Heteroaggregation between Al2O3 Submicrometer Particles and SiO2

Mar 1, 2008 - ... UMR 6638, ENSCI, CNRS, 47/73 AVenue Albert Thomas, 87065 Limoges, Cedex, France, and ..... randomly placed in the simulation box...
0 downloads 0 Views 402KB Size
Langmuir 2008, 24, 3001-3008

3001

Heteroaggregation between Al2O3 Submicrometer Particles and SiO2 Nanoparticles: Experiment and Simulation M. Cerbelaud,† A. Videcoq,*,† P. Abe´lard,† C. Pagnoux,† F. Rossignol,† and R. Ferrando*,‡ SPCTS, UMR 6638, ENSCI, CNRS, 47/73 AVenue Albert Thomas, 87065 Limoges, Cedex, France, and Dipartimento di Fisica dell’ UniVersita` di GenoVa, Via Dodecaneso 33, 16146 GenoVa, Italy ReceiVed July 13, 2007. In Final Form: December 14, 2007 The aggregation process of a two-component dilute system (3 vol %), made of alumina submicrometer particles and silica nanoparticles, is studied by Brownian dynamics simulations. Alumina and silica particles have very different sizes (diameters of 400 and 25 nm, respectively). The particle-particle interaction potential is of the DLVO form. The parameters of the potential are extracted from the experiments. The simulations show that the experimentally observed aggregation phenomena between alumina particles are due to the silica-alumina attraction that induces an effective driving force for alumina-alumina aggregation. The experimental data for silica adsorption on alumina are very well reproduced.

1. Introduction One of the main goals in materials processing using the colloidal route is to control the stabilization and destabilization of suspensions. This is crucial to obtaining appropriate rheological properties and particle arrangements. Therefore, there has been considerable interest in studying stabilization, aggregation, and sedimentation phenomena in suspensions both from the point of view of experiment and simulation.1-10 In aqueous media, the conventional method used to control the stability of one-component suspensions is based on electrostatic forces, which counteract van der Waals attraction.11 Indeed, it is possible to tune the strength of the electrostatic repulsion between identical colloids by changing their surface charge density. This can be achieved by modifying either the pH of the suspension or the surface chemistry of the particles. However, one can alter the ionic strength by changing either the ion valency or concentration in order to modify the charge screening and consequently the range of the electrostatic repulsion. Other methods are also possible for controlling the stability of inorganic suspensions. A possible strategy is based on adding oppositely charged particles to the suspension. This method, the first step of which is heteroaggregation, proved to be very versatile. * Corresponding authors. E-mail: [email protected], ferrando@ fisica.unige.it. † SPCTS. ‡ Universita ` di Genova. (1) Liu, J.; Shih, W. Y.; Kikuchi, R.; Aksay, I. A. J. Colloid Interface Sci. 1991, 142, 369-377. (2) Yasrebi, M.; Shih, W. Y.; Aksay, I. A. J. Colloid Interface Sci. 1991, 142, 357-368. (3) Harley, S.; Thompson, D. W.; Vincent, B. Colloids Surf. 1992, 62, 163176. (4) Kim, A. Y.; Berg, J. C. J. Colloid Interface Sci. 2000, 229, 607-614. (5) Tohver, V.; Smay, J. E.; Braem, A.; Braun, P. V.; Lewis, J. A. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 8950-8954. (6) Uricanu, V.; Eastman, J. R.; Vincent, B. J. Colloid Interface Sci. 2001, 233, 1-11. (7) Fisher, M. L.; Colic, M.; Rao, M. P.; Lange, F. F. J. Am. Ceram. Soc. 2001, 84, 713-718. (8) Kim, A. Y.; Hauch, K. D.; Berg, J. C.; Martin, J. E.; Anderson, R. A. J. Colloid Interface Sci. 2003, 260, 149-159. (9) Gilchrist, J. F.; Chan, A. T.; Weeks, E. R.; Lewis, J. A. Langmuir 2005, 21, 11040-11047. (10) Liu, J.; Luijten, E. Phys. ReV. E 2005, 72, 061401. (11) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, England, 1989.

