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Dubois, E.; Perzynski, R.; Boué, F.; Cabuil, V. Langmuir 2000, 16, 5617−5625. [ACS Full ... Phase Diagrams of Wyoming Na-Montmorillonite Clay. Infl...
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Langmuir 2002, 18, 1466-1473

Magnetic Colloidal Particles as Probes for the Determination of the Structure of Laponite Suspensions Fabrice Cousin,*,†,§ Vale´rie Cabuil,† and Pierre Levitz‡ Laboratoire des Liquides Ioniques et Interfaces Charge´ es, CNRS UMR 7612, case 63, Universite´ Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris Cedex 05, France, and Centre de Recherche sur la Matie` re Divise´ e, Centre National de la Recherche Scientifique, 45071 Orle´ ans Cedex 2, France Received June 22, 2001. In Final Form: December 5, 2001 A new way to probe the microscopic structure of suspensions of discotic particles of Laponite is reported. Magnetic spherical colloidal particles of maghemite are incorporated into the Laponite suspensions to study their spatial repartition and their microrheological behavior. Chemicals conditions are found for the synthesis of stable mixtures. The determination of the equation of state of the obtained mixtures by osmotic measurements shows that the inclusion of the probes does not modify the structure of Laponite suspensions which exhibit a fluid-solid transition at a given volume fraction. The transition is related to the appearance of a pseudoplateau in the equation of state of the system. SANS and microrheological measurements show that the probes are homogeneously dispersed in the mixture out ofthe pseudoplateau and that there is a microscopic phase separation between Laponite particles and maghemite probes in the region of the pseudoplateau of the equation of state. This microscopic phase separation is consistent with the description of Laponite suspensions as microscopically segregated in the region of the pseudoplateau.

1. Introduction Colloidal dispersions of particles exhibit phase transitions that are strongly dependent on the shape of the particles.1 The case of suspensions of spheres has been widely studied, both experimentally and theoretically, during the past 50 years.2 The suspensions of anisotropic particles, which may exhibit specific phase behaviors due to their anisotropy,3 are now under consideration. Langmuir decribed as early as 1938 the behavior of dispersions of bentonite clays.4 He observed that the suspensions of bentonite spontaneously separate into two phases: a nematic solid and an isotropic fluid. This phase separation has been lately explained as an Onsager transition.5 Contrary to the dispersions of rodlike particles that have been largely studied6-8 since the pioneering work of Langmuir, the dispersions of platelets or discotic particles have been scarcely studied. Suspensions of gibbsite platelets in apolar media have been recently described by Van der Kooij and Lekkerkerker who observe typical isotropic-nematic Onsager transitions.9 The case of aqueous suspensions appears to be more complex, as it combines long-range electrostatic * To whom correspondence should be addressed. † Universite ´ Pierre et Marie Curie. ‡ Centre National de la Recherche Scientifique. § Present address: Laboratoire Le ´ on Brillouin, CEA-CNRS UMR 12, CE-Saclay, 91191 Gif-sur-Yvette, France. (1) Forsyth, P. A.; Marcelja, S.; Mitchell, D. J.; Ninham, B. W. Adv. Colloid Interface Sci. 1978, 9, 37-60. (2) See for example Pusey, P. N. Colloidal suspensions. In Liquids, Freezing and Glass Transitions; Hansen, J. P., Levesque, D., ZinnJustin, J., Eds.; North-Holland: Amsterdam, 1991; pp 765-942. (3) Vroege, G. J.; Lekkerkerker, H. N. W. Rep. Prog. Phys. 1992, 55, 1241. (4) Langmuir, I. J. Chem. Phys. 1938, 6, 873. (5) Onsager, L. Ann. N.Y. Acad. Sci. 1949, 51, 627. (6) Zocher, H. Z. Anorg. Chem. 1925, 147, 97. (7) Buining, P. A.; Philipse, A. P.; Lekkerkerker, H. N. W. Langmuir 1994, 10, 2106-2114. (8) Davidson, P.; Bourgaux, C.; Schoutteten, L.; Sergot, P.; Williams, C.; Livage, J. J. Phys. II 1995, 5 (10), 1577-1596. (9) Van der Kooij, F. M.; Lekkerkerker, H. N. W. J. Phys. Chem. B 1998, 102, 7829-7832.

