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Competition between Entropy and Electrostatic Interactions in a Binary Colloidal Mixture of Spheres and Platelets Fabrice Cousin,*,†,‡ Vale´rie Cabuil,‡ Isabelle Grillo,§ and Pierre Levitz| Laboratoire Le´on Brillouin, CEA-CNRS, CEA-Saclay, 91191 Gif-sur-YVette, France, 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, Institut Laue LangeVin, 6 rue Jules Horowitz BP 156 - 38042 Grenoble Cedex 9, France, and Laboratoire de Physique de la Matie`re Condense´e, Ecole Polytechnique, Palaiseau 91128, France ReceiVed May 21, 2008. ReVised Manuscript ReceiVed July 24, 2008 We describe the phase behavior of an aqueous mixture of discotic nanoparticles of laponite and spherical magnetic nanoparticles of maghemite. To obtain stable mixtures from a chemical point of view, the maghemite nanoparticles are first coated by a thin layer of silica in order to adapt their surface chemistry to that of laponite nanoparticles: this enables one to raise volume fractions of maghemite Φmag in the laponite suspensions up to several percent. Although the system is out of equilibrium, a “fluid-solid” state diagram was established showing that the mixtures undergo a fluid-solid transition, similar to that of pure suspensions of laponite, over a given volume fraction of laponite Φlap* and over a given Φmag. An increase in Φmag shifts Φlap* toward the lower values. When a solid sample is just above Φlap*, the application of an external magnetic field gradient induces a solid-to-liquid transition if the sample is located not too far from Φlap* on the state diagram. The structure of the mixtures, determined either at small scale by small-angle neutron scattering (SANS) or at intermediate scales by optical microscopy, shows that the solid samples are phase separated at a local scale: they are made of densely connected domains of laponite nanoparticles surrounding liquid pockets of maghemite nanoparticles. The size of the pockets grows with time. The magnetic liquid pockets are responsible for the rupture of the solid samples when an external magnetic field gradient is applied since their deformation induces local mechanical stress, internally damaging the network formed by the solid domains of laponite. The microscopic phase separation is the result of two opposite effects: (i) entropic effects that tend to phase separate the system macroscopically when the packing entropy overcomes the orientational entropy and (ii) long-range electrostatic repulsions that freeze the system.
I. Introduction One of the current trends in colloidal formulation is the design of “smart materials” associating two types of colloids. The aim is to tune the macroscopic properties of one of the components (elasticity, hydrophobicity, wettability, etc.) using external stimuli provided by the properties of the other (pH-responsive, thermoresponsive, etc.). In this context, suspensions of magnetic nanoparticles (also known as “ferrofluids”1) are of a great importance, as they enable the synthesis of new magnetic materials. They have thus been incorporated in systems as varied as polymeric gels,2,3 polymeric matrix,4 nematics,5 smectics,6,7 emulsions,8 liposomes,9 and vesicles10). The main objective is * Corresponding author. E-mail:
[email protected]. † CEA-Saclay. ‡ Universite´ Pierre et Marie Curie. § Institut Laue Langevin. | Ecole Polytechnique. (1) Rosensweig, R. Ferrohydrodynamics; Cambridge University Press: Cambridge, U.K., 1985. (2) Varga, Z.; Filipcsei, G.; Zrinyi, M. Polymer 2006, 47, 227–233. and references therein. (3) Galicia, J.; Sandre, O.; Cousin, F.; Guemghar, D.; Me´nager, C.; Cabuil, V. J. Phys.: Condens. Matter 2003, 15, S1379-S1402. (4) Jestin, J.; Cousin, F.; Dubois, I.; Me´nager, C.; Oberdisse, J.; Schweins, R.; Boué, F. AdV. Mater. 2008, 20(13), 2533–2540. (5) Berejnov, V.; Bacri, J.-C.; Cabuil, V.; Perzynski, R.; Raikher, Y. Europhys. Lett. 1998, 41, 507–512. (6) Fabre, P.; Casagrande, C.; Veyssie´, M.; Cabuil, V.; Massart, R. Phys. ReV. Lett. 1990, 64(5), 539–542. (7) Me´nager, C.; Cabuil, V. J. Colloid Interface Sci. 1995, 169, 251–253. (8) Bibette, J. J. Magn. Magn. Mater. 1993, 122(1-3), 37–41. (9) Me´nager, C.; Belloni, L.; Cabuil, V.; Dubois, M.; Gulik.Krzywicki, T.; Zemb, T. Langmuir 1996, 12(14), 3516–3522. (10) Lecommandoux, S. B.; Sandre, O.; Checot, F.; Rodriguez-Hernandez, J.; Perzynski, R. AdV. Mater. 2005, 17(6), 712.
generally to incorporate them as a magnetic load, in order to obtain field-dependent materials. This is especially important for materials with original mechanicals properties, as they can be tuned by using a simple external magnetic field. The magnetic field can be applied either after the synthesis of the hybrid system, to get magneto-responsive mechanical materials,2,3,10,11 or during the synthesis, to create materials with controlled anisotropic mechanical properties.4 Following this idea, we describe here the design of a new magneto-responsive material endowed with much softer elasticity than the systems previously described. Our aim is to incorporate a large quantity of magnetic nanoparticles of maghemite γ-Fe2O3 in suspensions of anisotropic discotic nanoparticles of laponite. This type of laponite suspension exhibits a fluid-solid transition over a given volume fraction that depends on the salinity of the medium.12,13 Since the system is out of equilibrium,14 it exhibits aging properties: the suspensions can easily be turned to liquid by providing weak mechanical energy to a solid sample, but when they are left at rest they revert back to solid. We expect thus magnetorheological properties from a mixture of laponite and maghemite nanoparticles, and, in particular, the possibility of inducing a solid-to-fluid transition by a magnetic field gradient. Such potential properties implicitly require stable macroscopic homogeneous mixtures. Two difficulties must be overcome: (i) (11) Coquelle, C.; Bossis, G. Int. J. Solid Struct. 2006, 43, 7659–7672. (12) Mourchid, A.; Delville, A.; Lambard, J.; Le´colier, E.; Levitz, P. Langmuir 1995, 11(6), 1942–1950. (13) Levitz, P.; Lecolier, E.; Mourchid, A.; Delville, A.; Lyonnard, S. Europhys. Lett. 2000, 49(5), 672–677. (14) (a) Bonn, D.; Tanaka, H.; Wegdam, G.; Kellay, H.; Meunier, J. Europhys. Lett. 1998, 45(1), 52–57. (b) Bonn, D.; Kellay, H.; Tanaka, H.; Wegdam, G.; Meunier, J. Langmuir 1999, 15, 7534–7536.
