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X-Ray Scattering Investigation of Swelling Clay Fabric
Journal of Colloid and Interface Science 240, 211–218 (2001) doi:10.1006/jcis.2001.7690, available online at http://www.idealibrary.com on
X-Ray Scattering Investigation of Swelling Clay Fabric 1. The Dry State Isabelle Bihannic,∗,1 Denise Tchoubar,† Sandrine Lyonnard,‡ G´erard Besson,† and Fabien Thomas∗ ∗ Laboratoire Environnement et Min´eralurgie, INPL-ENSG-CNRS UMR 7569, 15, Avenue du Charmois, BP 40, 54501 Vandoeuvre Cedex, France; †Centre de Recherche sur la Mati`ere Divis´ee, CNRS-Universit´e d’Orl´eans, rue de Chartres, 45067 Orl´eans Cedex 2, France; and ‡Service de Chimie Mol´eculaire, CE Saclay, 91191 Gif sur Yvette Cedex, France Received January 30, 2001; accepted May 4, 2001; published online June 21, 2001
The solid phase geometry of a Na- and Ca-montmorillonite has been investigated by using ultra-small- and small-angle X-ray scattering and X-ray diffraction. The scattering domain covered by combining these techniques corresponds to characteristic distances ranging from a few angstroms to a micrometer. The intensity scattered on the whole scattering domain was decomposed into two terms, (i) one assigned to the structure of layers’ stacks and (ii) one ascribed to the porous network resulting from the entanglement of individual platelets. The comparison of experimental data with theoretical simulations revealed that the stacks of clay layers are complex and heterogeneous. Ordered stacks of approximately ˚ seem to be organized in larger parti10 layers separated by 9.5 A ˚ cles comprising around 100 layers. Distances between 25 and 150 A were observed within those particles. Both samples possess a low pore volume fraction of about a few percent, with pores characterized by a highly anisotropic shape. °C 2001 Academic Press Key Words: clay; montmorillonite; porosity; structure; texture; XRD; SAXS; USAXS.
INTRODUCTION
Clay minerals are finely divided silicates that are major components of soils and sediments, and that are widely used in many industrial applications (thickeners, drilling fluid, paints, etc.). Among the large variety of layered silicates, swelling clays such as smectites deserve special attention due to their specific interaction with water. The structure of these anisotropic minerals (about 1 nm thick with a lateral extension up to 1 µm) consists of two tetrahedral silica sheets sandwiching an aluminum or magnesium hydroxide octahedral sheet (1). The isomorphic substitutions in the tetrahedral and/or octahedral sheets by less charged cations generate a net negative layer charge compensated by interlayer exchangeable cations whose valency and hydration properties control both swelling and colloidal behavior (2–10).
1 To whom correspondence should be addressed. E-mail: isabelle.bihannic@ ensg.inpl-nancy.fr.
Since the pioneering work of Norrish (3) on Na-montmorillonite, clay scientists classically distinguish two swelling stages, i.e., intracrystalline and osmotic swelling. Intracrystalline swelling occurs for the lowest water contents (undersaturated systems) and corresponds to the first hydration steps of interlamellar spaces mainly through interlayer cation hydration (2, 4, 5, 11, 12). Osmotic swelling takes place for higher water contents (water activities around 0.98) and corresponds, for monovalent cations, to a further expansion of the clay layer spacing (3, 4, 13, 14). The beginning of osmotic swelling is associated with a large water uptake inducing major macroscopic modifications of the sample which evolves from a hydrated solid to a paste and then, for some monovalent cations, to a thixotropic gel. These changes in the mechanical and rheological properties not only involve the interlamellar spaces but also affect the whole range of porosity. For example, for water activities above 0.98 (water content >250–300 mg/g of dry clay for Na-montmorillonites (8, 15)), in addition to interlamellar spacings, all pore sizes (i.e., interparticulate and interaggregate pores (14, 16)) also begin to be concerned and are partially filled with water. A proper understanding of the textural modifications occurring upon water uptake and release and of the associated changes (swelling and shrinking) can then be obtained only from a multiscale description of the tridimensional organization of the clay structure under various water activities. This kind of approach has already been extensively used to describe water-saturated clay pastes by associating scattering experiments with rheology studies, to explore the arrangement and interrelationships of particles in the solvent (16–28). The combination of ultra-smallangle X-ray scattering (USAXS), small-angle X-ray scattering (SAXS), and X-ray diffraction (XRD) experiments appears to be an appropriate tool for such a purpose as it allows in situ investigations over all the desired length scales. The aim of the present study is to pursue this approach in the range classically defined as corresponding to crystalline swelling, i.e., water activities between 0 and 0.98. Instead of simply exploring layer expansion upon water addition, we will try to follow, from the angstrom to the micrometer level, all
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the textural and morphological changes associated with increasing water uptake in concentrated clay systems. However, in this kind of system, interpretation of scattering curves becomes more complex as upon concentration, due to entanglement, the notion of a structural unit starts to be inappropriate (29). For this reason, such a system must be interpreted using two complementary approaches focusing simultaneously on the quantitative and morphological evolutions of pores as well as on the structural changes in pore walls. This first paper describes in detail the organization of dry clay systems, for a reference swelling clay mineral, a Wyoming montmorillonite exchanged either with a monovalent (Na+ ) or with a divalent (Ca2+ ) interlayer cation.
holding scattering. The data were then desmeared according to an algorithm described by Lake (34). Small-angle scattering data were collected with a Huxley– Holmes type camera (CEA, Saclay) with CuK α radiation. The ˚ −1 to 0.4 A ˚ −1 . scattering domain covered ranges from 0.015 A The detector is a two-dimensional camera. Data were summed radially to express intensity as a function of the scattering vector. After correction of transmission and subtraction of the sampleholding scattering, intensity was directly expressed on an absolute scale, such that no desmearing procedure is needed. The overlapping of data obtained from both experiments validates the desmearing procedure used to process USAXS data. XRD
EXPERIMENTAL SECTION
Material The clay used in this study is a reference montmorillonite clay provided by the Clay Minerals Society (Swy-2, Crook County Repository, Wyoming). The clay was purified first by dispersion in pure water and sedimentation to remove impurities such as quartz and feldspars. Saturation of the exchange capacity was then achieved by successive dispersions in molar NaCl solutions and centrifugation. This step was repeated three times. The excess sodium chloride was removed by washing in pure water and centrifugation until the supernatant was chloride-free as checked by the silver nitrate test. The structural formula calculated from chemical analysis (30) can be written as (Si7.76 Al0.24 )IV (Al3.09 Mg0.49 Fe0.46 )V O20 (OH)4 (Na+ )0.73 .
The apparatus used for XRD measurements was specially developed to follow the different stages of hydration and dehydration of swelling clays (7, 8). This device includes a chamber that enables one to keep the sample under vacuum at a controlled temperature. The diffraction patterns were recorded using CoK α radiation in reflection geometry. The data were collected simultaneously over 60◦ (2θ ) with an INEL CPS 120 curved detector and were processed using a multichannel Varro analyzer (2048 channels for 60◦ ). The peaks were calibrated using the d001 and d002 peaks of standard kaolinite added in the oriented films. During the experiments, the samples were kept under a primary vacuum and the temperature was set at 30◦ C by circulating water in the jacket of the chamber. EXPERIMENTAL CURVES
The experimental diffraction patterns recorded for the sodium and calcium montmorillonites are displayed in Fig. 1.