effects and entropic effects. In the past few years, aqueous suspensions of discotic particles of Laponite have emerged as a model for dispersions of discotic systems in aqueous media.10-18 Aqueous suspensions of Laponite exhibit a fluid-solid transition over a given concentration, which depends on the ionic strength. The microscopic structure of the suspensions and the nature of this transition are still under debate. Especially microscopic inhomogeneities in the structure of apparently homogeneous solid suspensions of Laponite are suspected. We propose in this paper a new method to test this hypothesis: nanoscopic spherical particles are included as probes in the suspensions and their spatial repartition is studied by SANS. The chosen probes have to be chemically compatible with Laponite and must not modify the structure of the Laponite suspensions. The probes we use are spherical maghemite particles,19 which have specific magnetooptical properties that allow rheological measurements to be performed on a nanoscopic scale. As a matter of fact, if microscopic heterogeneities exist in Laponite solids, the investigation of the rheology of the system on a nanoscopic scale is a relevant problem. (10) Mourchid, A.; Delville, A.; Lambard, J.; Le´colier, E.; Levitz, P. Langmuir 1995, 11 (6), 1942-1950. (11) Gabriel, J.-C. P.; Sanchez, C.; Davidson, P. J. Phys. Chem. 1996, 100, 11139-11143. (12) Kroon, M.; Wedgam, H. G.; Sprik, R. Phys. Rev. E 1996, 54, 6. (13) Trizac, E.; Hansen, J.-P. Phys. Rev. E 1997, 56 (3), 3137-3149. (14) Pignon, F.; Piau, J. M.; Magnin, A. Phys. Rev. Lett. 1996, 56 (3), 3281-3289. (15) Mourchid, A.; Le´colier, E.; Van Damme, H.; Levitz, P. Langmuir 1998, 14, 4718-4723. (16) Bonn, D.; Tanaka, H.; Wegdam, G.; Kellay, H.; Meunier, J. Europhys. Lett. 1998, 45 (1), 52-57. (17) Bonn, D.; Kellay, H.; Tanaka, H.; Wegdam, G.; Meunier, J. Langmuir 1999, 15, 7534-7536. (18) Levitz, P.; Lecolier, E.; Mourchid, A.; Delville, A.; Lyonnard, S. Europhys. Lett. 2000, 49 (5), 672. (19) Bacri, J.-C.; Perzynski, R.; Salin, D.; Cabuil, V.; Massart, R. J. Magn. Magn. Mater. 1990, 85, 27-32.

10.1021/la010947u CCC: $22.00 © 2002 American Chemical Society Published on Web 02/01/2002

Determination of Structure of Laponite Suspensions

2. Background 2.1. Aqueous Suspensions of Laponite Particles. Laponite is a synthetic clay of the general formula Si8Mg5.45Li0.4H4O24Na0.7. Particles are discotic; SAXS measurements have shown that their diameter is around 30 nm and their thickness 1 nm, with a rather low polydispersity. The particles are usually dispersed in aqueous media at pH 10. The chemical pH stability range of the particles is narrow: Thompson and Butterworth have shown that below pH 9 the magnesium ions dissolve in solution.20 Above pH 10.5 the dissolution of silica is observed. The structural charge of the surface of particles is negative. The edge charge depends on the acid-base behavior of the Si-OH and Mg-OH amphoteric hydroxyl groups, which are the main species on the edge. At pH 10, this edge surface is weakly positive (the PZC of Mg-OH is pH 12.521]). The averaged surface charge of the particle is overall negative. The physicochemical conditions imposed to obtain stable dispersions of Laponite particles are strict: when the ionic strength in the suspension is higher than 2 × 10-2 mol/L, attractions in the system lead to flocculation. In the convenient conditions of pH (pH 10) and ionic strength (I < 2 × 10-2 mol/L), Laponite dispersions exhibit a rheological fluid-solid transition for a given volume fraction of particles. For an ionic strength higher than 10-4 mol/L, the transition is shifted toward low particles volume fraction when ionic strength increases.10 For an ionic strength lower than 10-4 mol/L, the slope of the transition’s line is inverted and the transition is shifted toward the high particles volume fraction when ionic strength increases18 as observed in spherical systems. Above 10-4 mol/L the transition is related to the appearance of a pseudoplateau in the equation of state of the system.10 The end of the pseudoplateau may be related to an ill-defined isotropic-nematic transition.11 Although this plateau in the equation of state is characteristic of a first-order transition, the Laponite suspensions stay macroscopically homogeneous and the existence of biphasic samples has never been reported. Nevertheless, the density of particles seems to fluctuate in the Laponite suspensions10,14 and the isotropic-nematic transition may occur only on a microscopic scale. The nature of the fluid-solid transition of Laponite is still under discussion and several theories are proposed. Quadripolar electrostatic attractions have been invoked as being at the origin of structures of “house of cards” due to the sticking of faces and edges.13 Long-time experiments have lead several authors to conclude on the non-ergodicity of the system and on the vitreous nature of the transition12,16,17 in the regime of low ionic strength (I < 10-4 mol/L), proving that the system has not reached equilibrium and that long-range electrostatic repulsions play an important role in Laponite suspensions. In the high ionic strength regime (I > 10-4 mol/L), the transition has also been described as an isotropic-nematic Onsager transition on the basis of the following arguments: The shift of the transition toward the low volume fraction with an increase of the effective anisotropy of the particles and the appearance of a liquid-solid and an isotropicnematic transitions at the borders of the pseudoplateau.10 The transition can be “frustrated” by long-range electrostatic interactions between faces and edges and occurs (20) Thompson, D. W.; Butterworth, T, J. Colloid Interface Sci. 1992, 151 (1), 236-243. (21) Stumm, W. Chemistry of the solid-liquid interface; John Wiley & Sons: New York, 1992.