10.1021/la8015595 CCC: $40.75 2008 American Chemical Society Published on Web 09/10/2008
Phase BehaVior of Platelet/Sphere Mixtures
chemical conditions must be found where both species are compatible, and (ii) we must avoid the phase separation occurring between spheres and anisotropic particles such as rods15 or discs16 due to depletion effects. In our first attempt to mix γ-Fe2O3 maghemite and laponite nanoparticles,17 we showed that the chemical ranges of stability of pH (9 < pH < 10.5) and salinity (I < 2 10-2 mol/L) of laponite nanoparticles strongly limit the amount of magnetic nanoparticles that can be included without specific surface treatment. Here we follow another route. To address the problem of chemical compatibility, we coat the maghemite nanoparticles with a thin layer of silica. This enables us to work with a high amount of nanoparticles Φmag at pH 10, a pH at which the naked maghemite nanoparticles are not stable (their isoelectric point is 7.2). The problem of the phase separation is a priori more difficult to solve. First, as previously predicted by Onsager,18 pure suspensions of anisotropic nanoparticles must undergo an isotropic-nematic transition at high volume fractions when the packing entropy overcomes the orientational entropy.19,20 This has been observed experimentally in suspensions of one dimensional objects21,22 and suspensions of two-dimensional objects23-25 and, more recently, on clay suspensions.26 Second, the depletion forces lead to phase separation in binary mixtures as soon as the size ratio γ between the two kinds of nanoparticles reaches a given value. For alloys of colloidal spheres, γ is equal to 5. This has been theoretically predicted27 and experimentally observed.27,28 When γ < 5, mixtures are stable, and, for specific values of γ, spectacular superstructures such as phases AB2 or AB13 can be obtained.29 The formation of these is the result of entropic effects.30 When one of the two components is of anisotropic shape, depletion effects are enhanced owing to the rotational entropy of the anisotropic objects. Here again there is competition between packing entropy and orientational entropy. In concentrated systems, the presence of spheres prevents the rotation of anisotropic objects. The system therefore prefers to separate into two phases, one containing the anisotropic objects and the other the spheres, if the rotational entropy gained by freeing the rotation of anisotropic objects is higher than the loss (15) Koenderink, G. H.; Vliegenthart, G. H.; Kluijtmans, S.G.J.M.; van Blaaderen, A.; Philipse, A. P.; Lekkerkerker, H. N. W. Langmuir 1999, 15, 4693– 4696. (16) Oversteegen, S. M.; Wijnhoven, J. G. E. J.; Vonk, C.; Lekkerkerker, H. N. W. J. Phys. Chem. B 2004, 108(47), 18158–18163. (17) Cousin, F.; Cabuil, V.; Levitz, P. Langmuir 2002, 18, 1466–1473. (18) Onsager, L. Ann. N. Y. Acad. Sci. 1949, 51, 627. (19) Vroege, G. J.; Lekkerkerker, H. N. W. Rep. Prog. Phys. 1992, 55(8), 1241–1309. (20) Forsyth, P. A.; Marcelja, S.; Mitchell, D. J.; Ninham, B. W. AdV. Colloid Interface Sci. 1978, 9, 37–60. (21) Buining, P. A.; Philipse, A. P.; Lekkerkerker, H. N. W. Langmuir 1994, 10, 2106–2114. (22) Davidson, P.; Bourgaux, C.; Schoutteten, L.; Sergot, P.; Williams, C.; Livage, J. J. Phys. II 1995, 5(10), 1577–1596. (23) (a) Van der Kooij, F. M.; Lekkerkerker, H. N. W. J. Phys. Chem. B 1998, 102, 7829–7832. (b) Van der Kooij, F. M.; Kassapidou, K.; Lekkerkerker, H. N. W. Nature 2000, 406, 868–861. (24) (a) Brown, A. B. D.; Clarke, S. M.; Rennie, A. R. Langmuir 1998, 14, 3129–3132. (b) Brown, A. B. D.; Ferrero, C.; Narayanan, T.; Rennie, A. R. Eur. Phys. J. B 1999, 11, 481–489. (25) (a) Van der Beek, D.; Lekkerkerker, H. N. W. Europhys. Lett. 2003, 61(5), 702–707. (b) Van der Beek, D.; Lekkerkerker, H. N. W. Langmuir 2004, 20(20), 8582–8586. (26) Michot, L. J.; Bihannic, I.; Maddi, S.; Funari, S. S.; Baravian, C.; Levitz, P.; Davidson, P. Proc. Natl. Acad. Sci. U.S.A. 2006, 103(44), 16101–16104. (27) Lekkerkerker, H. N. W.; Dhont, J. K. G.; Verduin, H.; Smits, C.; van Duijneveldt, J. S. Physica A 1995, 213, 18–29. (28) van Duijneveldt, J. S.; Heinen, A. W.; Lekkerkerker, H. N. W. Europhys. Lett. 1993, 21(3), 369–374. (29) (a) Bartlett, P.; Ottewill, R. H.; Pusey, P. N. J. Chem. Phys. 1990, 93(2), 1299–1312. (b) Bartlett, P.; Ottewill, R. H.; Pusey, P. N. Phys. ReV. Lett. 1992, 68(25), 3801–3804. (30) Lekkerkerker, H. N. W.; Stroobants, A. Nature 1998, 393, 305–307.
