Phase Diagrams of Wyoming Na-Montmorillonite Clay. Influence of

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Phase Diagrams of Wyoming Na-Montmorillonite Clay. Influence of Particle Anisotropy Laurent J. Michot,*,† Isabelle Bihannic,† Katharina Porsch,† Solange Maddi,† Christophe Baravian,‡ Julien Mougel,‡ and Pierre Levitz§ Laboratoire Environnement et Mine´ ralurgie, UMR 7569 CNRS-INPL-ENSG, 15 Avenue du Charmois, BP 40 54501 Vandœuvre Cedex, France, Laboratoire d’Energe´ tique et de Me´ canique The´ orique et Applique´ e, UMR 7563 CNRS-INPL-UHP, 2, Avenue de la Foreˆ t de Haye, BP160 54504 Vandœuvre Cedex, France, and Laboratoire de Physique de la Matie` re Condense´ e, UMR 7643 CNRS-Ecole Polytechnique, Ecole Polytechnique 91128 Palaiseau Cedex, France Received May 1, 2004. In Final Form: September 15, 2004 Natural Na-Wyoming montmorillonite was size fractionated by successive centrifugation. Polydisperse particles with average sizes of 400, 290, and 75 nm were then obtained. As the structural charge of the particles belonging to three fractions (determined by cationic exchange capacity measurements) is the same, such a procedure allows studying the effect of particle anisotropy on the colloidal phase behavior of swelling clay particles. Osmotic stress experiments were carried out at different ionic strengths. The osmotic pressure curves display a plateau whose beginning systematically coincides with the sol/gel transition determined by oscillatory stress measurements. The concentration corresponding to the sol/gel transition increases linearly with particle anisotropy, which shows that the sol/gel transition is not directly related to an isotropic/nematic transition of individual clay particles. Indeed, a reverse evolution should be observed for an I/N transition involving the individual clay particles. Still, when observed between crossed polarizer and analyzer, the gel samples exhibit permanent birefringent textures, whereas in the “sol” region, transient birefringence is observed when the samples are sheared. This suggests that interacting clay particles are amenable to generate, at rest and/or under shear, large anisotropic particle associations.

Introduction

* Corresponding author Tel: (33)3 83 59 62 94 Fax (33) 3 83 59 62 55. e-mail: [email protected]. † Laboratoire Environnement et Mine ´ ralurgie, UMR 7569 CNRSINPL-ENSG. ‡ Laboratoire d’Energe ´ tique et de Me´canique The´orique et Applique´e, UMR 7563 CNRS-INPL-UHP. § Laboratoire de Physique de la Matie ` re Condense´e, UMR 7643 CNRS-Ecole Polytechnique.

The situation is much less clear in the case of charged colloidal plates whose most studied members are natural swelling clays. Due to their widespread occurrence and physicochemical characteristics (high affinity for water and polar solvents, high surface area, sealing ability, gelling, etc.) swelling clay-based systems play a major role in the environment (soil stability, geocycling, water reserves, etc.) and are also extensively used in industry (waste management, paints, drilling fluids, etc.). Most of their properties are due to their particular structure. These sheet minerals (typical aspect ratios between 25 and 1000) bear a negative layer charge compensated by interlayer exchangeable cations whose valence and hydration properties control both swelling and colloidal behavior. Clay mineral suspensions do not exhibit a clear isotropic/ nematic phase transition with phase separation but, instead, at very low volume fractions (as low as 0.5 wt %11) a sol-gel transition turns out to be ubiquitous. The structure of the gel formed is still under debate. Two main models were proposed in the 1950s based either on the formation of a tridimensional network governed by electrostatic attraction between platelets12 or on the formation of an oriented network stabilized by repulsive forces caused by interacting double layers.13 Whereas most early work was devoted to the behavior of natural swelling clay minerals,4,12-15 which are highly

(1) Gabriel, J.-C. P.; Davidson, P. Adv. Mater. 2000, 12, 9. (2) Gabriel, J.-C. P.; Davidson, P. Top. Curr. Chem. 2003, 226, 119. (3) Onsager, L. Ann. N. Y. Acad. Sci. 1949, 51, 627. (4) Langmuir, I. J. Chem. Phys. 1938, 6, 838. (5) Van Bruggen, M. P. B.; Dhont, J. K. G.; Lekkerkerker, H. N. W. Macromolecules 1999, 32, 2256. (6) Bernal, J. D.; Fankuchen, I. J. Gen. Physiol. 1941, 25, 111. (7) (a) Davidson, P.; Batail, P.; Gabriel, J. C. P.; Livage, J.; Sanchez, C.; Bourgaux, C. Prog. Polym. Sci. 1997, 22, 913. (b) Pelletier, O.; Davidson, P.; Bourgaux, C.; Livage, J. Prog. Colloid Polym. Sci. 1999, 112, 121. (c) Pelletier, O.; Davidson, P.; Bourgaux, C.; Livage, J. Europhys. Lett. 1999, 48, 53.

