR time scale.99,100 While the 2H relaxation rate constant of free water is
well characterized, the variation of the transverse and longitudinal 2H relaxation rate constants as a function of clay concentration (Figure 13) represents a first approach for extracting the characteristic relaxation rate constants of the physisorbed water molecules.73,101 The results obtained at the two magnetic field (8.465 et 2.351 T) are somewhat surprising: while the longitudinal relaxation rate constant remains almost unchanged in the whole range of clay concentrations, the transverse relaxation rate constant markedly increases and strongly depends on the applied magnetic field. Only two phenomena can explain such a difference between the longitudinal and transverse relaxation rate constants: either a slow exchange between the two spin populations99,100,102 or a slow modulation of the magnetic couplings61,103 responsible for the spin relaxation. Quadrupolar and dipolar couplings are the two relaxation mechanisms able to drive the NMR relaxation of the deuterium atoms within heavy water in the presence of nontronite. First, the quadrupolar relaxation mechanism is very efficient within heavy water because of the strength of the corresponding quadrupolar coupling (i.e., 210 kHz in eq 2) monitored by the fast reorientation of the OD director in the static magnetic field. Second, due to the large amount of iron in the clay network,26 the heterogeneous dipolar coupling is also an efficient relaxation mechanism for water molecules.60 This dipolar magnetic coupling is modulated not only by the reorientation of the water molecule near to the clay surface but also by its diffusion.61,103 In order to separately quantify the relative contribution of both relaxation mechanisms, multiquantum NMR relaxation measurements (see section II.2) were performed. As illustrated in Figure 14, three classes of apparent relaxation rate constants are easily identified: (1) the relaxation rate constants of the zero-order coherences (T10 and T20) are almost negligible and remain independent of clay concentration (see also Figure 13 for the T10 coherence); (2) the relaxation rate constants of the first-order coherences (T11 and T21) slightly increase with clay concentration (see also Figure 13 for the T11 coherence); (3) the relaxation rate constant of the second-order coherence (T22) markedly increases with clay concentration, reaching 60 s1 at high clay concentration corresponding to 30 times the relaxation rate constant of bulk heavy water. 14259
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Figure 14. Variation of the multiquantum relaxation rate constants Rij measured at B0 = 8.465 T as a function of clay concentration c.
Figure 15. Spectral densities JRi extracted from the analysis of the multiquantum relaxation rate constants Rij (cf. Figure 14 and see text).
In the presence of a static residual quadrupolar coupling (ωQ), it is not possible to extract the complete set of spectral densities60,81 describing the quadrupolar (JQ m , m ∈{0, 1, 2}) and dipolar (JPm, m ∈ {0, 1, 2}) relaxation mechanisms from the measured relaxation rate constants (see above). By using previous published data,60,81 we obtain R10 ¼ J1Q ðω0 Þ þ 4J2Q ð2ω0 Þ þ
1 P C 3
ð7aÞ
R11 ¼ R21 ¼
3 Q 3 2 J ð0Þ þ J1Q ðω0 Þ þ J2Q ð2ω0 Þ þ J0P ð0Þ 2 0 2 9 þ
1 P 1 C þ J1P ðωS Þ 2 3
ð7bÞ
R20 ¼ 3J1Q ðω0 Þ þ CP R22 ¼ J1Q ðω0 Þ þ 2J2Q ð2ω0 Þ þ þ
ð7cÞ 8 P 1 J0 ð0Þ þ CP 9 3
4 P J ðωS Þ 3 1
ð7dÞ
where CP ¼
1 P J ðωs ω0 Þ þ J1P ðω0 Þ þ 2J2P ðω0 þ ωs Þ 3 0
ð7eÞ
ω0 and ωs are the resonance angular velocities of deuterium and iron in the static magnetic field B0, respectively. The four independent measurements (see Figure 14) are not enough to extract each of these eight different spectral densities. We therefore decide first to group three spectral densities within a single variable CP (see eq 7e), second to neglect the highfrequency contribution from JP1 (ωS), and finally to assume the equality between the high-frequency spectral densities describing Q Q the quadrupolar coupling (JQ 1 (ω0) = J2 (2ω0) = C ). The resulting set of four linear equations is numerically solved by a matrix inversion, leading to four spectral densities quantifying the relative influence of the quadrupolar and dipolar couplings. As displayed in Figure 15, the heterogeneous dipolar coupling is the dominant relaxation mechanism (JP0 (0) . JQ m , m ∈ {0, 1, 2}).