Homoionic calcium montmorillonite was also prepared by dispersing the sodium montmorillonite three times in molar CaCl2 solutions. Scattering Experiments USAXS and SAXS experiments were carried out in transmission geometry with clay films placed in a closed sample-holder containing P2 O5 as a desiccating agent (drying efficiency of P2 O5 :residual water < 1 mg in 40,000 l of dry air (31)). The films were prepared by drying a montmorillonite suspension onto a kapton sheet. Films were kept dry in a closed chamber containing P2 O5 . Ultra-small-angle X-ray scattering experiments were performed with a Bonse–Hart type camera (CEA, Saclay, France). This set-up, developed by Lambard and Zemb (32), consists of a pair of multiple reflection channel-cut Ge(111) crystals used as monochromator and analyzer, allowing high-resolution measurements on a scattering vector (q = 4π sin(θ )/λ) range ˚ −1 (33). The X-ray source was a ˚ −1 to 0.03 A from 2.5 × 10−4 A 18-kW CuK α rotating anode. Data were collected with a scintillator. The absolute intensity was obtained after normalization with the sample transmission and subtraction of the sample-
FIG. 1. Observed X-ray diffractograms recorded under primary vacuum a (CoK α1 radiation, λ = 1.7889 A). (a) Sodium montmorillonite, (b) calcium montmorillonite.
X-RAY SCATTERING STUDY OF SWELLING CLAY FABRIC
Besides peaks originating from the montmorillonite, a few ˚ correadditional peaks are observed. Peaks at 7.13 and 3.56 A spond to kaolinite used as an internal reference to calibrate the ˚ is due to the pharcurved detector. The small hump at 3.88 A maceutical gaze on which the suspension is poured and that is used to increase the mechanical strength of the sample. The dry state of the sodium montmorillonite (Fig. 1a) appears homogeneous and is characterized by a basal spacing value d001 ˚ and harmonics at 4.8 and 3.2 A. ˚ These d values are of 9.6 A characteristic of the dry state, with no water molecules in the interlamellar space (7). In the case of calcium montmorillonite (Fig. 1b), the dry state ˚ and appears less homogeneous with a d001 distance at 10.1 A ˚ This d001 value is slightly higher than harmonics at 5 and 3 A. that previously obtained (9) on a calcium-exchanged montmo˚ and may be assigned to the presence of a few rillonite (9.8 A), residual water molecules in the interlamellar space. Figure 2 presents the evolution of the scattered intensity as a function of the scattering vector q (= 4π sin(θ)/λ) for both Na- and Ca-montmorillonite films. Relative intensities can be converted in absolute intensities by a proportional relationship, provided that the film thickness is known. For Camontmorillonite, the measured thickness was about 28 µm. For the Na sample, the film thickness was a posteriori evaluated using Beer–Lambert’s law. Taking into account errors related to both experimental accuracy and mass absorption coefficient calculations, the calculated thickness can be estimated to lie between 40 and 65 µm. For this reason, the curve corresponding to Na-montmorillonite is presented in relative units. In both cases, intensity decreases monotonically with q although different fields can clearly be distinguished. For lower q ˚ −1 ) the intensity decreases following a values (q < 2 × 10−3 A −2.4 decay. For larger q values, the slopes of the decay on the q
log–log plots are −3.3 for the Na sample and −3.2 for the Ca sample, respectively. DISCUSSION
The power law decay observed in Fig. 2 could be interpreted as resulting from a medium with a fractal surface (35) which is reminiscent of numerous studies that have applied fractal geometrical concepts to describe the structure of fragmented soils and clayey aggregates (36–41). Still, instead of using a fractal formalism, we rather chose to analyze clay films as a porous medium formed by the entanglement of flexible and highly anisotropic sheet stacks enclosing pores. The use of such a framework could be debated as the experimental scattering curves do not exhibit a q −4 intensity decay (Porod’s law) typical of porous media (42). However, when porous media do not fulfill all the conditions required for observing a Porod behavior (constant electronic density over each phase, sharp interfaces), systematic deviations from Porod’s law are observed (43–45). A typical example of such a deviation was observed for graphite, on the one hand containing flake components a few angstroms thick, and on the other hand where the interlayer distances fluctuate around a mean value (46). A more recent study on anthracites (47) illustrates this kind of deviation from Porod’s law, when materials presenting a composite structure (i.e., flattened pores and lamellar organization) are concerned. On the basis of theoretical considerations Pons (48) suggested that such deviations could also be observed for other lamellar materials such as clay minerals. Following such assumptions, we tentatively assign the deviation from Porod’s law (−3.3, −3.2 decay) observed in our system to heterogeneities of the solid clay phase which can be considered as a lamellar material with both stacking faults and ˚ thick (20). additional lenticular micropores 30 to 40 A Scattering results will then be interpreted by considering a biphasic system where one phase is the clay matrix with numerous structural defects and the other phase corresponds to pores of various sizes and shapes. To quantify the extent of deviation from Porod’s law for which the scattering intensity follows a q −4 decay (42), the product q 4 I was plotted as a function of q 2 (Fig. 3). For the Na- (resp. ˚ −1 ˚ −1 < q < 0.04 A Ca-) montmorillonite, on the range 0.01 A ˚ −1 < q < 0.07 A ˚ −1 ), q 4 I is a linear function of q 2 . (resp. 0.03 A Over this scattering vector range, the total intensity can then be expressed as a sum of two terms: q 4 Itotal = aq 2 + b.
FIG. 2. Log–log plots of ultra-small- and small-angle X-ray scattering from montmorillonite in a dry state. (a) Sodium montmorillonite, (b) calcium montmorillonite.
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[1]
The constant b term follows Porod’s law and the intensity corresponding to this term can be called IPorod , where IPorod can be expressed as b/q 4 . IPorod corresponds to scattering by a porous medium. The additional component aq 2 is assigned to the contribution of the clay stack’s inner structure and the corresponding intensity called Istruct can be expressed as a/q 2 in this scattering vector range.
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˚ −1 , Istruct becomes predominant and the scattered intensity 0.1 A is mainly sensitive to local arrangement in pore walls (drawing 3, Fig. 4a). In the intermediate range, both structure and porosity have to be taken into account. Porous Medium
FIG. 3. Plots of the product q 4 I (q) as a function of q 2 . The product q 4 I (q) exhibits a linear deviation from Porod’s law. In this scattering vector range, q 4 I (q) can be expressed as a sum of two terms: the first one is called q 4 IPorod and follows Porod’s law, the second one q 4 Istruct is the linear deviation assigned to the structure.
Such a decomposition is illustrated in Fig. 4. For low q val˚ −1 ) the additional component is negligible. ues (q < 2 × 10−2 A Therefore, for the range of distances probed in such a q domain, the system can be assimilated to a true porous medium with two phases, both homogeneous in electronic density. In other words, on this scale, the structure of the solid matter is no longer apparent (drawing 2 in Fig. 4a). An increase in q corresponds to a zoom into the probed material, which progressively reveals more of the local structure, and consequently improves the relative proportion of Istruct over IPorod . For q values higher than
FIG. 4. Log–log plot of the total intensity decomposed into the two terms defined in Fig. 3. The schematic drawing shown in inset of (a) illustrates this decomposition: the first term called IPorod (2) corresponds to the intensity scattered by a porous medium whose pore walls have a uniform electronic density (without structure) and the second term Istruct (3) is relative to the structure of the walls.