(8) Van der Kooij, F. M. Thesis, Utrecht University, The Netherlands, 2000. (9) (a) Van der Kooij, F. M.; Lekkerkerker, H. N. W. J. Phys. Chem. B 1998, 102, 7829. (b) Van der Kooij, F. M.; Kassapidou, E.; Lekkerkerker, H. N. W. Nature 2000, 406, 868. (10) (a) Brown, A. D. B.; Clarke, S. M.; Rennie, A. R. Langmuir 1998, 14, 3129. (b) Brown, A. D. B.; Ferrero, C.; Narayanan, T.; Rennie, A. R. Eur. Phys. J. B 1999, 11, 481. (11) Lecolier E. Thesis, Universite´ d’Orle´ans, France, 1998. (12) Van Olphen, H. Discuss. Faraday Soc. 1951, 11, 82. (13) Norrish, K. Discuss. Faraday Soc. 1954, 18, 120.

Anisotropic colloids exhibit a rich and complex phase behavior due to possible orientational ordering which can lead to inorganic liquid crystals.1,2 In the case of rodlike particles, a theoretical description of the phase transitions was proposed in the 1930s and 1940s by Onsager.3 Considering the competition between orientational entropy and excluded volume entropy, he thus managed to explain the isotropic/nematic phase transition observed experimentally in various systems.4-7 As suggested in Onsager’s work, such a theory can also apply to the case of uncharged platelike colloids. This was experimentally demonstrated recently in the case of monodisperse or slightly polydisperse platelets that exhibited two clear phase transitions, the system evolving subsequently from isotropic to nematic and from nematic to columnar with increasing volume fraction.8-10

10.1021/la0489108 CCC: $27.50 © 2004 American Chemical Society Published on Web 11/10/2004

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polydisperse in terms of size, shape, and charge, most recent studies16-47 focus on laponite, a synthetic hectorite sample that can be approximated as monodisperse disks with a thickness of 1 nm and a diameter of 30 nm. Recent atomic force microscopy measurements47 reveal that the actual shape is in fact more ellipsoidal than discoidal. In that system, the “phase diagram” solid concentration/ionic strength exhibits, for low ionic strength (e10-4 M),11,29 i.e., when the Debye screening length is of the same order of magnitude as the particle diameter, a positive slope. In that region, there is a general agreement that the liquidsoft solid transition is mainly driven by electrostatic repulsions and that the sol/gel transition can be interpreted as a colloidal Wigner glass transition.28,29 Still, ultra-small-angle X-ray scattering measurements suggest a nonhomogeneous spatial distribution of particles.29,32 For higher ionic strength, i.e., when the Debye screening length becomes smaller than the particle size, the phase (14) Callaghan, I. C.; Ottewill, R. Faraday Discuss. Chem. Soc. 1974, 57, 110. (15) Rand, B.; Penkenc, E.; Goodwin, J. W.; Smith, R. W. J. Chem. Soc., Faraday Trans. 1980, 76, 225. (16) Avery, R. G.; Ramsay, J. D. F. J. Colloid Interface Sci. 1986, 109, 448. (17) Ramsay, J. D. F.; Swanton, S.; Bunce, J. J. J. Chem. Soc., Faraday Trans. 1990, 86, 3919. (18) Rosta, L.; Van Gunten, H. R. J. Colloid Interface Sci. 1990, 134, 497. (19) Thompson, D. W.; Butterworth: J. T. J. Colloid Interface Sci. 1992, 151, 236. (20) Ramsay, J. D. F.; Lindner, P. J. Chem. Soc., Faraday Trans. 1993, 89, 4207. (21) Mourchid, A.; Delville, A.; Lambard, J.; Le´colier, E.; Levitz, P. Langmuir 1995, 11, 1942. (22) Mourchid, A.; Delville, A.; Levitz, P. Faraday Discuss. 1995, 101, 275. (23) Gabriel, J.-C P.; Sanchez, C.; Davidson, P. J. Phys. Chem. 1996, 100, 11139. (24) Pignon, P.; Piau, J.-M.; Magnin, A. Phys. Rev. Lett. 1997, 79, 4689. (25) Mourchid A.; Le´colier, E.; Van Damme, H.; Levitz, P. Langmuir 1998, 14, 4718. (26) Porion, P.; Fauge`re, P. M.; Le´colier, E.; Gherardi, B.; Delville, A. J. Phys. Chem. B 1998, 102, 3477. (27) Saunders: J. M.; Goodwin, J. W.; Richardson, R. M.; Vincent, B. J. Phys. Chem. B 1999, 103, 9211. (28) Bonn, D.; Kellay, H.; Tanaka, H.; Wegdam, G.; Meunier, J. Langmuir 1999, 15, 7534. (29) Levitz, P.; Le´colier, E.; Mourchid A.; Delville, A.; Lyonnard, S. Europhys. Lett. 2000, 49, 672. (30) Knaebel, A.; Bellour, M.; Munch, J.-P.; Viasnoff, V.; Lequeux, F.; Harden, J. L. Europhys. Lett. 2000, 52, 73. (31) Nicolai, T.; Cocard, S. Langmuir 2000, 16, 8189. (32) Levitz, P.; Delville, A.; Le´colier, E.; Mourchid A. Prog. Colloid Polym. Sci. 2001, 118, 290. (33) Harnau, L.; Costa, D.; Hansen, J. P. Europhys. Lett. 2001, 53, 729. (34) Bonn, D.; Tanase, S.; Abou, B.; Tanaka, H.; Meunier, J. Phys. Rev. Lett. 2002, 89, 015701. (35) Schmidt, G.; Nakatani, A. I.; Butler, P. D.; Han, C. C. Macromolecules 2002, 35, 4725. (36) Lemaire, B. J.; Panine, P.; Gabriel, J. C. P.; Davidson, P. Europhys. Lett. 2002, 59, 55. (37) Trizac, E.; Bocquet, L.; Agra, R.; Weis, J.-J.; Aubouy, M. J. Phys. Condens. Matter 2002, 14, 9339. (38) Zhivkov, A. M.; Stoylov, S. P. Colloids Surf., A 2002, 209, 315. (39) Cousin, F.; Cabuil, V.; Levitz, P. Langmuir 2002, 18, 1466. (40) Bakk, A.; Fossum, J. O.; da Silva, G. J.; Adland, H. M.; Mikkelsen, A.; Elgsaeter, A. Phys. Rev. E 2002, 021502. (41) Martin, C.; Pignon, F.; Piau, J.-M.; Magnin, A.; Lindner, P.; Cabane, B. Phys. Rev. E 2002, 021401. (42) Bonn, D.; Coussot, P.; Huynh, H. T.; Bertrand, F.; Debregeas, G. Europhys. Lett. 2002, 786. (43) Wilhelm, C.; Elias, F.; Browaeys, J.; Ponton, A.; Bacri, J.-C. Phys. Rev. E 2002, 021502. (44) Bhatia, S.; Barker, J.; Mourchid, A. Langmuir 2003, 19, 532. (45) Porion, P.; Al-Mukhtar, M.; Fauge`re, A.-M.; Meyer, S.; Delville, A. Eur. Phys. J. E 2003, S17-S20. (46) Porion, P.; Al-Mukhtar, M.; Fauge`re, A.-M.; Pellenq, R. J. M.; Meyer, S.; Delville, A. J. Phys. Chem. B 2003, 107, 4012. (47) Balnois, E.; Durand-Vidal, S.; Levitz, P. Langmuir 2003, 19, 6633.