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only on a microscopic scale, explaining why the samples remain macroscopically monophasic in the region of the plateau of the equation of state. Nevertheless, the experimental volume fraction of the transition is 10 times lower than the one predicted by the Onsager theory for such an anisotropic ratio of particles. As the transition can be “frustrated” by long-range electrostatic interactions, one point has to be clarified: are the suspensions of Laponite microscopically biphasic in the region of the plateau of the equation of state when the ionic strength is above 10-4 mol/L? We propose here to include nanoscopic magnetic probes in Laponite suspensions to answer this question. 2.2. The Probes: Spherical Maghemite Nanoparticles. The probes we have chosen to test the Laponite suspensions are magnetic nanoparticles made of a ferric oxide of maghemite (γ-Fe2O3). (a) TEM pictures22 and measurements of the form factor of particles by SAXS23 show that the shape of the particles is spherical. Thus, they do not exhibit specific hard-core geometrical interactions with anisotropic particles. (b) They have a mean diameter of 8 nm, which is inferior to the supposed size of the heterogeneities of the Laponite suspensions. The size distribution is usually described by a log-normal law:24

P(d) )

1

x2πσd

[ ( )]

exp -

d 1 ln 2 d 2σ 0

2

(c) When coated by citrate species, they can be dispersed in aqueous media at pH 10 as negatively charged particles. Dispersions of citrate-coated particles are stable from pH 4 to pH 10. The adsorption equilibrium of the citrate species controls the number of surface charges: the plateau of adsorption is reached over a concentration of citrate in solution equal to 2 × 10-3 mol/L.25 The ionic strength of the medium is thus due to the unadsorbed species, that is, trisodium citrate, and dispersions are stabilized by electrostatic repulsions. The citrate-coated particles have the same counterions as Laponite particles (Na+).26,27 (d) The particularity of these maghemite particles is their magneto-optical properties that allow the viscosity in the neighborhood of the magnetic particles to be measured. Each particle bears a permanent magnetic moment. For the small particles, the magnetic moment is not locked in the crystallographic axes (superparamagnetic behavior) and the particles exhibit Neel relaxation after the cutoff of an applied magnetic field. For the biggest particles (for d0 > 7 nm), the magnetic moment is locked in the crystallographic axes (ferrimagnetic behavior) and the particles exhibit brownian relaxation.22 Particles have an intrinsic optical anistropy related to their magnetic anistropy, as evidenced by Hasmonay et al.27 When a magnetic field is applied, the ferrimagnetic particles orientate along the axis of the field if they are not mechanically blocked and the sample into which they are dispersed becomes macroscopically birefringent.26 The intensity of the birefringence signal of the sample ∆n is (22) Bacri, J.-C.; Perzynski, R.; Salin, D.; Cabuil, V.; Massart, R. J. Magn. Magn. Mater. 1986, 62, 36-46. (23) Cousin, F. Paris VI University thesis, 2000. (24) Bacri, J.-C.; Perzynski, R.; Salin, D.; Cabuil, V.; Massart, R. J. Colloid Interface Sci. 1988, 132 (1), 43. (25) Dubois, E.; Cabuil, V.; Boue´, F.; Perzynski, R. J. Chem. Phys. 1999, 111, 7147. (26) Bacri, J.-C.; Perzynski, R.; Salin, D.; Cabuil, V.; Massart, R. J. Magn. Magn Mater. 1987, 65, 285-288. (27) Hasmonay, E.; Dubois, E.; Bacri, J.-C.; Perzynski, R.; Raikher, Y.; Stepanov, V. I. Eur. Phys. J. B 1998, 5, 859-867.

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proportional to the number of magnetic particles able to rotate and is a function of the intensity of the applied magnetic field. When there are no aggregates in solution and no magnetic interactions between particles (i.e., for diluted suspensions), it follows the second Langevin law27:

(

∆n ) ∆ns 1 -

)

3 3 x tanh x x2

(1)

with

x ) µH/kT (µ is the magnetic moment of the particles, H the applied magnetic field, k the Boltzmann constant, and T the temperature) and ∆ns the birefringence intensity for an infinite applied magnetic field. If the magnetic field is progressively decreased, an eventual remanence of the birefringence signal in the sample indicates that, under a given magnetic field, the magnetic energy provided by the field is not sufficient to induce the rotation of the particles. When the field is cut off, the particles relax by brownian motion and the decay time, τ, of the birefringence intensity of the sample is related to the coefficient of rotational diffusion, D0, of the particles. The decrease of the birefringence signal is thus described by an exponential law: ∆n ) ∆nBe(-t/τ) with ∆nB being the intensity of birefringence of the sample at the given applied field and

τ)

ηV 1 ) 6D0 kT

(V is the volume of a particle, η the viscosity of the liquid carrier, T the temperature, and k the Boltzmann constant).28 When magnetic nanoparticles do not aggregate, the volume of the species is not modified and the relaxation time τ is a measure of the viscosity in the vicinity of the particles. The volume fraction of maghemite particles, Φmaghemite_particles, will be limited to 0.05% and we shall verify that the structure of Laponite suspensions is not modified by the introduction of such an amount of probes. 3. Experimental Section 3.1. Materials. 3.1.1. Laponite. Laponite particles are purchased from Laporte Industries Ltd. (Laponite RD). They have a high chemical purity. (A chemical study on such particles has shown that traces of metals such as iron, aluminum, and calcium are in negligeable quantities.29) They are dispersed on distilled water set to pH 10 with NaOH and stirred at 15 000 rpm with a homogeneizer device. 3.1.2. Maghemite Particles. Magnetic particles are synthesized using Massart’s method.30 Alkalanization of FeCl3 and FeCl2 mixtures leads to the precipitation of magnetite, which is chemically oxidized to maghemite in an acidic medium. Addition of trisodium citrate in the solution allows coating of particles with citrate ions. They are negativelly charged for all pH above 3 and can be dispersed in water. The parameters d0 and σ of the size distributions are deduced from a two-parameter fit of the shape of the magnetization curve. This magnetization curve is obtained with a vibrating sample magnometer device. For all experiments described in this paper, d0 is found equal to 7.5 nm and σ close to 0.35. 3.2. Procedure for the Synthesis of the Mixtures. The mixtures are prepared using the following procedure: citratecoated magnetic particles are synthesized and dispersed in distilled water (degassed to prevent any formation of CO3-) to (28) Perrin, J. J. Phys. Radium. 1934, 5, 33. (29) Le´colier, E. Orle´ans University thesis, 1998. (30) Massart, R. IEEE Trans. Magn. 1981, 17, 1247.