IPorod can be analyzed according to the formalism developed for porous media described in reference books (49, 50). The system is then considered as an isotropic two-phase system with constant electronic densities over each phase. The two phases are (i) the solid matter described by its electronic density ρm and volume fraction φm and (ii) the pores, with volume fraction (i.e., porosity) φ p (φm + φp = 1) and electronic density ρp . For such a system, the scattered intensity per unit volume can be expressed as Z I (q) = A2e (ρm − ρp )2 φm φp
4πr 2 γ0 (r )
sin(qr ) dr, qr
[2]
where A2e is the Thomson factor, i.e., the intensity scattered by an electron, and γ0 (r ) is the Porod’s characteristic correlation function normalized to 1 for r = 0. γ0 (r ) is proportional to the probability that if one point lies in phase m (resp. p) a second point distant from r also lies in m (resp. p) (42). This correlation function can be expressed as a function of intensity by inverse Fourier transform: 1 γ0 (r ) = 2 2 2π Ae (ρm − ρp )2 φm φp
Z q 2 I (q)
sin qr dq. qr
[3]
Resolution and maximum size of heterogeneities. The maximum particle or heterogeneity size that is fully probed in a scattering experiment is related to the minimum scattering vector qmin by the relation D ≤ π/qmin . For experimental reasons, the minimum scattering vector is different for both sam˚ and D ≤ 7850 A ˚ for Na- and Caples with D ≤ 11 200 A montmorillonite, respectively. The resolution in real space for γ0 (r ) is given by the sampling theorem of Fourier transform and by introducing a sampling distance that follows the condition 1r ≥ π/qmax , where qmax is the maximum experimental scattering vector. For our experiments, qmax was chosen as the q value for which Istruct becomes predom˚ and 1r ≥ 45 A ˚ inant. The calculated values are then 1r ≥ 78 A for the Na- and Ca-montmorillonite, respectively. Porosity. Assuming a pore-diluted system (φp ¿ 1) Eq. [2] can be simplified, which allows one to calculate the porosity owing to the normalizing condition γ0 (0) = 1: φp =
1 2 2 2π Ae (ρm − ρp )2
Z q 2 I (q) dq.
[4]
Porosity values calculated with Eq. [4] correspond to the porosity probed by X-ray scattering, i.e., resulting from electronic
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TABLE 1 Calculated Values Relative to Porosity and Pore Shape for Na- and Ca-Montmorillonite
Sodium montmorillonite Calcium montmorillonite
Porosity (%)
Pore’s mean chord length a (A)
Modal values of the distance distribution a f (r ) (A)
1.6–2.5 1.5
621 271
311 224
density heterogeneities. The calculated values then depend on the experimental conditions that impose both resolution (a few nanometers) and maximal length scale probed (around 1 µm). For Na-montmorillonite, two porosity values were calculated corresponding to the minimal and maximal values of the evaluated film thickness. The true porosity value is assumed to belong to this interval, between 1.6 and 2.5%. The porosity of the calcium montmorillonite was calculated to be 1.5% (Table 1). For both samples, the low porosity value obtained confirms the assumption of a pore-diluted system. The calculated porosity values reveal that the clay films are extremely compact as illustrated on the micrograph (Fig. 5) recorded with a Hitachi
FIG. 6. Schematic illustration of chords. A chord is the intercept segment between a line crossing the system and pores (lp ) or matter (lm ).
S 2500 scanning electron microscope on another dry calcium montmorillonite film. The observed clay film is a few micrometers thicker than the one used in SAXS and USAXS experiments. Pore’s mean chord length. With a pore-diluted system assumption, the pore’s mean chord length can be calculated from the asymptotic limit of Porod’s law: lim
q→∞
8π q 4 I (q) = , 2 2 Ae (ρm − ρp ) φp l¯p
[5]
where l¯p represents the pore’s mean chord length, as illustrated in Fig. 6. Calculated values are displayed in Table 1. It must be pointed out that these values do not correspond to true mean pore sizes and must be considered as dimension indicators. Distance distributions functions. Pore shape can be approached by calculating the distance distribution functions that are deduced from Porod’s characteristic function γ0 (r ). Two kinds of distance distribution functions (50) can be calculated:
FIG. 5. Scanning electron micrograph obtained, in secondary electron emission mode, on the section of a dry film of Ca-montmorillonite.
P(r ) = r 2 γ0 (r )
[6]
f (r ) = r γ0 (r ).
[7]
As γ0 (r ) is an autocorrelation function, i.e., the probability that a segment of length r is located within a pore, and P(r ) and f (r ) are equivalent to a square distance and a distance, respectively. Generally, f (r ) is used preferably for characterizing lamellar pores. The f (r ) distance distributions calculated for both samples are shown in Fig. 7. In order to obtain more information about the physical meaning of such distributions, similar distribution functions were calculated for a set of ellipsoids with two equal ˚ and a variable half-axes c (50). half-axes a and b (= 5000 A) The ratio v (= c/a) is then indicative of the spheroidal character of those ellipsoids. Figure 7 clearly reveals that an elongated ellipsoid with a v value around 0.07 represents the best
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Structure The structure of particles can be analyzed using two different sets of experimental data: (i) the additional component Istruct originating from small-angle scattering and (ii) XRD patterns. In contrast with the procedure used for interpreting USAXS and SAXS data, a joint analysis of Istruct and XRD data cannot be achieved as XRD data were obtained in reflection mode while SAXS data were recorded using a transmission mode. As a consequence XRD results and SAXS results will be examined separately. Bragg angular domain. XRD patterns were used to analyze the characteristic distances inside layer stacks. They were simulated using the formalism developed for studying diffraction by lamellar structures (51), that was applied on many clay systems to study swelling and/or structure (7–9, 18–20, 52–56). According to such a formalism, the intensity diffracted by a powder formed by infinite layered particles can be written as I00 (q) ≈
1 X α(M)Spur{Re{[F][W ][R]}}, q2 M
[8]
where α(M) is the distribution of the number of layers per stack, and [F] and [W ] are respectively a diagonal matrix containing the relative proportions of the different types of layers and a square matrix containing the structure factors. The elements of the matrix [Q] are dependent on all the possible phase differences between the waves diffracted by adjacent layers. The XRD patterns were simulated using the above equation with software developed by Besson and Kerm (55) at CRMD, University of Orl´eans, France. As previously discussed (8), the comparison of simulated XRD patterns with experimental ones is not straightforward due to the experimental procedure used, i.e., reflection conditions associated with a curved detector. As a consequence, the criterion of agreement between experimental and calculated curves relies more on peak positions (main reflections and harmonics) than on peak shapes and relative intensities. The values derived from the simulation procedure are displayed in Table 2. For sodium
FIG. 7. Distance distribution functions f (r ). The functions displayed in (c) a are calculated for three ellipsoids with two equal half-axes a and b (= 5000 A), and a variable half-axis c. v is the ratio c/a, and is indicative of the ellipsoid’s spheroidal character.
approximation for matching the experimental f (r ) of both Naand Ca-montmorillonites. This confirms the lenticular character ˚ A full modeling of experiof pores in the range 50–7000 A. mental distance distributions would require the introduction of both size and shape polydispersity, which is rather difficult to implement.