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of entropy of mixing. Maximal free space can be obtained for rods if the spheres are optimally packed, i.e., when they form crystal domains in the suspensions. It has been shown experimentally in systems of rods and spheres15 and platelets and spheres16 that depletion forces by anisotropic particles induce the crystallization of the spheres. It is nevertheless difficult to predict the structures of the phases if the volume fraction of isotropic and anisotropic objects are large. Adams et al. for example have obtained various phases (layers or columns of spheres and rods) by mixing TVM rods with spheres.31 But obtaining such peculiar phases with colloidal alloys is only possible when the system is able to explore all the configurations of the phase space. A good way to avoid phase separation therefore is by freezing. We believe that the properties of laponite suspensions are such that they would probably avoid phase separation with maghemite nanoparticles in binary mixtures. First, the diameter of the nanoparticles is around 30 nm, and their thickness 1 nm; this is on the order of the diameter of the maghemite nanoparticles (∼8 nm). Second, they are frozen by long-range electrostatic repulsions that prevent the isotropic-nematic transition to occur macroscopically in a pure solution. It has been proven that their rheological fluid-solid transition is strongly related to electrostatic screening. For very low ionic strength (I < 10-4), the transition is shifted toward the high volume fraction of nanoparticles as ionic strength increases13 (as observed in spherical systems). The transition occurs here when the effective volume fraction of nanoparticles reaches ∼0.5, taking as an effective diameter the sum of the geometrical diameter of the nanoparticle and the Debye length. At intermediate ionic strength (10-2 > I > 10-4), the slope of the threshold is inverted because the transition is shifted toward low particle volume fractions. It is related here to the appearance of a pseudoplateau in the equation of state of the system.12 The presence of a pseudoplateau, characteristic of a first-order transition, may be related to an isotropic-nematic transition. An increase of the ionic strength increases the effective anisotropy of shape of the laponite nanoparticles and shifts thus fluid-solid transition toward low value of volume fraction. But the samples of laponite remain macroscopically homogeneous, even for volume fractions beyond the end of the pseudoplateau. It has been suggested that the transition is ill-defined12,32 and only occurs on a microscopic scale because it is frozen by the long-range electrostatic repulsions evidenced at low ionic strength. The competition between electrostatic freezing and entropic demixing is highlighted by the fact that the change of behavior in the phase diagram occurs for I ) 10-4 mol/L when the Debye length corresponds to the diameter of the nanoparticles. At high ionic strength (I > 10-2), the electrostatic interactions are strongly screened, and the Debye length becomes small compared to the nanoparticle diameter ( 0.16%. The mixture of γ-Fe2O3 particles and silica is stirred for 2 h at room temperature. For Φmag ) 0.16% and a pH of 12, the conductivity of the mixture is 1.2 mS (34) Jabbari-Farouji, S.; Wegdam, H. G. J.; Bonn, D. Phys. ReV. Lett. 2007, 99(6), 065701. (35) Thompson, D. W.; Butterworth, T. J. Colloid Interface Sci. 1992, 151(1), 236–243. (36) Mourchid, A.; Levitz., P. Phys. ReV. E 1998, 57(5), R4887–R4890. (37) (a) Massart, R. IEEE Trans. Magn. 1981, 17, 1247. (b) Massart, R. French Patent, 79-188-42, 1979; U.S. Patent, 4-329-241, 1982. (38) Philipse, A. P.; Bruggen, M. P. B.; Pathmamanoharan, C. Langmuir 1994, 10, 92–99.
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after stirring. The dispersion of the silica-coated maghemite nanoparticles is then dialyzed against a reservoir constituted by a NaOH solution at pH 10 in order to eliminate excess silica oligomers. To avoid any possible desorption of silica from the surface, the dialysis is stopped when the pH is 10 and the conductivity of the mixture reaches 260 µS. No hypothesis will be made here on the exact nature of the silica species in solution. The ionic strength will be considered constant and equal to that of a reference solution of sodium silicate with a conductivity of 260 µS at pH 10. In order to increase Φmag at the end of the dialysis while keeping the ionic strength constant, we perform an osmotic stress on the suspension. The suspension is placed in a dialysis bag in a reservoir containing a solution of dextran (Mw ) 110 000 g/mol) dissolved in a solution of NaOH and silicate (pH 10, conductivity 260 µS). The osmotic pressure of the reservoir, fixed by the dextran concentration and independent of ionic strength and pH, is set to 3000 Pa. The equation of state of dextran can be found in reference 39. The reservoir bath is changed as often as necessary to reach equilibrium. At the end of the stress, Φmag can increase up to ∼4%. It is determined by the saturation of the magnetization curve of the suspension. The conductivity of the suspension is precisely set to 260 µS. Since almost all the N(CH3)4+ ions are removed from the suspension, the counterions of the nanoparticles are Na+, similar to those of laponite nanoparticles. Surface Charge of Silica-Coated Nanoparticles. The approximate potential of zero charge (PZC) of the silica-coated particles was determined by turbidity measurements of the suspensions as a function of the pH. The turbidity is obtained by measuring the optical transmission of suspensions at 700 nm with a spectrophotometer. The suspensions were found to be stable between pH 4 and pH 10. Stability was only impaired at pH lower than 4. The PZC of the coated nanoparticles is inferior to 3, close to that of silica (2.5). This proves that the surface of the maghemite nanoparticles was chemically modified, given that the PZC of naked γ-Fe2O3 is initially 7.2. The modification of the surface charge of the γ-Fe2O3 nanoparticles by the silica-coating treatment has also been confirmed by measuring the ζ potential (at Φ ) 0.016) on a commercial zetameter setup. The ζ potential increases in absolute value from -39 mV for naked γ-Fe2O3 nanoparticles (at pH 12) up to - 49 mV for silica-coated nanoparticles. 2. Binary Mixtures. The laponite nanoparticles were purchased from Laporte Industries, Ltd. (laponite RD). Laponite is a synthetic clay of general formula Si8Mg5.45Li0.4H4O24Na0.7. The nanoparticles have high chemical purity (a chemical study on these nanoparticles has shown negligible traces of metals such as iron, aluminum, and calcium40). The maghemite/laponite mixtures are obtained by dispersing the laponite nanoparticles in silica-coated maghemite particle suspensions by ultrasonication. Φmag is first set by diluting a concentrated suspension of silica-coated maghemite nanoparticles in a NaOH solution containing silica species (pH 10, conductivity equal to 260 µS). The mixtures are either liquid or solid and always appear macroscopically homogeneous. They resemble pure suspensions of laponite nanoparticles, although red in color owing to the presence of maghemite nanoparticles. (39) http://www.brocku.ca/researches/peter_rand/osmotic/data/ (40) Lecolier E., Thesis, Universite´ d’Orle´ans, 1998;available at http:// cat.inist.fr/.