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diagram exhibits a nose and the transition line from a liquid to a soft solid then presents a negative slope as a function of ionic strength.11,21-23,25,29,32,39 The interpretation of this region of the phase diagram is much more controversial as long-range and anisotropic short-range interactions are mixed in a nontrivial way. Some authors propose an interpretation based on an electrostatically frustrated isotropic/nematic phase transition1,11,21,22,23,25,36,39,44 or a spinodal decomposition.39 Other authors propose the existence of a fractal network and/or of retarded aggregation processes to explain this region of the phase diagram24,31,40,41 whereas an interpretation in terms of glass transition has also been put forward.28,30,34,42 In summary, there is at the moment no univocal interpretation that can reconcile all the experimental observations on laponite suspensions. Despite its wide acceptance as a model charged colloidal platelet, laponite particles present two main drawbacks: (i) their window of chemical stability (pH g 9-10) is rather narrow which obliges one to take serious precautions to avoid any possible acidification of the suspension; (ii) their particle size is small compared to the range of aspect ratios that can be encountered in natural clay minerals. For these reasons, our approach to the study of phase behavior in charged colloidal platelets is dual. On one hand, we try to focus on synthetic particles with adjustable charge and aspect ratios such as layered double hydroxides.48 On the other hand, we use various natural smectite clay minerals which, though polydisperse, can provide a wide range of shape size and charge that allow simultaneous exploration of the influence of various parameters on colloidal behavior.49 The present paper focuses on one montmorillonite sample (Wyoming montmorillonite) by combining osmotic pressure measurements, rheological experiments, and birefringence observations. Three different average aspect ratios are studied to explore the influence of anisotropy on the phase diagrams. Materials and Methods Wyoming montmorillonite Swy2 was purchased from the Source Clays Minerals repository at the University of Missouri. A 50 g/L clay suspension was first exchanged three times in 1 M NaCl. The suspension was then washed repeatedly by centrifugation and redispersion of the solid in MilliQ water until the supernatant was chloride free as judged from the silver nitrate test. After each centrifugation, the bottom of the centrifuge tube that contains various impurities (quartz, silica, feldspar, mica, iron oxyhydroxides, etc.) was discarded. The structural formula of the pure montmorillonite thus obtained can be written as (Si7.94Al0.06)(Al2.88Fe0.5Mg0.62)O20(OH)4Na0.68. The thickness of the particles is around 1 nm, and the cationic exchange capacity (CEC) measured by exchange with cobaltihexamine50 is equal to 91 mequiv/100 g of clay. The final suspension was adjusted to a solid concentration of ≈12 g/L by dilution. Size fractionation was also carried out for trying to reduce the polydispersity of clay platelets. For this purpose, a clay suspension obtained after purification was centrifuged at 5000g during 90 min. The bottom section was separated and will be referred to as SWy2-size 1. The supernatant was then recentrifuged at 12000g during 90 min to yield SWy-2 size 2, and the procedure was repeated at 35000g during 90 min to yield SWy-2 size 3. The three sizes were then rediluted in MilliQ water to adjust the solid concentration of the suspensions at ≈12 g/L. CEC measurements were carried out on the three sizes and yield values of 90.5, 93, and 91.5 mequiv/ 100 g for sizes 1-3, respectively, which proves that, in Wyoming montmorillonites, the average layer charge does not depend on particle size. (48) Michot, L. J.; Ghanbajaa, J.; Tirtaamadja, V.; Scales, P. J. Langmuir 2001, 17, 2100. (49) Vantelon, D. Thesis, Institut National Polytechnique de Lorraine, France, 2001. (50) Re´my, J. C.; Orsini, L. Sci. Sol 1976, 4, 269.