It can be used for either stabilizing or destabilizing colloidal suspensions.12-14 From the theoretical point of view, the electrostatic interaction between colloidal particles in suspension is typically modeled by the DLVO theory, proposed by Derjaguin, Landau,15 Verwey, and Overbeek.16 The colloids are assumed to be spherical particles of a given size, with a given surface charge density or surface potential, and the counter ions that are screening the interactions are assumed to be point charges following the Boltzmann distribution around the colloidal particles. Although the DLVO theory does not present precise information concerning the particle arrangement, it usually provides satisfactory predictions about the tendency of suspensions to undergo aggregation. When two kinds of particles are present in suspension, the situation is more complex so that predicting the tendency toward aggregation or dispersion is not a simple task. Indeed, the DLVO theory provides a description of direct interactions between particles, but we need to understand what effective forces arise from the combination of direct and indirect interactions, with the latter being mediated through other particles. In such a situation, numerical simulations can be very helpful. For example, Liu and Luijten10 addressed the problem of a colloidal suspension dispersion containing micrometer-sized silica spheres and zirconia nanoparticles5 by means of canonical Monte Carlo simulations. In their case, silica spheres tend to aggregate, but the addition of zirconia nanocolloids induces an effective repulsion that suppresses aggregation. Aggregation is again possible at high nanoparticle concentration. In this article, we study a case in which the behavior is the opposite to that reported for the silica-zirconia system. We consider a dilute system consisting of alumina submicrometer particles (d1 ) 400 nm) and silica nanoparticles (d2 ) 25 nm) suspended in water. The experiments17,18 show that alumina submicrometer particles in suspension do not undergo aggregation (12) Kong, D.; Yang, H.; Yang, Y.; Wei, S.; Wang, J.; Cheng, B. Mater. Lett. 2004, 58, 3503-3508. (13) Zhu, X.; Jiang, D.; Tan, S.; Zhang, Z. J. Eur. Ceram. Soc. 2001, 21, 2879-2885. (14) Tohver, V.; Chan, A.; Sakurada, O.; Lewis, J. A. Langmuir 2001, 17, 8414-8421. (15) Derjaguin, B. V.; Landau, L. Acta Physicochim. URSS 1941, 14, 633662. (16) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948.

10.1021/la702104u CCC: $40.75 © 2008 American Chemical Society Published on Web 03/01/2008

3002 Langmuir, Vol. 24, No. 7, 2008

Cerbelaud et al.

Figure 1. pH of the suspension as a function of the amount of silica added to the alumina suspension.

but that aggregation is induced when silica nanocolloids are added to the suspension. To investigate the aggregation process, we develop a model for the alumina-silica system in which the interactions between particles are given by the DLVO potential, whose parameters are directly extracted from our experimental measurements. The model is studied by Brownian dynamics simulations. The simulation results are then compared to the experiments, obtaining very good agreement both qualitatively and quantitatively. 2. Experimental System The alumina powder is AKP30 alumina from the Sumitomo Chemical Company (d50 ) 400 nm diameter, purity 99.99%, specific surface area 7 m2/g). Suspensions containing 3 vol % solids loading are used. The solvent is deionized water, and no salt is added. The measured pH of the alumina suspension is 6.5. At this pH, alumina particles are positively charged with a zeta potential of about 50 mV so that the suspension is stable for long time periods (several weeks). Silica particles are taken from a commercial, aqueous suspension of Ludox TM50 (50 wt % SiO2, d50 ) 25 nm diameter, purity 99.56%, specific surface area 140 m2/g) obtained from Grace Davison. This suspension is prepared in an alkaline medium (Na+ counterion), and its pH is 9. At this pH, silica nanoparticles are negatively charged, with a zeta potential of about -35 mV, leading to a well-dispersed suspension. The alumina and silica suspensions are oppositely charged; therefore, they are prone to heteroaggregation. To probe this phenomenon, silica nanoparticles are added to the alumina suspension. Mass ratios of r ) (mSiO2)/(mAl2O3) (× 100%) in the range of 0 e r e 4.6% are considered. We note that r is the ratio of the total mass of added silica divided by the total mass of alumina in the suspension. r values are always given as percentages in the following text. From the mass ratio, one may evaluate the ratio rn between the numbers (nSiO2 and nAl2O3) of silica and alumina particles in the suspension as follows rn )

nSiO2 nAl2O3

)