TABLE 2 Parameters Used to Simulate the XRD Patterns
M (mean number of layers per stack) Interlamellar distances distribution
Sodium montmorillonite
Calcium montmorillonite
10
10
a 100% at 9.55 A (dry sate)
a 90% at 9.55 A (dry sate) a 10% at 12.5 A (one water layer)
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CONCLUDING REMARKS
FIG. 8. Simulation of Istruct in the intermediate domain between diffraction and small-angle scattering. The distance distributions used in the calculations are displayed on the plots in the inset.
montmorillonite, the dry state is quasi homogeneous, with a ˚ The interlamellar space does not distance repetition of 9.55 A. appear to contain any water molecules. The mean number of layers per stack is estimated to be around 10. For calcium montmorillonite, some water molecules are still present in the inter˚ a value layer space: about 10% of the layers are at 12.55 A, characterizing the one-water-layer hydrated state. Such a difference between Na- and Ca-montmorillonite can be assigned to the high hydration energy of Ca2+ ions that are then difficult to fully dehydrate. Intermediate domain between diffraction and small-angle scattering. The intensity increase toward the small-angle scattering domain was simulated using the same equation ([8]) as the one used to model XRD patterns. Larger distances and larger stack thickness were introduced to account for the larger angular domain probed. The simulation results are displayed in Fig. 8. Calculations were performed using stacks formed by 100 el˚ distances ementary layers per stack. In addition to the 9.5-A corresponding to the dry state, larger distances between 25 and ˚ (resp. 100 A) ˚ for the Na- (resp. Ca-) montmorillonite 150 A were needed to obtain a proper fit. The distribution of these large distances is almost homogeneous which can be interpreted as corresponding to areas where substacks of dry layers are separated from each other by continuously varying distances. On this length scale the material appears less compact with an intermediate porosity introduced by the largest distances. The amount of such a porosity is not negligible as the probability of find˚ is roughly the same as the ing an open space (larger than 20 A) probability of having a dry compact stacking with an interlayer ˚ distance of 9.5 A.
Using a combination of X-ray scattering and X-ray diffraction experiments, the structure of clay films can be probed in situ over a wide distance range, i.e., from a few angstroms to about a micrometer. Our interpretation is based on the assumption that dry clays can be considered as porous materials with a ˚ µm observation domain, structured solid phase. In the 50 A–1 the medium appears as rather dense with a low porosity (1– 2%) formed by anisotropically shaped pores (lenticular pores). Calcium montmorillonite appears slightly less porous and exhibits lower mean chord lengths and lower modal values of f (r ) (Table 1). This suggests a denser packing which could be due to the lower flexibility of Ca-montmorillonite stacks compared with Na-montmorillonite ones (40, 57). However, the observed differences may also be due to variations in the polydispersity of pore size and shapes that are rather difficult to approach. ˚ domain, the combination of XRD and SAXS In the 5–100 A reveals a complex and heterogeneous nature of pore walls. Or˚ seem dered stacks of approximately 10 layers separated by 9.5 A to be organized in larger particles comprising around 100 layers. ˚ are observed In those particles, distances between 25 and 150 A which may be tentatively assigned to lenticular micropores. The porosity introduced by the largest distances in an additional porosity that is not taken into account in the porosity values calculated in the largest length scale range (Porod’s region). Indeed, the distance distribution functions were calculated from the term Istruct after separation of the total intensity into two terms. In contrast, the calculated porosities were derived from the second term, i.e., IPorod . As in the previous observation domain, Ca-montmorillonite ˚ are appears less porous as no distances higher than 100 A
FIG. 9. Schematic illustration of the dry clay system according to the 3scale domains individualized to describe the clay fabric. (1) Ultra-small-angle scattering range, (2) intermediate domain between diffraction and scattering, and (3) XRD area.
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detected. A clearer picture of the organization in this size range would certainly be obtained if XRD patterns were recorded in transmission mode, allowing a real joint analysis on the complete q scattering vector domain. The general picture derived from this observation (Fig. 9) reveals a really complex organization where no structural unit corresponding to each observation scale can be clearly defined. This is particularly acute in what we referred to as the intermediate zone between XRD and SAXS as in this size range, various distances can be observed which are difficult to assign unambiguously. In that regard, the separation we performed in different ranges may be partially artificial. Still, the picture obtained in this study represents a sound basis for understanding the textural and morphological evolution of clay systems upon water adsorption as will be described in a forthcoming paper. ACKNOWLEDGMENTS The authors thank Dr. Pierre Levitz (CRMD) for very fruitful discussions and assistance with USAXS experiments. Drs. L. J. Michot and B. S. Lartiges are acknowledged for their help. I.B. thanks R´egion Centre for financial support.
REFERENCES 1. Newman, A. C. D., Ed., “Chemistry of Clays and Clay Minerals,” Mineralogical Society, London, 1987. 2. Mooney, R. W., Keenan, A. G., and Wood, L. A., J. Am. Chem. Soc. 74, 1371 (1952). 3. Norrish, K., Discuss. Faraday Soc. 18, 120 (1954). 4. Norrish, K., and Raussell-Colom, J. A., Clays Clays Miner. 10, 123 (1963). 5. Sposito, G., and Prost, R., Chem. Rev. 82, 553 (1982). 6. Slade, P. G., and Quirk, J. P., J. Colloid Interface Sci. 176, 308 (1991). 7. Cases, J. M., B´erend, I., Besson, G., Fran¸cois, M., Uriot, J. P., Thomas, F., and Poirier, J. E., Langmuir 8, 2730 (1992). 8. B´erend, I., Cases, J. M., Fran¸cois, M., Uriot, J. P., Michot, L. J., Masion, A., and Thomas, F., Clays Clay Miner. 43, 324 (1995). 9. Cases, J. M., B´erend, I., Fran¸cois, M., Uriot, J. P., Michot, L. J., and Thomas, F., Clays Clay Miner. 45, 8 (1997). 10. Helmy, A., J. Colloid Interface Sci. 207, 128 (1998). 11. Glaeser, R., and M´ering, J., C. R. Acad. Sci. Paris t. 267 S´erie D, 463 (1968). 12. Suquet, H., and Pezerat, H., Clays Clay Miner. 35, 353 (1987). 13. Van Olphen, H., “An introduction to clay colloid chemistry,” 2nd Ed., Wiley, New York, 1977. 14. G¨uven, N., in “Clay–water interface and its rheological implications” (N. G¨uven and R. M. Pollastro, Eds.), p. 2, CMS Workshop Lectures, Clay Minerals Society, Boulder, CO, 1992. 15. Boek, E. S., Coveney, P. V., and Skipper, N. T., Langmuir 11, 4629 (1995). 16. Touret, O., Pons, C. H., Tessier, D., and Tardy, Y., Clay Miner. 25, 217 (1990). 17. Cebula, D. J., Thomas, R. K., Middleton, S., Ottewill, R. H., and White, J. W., Clays Clay Miner. 27, 39 (1979). 18. Pons, C. H., Rousseaux, F., and Tchoubar, D., Clay Miner. 16, 23 (1981). 19. Pons, C. H., Rousseaux, F., and Tchoubar, D., Clay Miner. 17, 327 (1982). 20. Ben Rha¨ıem, H., Tessier, D., and Pons, C. H., Clay Miner. 21, 9 (1986). 21. Ramsay, J. D. F., J. Colloid Interface Sci. 109, 441 (1986).