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Figure 1. TEM micrographs of Na-Wyoming montmorillonite. Transmission electron microscopy (TEM) micrographs of clay platelets were obtained on a Philips microscope operating at 100 kV. Dilute suspensions (≈1 g/L) of montmorillonite were stirred with Masquol, a polyphosphonate-based dispersant. A drop of this suspension was deposited on a copper grid and observed under the microscope. Osmotic pressure measurements were carried out using Visking dialysis tubes with a cutoff of 14000 Da. Prior to the experiment, the membranes were first rinsed two times with 10-3 M sodium azide to remove impurities and prevent bacterial contamination. The membranes were then washed two more times in MilliQ water and conditioned during one night at the ionic strength of the experiment. Dextran 110000 (Fluka) solutions were prepared by dilution in sodium chloride solutions. Under such conditions, the ionic strength is fixed in the reservoir, which avoids problems related with the Donnan effect.51 For solutions with low osmotic pressures (πi e 1000 Pa), 25 mL of clay suspensions (≈12 g/L) were introduced in the dialysis tubes and placed in 250 mL of Dextran solutions. For higher osmotic pressures, 50 mL of clay suspensions were placed in 500 mL of Dextran solutions. In all cases, the conditions were that of an osmotic stress. The duration of the experiment was fixed at 4 weeks as it was shown for latexes52 and laponite11 suspensions that osmotic equilibrium was reached in those conditions. At the end of the experiment, the concentrated clay suspension was recovered and its solid content was determined after oven-drying. To determine a “true” weight fraction, the relative humidity was measured and taken into account according to the water adsorption data determined for Na-Wyoming montmorillonite.53 The final Dextran solutions were analyzed by high-pressure liquid chromatography (Hewlett-Packard series 1100) using a refractive index detector and a sequence previously designed for measuring polysaccharides in activated sludges54 from wastewater treatment. Such a procedure yields the final Dextran concentration and thus the osmotic pressure according to the calibration law11,52 log Π ) 1.826 + 1.715w0.297, where Π is the osmotic pressure in dyn/cm2 and w the weight percent of Dextran. In addition, the use of such a procedure also allows checking for any Dextran degradation from the shape of the chromatographic profile. Rheological measurements were carried out using an Aspect 2000 rheometer from TA instruments with a cone and plate (51) Dubois, M.; Zemb, T.; Belloni, L.; Delville, A.; Levitz, P.; Setton, R. J. Chem. Phys. 1992, 96, 2278. (52) Bonnet-Gonnet, C. Thesis, Universite´ Paris VI, France, 1993. (53) Be´rend, I.; Cases, J. M.; Franc¸ ois, M.; Uriot, J. P.; Michot, L.; Masion, A.; Thomas, F. Clays Clay Miner. 1995, 43, 324. (54) Gorner, T.; de-Donato, P.; Ameil, M.-H.; Montarge`s-Pelletier, E.; Lartiges, B. S. Water Res. 2003, 37, 2388.

Figure 2. Size distribution of Na-Wyoming montmorillonite deduced from the TEM images. geometry. The elastic and viscous moduli G′ and G′′ were determined from oscillatory stress measurements using frequencies between 0.02 and 10 Hz. The birefringent nature of the various samples was assessed in two different ways. For macroscopic experiments, the clay samples were introduced in 2 mL glass vials with a diameter of 5 mm and were then observed between crossed polarizers. Such a procedure can only be applied for moderately concentrated systems as concentrated systems absorb too much light. In parallel, the samples were introduced into 100 µm flat optical capillaries and observed using a Nikon optical microscope equipped with a polarizer and an analyzer.

Results Size Measurements. Figure 1 presents some clay platelets observed by transmission electron microscopy. The platelets are polydisperse both in size and in shape. The smallest ones generally exhibit rather regular lath shapes, whereas the larger ones are much more irregular and exhibit torn edges. The size distribution deduced from

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Figure 3. Size distribution of the three fractions obtained by centrifugation of Na-Wyoming montmorillonite: (A) size 1; (B) size 2; (C) size 3.