set their volume fraction at 0.05%. pH and Na3Cit concentration in the solution are imposed by dialysis. The reservoir is a solution of Na3Cit (2.5 × 10-3 mol/L) in NaOH (10-4 mol/L). Equilibrium is controlled measuring the conductivity of the solution. The liquid of the reservoir is replaced as many times as necessary. When equilibrium is reached, the clay is dispersed in the magnetic particles dispersion and stirred vigorously at 15 000 rpm for 10 min using a homogenizer device. It is impossible to synthesize samples with a volume fraction of Laponite particles higher than 2% because the gel becomes so viscous that the dispersions obtained are not homogeneous, even for such vigorous stirring. The suspensions are then allowed 10 days at rest before some measurements are performed. 3.3. Techniques for Characterization of the Mixtures. 3.3.1. Osmotic Pressure Measurements. Colloidal suspensions are often described with the same formalism as simple liquid systems.2 The osmotic pressure in colloidal suspensions is the analogue of the pressure in simple liquid systems and its measurement as a function of the volume fraction gives the equation of state of the suspension. We use two different techniques to obtain the osmotic pressure of the systems: direct measurements with a membrane osmometer and osmotic stress. (a) Membrane Osmometer: The measurements are performed using a membrane osmometer Knauer (model A0330). This apparatus is divided into two parts, one containing the colloidal dispersion and the other one (the so-called “reservoir”) containing an aqueous solution at the same ionic strength. These two parts are separated by a membrane, allowing the small ions to diffuse across. The pressure difference between the two parts is exactly the osmotic pressure due to colloidal particles. It is measured by a sensitive pressure sensor. The apparatus is thermalized. Before the measurements, the ionic strength of the colloidal dispersion is adjusted to the desired value through dialysis. It is not possible to study a solid sample with the osmometer. (b) Osmotic stress: This method allows osmotic pressure measurements in a large range of osmotic pressures and volume fractions to be performed without modifying the chemical composition of the samples.31 These samples are dialyzed against a liquid reservoir that has the required ionic strength and pH. A Dextran polymer (Mw ) 110 000 g/mol) is added in the bath and imposes its own osmotic pressure, fixing the chemical potential of water. This osmotic pressure is dependent on neither ionic strength nor pH. The phenomenological law followed by the osmotic pressure as a function of the concentration of polymer has been established elsewhere:10 log 10(Πdyn/cm2) ) 1.826 + 1.715w0.297 (100w is the massic fraction of polymer in solution) and is easily experimentally verified using the membrane osmometer. The reservoir is replaced as many times as necessary to reach the equilibrium, which takes 3 weeks. The new volume fraction of particles in the suspension is then determined by gravimetry. 3.3.2. SANS. The spatial repartition of the magnetic spherical particles is studied by SANS. The total amplitude AT(q) of the wave scattered by the binary mixture is AT(q) ) Al(q) + Ap(q) where l corresponds to Laponite particles and p to probes. Thus,

IT(q) ) |Al(q)|2 + |Ap(q)|2 + 2|Al(q)Ap(q)*|

(2)

IT(q) ) Il + Ip + Ilp

(3)

By playing on the ratio of deuterated water in the solvent, it is possible to realize the extinction of Laponite particles and IT(q) reduces to Ip. As the density of the diffusion scattering length of Laponite is 3.91 × 1010 cm-2, we use mixtures containing 64.9% of D2O and 35.1% of H2O.

Ip(q) ) np∆Fp2Pp(q)Spp(q)

(4)

with np is the density of the probes, ∆Fp2 the contrast between the probes and the solvent, Pp(q) the form factor of the probes, and Spp(q) the partial structure factor between probes in the suspension. (31) Parsegian, V. A.; Fuller, N.; Rand, R. P. Proc. Natl. Acad. Sci. 1979, 76 (6), 2750.

Determination of Structure of Laponite Suspensions

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Figure 2. Comparison of the stability range of Laponite suspensions and maghemite suspensions for pH (a) and ionic strength (b). Stable domains are represented in light gray and unstables ones in dark gray. The arrows correspond to the experimental conditions of the mixtures.