22. Ramsay, J. D. F., Swanton, S. W., and Bunce, J., J. Chem. Soc., Faraday Trans. 86, 3919 (1990). 23. Ramsay, J. D. F., and Lindner, P., J. Chem. Soc., Faraday Trans. 89, 4207 (1993). 24. Morvan, M., Espinat, D., Lambard, J., and Zemb, Th., Colloids Surf. 82, 193 (1994). 25. Morvan, M., Espinat, D., Vascon, R., Lambard, J., and Zemb, Th., Langmuir 10, 2566 (1994). 26. Mourchid, A., Delville, A., Lambard, J., L´ecolier, E., and Levitz, P., Langmuir 11, 1942, (1995). 27. Abend, S., and Lagaly, G., Appl. Clay Sci. 16, 201 (2000). 28. Levitz, P., L´ecolier, E., Mourchid, A., Delville, A., and Lyonnard, S., Europhys. Lett. 49, 672 (2000). 29. Tessier, D., in “Soil Colloids and their Associations in Aggregrates” (M. F. De Boodt, M. H. B. Hayes, and A. Herbillon, Eds.), p. 387, NATO ASI Series, Plenum Press, New York, 1990. 30. Vantelon, D., Pelletier, M., Barres, O., Thomas, F., Michot, L. J., Clay Miner. (2001), in press. 31. “CRC Handbook of Chemistry and Physics” (D. R. Lide and H. P. R. Frederikse, Eds.), pp. 15–26, CRC Press, Boca Raton, 1993. 32. Lambard, J., and Zemb, Th., J. Appl. Crystallogr. 24, 555 (1991). 33. Lambard, J., Lesieur, P., and Zemb, Th., J. Phys. I Fr. 2, 1191 (1992). 34. Lake, J. A., Acta Crystallogr. 23, 938 (1967). 35. Schmidt, P. W., in “Characterization of Porous Solids” (K. K. Unger et al., Eds.), Elsevier, Amsterdam, 1988. 36. Van Damme, H., and Ben Ohoud, M., in “Disorder and Fracture” (J. C. Charmet et al., Eds.), p. 105, Plenum Press, New York, 1990. 37. Rieu, M., and Sposito, G., Soil Sci. Soc. Am. J. 55, 1231 (1991). 38. Rieu, M., and Sposito, G., Soil Sci. Soc. Am. J. 55, 1239 (1991). 39. Erzan, A., and G¨ung¨or, N., J. Colloid Interface Sci. 176, 301 (1995). 40. Van Damme, H., in “Fractals in Soil Science” (P. Baveye, J. Y. Parlange, and B. A. Stewart, Eds.), p. 55, CRC Press, Boca Raton, 1998. 41. Lee, J.-F., Lee, C.-K., and Juang, L.-C., J. Colloid Interface Sci. 217, 172 (1999). 42. Porod, G., in “Small angle X-ray scattering” (O. Glatter and O. Kratky, Eds.), p. 17, Academic Press Inc., London, 1982. 43. Ruland, W., J. Appl. Crystallogr. 4, 70 (1971). 44. Perret, R., and Ruland, W., J. Appl. Crystallogr. 1, 308 (1968). 45. Perret, R., and Ruland, W., J. Appl. Crystallogr. 2, 209 (1969). 46. Schiller, C., and M´ering, J., C. R. Acad. Sci. Paris t. 264, 247 (1967). 47. Cohaut, N., Blanche, C., Dumas, D., Guet, J. M., and Rouzaud, J. N., Carbon 38, 1391 (2000). 48. Pons, C. H., “Mise en e´ vidence des relations entre la texture et la structure dans les syst`emes eau-smectites par diffusion aux petits angles du rayonnement X synchrotron,” Thesis, Universit´e d’Orl´eans, France, 1980. 49. Guinier, A., and Fournet, G., “Small-angle scattering of X-rays,” Wiley, New York, 1955. 50. Glatter, O., and Kratky, O., “Small angle X-ray scattering,” Academic Press Inc., London, 1982. 51. Drits, V. A., Tchoubar, C., “X-ray diffraction by disordered lamellar structures,” Springer-Verlag, Berlin, 1990. 52. Plan¸con, A., and Tchoubar, C., J. Appl. Crystallogr. 9, 279 (1976). 53. Besson, G., Glaeser, R., Tchoubar, C., Clay Miner. 18, 11 (1983). 54. Ben Brahim, J., Armagan, N., Glaeser, R., and Tchoubar, C., Clay Miner. 21, 111 (1986). ´ 55. Kerm, A. G., “Etude et caract´erisation des premiers stades d’hydratation d’une nontronite,” Thesis, Universit´e d’Orl´eans, France, 1988. 56. Faisandier, K., Pons, C. H., Tchoubar, D., and Thomas, F., Clays Clay Miner. 46, 636 (1998). 57. Zabat, M., Vayer-Besan¸con, M., Harba, R., Bonnamy, S., and Van Damme, H., Prog. Colloid Polym. Sci. 105, 96 (1997).
X-Ray Scattering Investigation of Swelling Clay Fabric 1. The Dry State Isabelle Bihannic,∗,1 Denise Tchoubar,† Sandrine Lyonnard,‡ G´erard Besson,† and Fabien Thomas∗ ∗ Laboratoire Environnement et Min´eralurgie, INPL-ENSG-CNRS UMR 7569, 15, Avenue du Charmois, BP 40, 54501 Vandoeuvre Cedex, France; †Centre de Recherche sur la Mati`ere Divis´ee, CNRS-Universit´e d’Orl´eans, rue de Chartres, 45067 Orl´eans Cedex 2, France; and ‡Service de Chimie Mol´eculaire, CE Saclay, 91191 Gif sur Yvette Cedex, France Received January 30, 2001; accepted May 4, 2001; published online June 21, 2001
The solid phase geometry of a Na- and Ca-montmorillonite has been investigated by using ultra-small- and small-angle X-ray scattering and X-ray diffraction. The scattering domain covered by combining these techniques corresponds to characteristic distances ranging from a few angstroms to a micrometer. The intensity scattered on the whole scattering domain was decomposed into two terms, (i) one assigned to the structure of layers’ stacks and (ii) one ascribed to the porous network resulting from the entanglement of individual platelets. The comparison of experimental data with theoretical simulations revealed that the stacks of clay layers are complex and heterogeneous. Ordered stacks of approximately ˚ seem to be organized in larger parti10 layers separated by 9.5 A ˚ cles comprising around 100 layers. Distances between 25 and 150 A were observed within those particles. Both samples possess a low pore volume fraction of about a few percent, with pores characterized by a highly anisotropic shape. °C 2001 Academic Press Key Words: clay; montmorillonite; porosity; structure; texture; XRD; SAXS; USAXS.
INTRODUCTION
Clay minerals are finely divided silicates that are major components of soils and sediments, and that are widely used in many industrial applications (thickeners, drilling fluid, paints, etc.). Among the large variety of layered silicates, swelling clays such as smectites deserve special attention due to their specific interaction with water. The structure of these anisotropic minerals (about 1 nm thick with a lateral extension up to 1 µm) consists of two tetrahedral silica sheets sandwiching an aluminum or magnesium hydroxide octahedral sheet (1). The isomorphic substitutions in the tetrahedral and/or octahedral sheets by less charged cations generate a net negative layer charge compensated by interlayer exchangeable cations whose valency and hydration properties control both swelling and colloidal behavior (2–10).