Figure 4. Osmotic pressure curves obtained for the three size fractions of Na-Wyoming montmorillonite: (A) size 1; (B) size 2; (C) size 3.

the analysis of around 500 particles is displayed in Figure 2. In view of the irregular shape of the particles, the size chosen for this analysis corresponds to the longest chord inside the particle. The polydisperse nature of the clay platelets is well illustrated by this graph with sizes extending over 2 orders of magnitude between 5 and 750 nm with an average size around 250 nm and a standard deviation around 180 nm. The size distribution histograms of the three size fractions are displayed in Figure 3. Polydispersity is obviously reduced with average sizes of 410, 295, and 75 nm for sizes 1-3, respectively with corresponding standard deviations of 130, 100, and 50 nm. Still, even after fractionation, the samples remain rather polydisperse. Osmotic Pressure Measurements. The osmotic pressures curves obtained for the three size fractions at four ionic strengths are displayed in Figure 4. Whatever the ionic strength, the shape of the curve is similar: for low solid contents, one can observe a moderate increase in osmotic pressure up to values around 500 Pa, followed by a pseudoplateau where the osmotic pressure remains nearly constant for increasing solid fractions. At the end of the plateau, the osmotic pressure increases sharply. Such a general shape is similar to what was obtained for laponite,11,21,25 which suggests that the existence of a pseudoplateau could be typical of charged colloidal

platelets and that it is only marginally affected by polydispersity. However, in comparison with laponite, the influence of ionic strength is much less marked in the case of montmorillonite. Indeed, in that latter case, the influence of ionic strength on the osmotic pressure at the pseudoplateau remains limited. This fact may be linked to results previously obtained showing that the zeta potential of Wyoming montmorillonite is nearly independent of ionic strength at neutral pH.49,55-58 The main influence of ionic strength lies in the extension of the plateau that is more horizontal and more extended with increasing ionic strength. Figure 5 displays the osmotic pressure curves obtained for the three size fractions at a given ionic strength. Increasing size significantly shifts the curves toward higher solid content, this influence being particularly marked for the second increase in osmotic pressure at high solid concentration. It is worth mentioning that the curves obtained for Wyoming montmorillonite before size separation (average size 250 nm) are located (55) Chan, D. Y. C.; Pashley, R. M.; Quirk, J. P. Clays Clay Miner. 1984, 32, 131. (56) Low, P. F. Langmuir 1987, 3, 18. (57) Horikawa, Y.; Murray, R. S.; Quirk, J. P. Colloids Surf. 1988, 32, 181. (58) Thomas, F.; Michot, L. J.; Vantelon, D.; Montarge`s, E.; Pre´lot, B.; Cruchaudet, M.; Delon, J.-F. Colloids Surf., A 1999, 159, 351.

Phase Diagrams of Clay

Figure 5. Effect of average size on the osmotic pressure curves of Na-Wyoming montmorillonite: (A) 10-5 M NaCl; (B) 10-4 M NaCl; (C) 10-3 M NaCl; (D) 10-2 M NaCl.

close to the curves obtained for size fraction 2 (average size 295 nm) which suggests that average size is the key parameter defining the equation of state and that polydispersity only plays a moderate role. Rheological Characterization. Figure 6 presents the frequency dependence of the storage modulus (G′) for some selected montmorillonite suspensions of the three size fractions obtained by osmotic stress at ionic strengths of 10-5, 10-4, 10-3, and 10-2 M. For the higher solid contents, G′(ω) is significantly higher than G′′(ω) and does not vary much with frequency in the dynamical range between 10-2 and 10 Hz. These two features indicate a gel-type behavior. In contrast, for lower solid content, G′(ω) and G′′(ω) are both weak with roughly similar magnitudes indicating a slightly viscous suspension. The rheological behavior of the gels can be interpreted as corresponding to repulsive gels. Indeed, a more detailed analysis was recently published for Wyoming montmorillonite59 that leads to the determination of repulsive interaction potentials between clay platelets. Figure 7 displays the evolution of G′ at an arbitrarily chosen frequency of 1 Hz for various solid contents and ionic strengths. In addition, the curve obtained for the nonfractionated Wyoming montmorillonite is also displayed (Figure 7D). The curves obtained display a power law behavior as observed for various systems of charged colloidal platelets such as laponite,11,21,25 montmorillonite,60,61 or takovite.48 The dependency of G′ on ionic strength remains rather limited, in contrast with what was observed for other systems such as laponite11,21,25 or takovite48 where for a given solid concentration G′ (59) Baravian, C.; Vantelon, D.; Thomas, F. Langmuir 2003, 19, 8109. (60) Ramsay, J. D. F. J. Colloid Interface Sci. 1986, 109, 441. (61) Sohm, R.; Tadros, Th., F. J. Colloid Interface Sci. 1989, 132, 62.

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Figure 6. Evolution of G′ with the oscillatory frequency for different size fractions and ionic strengths: (A) size 1, 10-5 M NaCl; (B) size 1, 10-3 M NaCl; (C) size 2, 10-4 M NaCl; (D) size 2, 10-2 M NaCl; (E) size 3, 10-4 M NaCl; (F) size 3, 10-3 M NaCl.