()

FAl2O3 a1 3 r FSiO2 a2 100

(1)

where a1 ) 200 nm and a2 ) 12.5 nm are the average particle radii of alumina and silica particles, respectively, and FAl2O3 ) 3.98 g/cm3 and FSiO2 ) 2.20 g/cm3 are the mass densities of alumina and silica. The factor of 100 is needed because r is expressed as a percentage. (17) Garcia-Perez, P.; Pagnoux, C.; Rossignol, F.; Baumard, J.-F. Colloids Surf., A 2006, 281, 58-66. (18) Garcia-Perez, P.; Pagnoux, C.; Pringuet, A.; Videcoq, A.; Baumard, J.-F. J. Colloid Interface Sci. 2007, 313, 527-536.

Figure 2. Zeta potentials of alumina (9) and silica (2) as a function of pH. The pH of the binary suspension depends on its composition. Before adding silica, the pH is =6.5, and this value increases with the amount of added silica (Figure 1).17 This increase in pH might be mainly due to the following chemical reaction that takes place at the surface of silica particles when they encounter a more acidic medium: Si-O- + H+ f Si-OH

(2)

This reaction causes an increase in pH because it consumes H+ ions. We note that the pH increase is an effect of the higher buffer capacity of the silica suspension compared to that of the alumina suspension. The pH-dependent zeta potential of both particle types has been measured over a large pH range using an electrokinetic sonic amplitude (ESA) measurement apparatus (model ESA8000 Matec, Northborough, MA).17 The results in Figure 2 show that in pH range of 6.5-8.5 alumina and silica particles are oppositely charged and thus heteroaggregation is expected.18 In our experiments, the possible modification of the surface potential of alumina due to the dissolution of both oxides (Healy et al.)19,20 should be negligible. In fact, it has been shown that for pure R-alumina, which is used in this case, there is no interaction between the silicic acid, which originates from the partial solubility of silica, and the alumina surface.21 In addition, a significant recondensation of silicic acid on the alumina surface should be mediated by Al3+ or polybasic Al ions coming from the dissolution of alumina.21 In our pH range and aggregation time scale (compared to those in Healy et al.),19,20 this dissolution is expected to be very limited. Although the ion concentration in suspension slightly depends on the amount of added silica, it is assumed to be equal to 10-3 mol/L. All suspensions are dilute with a solid loading of 3 vol %. The amount of silica adsorbed on alumina is determined by employing inductively coupled plasma (ICP) analysis.17 We investigate the behavior of suspensions with mass ratios of 1.1, 2.2, 2.75, 3.3, and 4.6%, corresponding to a pH range of 6.58.5 (Figure 1). In Table 1, we report the number ratio, the pH, and the zeta potentials corresponding to these mass ratios.

3. Model and Simulation Method 3.1. DLVO Potential. In the following text, all particles are assumed to be spherical, and within each particle type, all sizes are equal. These are of course approximations, especially for (19) Healy, T. W.; Wiese, G. R.; Yates, D. E.; Kavanagh, B. V. J. Colloid Interface Sci. 1973, 42, 647-649. (20) Wiese, G. R.; Healy, T. W. J. Colloid Interface Sci. 1975, 52, 452-457. (21) Iler, R. K. The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties; Wiley: New York, 1979.