1 To whom correspondence should be addressed. E-mail: isabelle.bihannic@ ensg.inpl-nancy.fr.
Since the pioneering work of Norrish (3) on Na-montmorillonite, clay scientists classically distinguish two swelling stages, i.e., intracrystalline and osmotic swelling. Intracrystalline swelling occurs for the lowest water contents (undersaturated systems) and corresponds to the first hydration steps of interlamellar spaces mainly through interlayer cation hydration (2, 4, 5, 11, 12). Osmotic swelling takes place for higher water contents (water activities around 0.98) and corresponds, for monovalent cations, to a further expansion of the clay layer spacing (3, 4, 13, 14). The beginning of osmotic swelling is associated with a large water uptake inducing major macroscopic modifications of the sample which evolves from a hydrated solid to a paste and then, for some monovalent cations, to a thixotropic gel. These changes in the mechanical and rheological properties not only involve the interlamellar spaces but also affect the whole range of porosity. For example, for water activities above 0.98 (water content >250–300 mg/g of dry clay for Na-montmorillonites (8, 15)), in addition to interlamellar spacings, all pore sizes (i.e., interparticulate and interaggregate pores (14, 16)) also begin to be concerned and are partially filled with water. A proper understanding of the textural modifications occurring upon water uptake and release and of the associated changes (swelling and shrinking) can then be obtained only from a multiscale description of the tridimensional organization of the clay structure under various water activities. This kind of approach has already been extensively used to describe water-saturated clay pastes by associating scattering experiments with rheology studies, to explore the arrangement and interrelationships of particles in the solvent (16–28). The combination of ultra-smallangle X-ray scattering (USAXS), small-angle X-ray scattering (SAXS), and X-ray diffraction (XRD) experiments appears to be an appropriate tool for such a purpose as it allows in situ investigations over all the desired length scales. The aim of the present study is to pursue this approach in the range classically defined as corresponding to crystalline swelling, i.e., water activities between 0 and 0.98. Instead of simply exploring layer expansion upon water addition, we will try to follow, from the angstrom to the micrometer level, all
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the textural and morphological changes associated with increasing water uptake in concentrated clay systems. However, in this kind of system, interpretation of scattering curves becomes more complex as upon concentration, due to entanglement, the notion of a structural unit starts to be inappropriate (29). For this reason, such a system must be interpreted using two complementary approaches focusing simultaneously on the quantitative and morphological evolutions of pores as well as on the structural changes in pore walls. This first paper describes in detail the organization of dry clay systems, for a reference swelling clay mineral, a Wyoming montmorillonite exchanged either with a monovalent (Na+ ) or with a divalent (Ca2+ ) interlayer cation.
holding scattering. The data were then desmeared according to an algorithm described by Lake (34). Small-angle scattering data were collected with a Huxley– Holmes type camera (CEA, Saclay) with CuK α radiation. The ˚ −1 to 0.4 A ˚ −1 . scattering domain covered ranges from 0.015 A The detector is a two-dimensional camera. Data were summed radially to express intensity as a function of the scattering vector. After correction of transmission and subtraction of the sampleholding scattering, intensity was directly expressed on an absolute scale, such that no desmearing procedure is needed. The overlapping of data obtained from both experiments validates the desmearing procedure used to process USAXS data. XRD
EXPERIMENTAL SECTION
Material The clay used in this study is a reference montmorillonite clay provided by the Clay Minerals Society (Swy-2, Crook County Repository, Wyoming). The clay was purified first by dispersion in pure water and sedimentation to remove impurities such as quartz and feldspars. Saturation of the exchange capacity was then achieved by successive dispersions in molar NaCl solutions and centrifugation. This step was repeated three times. The excess sodium chloride was removed by washing in pure water and centrifugation until the supernatant was chloride-free as checked by the silver nitrate test. The structural formula calculated from chemical analysis (30) can be written as (Si7.76 Al0.24 )IV (Al3.09 Mg0.49 Fe0.46 )V O20 (OH)4 (Na+ )0.73 .
The apparatus used for XRD measurements was specially developed to follow the different stages of hydration and dehydration of swelling clays (7, 8). This device includes a chamber that enables one to keep the sample under vacuum at a controlled temperature. The diffraction patterns were recorded using CoK α radiation in reflection geometry. The data were collected simultaneously over 60◦ (2θ ) with an INEL CPS 120 curved detector and were processed using a multichannel Varro analyzer (2048 channels for 60◦ ). The peaks were calibrated using the d001 and d002 peaks of standard kaolinite added in the oriented films. During the experiments, the samples were kept under a primary vacuum and the temperature was set at 30◦ C by circulating water in the jacket of the chamber. EXPERIMENTAL CURVES
The experimental diffraction patterns recorded for the sodium and calcium montmorillonites are displayed in Fig. 1.
Homoionic calcium montmorillonite was also prepared by dispersing the sodium montmorillonite three times in molar CaCl2 solutions. Scattering Experiments USAXS and SAXS experiments were carried out in transmission geometry with clay films placed in a closed sample-holder containing P2 O5 as a desiccating agent (drying efficiency of P2 O5 :residual water < 1 mg in 40,000 l of dry air (31)). The films were prepared by drying a montmorillonite suspension onto a kapton sheet. Films were kept dry in a closed chamber containing P2 O5 . Ultra-small-angle X-ray scattering experiments were performed with a Bonse–Hart type camera (CEA, Saclay, France). This set-up, developed by Lambard and Zemb (32), consists of a pair of multiple reflection channel-cut Ge(111) crystals used as monochromator and analyzer, allowing high-resolution measurements on a scattering vector (q = 4π sin(θ )/λ) range ˚ −1 (33). The X-ray source was a ˚ −1 to 0.03 A from 2.5 × 10−4 A 18-kW CuK α rotating anode. Data were collected with a scintillator. The absolute intensity was obtained after normalization with the sample transmission and subtraction of the sample-
FIG. 1. Observed X-ray diffractograms recorded under primary vacuum a (CoK α1 radiation, λ = 1.7889 A). (a) Sodium montmorillonite, (b) calcium montmorillonite.
X-RAY SCATTERING STUDY OF SWELLING CLAY FABRIC
Besides peaks originating from the montmorillonite, a few ˚ correadditional peaks are observed. Peaks at 7.13 and 3.56 A spond to kaolinite used as an internal reference to calibrate the ˚ is due to the pharcurved detector. The small hump at 3.88 A maceutical gaze on which the suspension is poured and that is used to increase the mechanical strength of the sample. The dry state of the sodium montmorillonite (Fig. 1a) appears homogeneous and is characterized by a basal spacing value d001 ˚ and harmonics at 4.8 and 3.2 A. ˚ These d values are of 9.6 A characteristic of the dry state, with no water molecules in the interlamellar space (7). In the case of calcium montmorillonite (Fig. 1b), the dry state ˚ and appears less homogeneous with a d001 distance at 10.1 A ˚ This d001 value is slightly higher than harmonics at 5 and 3 A. that previously obtained (9) on a calcium-exchanged montmo˚ and may be assigned to the presence of a few rillonite (9.8 A), residual water molecules in the interlamellar space. Figure 2 presents the evolution of the scattered intensity as a function of the scattering vector q (= 4π sin(θ)/λ) for both Na- and Ca-montmorillonite films. Relative intensities can be converted in absolute intensities by a proportional relationship, provided that the film thickness is known. For Camontmorillonite, the measured thickness was about 28 µm. For the Na sample, the film thickness was a posteriori evaluated using Beer–Lambert’s law. Taking into account errors related to both experimental accuracy and mass absorption coefficient calculations, the calculated thickness can be estimated to lie between 40 and 65 µm. For this reason, the curve corresponding to Na-montmorillonite is presented in relative units. In both cases, intensity decreases monotonically with q although different fields can clearly be distinguished. For lower q ˚ −1 ) the intensity decreases following a values (q < 2 × 10−3 A −2.4 decay. For larger q values, the slopes of the decay on the q
log–log plots are −3.3 for the Na sample and −3.2 for the Ca sample, respectively. DISCUSSION
The power law decay observed in Fig. 2 could be interpreted as resulting from a medium with a fractal surface (35) which is reminiscent of numerous studies that have applied fractal geometrical concepts to describe the structure of fragmented soils and clayey aggregates (36–41). Still, instead of using a fractal formalism, we rather chose to analyze clay films as a porous medium formed by the entanglement of flexible and highly anisotropic sheet stacks enclosing pores. The use of such a framework could be debated as the experimental scattering curves do not exhibit a q −4 intensity decay (Porod’s law) typical of porous media (42). However, when porous media do not fulfill all the conditions required for observing a Porod behavior (constant electronic density over each phase, sharp interfaces), systematic deviations from Porod’s law are observed (43–45). A typical example of such a deviation was observed for graphite, on the one hand containing flake components a few angstroms thick, and on the other hand where the interlayer distances fluctuate around a mean value (46). A more recent study on anthracites (47) illustrates this kind of deviation from Porod’s law, when materials presenting a composite structure (i.e., flattened pores and lamellar organization) are concerned. On the basis of theoretical considerations Pons (48) suggested that such deviations could also be observed for other lamellar materials such as clay minerals. Following such assumptions, we tentatively assign the deviation from Porod’s law (−3.3, −3.2 decay) observed in our system to heterogeneities of the solid clay phase which can be considered as a lamellar material with both stacking faults and ˚ thick (20). additional lenticular micropores 30 to 40 A Scattering results will then be interpreted by considering a biphasic system where one phase is the clay matrix with numerous structural defects and the other phase corresponds to pores of various sizes and shapes. To quantify the extent of deviation from Porod’s law for which the scattering intensity follows a q −4 decay (42), the product q 4 I was plotted as a function of q 2 (Fig. 3). For the Na- (resp. ˚ −1 ˚ −1 < q < 0.04 A Ca-) montmorillonite, on the range 0.01 A ˚ −1 < q < 0.07 A ˚ −1 ), q 4 I is a linear function of q 2 . (resp. 0.03 A Over this scattering vector range, the total intensity can then be expressed as a sum of two terms: q 4 Itotal = aq 2 + b.