increased significantly with increasing ionic strength. If one makes the assumption that the gelation mechanism is the same whatever the ionic strength, then all the data obtained can be placed on a master curve according to a power law behavior G′ (1 Hz) ) A(C - C0)R, where C0 is the solid concentration for the sol/gel transition. It must be pointed out that only one curve cannot be adjusted properly on the master curves displayed in Figure 7, i.e., the curve corresponding to size fraction 3 at an ionic strength of 10-2 M/L. This could indicate that the gelation mechanism in that case may be slightly different, a point that will be examined in the following sections of this paper. In the fitting curves of Figure 7, the prefactor A remains constant at -0.1 whereas the exponent R increases with the average size of clay platelets with values of 2.75, 2.73, and 2.39 for sizes 1-3, respectively. For the whole Wyoming montmorillonite, the prefactor value is equal to 2.71. These four values are higher than that obtained for smaller particles such as takovite48 and laponite.11 On the basis of the values derived from the sol-gel transition, it is possible to draw the rheological phase diagram for the three size fractions as well as for the whole Wyoming montmorillonite (Figure 8). The dotted line corresponding to the flocculation transition was not directly determined experimentally and is plotted according to the data published by Abend and Lagaly.62 It corresponds to what they called the transition between repulsive and attractive gels. Contrary to what is observed in the case of laponite,11,21-23,25,29,32,39 or takovite,48 these phase diagrams exhibit transition lines with slightly positive slopes, except at high ionic strength for the two smaller size fractions (parts B and C of Figure 8) where (62) Abend, S.; Lagaly, G. Appl. Clay Sci. 2000, 16, 201.

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Figure 7. Evolution of G′ with the reduced solid concentration C - C0, where C0 is the concentration corresponding to the sol/gel transition: (A) size 1; (B) size 2; (C) size 3; (D) whole Na-montmorillonite before size fractionation.

a slightly negative slope is observed. The existence of such a nose in the phase diagram has recently been experimentally observed and analyzed29 and theoretically predicted for charged colloidal disks.37 However, as for an ionic strength of 10-2 M, the suspensions appear slightly more turbid than those at lower ionic strength, and this slope change in the phase diagram could also be attributed to aggregation processes that may start playing a significant role at such elevated ionic strength. In Figure 8, the position of the first break in the osmotic pressure curves (beginning of the pseudoplateau) is also reported. It appears to be located close to the transition line determined from rheological measurements. Birefringence Measurements. Figure 9 displays some photographs of selected samples observed between crossed polarizer and analyzer. Permanent birefringent textures with numerous threadlike defects reminiscent of nematic ordering are observed as already shown for Laponite RD11,25 and Laponite B.23 The concentration at which permanent birefringence appears is reported in Figure 8. Contrary to what was observed for laponite,25 permanent birefringence does not appear at the end of the pseudoplateau of the osmotic pressure. In the case of the smallest size fraction (Figure 8C), the appearance of permanent birefringence coincides with the sol-gel transition. For all the other samples, permanent birefringence appears at clay concentrations higher than the sol-gel transition but lower than that corresponding to the end of the pseudoplateau. In those three cases, it is then possible to define two types of gels, an isotropic one and a birefringent one. In contrast, for the smallest size fraction only a birefringent gel phase is present.

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Figure 8. Rheological phase diagrams: the filled circles correspond to the sol/gel transition deduced from oscillatory stress measurements, the filled triangles correspond to the start of the plateau of the osmotic pressure curves of Figure 4, the open squares correspond to the apparition of permanent birefringence, the open triangles correspond to the end of the plateau of the osmotic pressure curves of Figure 4; (A) size 1, (B) size 2, (C) size 3, (D) whole Na-montmorillonite before size fractionation.

Figure 9. Birefringence exhibited by the samples between crossed polarizer and analyzer: (A) from left to right, size 3 13.8 g/L for 10-5 M NaCl, size 3 15.2 g/L for 10-5 M NaCl, size 3 16.9 g/L for 10-5 M NaCl; (B) from left to right, size 3 37.1 g/L for 10-3 M NaCl, size 3 43.0 g/L for 10-3 M NaCl, size 3 44.4 g/L for 10-3 M NaCl, size 3 48.7 g/L for 10-3 M NaCl; (C) size 3 43.3 g/L for 10-5 M NaCl; (D) size 3 38.2 g/L for 10-5 M NaCl.

Discussion As shown in Figures 8 and 10, the sol/gel transition deduced from rheological measurements coincides with the change of slope revealed in osmotic pressure measurements. Such a coincidence was already observed for laponite.11,21,22,25,29 Considering the fact that birefringence is observed in the gels, it would be rather tempting to assign the formation of a gel to a missed first-order transition that could be an isotropic/nematic one. In the case of an isotropic/nematic transition, for infinitely thin

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Figure 10. Evolution of the concentration corresponding to the sol/gel transition with the average anisotropy of the particles.

platelets the coexisting densities and pressure at the I/N transition are written as63,64