Figure 1. (a) Experimental setup for the measurement of the birefringence’s relaxation time. (b) Example of birefringence’s relaxation time curve. It is not possible to achieve the extinction of the maghemite probes because their density of diffusion scattering length is out of the reachable range for H2O/D2O mixtures (6.96 × 1010 cm-2). Measurements have been performed at ILL (Grenoble, France) on a D11 spectrometer. The scattering vector ranges from 1.6 × 10-3 to 3 × 10-2 Å-1. 3.3.3. Birefringence Measurements. Two kinds of experiments are performed: a static measurement of the birefringence intensity as a function of an applied magnetic field and a dynamic measurement of the birefringence intensity after the cutoff of the field. (a) Static birefringence: The sample is placed between crossed polarizers and is submitted to a magnetic field varying from 0 to 1 T (the direction of the field forms an angle of π/4 with the axes of polarizers). A photodiode detects the signal of a laser beam (He-Ne, 632 nm) passing through the common axis of the polarizers and the sample and allows detection of ∆n. The intensity of the magnetic field is measured with a gaussmeter. (b) Dynamic birefringence: The experimental device is similar to the one for static birefringence and is presented in Figure 1. The sample is submitted to pulses of magnetic field of 0.017 T. The relaxation time τ is deduced from the signal of the photodiode. This device allows one to determine if some magnetic particles are mechanically blocked in the samples for a given magnetic field B: The comparison of the value of the birefringence of the sample ∆nB (renormalized by the optical transmission factor of the sample at the wavelength of the laser) is compared to the one of a suspension of magnetic particles at the same volume fraction to calculate the volume fraction Φblocked of blocked particles in the sample by

Φblocked )

(∆nB)sample/Tsample (∆nB)ferrofluid/Tferrofluid

(5)

The value of the volume fraction Φblocked is characteristic of the intensity of the applied magnetic field (here 0.017 T) and may underestimate the volume fraction of blocked magnetic particles at zero magnetic field.

4. Results 4.1. Getting Stable Mixtures: Chemical and Physicochemical Conditions. First of all, one has to find the

conditions of pH and ionic strength for which mixtures of Laponite and maghemite particles are stable. As there is an adsorption equilibrium of trisodium citrate at the surface of the maghemite particles, the ionic strength is imposed by sodium and citrate ions. There is a narrow pH range where stable mixtures are produced (Figure 2a): under pH 9, the Laponite particles chemically dissolve and over pH 10 desorption of citrate ions from the surface of the maghemite occurs due to a replacement of citrate ions by OH- ions and Laponite particles dissolve too. The compatible range for the ionic strength is also narrow (Figure 2b). The adsorption isotherm for citrate species on maghemite particles presents a plateau for a concentration of Na3Cit ) 2 × 10-3 mol/L. It is thus impossible to use lower concentrations in the mixtures. On the other hand, suspensions of Laponite flocculate for ionic strength above 2 × 10-2 mol/L.10 Trisodium citrate being a 3:1 electrolyte, this threshold corresponds to [Na3Cit] ) 3.3 × 10-3 mol/L. We experimentally measure this threshold at [Na3Cit] ) 3 × 10-3 mol/L. The range of suitable ionic strength corresponds thus to 2 × 10-3 < Na3Cit < 3 × 10-3. According to Figure 2, we have fixed the pH to 10 and the ionic strength to [Na3Cit] ) 2.5 × 10-3 mol/L in all mixtures. The pH and the ionic strength are imposed by dialysis. This Na3Cit concentration is equivalent to an ionic strength of

I)

1 2

∑i cizi2

of 1.5 × 10-2 mol/L (ci is the concentration of the species i and zi is its valency). It corresponds to the regime of ionic strength where the fluid-solid transition of Laponite suspensions is shifted toward low volume fraction as the ionic strength increases. 4.2. Equation of State of Mixed Laponite/Maghemite Suspensions. As described above, the osmotic pressure of the aqueous suspensions of Laponite has been measured by Mourchid et al.10 as a function of the ionic strength. These authors have always imposed the ionic strength of the system by a 1-1 electrolyte (NaCl). In the present work a 3-1 electrolyte (Na3Cit) is used. Therefore, we have characterized Laponite suspensions in these conditions, that is, in the presence of an ionic strength related to [Na3Cit] ) 2.5 × 10-3 mol/L. Macroscopically, suspensions are liquid for Laponite volume fractions lower than 0.57% and solidlike over this threshold. The most concentrated samples (over a volume fraction of 2%) become birefringent on a time scale of several weeks but it is difficult to appreciate if there is a well-defined volume fraction threshold above which such a birefringence is observed.

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Figure 3. Equation of state of Laponite suspensions in a Na3Cit solution (2.5 × 10-3 mol/L) at pH 10 (open dots) and equation of state of mixtures of Laponite and maghemite particles in the same chemical conditions (filled dots). The dotted lines separate the three characteristic domains of the equation of state of mixtures considered in the text and denoted respectively 1 for the range of Laponite volume fraction preceding the pseudoplateau, 2 for the pseudoplateau, and 3 for the range of Laponite volume fraction after the pseudoplateau.