FIG. 2. Log–log plots of ultra-small- and small-angle X-ray scattering from montmorillonite in a dry state. (a) Sodium montmorillonite, (b) calcium montmorillonite.
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[1]
The constant b term follows Porod’s law and the intensity corresponding to this term can be called IPorod , where IPorod can be expressed as b/q 4 . IPorod corresponds to scattering by a porous medium. The additional component aq 2 is assigned to the contribution of the clay stack’s inner structure and the corresponding intensity called Istruct can be expressed as a/q 2 in this scattering vector range.
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˚ −1 , Istruct becomes predominant and the scattered intensity 0.1 A is mainly sensitive to local arrangement in pore walls (drawing 3, Fig. 4a). In the intermediate range, both structure and porosity have to be taken into account. Porous Medium
FIG. 3. Plots of the product q 4 I (q) as a function of q 2 . The product q 4 I (q) exhibits a linear deviation from Porod’s law. In this scattering vector range, q 4 I (q) can be expressed as a sum of two terms: the first one is called q 4 IPorod and follows Porod’s law, the second one q 4 Istruct is the linear deviation assigned to the structure.
Such a decomposition is illustrated in Fig. 4. For low q val˚ −1 ) the additional component is negligible. ues (q < 2 × 10−2 A Therefore, for the range of distances probed in such a q domain, the system can be assimilated to a true porous medium with two phases, both homogeneous in electronic density. In other words, on this scale, the structure of the solid matter is no longer apparent (drawing 2 in Fig. 4a). An increase in q corresponds to a zoom into the probed material, which progressively reveals more of the local structure, and consequently improves the relative proportion of Istruct over IPorod . For q values higher than
FIG. 4. Log–log plot of the total intensity decomposed into the two terms defined in Fig. 3. The schematic drawing shown in inset of (a) illustrates this decomposition: the first term called IPorod (2) corresponds to the intensity scattered by a porous medium whose pore walls have a uniform electronic density (without structure) and the second term Istruct (3) is relative to the structure of the walls.
IPorod can be analyzed according to the formalism developed for porous media described in reference books (49, 50). The system is then considered as an isotropic two-phase system with constant electronic densities over each phase. The two phases are (i) the solid matter described by its electronic density ρm and volume fraction φm and (ii) the pores, with volume fraction (i.e., porosity) φ p (φm + φp = 1) and electronic density ρp . For such a system, the scattered intensity per unit volume can be expressed as Z I (q) = A2e (ρm − ρp )2 φm φp
4πr 2 γ0 (r )
sin(qr ) dr, qr
[2]
where A2e is the Thomson factor, i.e., the intensity scattered by an electron, and γ0 (r ) is the Porod’s characteristic correlation function normalized to 1 for r = 0. γ0 (r ) is proportional to the probability that if one point lies in phase m (resp. p) a second point distant from r also lies in m (resp. p) (42). This correlation function can be expressed as a function of intensity by inverse Fourier transform: 1 γ0 (r ) = 2 2 2π Ae (ρm − ρp )2 φm φp
Z q 2 I (q)
sin qr dq. qr
[3]
Resolution and maximum size of heterogeneities. The maximum particle or heterogeneity size that is fully probed in a scattering experiment is related to the minimum scattering vector qmin by the relation D ≤ π/qmin . For experimental reasons, the minimum scattering vector is different for both sam˚ and D ≤ 7850 A ˚ for Na- and Caples with D ≤ 11 200 A montmorillonite, respectively. The resolution in real space for γ0 (r ) is given by the sampling theorem of Fourier transform and by introducing a sampling distance that follows the condition 1r ≥ π/qmax , where qmax is the maximum experimental scattering vector. For our experiments, qmax was chosen as the q value for which Istruct becomes predom˚ and 1r ≥ 45 A ˚ inant. The calculated values are then 1r ≥ 78 A for the Na- and Ca-montmorillonite, respectively. Porosity. Assuming a pore-diluted system (φp ¿ 1) Eq. [2] can be simplified, which allows one to calculate the porosity owing to the normalizing condition γ0 (0) = 1: φp =
1 2 2 2π Ae (ρm − ρp )2
Z q 2 I (q) dq.
[4]
Porosity values calculated with Eq. [4] correspond to the porosity probed by X-ray scattering, i.e., resulting from electronic
X-RAY SCATTERING STUDY OF SWELLING CLAY FABRIC
215
TABLE 1 Calculated Values Relative to Porosity and Pore Shape for Na- and Ca-Montmorillonite
Sodium montmorillonite Calcium montmorillonite
Porosity (%)
Pore’s mean chord length a (A)
Modal values of the distance distribution a f (r ) (A)
1.6–2.5 1.5
621 271
311 224
density heterogeneities. The calculated values then depend on the experimental conditions that impose both resolution (a few nanometers) and maximal length scale probed (around 1 µm). For Na-montmorillonite, two porosity values were calculated corresponding to the minimal and maximal values of the evaluated film thickness. The true porosity value is assumed to belong to this interval, between 1.6 and 2.5%. The porosity of the calcium montmorillonite was calculated to be 1.5% (Table 1). For both samples, the low porosity value obtained confirms the assumption of a pore-diluted system. The calculated porosity values reveal that the clay films are extremely compact as illustrated on the micrograph (Fig. 5) recorded with a Hitachi
FIG. 6. Schematic illustration of chords. A chord is the intercept segment between a line crossing the system and pores (lp ) or matter (lm ).
S 2500 scanning electron microscope on another dry calcium montmorillonite film. The observed clay film is a few micrometers thicker than the one used in SAXS and USAXS experiments. Pore’s mean chord length. With a pore-diluted system assumption, the pore’s mean chord length can be calculated from the asymptotic limit of Porod’s law: lim
q→∞
8π q 4 I (q) = , 2 2 Ae (ρm − ρp ) φp l¯p
[5]
where l¯p represents the pore’s mean chord length, as illustrated in Fig. 6. Calculated values are displayed in Table 1. It must be pointed out that these values do not correspond to true mean pore sizes and must be considered as dimension indicators. Distance distributions functions. Pore shape can be approached by calculating the distance distribution functions that are deduced from Porod’s characteristic function γ0 (r ). Two kinds of distance distribution functions (50) can be calculated:
FIG. 5. Scanning electron micrograph obtained, in secondary electron emission mode, on the section of a dry film of Ca-montmorillonite.
P(r ) = r 2 γ0 (r )
[6]
f (r ) = r γ0 (r ).