nID3 ≈ ×93 3.7

nND3 ≈ 4.0

Πn ≈ 15

where nI and nN are the number densities of platelets in the isotropic and nematic phase, respectively, D is the particle diameter, and Πn ) ΠD3/kT is the reduced osmotic pressure. Taking into account the average sizes of fractions 1-3, such equations would predict for an ionic strength of 10-2 M, an I/N transition located between 10.8 and 11.6 g/L for size fraction 1, between 14.5 and 15.7 g/L for size fraction 2, and between 57.4 and 62.1 g/L for size fraction 3. The associated osmotic pressures would be around 1, 2, and 150 Pa for size fractions 1-3, respectively. For an ionic strength of 10-3 M, taking into account the Debye Length and assuming that the particles can still be considered as infinitely thin platelets, the I/N transitions would be located between 10.7 and 11.5 g/L for size fraction 1, between 14.4 and 15.6 g/L for size fraction 2, and between 55.2 and 59.7 g/L for size fraction 3. The associated osmotic pressures would be around 1, 2, and 130 Pa for size fractions 1-3, respectively. For an ionic strength of 10-4 M the values would then be 10.0 and 10.8 g/L for size fraction 1, 13.2 and 14.3 g/L for size fraction 2, and 41.0 and 44.3 g/L for size fraction 3 with associated osmotic pressures around 1, 2, and 55 Pa. Finally for an ionic strength of 10-5 M, the values would be 8.2 and 8.9 g/L for size fraction 1, 10.1 and 11.0 g/L for size fraction 2, and 22.1 and 23.9 g/L for size fraction 3 with associated osmotic pressures around 0.5, 1, and 8 Pa. However, in these two latter cases, it is rather doubtful to assume that the particles can still be considered as infinitely thin platelets. It was for instance convincingly shown that at very low ionic strength, laponite particles behave nearly as isotropic particles.11,29 The values corresponding to the theoretical I/N transition are of the same order of magnitude as those corresponding to the sol/gel transition. However, in such (63) Bates, M. A.; Frenkel, D. J. Chem. Phys. 1999, 110, 6553. (64) Van der Kooij, F. M.; Van der Beek, D.; Lekkerkerker, H. N. W. J. Phys. Chem. B 2001, 105, 1696.

a framework where the sol-gel transition would correspond to a missed isotropic/nematic transition, the concentration corresponding to the transition should decrease with an increase in the anisotropy of the elementary particles. In fact, Wyoming montmorillonite displays an opposite behavior as lower anisotropy shifts the sol/gel transition toward lower solid content. Figure 10 presents the evolution of the concentration corresponding to the sol/gel line determined from rheological measurements with the average aspect ratio (diameter/ thickness) of the particles. The relationship thus obtained is linear for all the ionic strengths investigated with a slightly less convincing relationship for an ionic strength of 10-2 M. This poorer agreement can once again be related to aggregation processes that may well start playing a significant role at ionic strengths g10-2 M. It must be pointed out that in a remarkable study carried out in 1937, Hauser and Reed66 worked on size fractionated Wyoming montmorillonites and formed gels by adding to the suspensions KOH or KCl. In the case of the attractive gels thus formed at high ionic strength, they observed a similar trend with particle size as the one we observe at low ionic strength for repulsive gels, i.e., smaller particles exhibited gel formation at lower solid concentration that larger particles. The relationship between anisotropy and gel formation then seems to extend over a large range of ionic strength for both attractive and repulsive gels. In any case, the inverse linear relationship observed between sol-gel concentration and particle anisotropy tends to discard the interpretation of the sol-gel transition as being the fingerprint of the start of an isotropic/nematic phase transition for clay minerals. A jamming transition should also display a decrease of the concentration corresponding to the sol-gel transition with increasing anisotropy. It could then be suggested that many particles correlation must play a role in the appearance of a soft solid. Such correlations could be linked somehow to the edge faces whose amount increases linearly with decreasing particle anisotropy. Recent calculations on the relative orientation of two charged disks32,65 have shown that the most energetically favorable orientations are those in which particles take edge-edge configurations with a tilt. The sol-gel transition could then occur when a sufficiently high number of particles are blocked in their most favorable relative orientation. Such an explanation could also account for the long-term evolution of clay gels whose characteristic times exceed a week.67,68 One of the remaining questions in such an hypothetical scheme relates to the existence of birefringent textures that indicate long-range order in the gels. As can be seen in Figure 8, permanent birefringence starts appearing either at the sol-gel transition for size fraction 3 or for slightly higher concentrations in the other samples. As in the case of laponite, flow birefringence (observed by flowing the gel in a pipet,11,25 an experiment similar to that described by Langmuir in 19384) started appearing at the first break of the osmotic pressure curve. It seemed relevant to study transient birefringence in montmorillonite suspensions when subjected to shear. In view of the small amounts of sample available, and to try to obtain reproducible shear conditions, 2 mL vials were totally filled with montmorillonite suspensions. Eight microballs of zirconia, 1 mm in diameter, were introduced in the filled (65) Meyer, S.; Levitz, P.; Delville, A. J. Phys. Chem. B 2001, 105, 10684. (66) Hauser, E. A.; Reed, C. E. J. Phys. Chem. 1937, 41, 911. (67) Willenbacher, N. J. Colloid Interface Sci. 1996, 182, 501. (68) Bellour, M.; Knaebel, A.; Harden, J.-L.; Lequeux, F.; Munch, J.-P. Phys. Rev. E 2003, 031405.