The equation of state of Laponite suspensions is presented in Figure 3. Measurements are conducted using the membrane osmometer for the low volume fractions of Laponite as long as the suspension stays liquid. Osmotic stress experiments are performed for higher volume fractions. The equation of state presents a characteristic pseudoplateau. The beginning of the plateau corresponds to the liquid-solid transition as observed by visual inspection. 4.3. Structure of Laponite Suspensions Including Magnetic Spherical Probes. A first question has to be clarified: How perturbative is the addition of probes in Laponite suspensions? Mixtures are fluids for a low volume fraction of Laponite particles and form isotropic solids as the volume fraction of Laponite particles increases. Some birefringence appears for the most concentrated samples after a time. The aspect of the solid mixtures is the same as the one of suspensions of Laponite, except their color, which is homogeneously orange because of the ferric oxide species dispersed in the medium. The volume fraction of Laponite for which the liquid-solid transition appears is the same as the one in the absence of the probes (ΦLaponite ) 0.57%). The osmotic pressure of mixtures has been measured by osmotic stress. Obviously, the change of the particles volume fraction induced by the osmotic stress does not allow one to work with a constant volume fraction of magnetic particles. The constant parameter is thus the ratio Vclay_particles/Vspherical_particles, which is set to 7.6. This ratio ensures that, during the experiment, whatever ΦLaponite, Φmaghemite particles stays higher than 0.05% and is chosen considering the relative osmotic pressures of Laponite suspensions and maghemite suspensions: the osmotic pressure due to Laponite particles is much higher than the one due to maghemite particles. The equation of state experimentally obtained is given in Figure 4 and compared with the one of a Laponite suspension without magnetic probes. The osmotic pressure is given as a function of the volume fraction of Laponite particles in the case of the mixtures. It still presents a pseudoplateau. Three distincts regions are observed (before, along, and after the plateau) denoted hereafter 1, 2, and 3 (see Figure 3).

Cousin et al.

Figure 4. Effective structure factor of magnetic probes in mixtures. Φmaghemite is set constant (0.05%). The volume fractions of Laponite particles correspond respectively to the first part of the equation of state (Φ ) 0.18%), the beginning of the pseudoplateau (Φ ) 0.59%), the end of the pseudoplateau (Φ ) 0.1.48%), and the third part of the equation of state (Φ ) 2.00%).

4.4. Spatial Repartition of Spherical Magnetic Probes in the Laponite Suspensions. Four mixtures belonging respectively to the three regions of the equation of state are characterized by SANS: a fluid sample of ΦLaponite ) 0.18% (region 1 of the equation of state), two solids samples of ΦLaponite ) 0.59% and ΦLaponite ) 1.48% corresponding to the beginning and the end of the pseudoplateau of the equation of state, and a solid sample of ΦLaponite ) 2.0% above the pseudoplateau in region 3. The neutron scattering length density of the solvent is adjusted to the one of Laponite particles to match them in all the samples. Φmaghemite is set constant to 0.05%. Figure 4 presents the effective structure factors Sprobes-probes. The effective structure factors are obtained by dividing absolute intensities measured on binary mixtures by the form factor of maghemite particles. This form factor has been determined on a diluted suspension of maghemite particles free of Laponite particles. 4.5. Viscosity in the Vicinity of the Spherical Magnetic Probes in the Laponite Suspensions. 4.5.1. Static Birefringence. The birefringence of three mixtures, with ΦLaponite ) 0.37% (region 1), ΦLaponite ) 1.11% (region 2), and ΦLaponite ) 1.48% (region 2, end of the plateau), and a constant volume fraction of maghemite particles (0.05%) have been recorded as a function of the applied magnetic field and treated as described in ref 27. The samples containing 0.37% and 1.11% of Laponite follow the same Langevin second law as a suspension of 0.05% maghemite particles (Figure 5a). Figure 5b presents the curve obtained for the sample containing 1.48% of Laponite, exhibiting a small remanence. The presence of mechanically blocked probes in the direction of the imposed applied magnetic field also give a remanent magnetization which disappears after a few hours. The value of the magnetization is very weak due to the small number of blocked particles and does not allow quantitative measurements. 4.5.2. Relaxation of Birefringence. Four mixtures corresponding to the three regions of the equation of state are characterized by birefringence relaxation measurements: a liquid sample of ΦLaponite ) 0.18% (region 1) and three solids samples of ΦLaponite ) 1.11% (region 2), ΦLaponite ) 1.48% (region 2, end of the plateau), and ΦLaponite ) 1.85% (region 3). The results obtained on a suspension of maghemite particles (Φ ) 0.05%) are presented for comparison. Figure 6 presents the ratio of blocked probes as a function of Laponite volume fraction and Table 1