[7]
As γ0 (r ) is an autocorrelation function, i.e., the probability that a segment of length r is located within a pore, and P(r ) and f (r ) are equivalent to a square distance and a distance, respectively. Generally, f (r ) is used preferably for characterizing lamellar pores. The f (r ) distance distributions calculated for both samples are shown in Fig. 7. In order to obtain more information about the physical meaning of such distributions, similar distribution functions were calculated for a set of ellipsoids with two equal ˚ and a variable half-axes c (50). half-axes a and b (= 5000 A) The ratio v (= c/a) is then indicative of the spheroidal character of those ellipsoids. Figure 7 clearly reveals that an elongated ellipsoid with a v value around 0.07 represents the best
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Structure The structure of particles can be analyzed using two different sets of experimental data: (i) the additional component Istruct originating from small-angle scattering and (ii) XRD patterns. In contrast with the procedure used for interpreting USAXS and SAXS data, a joint analysis of Istruct and XRD data cannot be achieved as XRD data were obtained in reflection mode while SAXS data were recorded using a transmission mode. As a consequence XRD results and SAXS results will be examined separately. Bragg angular domain. XRD patterns were used to analyze the characteristic distances inside layer stacks. They were simulated using the formalism developed for studying diffraction by lamellar structures (51), that was applied on many clay systems to study swelling and/or structure (7–9, 18–20, 52–56). According to such a formalism, the intensity diffracted by a powder formed by infinite layered particles can be written as I00 (q) ≈
1 X α(M)Spur{Re{[F][W ][R]}}, q2 M
[8]
where α(M) is the distribution of the number of layers per stack, and [F] and [W ] are respectively a diagonal matrix containing the relative proportions of the different types of layers and a square matrix containing the structure factors. The elements of the matrix [Q] are dependent on all the possible phase differences between the waves diffracted by adjacent layers. The XRD patterns were simulated using the above equation with software developed by Besson and Kerm (55) at CRMD, University of Orl´eans, France. As previously discussed (8), the comparison of simulated XRD patterns with experimental ones is not straightforward due to the experimental procedure used, i.e., reflection conditions associated with a curved detector. As a consequence, the criterion of agreement between experimental and calculated curves relies more on peak positions (main reflections and harmonics) than on peak shapes and relative intensities. The values derived from the simulation procedure are displayed in Table 2. For sodium
FIG. 7. Distance distribution functions f (r ). The functions displayed in (c) a are calculated for three ellipsoids with two equal half-axes a and b (= 5000 A), and a variable half-axis c. v is the ratio c/a, and is indicative of the ellipsoid’s spheroidal character.
approximation for matching the experimental f (r ) of both Naand Ca-montmorillonites. This confirms the lenticular character ˚ A full modeling of experiof pores in the range 50–7000 A. mental distance distributions would require the introduction of both size and shape polydispersity, which is rather difficult to implement.
TABLE 2 Parameters Used to Simulate the XRD Patterns
M (mean number of layers per stack) Interlamellar distances distribution
Sodium montmorillonite
Calcium montmorillonite
10
10
a 100% at 9.55 A (dry sate)
a 90% at 9.55 A (dry sate) a 10% at 12.5 A (one water layer)
X-RAY SCATTERING STUDY OF SWELLING CLAY FABRIC
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CONCLUDING REMARKS
FIG. 8. Simulation of Istruct in the intermediate domain between diffraction and small-angle scattering. The distance distributions used in the calculations are displayed on the plots in the inset.
montmorillonite, the dry state is quasi homogeneous, with a ˚ The interlamellar space does not distance repetition of 9.55 A. appear to contain any water molecules. The mean number of layers per stack is estimated to be around 10. For calcium montmorillonite, some water molecules are still present in the inter˚ a value layer space: about 10% of the layers are at 12.55 A, characterizing the one-water-layer hydrated state. Such a difference between Na- and Ca-montmorillonite can be assigned to the high hydration energy of Ca2+ ions that are then difficult to fully dehydrate. Intermediate domain between diffraction and small-angle scattering. The intensity increase toward the small-angle scattering domain was simulated using the same equation ([8]) as the one used to model XRD patterns. Larger distances and larger stack thickness were introduced to account for the larger angular domain probed. The simulation results are displayed in Fig. 8. Calculations were performed using stacks formed by 100 el˚ distances ementary layers per stack. In addition to the 9.5-A corresponding to the dry state, larger distances between 25 and ˚ (resp. 100 A) ˚ for the Na- (resp. Ca-) montmorillonite 150 A were needed to obtain a proper fit. The distribution of these large distances is almost homogeneous which can be interpreted as corresponding to areas where substacks of dry layers are separated from each other by continuously varying distances. On this length scale the material appears less compact with an intermediate porosity introduced by the largest distances. The amount of such a porosity is not negligible as the probability of find˚ is roughly the same as the ing an open space (larger than 20 A) probability of having a dry compact stacking with an interlayer ˚ distance of 9.5 A.
Using a combination of X-ray scattering and X-ray diffraction experiments, the structure of clay films can be probed in situ over a wide distance range, i.e., from a few angstroms to about a micrometer. Our interpretation is based on the assumption that dry clays can be considered as porous materials with a ˚ µm observation domain, structured solid phase. In the 50 A–1 the medium appears as rather dense with a low porosity (1– 2%) formed by anisotropically shaped pores (lenticular pores). Calcium montmorillonite appears slightly less porous and exhibits lower mean chord lengths and lower modal values of f (r ) (Table 1). This suggests a denser packing which could be due to the lower flexibility of Ca-montmorillonite stacks compared with Na-montmorillonite ones (40, 57). However, the observed differences may also be due to variations in the polydispersity of pore size and shapes that are rather difficult to approach. ˚ domain, the combination of XRD and SAXS In the 5–100 A reveals a complex and heterogeneous nature of pore walls. Or˚ seem dered stacks of approximately 10 layers separated by 9.5 A to be organized in larger particles comprising around 100 layers. ˚ are observed In those particles, distances between 25 and 150 A which may be tentatively assigned to lenticular micropores. The porosity introduced by the largest distances in an additional porosity that is not taken into account in the porosity values calculated in the largest length scale range (Porod’s region). Indeed, the distance distribution functions were calculated from the term Istruct after separation of the total intensity into two terms. In contrast, the calculated porosities were derived from the second term, i.e., IPorod . As in the previous observation domain, Ca-montmorillonite ˚ are appears less porous as no distances higher than 100 A
FIG. 9. Schematic illustration of the dry clay system according to the 3scale domains individualized to describe the clay fabric. (1) Ultra-small-angle scattering range, (2) intermediate domain between diffraction and scattering, and (3) XRD area.
218
BIHANNIC ET AL.
detected. A clearer picture of the organization in this size range would certainly be obtained if XRD patterns were recorded in transmission mode, allowing a real joint analysis on the complete q scattering vector domain. The general picture derived from this observation (Fig. 9) reveals a really complex organization where no structural unit corresponding to each observation scale can be clearly defined. This is particularly acute in what we referred to as the intermediate zone between XRD and SAXS as in this size range, various distances can be observed which are difficult to assign unambiguously. In that regard, the separation we performed in different ranges may be partially artificial. Still, the picture obtained in this study represents a sound basis for understanding the textural and morphological evolution of clay systems upon water adsorption as will be described in a forthcoming paper. ACKNOWLEDGMENTS The authors thank Dr. Pierre Levitz (CRMD) for very fruitful discussions and assistance with USAXS experiments. Drs. L. J. Michot and B. S. Lartiges are acknowledged for their help. I.B. thanks R´egion Centre for financial support.
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