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Figure 11. Transient birefringence of the samples between crossed polarizer and analyzer. Evolution of the relaxation time of birefringence with the reduced solid concentration C - C0, where C0 is the concentration corresponding to the sol/gel transition: (A) 10-5 M NaCl; (B) 10-4 M NaCl; (C) 10-3 M NaCl.

vials. The samples were then shaken during 5 s. The whole process was carried out between crossed polarizer and analyzer and in all cases birefringence flashes were observed upon application of shear. After the shear was stopped, the time required for the shear-induced birefringent textures to disappear was measured. Figure 11 presents an example of the extinction of birefringence and the evolution of the thus determined relaxation time as a function of the reduced concentration C - C0 where C0 is the concentration of the sol-gel transition. It appears that all the samples display shear-induced birefringence even when they are located in the liquid region of the phase diagram far from the sol/gel transition. In all cases, the relaxation times are higher than 1 s, i.e., values that are much higher than the relaxation time of an individual particle. Indeed, for a disk-shaped particle, the rotational diffusion can be approximated according to the formula69 Dr ≈ 3kT/32ηb3, where η is the viscosity and b the disk diameter. Taking into account the average diameter of sizes 1-3, the relaxation time of individual particles can then be estimated around 3 × 10-3, 10-3, and 2 × 10-5 s. In the liquid region, for suspensions located at the same distance from the sol-gel transition line, the relaxation time varies with the aspect ratio of the individual particles, smaller particles leading to faster-relaxing structures. In contrast, the relaxation time diverges faster for smaller particles when the suspensions get closer to the sol-gel transition line. In addition, for all sizes, the relaxation time decreases with increasing ionic strength, which confirms that the system is repulsive. All these results could suggest that shear-induced birefringence is linked to the formation of oriented large-scale structures much larger than the individual particles. As a support to this tentative assumption, it must be pointed out that large scale millimetric structures were indeed observed in Wyoming montmorillonite gels by synchrotron X-ray fluorescence.70 (69) Hunter, R. J. Foundations of Colloidal Science; Oxford Science Publishers: 1987; Vol. 1.

Concluding Remarks To sum up, the results obtained in the present study show that the sol/gel transition is not directly related to the emergence of an ill-defined isotropic/nematic transition involving individual clay particles. Indeed, even if the sol/ gel transition is never far from Onsager’s prediction except for size 3 (small particles), the experimental sol/gel transition increases linearly with particle size, as shown in Figure 10. A reverse evolution should be observed for an I/N transition involving the individual clay particles. In terms of phase diagrams and influence of anisotropy, smectite clay minerals behave differently from other systems of charged colloidal platelets. For high charge Mg/Al layered double hydroxides (LDH)71 and for gibbsite particles treated with Al13 Keggin ions,72 an isotropic/ nematic transition with phase separation was recently observed before gel formation. For lower charge Ni/Al LDHs,48 gel formation was observed with no phase separation and the influence of particle anisotropy was the opposite of the one we observe in the present study, i.e., the largest particles underwent a sol/gel transition at much lower solid content than the smallest ones. This illustrates a statement given in ref 72: “the theoretical understanding of the phase behavior of charged colloidal platelets is still in its infancy”. Obviously, the interplay between charge, anisotropy and ionic strength is still far from being understood. In the case of smectite clay samples, one of the key issues is to better understand what we call the “sol”. The observation of an important transient birefringence under shear suggests that interacting clay particles are amenable (70) Bihannic, I.; Michot, L. J.; Lartiges, B. S.; Vantelon, D.; Labille, J.; Thomas, F.; Susini, J.; Salome´, M.; Fayard, B. Langmuir 2001, 17, 8A. (71) Liu, S. Y.; Zhang, J.; Wang, N.; Liu, W. R.; Zhang, C. G.; Sun, D. J. Chem. Mater. 2003, 15, 3240. (72) Van der Beek, D., Lekkerkerker, H. N. W. Europhys. Lett. 2003, 61, 702. (73) Segre, P. N.; Prasad, V.; Schofield, A. B.; Weitz, D. A. Phys. Rev. Lett. 2001, 86, 6042.

Phase Diagrams of Clay

to generate, at rest and/or under shear, large anisotropic particle associations. These permanent or transient clusters are certainly mechanically disconnected. Two interesting questions can then be raised: (i) Are these associations (or clusters or tactoids) stable at rest, making the “sol” an heterogeneous suspension? (ii) Is there a location inside the pseudophase diagram shown in Figure 8, at low particle concentration and/or low ionic strength, where the suspension can be considered as a liquid of individual particles homogeneously distributed in space. What could be the status of the sol/gel transition for clay samples? Two possible alternatives are conceivable: a jamming transition or a percolation threshold.73 The first mechanism occurs when the crowding of clusters formed in the sol cause them to touch in a close packed way whereas the percolation transition will induce a heterogeneous elastic network where the correlation length between two connections is well above the characteristic particle size. The evolution of G′, shown in Figure 7, could be considered as a typical feature of an elasticity

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percolation in three-dimensions. According to both these hypothetical mechanisms, the experimental evolution of the sol/gel transition with particle size imposes that the connecting clusters or percolating threads are much larger than the size of the disklike clay particles. In the future, we will focus our work on the understanding of the dependence of the sol/gel transition with particle size and on the structure of the “sol” phase near the sol/gel transition. The influence of particle charge will also be investigated by using different natural clay samples. Acknowledgment. The authors thank Dominique Poly for her help in the osmotic pressure measurements and Dr. Patrick Davidson for enlightening discussions. The authors also thank one anonymous reviewer for his/ her fruitful comments and for attracting our attention to ref 66. LA0489108