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Figure 1. Rheological state diagram of the spheres/discs mixtures as a function of time after the synthesis: (a) ∼25 h; (b) ∼100 h (the red symbols on this diagram correspond to the samples probed by SANS experiments; see Section IV); (c) ∼450 h; (d) ∼1200 h. The samples described as “close to transition” correspond to suspensions that do not flow but break when the tubes into which they are placed are turned upside down by gravity. The dotted lines are only guides for the eyes.
III. Macroscopic Behavior 1. Samples at Rest. The solid-liquid state diagram of the suspension is determined by visual inspection: suspensions are considered liquid if they flow and solid if they do not. Since the time taken to reach equilibrium can be very long, this diagram is measured at different times after the mixture synthesis. The suspensions are kept in sealed tubes under nitrogen atmosphere. Figure 1 shows the diagram for different times after the synthesis. Its evolution over time shows that the suspensions are nonequilibrium systems like pure suspensions of laponite nanoparticles. There is an important evolution over the first 100 h, slowing down thereafter. A sample is considered a solid if it can sustain its own weight, i.e., if it does not flow when the tube into which it is placed is turned upside down. The solid samples exhibit shear thinning: their viscosity decreases when they are submitted to a shear stress. The samples are thus yield-stress fluids.41 The relevant parameter for a deep establishment of the rheological phase diagram would thus be the determination of the yield stress of the samples. However, as explained in the recent review of Moller et al.,41 the experimental determination of the yield stress of a given sample is very difficult because shear localization is an intrinsic property of yield-stress fluids. The experimental results may thus depend on the procedure and of the time of measurement, even for cone-plane geometry. We have thus decided to limit ourselves to the visual inspection of the samples. Figure 1 shows that the volume fraction of laponite Φlap* at the threshold of the fluid-solid transition for pure suspensions is ∼0.45% (∼1.2% in mass fraction) in our buffer containing the remaining sodium silicate at pH 10. On the basis of state diagram established in the literature for suspensions in pure NaCl solutions at pH 10,12,13 we can consider our buffer to have the same ionic strength equivalent Iequ at pH 10 as these. For Φlap* ∼ 0.45, we obtain Iequ ∼ 5 × 10-3 mol/L, far from the region of the phase diagram of pure laponite suspensions where suspensions flocculate. (41) Moller, P. C. F.; Mewis, J.; Bonn, D. Soft Matter 2006, 2, 274–283.
Although the diagram evolves kinetically, the introduction of the maghemite nanospheres has a clear influence on the threshold of the fluid-solid solution of laponite suspensions Φlap*. Whatever the time of measurement, the presence of spheres shifts Φlap* toward low Φlap. This shift increases with an increase of Φmag and is very marked. At equilibrium, an introduction of 1% of maghemite nanospheres shifts it by a factor of 2! This shift is induced by the presence of the maghemite nanospheres, and not simply by the increased ionic strength due to the counterions of the nanospheres. This is proved by the following fast calculation: Considering that the surface of the maghemite nanospheres is similar to that of the silica nanoparticles, their surface charge should be ∼0.02 C/m2.42 For Φmag ) 0.01, the dissociation of the species at the surface corresponds to an ionic strength of 1.4 × 10-3 mol/L (taking a sphere radius of 45 Å; see Section IV). This increase in ionic strength can not explain the shift of Φlap* down to ∼0.22, as observed when Φmag ) 0.01, because it would correspond roughly to an ionic strength of 10-2,12,13 much higher than that within the mixtures. 2. Behavior of the Mixtures under an External Magnetic Field Gradient. The application of an external magnetic field gradient created by a magnetic field of ∼0.02 T allows some solid mixtures to be turned back into liquid. The transition is conditioned by the Φmag/Φlap ratio: an increase of Φmag facilitates the solid-fluid transition by the application of the magnetic field gradient, although an increase of Φlap has the reverse effect. When the magnetic field gradient is removed, the suspensions solidify again. The time taken to revert to solid state also depends on Φmag and Φlap. It is reduced if one of the two volume fractions is increased. It is nevertheless always much shorter than the time taken to solidify after the synthesis.