Determination of Structure of Laponite Suspensions

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5. Discussion

dispersions of Laponite. Under these conditions (pH 10, presence of a 3:1 electrolyte) the osmotic pressure of Laponite follows the same experimental law as a suspension of Laponite in the presence of a 1-1 electrolyte. A pressure plateau is observed and a macroscopic fluidsolid transition occurs at the beginning of the plateau. The ionic environment we impose does not perturb the structure of Laponite suspensions. The inclusion of magnetic probes in the Laponite suspensions does not macroscopically modify the phase behavior of such suspensions: the volume fraction of the fluid-solid transition does not evolve. As shown in Figure 3, osmotic pressures of Laponite suspensions with and without a small amount of magnetic particles are identical. Therefore, the equation of state of Laponite suspensions is not modified by the adjunction of probes. Especially the pseudoplateau still exists and is not shifted. The structure of Laponite suspension does not appear to be modified by the inclusion of the probes. As a matter of fact, in a binary mixture, if one of the two components of the system has a much higher osmotic pressure than the other one, it imposes its structure on the system. The osmotic pressure of a suspension of citratecoated particles stays lower than 5 Pa for a volume fraction of 0.05% and lower than 25 Pa for a volume fraction of 0.45% (the greater volume fraction of maghemite particles reached in mixtures by osmotic stress) and is indeed highly inferior to the osmotic pressure of Laponite (see Figure 3). Experimental determination of the osmotic pressure of dispersions of citrate-coated particles using the membrane osmometer has not been possible. Pressures are so weak in the range of the very low volume fractions presented in this study that experimental errors on osmotic measurements with the membrane osmometer become very important. These osmotic pressures were estimated using a second-virial development which is sufficient to describe the osmotic pressures of suspensions for volume fractions below 2%.32 The second virial coefficient has been recently measured by SANS by Dubois et al.33 It has to be noticed that even if the structure of the Laponite suspension is not modified by the probes, the introduction of these probes can promote new interparticular interactions. The signature of such a modification in the interaction balance would be a difference between the osmotic pressure of the mixture and the sum of the osmotic pressures of the individual systems: an increase of osmotic pressure would indicate that repulsions have been added and a decrease of osmotic pressure would point out a diminution of repulsions. Figure 7 compares the osmotic pressure of the mixture to the sum of the pressures of the individual components. These pressures are exactly similar. It means that including maghemite particles in Laponite suspension does not imply specific repulsion or attraction between the two kinds of particles. As the probes do not perturb Laponite suspensions, we feel we are allowed to study their spatial repartition and their mechanical behaviors in such suspensions and to deduce some conclusions concerning Laponite suspensions: (a) The SANS spectra of maghemite particles in matched Laponite suspensions (Figure 4) point out that the spatial repartition of the probes differs in the three regions of the equation of state. In region 1 where the suspensions are fluid, the effective structure factor Sprobes-probes is equal to 1 in the whole range of q. That means that the probes behave as a

This work shows that it is possible to find chemical and physicochemical conditions that allow a small amount of maghemite particles to be introduced into aqueous

(32) Cousin, F.; Cabuil, V. J. Mol. Liq. 1999, 83, 1, 203. (33) Dubois, E.; Perzynski, R.; Boue´, F.; Cabuil, V. Langmuir 2000, 16, 5617-5625.

Figure 5. Measurements of the birefringence’s intensity of mixtures when applying a magnetic field for two volume fractions corresponding to the middle of the pseudoplateau (a) and to the end of the pseudoplateau (b).

Figure 6. Ratio of the free maghemite probes in mixtures when increasing the volume fraction of Laponite particles. The three domains correspond to the three regions of the equation of state. Table 1. Relaxation Time of the Maghemite Probes as a Function of the Laponite Volume Fraction; for Each Sample, the Time Relaxation Is Measured Three Times samples reference: suspension of maghemite particles without Laponite: Φmaghemite 0.05% ΦLaponite 0.37% (region 1) ΦLaponite 1.11% (region 2) ΦLaponite 1.48% (region 2, end of the plateau) ΦLaponite 1.85% (region 3)

time relaxation (µS) 8.3 7.8 7.4 7.9 6.7

presents the relaxation time of maghemite particles in the Laponite suspensions.

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Figure 7. Comparison between the osmotic pressure of the mixture (open dots) and the sum of the osmotic pressures of the individual components (empty dots). The osmotic pressure of Laponite particles is measured and the one of maghemite particles is calculated according to ref 29.

perfect “gas”. They are thus homogeneously dispersed in the Laponite suspension. At the beginning of the peusoplateau, Sprobes-probes increases at small q. The probes behave as an attractive system. The distances between probes is reduced. As the volume fraction of probes is set constant, magnetic particles concentrate in some specific regions of the space. As shown furthermore in this discussion, this increase of local concentration occurs without formation of aggregates. The effective attractions are related to the confinement induced by Laponite particles. At the end of the pseudoplateau, the divergence of Sprobes-probes at small q is very large. The probes behave as a strong attractive system. Along the pseudoplateau, the probes concentrate thus more and more in some specific region of the space as the volume fraction of Laponite particles is increased. In region 3 of the equation of state, when the end of the pseudoplateau is reached, Sprobes-probes decreases at small q and becomes largely inferior to 1. The effective interactions between particles are thus repulsive, indicating that the probes are homogeneously dispersed in the sample as in region 1 of the equation of state. (b) Concerning the birefringence measurements, the characteristic decay time of the magnetically induced birefringence signal measured in the mixtures is only due to magnetic particles. As a matter of fact, spontaneous nematic orientation of a suspension of Laponite particles under a magnetic field has never been observed in our experimental conditions. Moreover, if the maghemite particles had induced an orientation of the Laponite particles, the birefringence relaxation time should at least be on the same order of magnitude as the relaxation time of a single Laponite particle (about 100 µs34). This is 1 order of magnitude larger than the measured relaxation time (8 µS). The birefringence measurements show that the behavior of the maghemite probes in the Laponite suspensions in regions 1 and 2 of the equation of state are not modified compared to their behavior when they are dispersed in water: the static birefringence as a function of the applied magnetic field follows the Langevin second law without remanence and the relaxation measurements indicate that all the particles are unblocked in the mixture for samples containing ΦLaponite ) 0.37% (region 1) and ΦLaponite ) 1.11% (region 2): The characteristic time of the birefringence decay is the same in the solid sample containing Laponite (34) Tassin, J. F.; Robert, G.; Benyahia, L. Cahiers Rhe´ ol. 1996, 15 (1), 238-245.