Figure 16. Temperature variation of the multiquantum relaxation rate constants Rij (c = 34.19 g/L).
Figure 15 further confirms the condition of slow modulation of Q Q P magnetic couplings since JQ 0 (0) > Jm = C , m ∈ {1, 2}, and J0 (0) P . C . This last observation is fully compatible with our approach in which the high-frequency contribution from JP1 (ωS) has been neglected. Finally, the temperature variation of the multiquantum relaxation rate constants (Figure 16) is fully compatible with the fast exchange between the two spin populations pertaining respectively to the free and physisorbed water molecules. One may wonder about the large value of the spectral density (JP0 (0)) describing the heterogeneous dipolar coupling. On the basis of the previous evaluation of the fraction of the surface water molecules (eq 6), the values of JP0 (0) reported in Figure 15 require an intrinsic spectral density JP0 (0) 104 s1 for water molecules in the first hydration layer of the nontronite. Starting from our previous evaluation of the heterogeneous dipolar relaxation mechanism for water molecules confined between montmorillonite clay platelets,54,60 we multiply the corresponding spectral density by a factor of 10 in order to take into account the amount of iron within the network of nontronite.26 As displayed in Figure 17, the intrinsic spectral density describing the NMR relaxation of physisorbed water molecules becomes as high as 4000 s1 if their average residence time at the clay surface becomes as large as 100 ps. Such a residence time does not 14260
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Figure 17. Variation of the spectral density JP0 (0) describing the order of magnitude of the heterogeneous dipolar coupling as a function of the average residence time of water molecules physisorbed on the basal surface of nontronite clay platelets.
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and magnetic field strength. This analysis reveals a transition between two dynamical regimes corresponding to free and collective orientation of these anisotropic clay platelets. Since the transition detected by the NMR measurements occurs at clay concentration smaller than the concentrations corresponding to both the isotropic/biphasic/nematic and the sol/gel transitions, the analysis of the variation of the 2H residual quadrupolar splitting provides a very sensitive probe of the influence of interparticle couplings on the mechanical and dynamical behavior of these clay dispersions. Multiquantum NMR relaxation measurements were also performed in order to identify heterogeneous dipolar coupling as the main source of the 2H NMR relaxation within such aqueous dispersions of iron-rich clay platelets. Finally, the temperature variation of the 2H NMR relaxation rate constants is compatible with a fast exchange between the two spin populations corresponding to free and physisorbed water molecules, respectively. This result validates the central assumption used for analyzing the measured 2H residual quadrupolar splitting.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (A.D.);
[email protected] (P.P.).
’ ACKNOWLEDGMENT The DSX100 and DSX360 Bruker spectrometers used for that NMR study were purchased thanks to grants from Region Centre (France). ’ REFERENCES
Figure 18. Master curve suggesting a renormalization of the 2H residual quadrupolar splitting νQ and the difference of the relaxation rate constants R2 R1 as a function of the strength of the static magnetic field B0.
appears excessive since it corresponds to the time required by confined water molecules, with a self-diffusion coefficient56around 109 m2/s, to travel across 4 Å, i.e., the thickness of the first hydration layer (see Figure 7). An average residence time of 100 ps is also fully compatible with the condition of fast exchange between the two spin populations corresponding to free and physisorbed water molecules, respectively. Finally, Figure 18 may be used as a master curve for renormalizing the influence of magnetic field on the degree of ordering of clay platelets. This master curve fully reproduces the large influence of magnetic field strength B0 on both the residual quadrupolar coupling νQ (see Figure 6) and transverse relaxation rate constant R2 (see Figure 14).
IV. CONCLUSIONS Magnetic-field-induced orientation of clay nanoplatelets within dilute aqueous dispersions was determined by analyzing the variations of the 2H NMR residual quadrupolar splitting of physisorbed heavy water as a function of clay concentration
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