IV. SANS Experiment We have performed a number of SANS experiments to determine the structure of the binary mixture at the typical scale of the objects (from ∼100 Å to several thousand angstroms). In a SANS experiment made on our aqueous binary mixture, the scattered intensity is
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I(q)(cm-1) ) klap2Ilap_lap(q) + 2klapkmagIlap_mag(q) + kmag2Imag_mag(q) (1) where Ilap_lap is the scattering from the laponite nanoparticles, Imag_mag is the scattering from the maghemite nanoparticles, Ilap_mag is the interference term due to the correlations between laponite and maghemite nanoparticles, klap is the difference of scattering length density between the laponite and the solvent (in cm-2), and kmag is the difference of scattering length density between the maghemite and the solvent. Because we are using neutrons, the neutron length density of the aqueous solvent can be continuously tuned between the value of heavy water (-0.53 × 1010 cm-2) and deuterated water (6.38 × 1010 cm-2). The scattering length of laponite (3.91 × 1010 cm-2) can be completely matched by that of a 65% D2O/35% H2O mixture. In this case, klap becomes nil, and the scattering of the mixtures is reduced to kmag2Imag_mag. The scattering length of maghemite (6.96 × 1010 cm-2) can never be matched, however. In the methodology described below, we measure all of our samples both in pure water, where all correlations are visible, and in the 65% D2O/35% H2O mixture that provides the extinction of laponite nanoparticles.17 One may wonder whether the mechanical properties of the mixture are affected by the differences in the chemical compositions of the solvents (pure H2O versus 65% D2O/35% H2O). Behavorial differences induced by isotopic substitution are usually observed for systems in which the hydrogen bond plays a huge role, the hydrogen bond being strongly modified in D2O compared to H2O. In our system, however, the parameters that act on the structure are electrostatic interactions and entropy. We therefore assume in the following that the structure of suspensions does not depend on the amount of D2O in the mixture. This is macroscopically confirmed by the fact that the samples prepared in the two different solvents look exactly similar. Technical Aspects. SANS measurements were performed on the D11 spectrometer at the Institut Laue Langevin (Grenoble, France) in a q-range of between 2.2 × 10-3 and 5.6 × 10-2 Å-1. All measurements were carried out under atmospheric pressure and at room temperature. Standard corrections for sample volume, neutron beam transmission, empty cell signal subtraction, and detector efficiency were applied to obtain the scattered intensities in absolute scale. The incoherent scattering of the two different solvents (pure H2O and 65% D2O/35% H2O mixture) was measured independently of the samples and was subtracted from the scattering of the samples. Silica-Coated Magnetic Nanoparticles. Prior to preparing the mixtures, we checked that the silica-coating process did not induce aggregation of the nanoparticles and that the layer of silica remained small compared to the magnetic core. A sample of pure silica-coated maghemite nanoparticles was measured at Φ ) 1% in pure water. It is presented in Figure 2. For centrosymmetrical objects such as spherical nanoparticles, the scattering can be written as follows:
I(q)(cm-1) ) kmag_H2O2ΦmagP(q)S(q)
(2)
where kmag_H2O is the difference of scattering length density between maghemite nanoparticles and the pure H2O solvent, P(q) is the form factor, and S(q) is the structure factor. A plateau appears on the scattering curve at low q in a q-range where the form factor of the nanoparticles is close to 1. It shows that the structure factor is also close to 1 in this q-range, indicating (42) Kosmulski, M. Chemical Properties of Material Surfaces; Marcel Dekker, Inc.: New York, 1998; Chapter 3.
Figure 2. Scattered intensity by a suspension of pure silica-coated maghemite nanospheres for particles of Φmag ) 0.01 in pure H2O.
that there are no aggregates in the suspension. Since Φmag is weak, the behavior of the system resembles that of a noninteracting system. The scattering can thus be roughly identified to the form factor of the objects. It was then modeled on an absolute scale by the form factor of spherical objects with a log-normal distribution of radii with a characteristic radius R0 of 48 Å, and a mean standard deviation σ of 0.35. The modeling used an absolute scale where Φmag ) 0.01 and kmag_H2O2 ) 5.65 × 1021 cm-4. The parameters obtained are very close to the ones obtained by magnetization measurements. Please note that the scattering curve proves that the silica shell remains very thin compared to the maghemite core radius: it would otherwise significantly enhance the scattering at low q, and some extinctions would appear at intermediate q-range induced by destructive interference between the core and the shell of the nanoparticles. The magnetic properties of the nanoparticles are thus not altered by the coating. Scattering of Binary Mixtures. Ten samples were characterized corresponding to two volume fractions of laponite Φlap (0.38% and 0.53%) and five volume fractions of maghemite Φmag (0.2%, 0.4%, 0.6%, 0.8%, 1%). The measurements were performed roughly 100 h after their synthesis. For both Φlap, the samples were macroscopically solid for the two highest Φmag (0.8%, 1%) and liquid for the lowest Φmag (0.2%, 0.4%). For Φmag ) 0.6%, the sample was close to the transition for Φlap ) 0.38% and solid for Φlap ) 0.53%. The location of these samples on the rheological state diagram is presented in Figure 1b. We start with the case of the samples in the 65% D2O/35% H2O mixture. In this case, eq 1 is reduced to the term corresponding to kmag2Imag_mag. The scattering could thus be identified with eq 2. S(q) is an effective structure factor Seff(q) because it takes into account the effective interactions induced by the laponite nanoparticle (which are invisible from a neutron point of view) between maghemite nanoparticles. These effective structure factors are presented in Figure 3. They are obtained by dividing the scattering intensities by the form factor of the nanospheres measured in the previous section. The series of scattering intensities at Φlap ) 0.38% is very close to the one at Φlap ) 0.53%. Two kinds of behavior can be clearly distinguished: (i) For fluid suspensions, the effective structure factor increases progressively as q tends toward 0. The maghemite nanoparticles are thus sensitive to effective attractive interactions. These attractions are necessarily induced by the presence of laponite nanoparticles, since, as shown above, a pure suspension of silicacoated maghemite nanospheres at Φmag ) 1% is close to a system without interactions. Seff(q) is typical of an heterogeneous attractive system. The effective attractions between maghemite nanospheres recall depletion interactions and thus correspond to a progressive spatial exclusion of the two kinds of nanoparticles.