Cousin et al.

sample as in the aqueous suspension of maghemite. This observation proves that the magnetic particles do not aggregate in Laponite. The large increase of the structure factor Sprobes-probes at small q is then related to a local concentration of probes without aggregation in region 2 (the pseudoplateau). Although the samples are macroscopically solids, the viscosity in the vicinity of the maghemite particles is the one of pure water. The behavior of the mixture containing 1.48% of Laponite particles that corresponds to the end of the plateau is slightly different: a weak remanence in the birefringence curve is observed, indicating that about 10% of the maghemite particles are blocked in the solid. The relaxation time for these samples is still the same as the one of a diluted suspension of maghemite. Thus, most of the maghemite particles are still unblocked in the mixture. In region 3 of the equation of state, an important amount of maghemite particles is blocked as indicated by the experiments performed for samples containing 1.85% of Laponite particles. The low value of the birefringence relaxation time indicates that the mean diameter of the particles able to rotate in such solid is smaller than the one in a suspension of maghemite particles. The blocked particles are thus the biggest. According to structural and viscosity experiments, we propose the following structure for the mixtures in the three parts of the equation of state: (a) In the first part (region 1) suspensions are macroscopically fluids and Laponite particles do not induce effective interactions between the probes: these probes are homogeneously dispersed, totally unblocked. (b) Along the pseudoplateau (region 2), the probes become confined in some parts of the space where the viscosity is the one of water. The samples are macroscopically homogeneous and solids: the probes are thus located in liquid pockets in the solidlike suspensions and are excluded from domains where Laponite particles are localized. When the volume fraction of Laponite particles is increased, the size of these dense domains grow and liquid pockets shrink. This evolution explains why the magnetic probes concentrate more when the Laponite volume fraction is increased. At the end of the pseudoplateau, the free space left to the probes is so narrow that some probes become blocked in the system. (c) In the last part of the equation of state (region 3), the probes are homogeneously dispersed and partly blocked in Laponite suspensions. There are effective repulsions between probes due to the presence of Laponite particles which fill all the space and prevent the probes from moving freely. Possible spatial distributions of magnetic particles in Laponite suspensions are illustrated in Figure 8 for the three different regions of the equation of state. These results are in good accordance with the hypothesis of a microscopically biphasic structure for the Laponite suspensions (coexistence of diluted and concentrated regions). The fluid-solid transition appearing at the beginning of the pseudoplateau may thus be a ‘‘frustrated” transition. Although two regimes of structures have been identified before and after the end of the pseudoplateau, it is not possible to link the end of this pseudoplateau to a welldefined transition between biphasic area and a monophasic nematic area: the transition between the two regimes appears progressively as shown by the presence of blocked magnetic probes in mixtures before the end of the pseudoplateau. As a matter of fact, the free space allowed the objects for their motion is strongly reduced when the volume fraction of Laponite particles increases. The dynamics of objects is thus greatly slowed. It explains

Determination of Structure of Laponite Suspensions

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Figure 8. Schematic description of the Laponite suspensions including a constant volume fraction of magnetic probes (Φ ) 0.05%) for the different parts of the equation of state. Picture (2a) and picture (2b) correspond respectively to the beginning and to the end of the pseudoplateau.

why the remanent birefringence and remanent magnetization observed on concentrated samples after the application of a magnetic field, due to magnetic probes, disappears on long time scales. It also explains why the appearance of macroscopic birefringence in concentrated samples, due to Laponite particles, occurs on a very long time scale. Conclusion We investigate in this paper the structure of Laponite suspensions by the use of magnetic spherical particles of maghemite included in suspensions. Chemical conditions are found for which it is possible to achieve the inclusion of the maghemite probes without disturbing the chemistry of Laponite. The equation of state of the system shows that the mixtures have the same structure as the Laponite suspensions. This equation of state presents a pseudoplateau. The beginning of the pseudoplateau is linked with a rheological fluid-solid transition of the mixture. Samples stay nevertheless macroscopically homogeneous in the region of the pseudoplateau. SANS and viscosity mea-

surements have shown that the probes are homogeneously dispersed in Laponite suspensions, except in the region of this pseudoplateau, for which probes are confined in low densified area of Laponite, indicating that Laponite suspensions are microspically biphasic in the region of the pseudoplateau of the equation of state. Such a result is consistent with a possible spinodal decomposition or a frustrated Onsager transition. A very interesting point concerns the effect of the increase of the proportion of maghemite particles in Laponite suspensions at high volume fraction. New magnetorheological properties can be expected for such mixed suspensions. They will be discussed in a forthcoming paper. Acknowledgment. The authors are indebted to I. Grillo (ILL, Grenoble) for her help during SANS measurements and to E. Hasmonay and R. Perzynski (LMDH, Paris) for their help during the realization of the birefringence measurements and for fruitful discussions. LA010947U