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Figure 3. Effective sphere-sphere structure factors of maghemite nanoparticles within the maghemite/laponite mixtures: (a) Φlap ) 0.38%; (b) Φlap ) 0.53%. The insets show 1/q versus q2 for the determination of ξ (see text).
(ii) For solid suspensions, Seff(q) is close to 1 at intermediate q (up to 0.006 Å-1). The maghemite nanoparticles are thus not sensitive to effective attractions at short scales. It then increases at low q, showing that the maghemite nanoparticles are heterogeneously distributed within the macroscopically homogeneous mixture: There are regions with a high content of maghemite and regions with poor content. Since the maghemite nanoparticles behave like a perfect gas on a local scale (i.e., Seff(q) ∼ 1 for q > 0.006 Å-1), they are no longer sensitive to the laponite nanoparticles’ effective interactions. The low q increase suggests a local segregation between the two types of nanoparticle because the spatial regions that are dense in maghemite nanoparticles must be almost free of laponite nanoparticles. These regions rich in maghemite form liquid pockets. Since the samples are macroscopically solid, it is necessarily the domains rich in laponite nanoparticles organized in a percolating network that make the sample solid, as in pure laponite solutions. Finally, it should be noted that the low q increase is more pronounced when either Φmag or Φlap is increased, suggesting that the segregation is enhanced by the introduction of one of the two types of nanoparticles. One important question is to know whether the maghemite nanoparticles form dense concentrated zones or if they are aggregated. The shape of the structure factor strongly supports the scenario of concentrated zones because (i) the structure factor is very flat in the q-range 0.005 Å-1 < q < 0.015 Å-1, and (ii) the upturn of the scattering at low q increases less than a q-1 decay. In the case of dense aggregates of spherical nanoparticles, one would expect a correlation peak at 2π/d0 at large q due to the contact between nanoparticles in the structure factor, a correlation hole at intermediate q, and a strong increase of the scattering factor at low q such as q-4. The lack of correlation hole clearly dismisses the hypothesis of formation of dense aggregates. In the case of open aggregates with a fractal dimension Df, one would expect the structure factor to scale like q-Df starting from 4π/d0. Since the lowest Df that can be obtained for aggregates of spheres is 1, the weak increases of the structure factor at low q also dismisses the formation of open aggregates. Moreover it has to be noted that a system of electrostatically stabilized maghemite nanoparticles of typical diameter d0 ∼ 8 nm would probably form aggregates with a fractal dimension close to 2 like colloids interacting through an isotropic interparticle potential43 because it has been shown that dipolar interactions out of magnetic field have a negligible influence in such a system.44 The (43) (a) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Phys. ReV. A 1990, 41(5), 2005–2020. (b) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. J. Phys.: Condens. Matter 1990, 2, 3093–3113. (44) Cousin, F.; Dubois, E.; Cabuil, V. Phys. ReV. E 2003, 68(2), 021405.
Figure 4. The density fluctuations of maghemite nanoparticles within the mixtures.
maghemite nanoparticles must thus mainly be located in dense concentrated area, even if it is possible that there are a few aggregates within the sample. In order to compare the strength of the effective attractions from one sample to another, we measured their compressibility by measuring the correlation length of the density fluctuations in the system. Assuming that the spatial decay of the density correlation of the fluctuations is fast, the correlation pair function gmag_mag(r) can be written as
gmag_mag(r) ) K
e-r⁄ξ r
(3)
where K is a constant, and ξ is the correlation length. The structure factor is thus a Lorentzian S(q)∝1/(q2 + ξ-2). The insets of Figure 3a,b show 1/S(q) versus q2 for all the samples. Curves are linear, thus validating the hypothesis on gmag_mag(r). The value of 1/S(q))q2f0 allows one to determine 1/ξ2. The results are summarized in Figure 4. They highlight the two behaviours described previously. For fluid samples, the density fluctuations remain weak and constant. On the contrary, they strongly increase linearly with Φmag for solid samples. This shows that the local segregation between the two kinds of particles is very efficient when Φmag increases for a constant Φlap. It also appears that the density fluctuations are slightly higher when Φlap increases for a constant Φmag in solid samples. We turn now to the case where the samples are prepared in pure H2O. In this case, the three terms of eq 1 are present. The kmag2Imag_mag term can be subtracted from the total scattered intensities, as it was measured independently in the 65% D2O/ 35% H2O mixture. The neutron contrast between the two experiments is taken into account via (kmag_65%D2O/35%H2O/ kmag_H2O)2. The results are presented in Figure 5.
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Figure 5. The scattering remaining after subtracting the term kmag2Imag_mag from the total scattering of the binary mixtures: (a) Φlap ) 0.38%; (b) Φlap ) 0.53%. The insets show the same plots in a log-linear scale.
Since klap ∼ 0.6 kmag in the pure H2O solvent, it is not possible to neglect Ilap_mag or Ilap_lap in the scattered intensities presented in Figure 5. It is thus not possible to extract quantitative information from these spectra. But they nevertheless show two different types of behavior between solid and liquid samples. Solid samples show a maximum of intensity around 0.01 Å-1, not shown by fluid samples. In this q-region where local scales are probed, the maghemite-laponite correlations must be negligible owing to spatial segregation between the two kinds of nanoparticles. Since both types of nanoparticles are negatively charged at pH 10, we assume that electrostatic repulsions are sufficient to avoid aggregation between maghemite and laponite nanoparticles. This maximum must therefore come from laponite-laponite correlations. This scattering is reminiscent of that observed by SAXS in pure solutions of laponite:12,45,46 there is a correlation hole below 0.01 Å-1 in concentrated solid samples that dilute solids do not show (the resulting scattering seems to have a maximum around 0.01 Å-1). This correlation hole is the signature of nanoparticle density fluctuations within the samples. Since we observe a correlation hole of this type in our binary mixture, dense regions of pure laponite must be formed within the solid samples. It is especially important to note that this correlation hole arises for low volume fractions of laponite, in a range of Φlap where pure samples of laponite stay fluid. There exists a Φmag* threshold for the appearance of the correlation hole. Moreover it is much more marked when Φmag increases for a given Φlap. All these observations reinforce the picture of the local phase separation between the two kinds of nanoparticles in the system. Such local phase separation seems to be more important as Φlap or Φmag increases. The solid structure of the mixtures is formed by a network of dense domains of laponite particles surrounding liquids pockets of aqueous dispersions of maghemite particles. At large q values (above 0.01 Å-1), the scattering strongly decreases in log-log scale with a slope lying between -2 for the samples with the lowest concentration of maghemite nanoparticles and -4 for the samples with the highest concentration of maghemite nanoparticles. In this q-region, one probes the form factor of the two objects. It is thus a linear combination between the form factor of the laponite, which decays like q-2 because it has a discotic shape47 and the form factor of maghemite, which decays like q-4 because it has a spherical shape.47 The decay is thus close to q-2 for suspensions concentrated in discs and close to q-4 for suspensions concentrated in spheres. (45) Nallet, F. J. Phys. IV France 1999, 9, 95–107. (46) Kroon, M.; Wedgam, H. G.; Sprik, R. Phys. ReV. E 1996, 54(6), 6541– 6550. (47) Pignon, F.; Piau, J. M.; Magnin, A. Phys. ReV. Lett. 1996, 56(3), 3281– 3289.
At very low q, the spectra diverges when Φlap or Φmag increases. The divergence is very marked when one of these two volume fractions is increased. Here again, this is coherent with the mutual segregation of the two types of nanoparticle enhanced by both Φlap and Φmag.
V. Optical Microscopy 1. Samples at Rest. In order to get a picture of the structure of the binary mixture at a larger scale than that probed by SANS, the mixtures were investigated by optical microscopy. Since red maghemite nanoparticles absorb light in the visible light range and laponite nanoparticles do not, the measurement was limited to determining potential dense regions in maghemite nanoparticles. It was performed by placing a suspension in a cell composed of two glass plates separated by a spacer of about 10 µm and observing the suspension with an optical microscope. It was not therefore possible to detect heterogeneities bigger than 10 µm. Although the SANS results indicate that there is partial local phase separation of the two kinds of particles in the system, the liquid pockets of maghemite nanoparticles are not visible at larger scales than SANS, (i.e., to optical microscopy), after a lapse of about 100 h. The system has not reached equilibrium at this stage, however, and the pockets grow with time. They are finally visible to optical microscopy about ∼2 months after synthesis of the mixture. Figure 6a presents the picture obtained by optical microscopy of a mixture containing Φmag ) 0.8% and Φlap ) 0.38%, 2500 h after the synthesis. Please note that this sample was partially phase-separated at a local scale after 100 h, as clearly evidenced by SANS in the previous section. A number of dark areas can be seen, corresponding to the regions with high concentrations of maghemite nanoparticles, and these are surrounded by lighter areas corresponding to the regions with high concentrations of laponite nanoparticles. The lighter domains do indeed resemble those of a solid laponite suspension without maghemite nanoparticles. The areas concentrated with maghemite nanoparticles are confined in a network of fractures existing between the laponite-rich domains. The pockets of liquid do not appear turbid: this excludes the possibility of an aggregation of maghemite particles on large scales. It confirms that the divergence of the scattered intensity at low q observed by SANS when laponite is matched is induced, and confirms the presence of effective interactions but not by aggregation. 2. Behavior of the Mixtures under a Magnetic Field Gradient. We have tested the effect of a magnetic field gradient created by a maghetic field of ∼0.02 T on the structure of the solid sample described in the previous section. Macroscopically, the sample remained solid when the magnetic field gradient was applied. Figure 6b-e shows the pictures taken by microscopy
Phase BehaVior of Platelet/Sphere Mixtures
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Figure 6. Observation of a mixture by optical microscopy (Φmag ) 0.8%, Φlap ) 0.38%). (a) Sample at rest 2500 h after synthesis of the mixture. (b-e) Sample under the application of a magnetic field gradient. The pictures are taken at intervals of 1.5 s. (f) Sample at rest after the application of a magnetic field gradient. The crosses on the upper left of the picture indicate that suspensions are at rest; the arrows indicate the application of the external magnetic field gradient and its direction. The dashed lines merely help the eye to focus on the liquid pocket.
when the magnetic field gradient was applied. The time between two pictures is 1.5 s. These pictures may be compared with the sample at rest before application (Figure 6a) and after (Figure 6f). There is a dark area at the center of the pictures in Figure 6 that corresponds to a region dense in maghemite nanoparticles; this is a liquid pocket. It appears that the pocket is deformed by the application of the magnetic field gradient, as a droplet of ferrofluid would be.48 The fractures between solid domains of laponite are enlarged. When the field is cut off, however, the system returns to its initial state, at least on the scale probed by microscopy. The elastic modulus of the solid domains is therefore strong enough to restore the initial structure to the system. 3. Tests under Polarized Light. We also performed optical microscopy tests under polarized light. With no magnetic field applied, the sample displays no birefringence, unlike pure laponite suspensions far above the fluid-solid transition.32 This can be explained by the fact that the sample studied was very close to the fluid-transition threshold on the diagram of state.
VI. Discussion: Origin of the Local Phase Separation between the Two Types of Nanoparticles The combination of SANS experiments and optical microscopy leads us to the conclusion that there is a microscopic phase separation between the two types of nanoparticles. The evolution of the solid-liquid state diagram of the system (Figure 3) shows that the system is out of equilibrium, at least on the time scale of several weeks, because is evolves slowly over time. We see the progressive appearance of dense domains of maghemite nanoparticles and dense domains of laponite nanoparticles, without maghemite-maghemite aggregation. In the dense laponite nanoparticle regions, the local concentration in laponite nanoparticles increases progressively with time until the threshold of the fluid/solid transition of pure solution of laponite is reached. These dense domains of laponite then form in a network, confining the concentrated regions of maghemite nanoparticles, and transform the whole volume into a solid. This explains why the fluid-solid transition threshold in the laponite concentration is reduced as Φmag increases, because the volume inaccessible to the laponite nanoparticles, i.e., the volume containing pockets of magnetic liquids, increases. (48) Sandre, O.; Browaeys, J.; Perzynski, R.; Bacri, J.-C.; Cabuil, V.; Rosensweig, R. E. Phys. ReV. E 1999, 59(2), 1736–1746.
In summary, starting from a diluted liquid mixture with a rather homogeneous spatial distribution of spherical maghemite nanoparticles and laponite discotic nanoparticles, an increase of either Φmag or Φlap induces the microscopic phase separation of the system. The size of the dense domains of laponite particles or of the domains of maghemite particles depends on the Φmag/ Φlap ratio (see Figure 4). This is recalled in Figure 7. The partial phase separation between the two kinds of particles results from two opposite effects: (i) the entropic effects that tend to induce the total phase separation (as observed in mixtures of spheres and discs interacting through a hard-core potential system16 over a given threshold volume fraction of either spheres or discs), when the loss of entropy of mixing is overcome by the gain of rotational entropy of the discs induced by the release of excluded volume associated with the packing of spheres, and (ii) the long-range electrostatic repulsions that freeze the system. The long-range electrostatic repulsions in the system do not allow the system to explore the entire space of the phases. The system undergoes a vitreous transition similar to many charged colloidal systems when they become solid. The transition is similar in principle to the mechanisms of transition of pure suspensions of laponite at intermediate ionic strength; it is enhanced here by the volume inaccessible to the nanospheres. It explains why the partial phase separation between the species is kinetically long. In pure solid laponite suspensions consisting of either poor or rich domains of nanoparticles it has been shown that the nanoparticles located in the rich domains have very long diffusion times.14,33,34 This should also be the case in the binary mixtures for the maghemite nanoparticles; they are initially embedded and trapped within cages in domains concentrated in laponite nanoparticles. A long time is therefore required for their release from these dense domains of laponite. This explains why the dynamics of pocket formation is low. Phase separation occurs within a microscopic range during the synthesis of the mixture and extends progressively on a larger scale with time. When an external magnetic field gradient field is applied on a sample, it deforms the large liquid pockets of magnetic fluid. This induces a local mechanical stress within the sample that can break some solid domains of laponite to form smaller dense domains of laponite. If the local mechanical stress is sufficiently high, the number of solid domains of laponite that are broken is large enough to destroy the percolating network, and the sample
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Figure 7. Schematic representation of the mixtures of maghemite nanospheres (red) and laponite nanodiscs (white) in aqueous solvent. (a) Suspension with low Φmag and low Φlap; the sample is macroscopically liquid. (b) Increase of Φlap in the suspension pictured in panel a; the sample is macroscopically solid from the rheological point of view. (c) Increase of Φmag in the suspension pictured in panel a; the sample is macroscopically solid.
returns to liquid state. However, there remains in solution small dense solid domains of laponite since it is favorable for the system to phase separate in regions rich in maghemite nanoparticles and regions rich in laponite nanoparticles. The network formed by the dense domains of laponite can thus be quickly reformed. This explains why the time taken by the sample to resolidify after the application of the magnetic field gradient is much lower than the time required for the solid to form in the first time.
VII. Conclusion In this paper we describe the phase behavior of a mixture of discotic nanoparticles of laponite and spherical magnetic nanoparticles of maghemite. The maghemite naoparticles were first coated with a thin layer of silica in order to adapt their surface chemistry to that of the laponite nanoparticles, enabling us to raise the Φmag in the laponite suspensions up to several percent. The establishment of the solid-liquid state diagram of the system has shown that (i) the system is out of equilibrium and that it evolves kinetically over a time scale of several weeks, (ii) the system undergoes a fluid-solid transition comparable to the one of pure suspensions of laponite over a given fraction of laponite Φlap*, (iii) an increase of Φmag shifts the threshold of transition toward low Φlap, and (iv) the application of an external magnetic field gradient may induce a solid-to-liquid transition on a sample if it is located just above Φlap* on the solid-liquid state diagram. Structural studies, performed either at a small scale by SANS or at an intermediate scale by optical microscopy, have shown that the solid samples are microscopically phase separated: they are made of dense connected domains of laponite nanoparticles
surrounding liquid pockets of maghemite nanoparticles. The size of the pockets grows with time. When an external magnetic field gradient is applied, the local mechanical stress induced by the deformation of the magnetic liquid can break the network formed by the solid domains of laponite and revert the solid to liquid. The origin of the microscopic phase separation lies in the opposition between entropic effects (that tend to phase separate the system macroscopically when the packing entropy overcomes the orientational entropy) and the long-range electrostatic repulsions that freeze the system. We have therefore demonstrated in this way that it is possible to design materials with magneto-responsive mechanical properties by exploiting the opposition between entropic effects and the effects of long-ranged electrostatic interactions. Further developments could involve the following ingredients: (i) the volume fraction of maghemite nanoparticles Φmag, which influences the strength of the local mechanical stress applied to the system by an external magnetic field gradient, and (ii) the volume fraction of laponite Φlap, which influences the time taken for the sample to resolidify (the higher Φlap, the faster the liquid-solid transition). We could expect to achieve enhanced magnetorheological properties if the Φmag content were to increase to 10% or 15% in suspensions containing Φlap of a few percent. Solid suspensions may be broken under the application of strong magnetic gradients and instantaneously resolidify if the field is cut. Acknowledgment. The authors thank Robert Corner for his careful reading of the manuscript. LA8015595