Heteroaggregation between Al2O3 and SiO2 Particles

Langmuir, Vol. 24, No. 7, 2008 3003

Table 1. Mass Ratio r (Percentage), Number Ratio rn, pH, and Zeta Potentials ζ1 and ζ2 (in mV) of Alumina and Silica, Respectively r rn pH ζ1 ζ2

0.2 15 6.9 45 -20

1.1 82 7.5 30 -26

2.2 163 7.8 24 -27

2.75 204 7.9 22 -27

3.3 245 8.0 20 -28

4.6 341 8.3 12 -32

alumina particles, whose shapes are often far from being spherical and whose size distribution is not very narrow. To describe the interaction between the colloids, we have used an extension of DLVO theory to nonidentical particles.22 The interaction is the sum of two contributions: attraction due to van der Waals forces UvdW and electrostatic double layer ij interaction Uelij due to the surface charges of the colloids:

UDLVO ) UvdW + Uelij ij ij

(3)

For the van der Waals contribution, the following expression is employed23

UvdW ij (rij) ) -

[

Aij 2aiaj + 2 6 r - (a + a )2 ij i j 2aiaj rij2 - (ai - aj)2

(

+ ln

)]

rij2 - (ai + aj)2

rij2 - (ai - aj)2

(4)

where Aij is the Hamaker constant that depends on the polarizability of particles i and j and of the solvent. The values chosen for alumina-alumina, silica-silica, and alumina-silica interactions in water are respectively A11 ) 4.76 × 10-20 J, A22 ) 4.6 × 10-21J, and A12 ) xA11A22 ) 1.48 × 10-20 J.24,25 For the electrostatic term, we used the Hogg-HealyFuerstenau (HHF) equation26 under the condition of constant surface potential

Uelij (rij) ) π

aiaj (ψ 2 + ψj2) × ai + aj i 2ψiψj 1 + e-κhij ln + ln(1 - e-2κhij ) (5) ψi2 + ψj2 1 - e-κhij

[

(

)

]

where  ) 0r is the dielectric constant of the solvent. Here, r equals 81 for water. ψi is the surface potential of particle i. hij ) rij - (ai + aj) is the surface-to-surface separation distance, and κ is the inverse Debye screening length, which is given by

κ)

x

2e2z2NAI103 kBT

(6)

for a symmetric z - z electrolyte, with z being the counterion valence. In the system studied here, counterions of alumina are OH- ions and counterions of silica are Na+ ions, so z is equal to 1. e is the elementary electronic charge, NA is Avogadro’s number, and I is the ionic concentration (I ) 10-3mol/L). On the basis of these values, κ ) 108 m-1 is used in our simulations. (22) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. A. Particle Deposition and Aggregation: Measurement, Modelling and Simulation; ButterworthHeinemann: Oxford, England, 1995. (23) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: London, 1991; Vol. 1. (24) Bergstro¨m, L. AdV. Colloid Interface Sci. 1997, 70, 125-169. (25) Hu¨tter, M. J. Colloid Interface Sci. 2000, 231, 337-350. (26) Hogg, R.; Healy, T. W.; Fuerstenau, D. W. Trans Faraday Soc. 1966, 62, 1638-1651.

For the values of the particle surface potential (ψi), we have taken the zeta potential measured experimentally (Figure 2 and Table 1). Different approximations are available in the literature for the electrostatic interaction potential. The HHF equation (eq 5) is appropriate for the system studied here. Although the linearized Poisson-Boltzmann theory, which is used in its derivation, assumes surface potentials of ψi e 25 mV, this is a reasonable approximation for our experimental system (Table 1). However, the Derjaguin integration method, also used in the derivation of eq 5, is valid only for small κh. Nevertheless, a comparison with the linear superposition approximation22 shows a negligible difference between the two formulas for high κh, at least for our parameters. Finally, we note that, following the assumption of a constant surface potential in eq 5, the surface charges of the particles can vary as the particles approach each other. We believe that this approximation provides a better description of our system than the constant charge approximation. The DLVO potential (eqs 3-5) is plotted in Figure 3 for some of the parameter values used in the simulations. The interaction between identical particles is mainly repulsive, except when the surface potential is so weak that the electrostatic repulsion does not counteract the van der Waals attraction (dotted line in Figure 3a, where ψ1 ) 12 mV). For the interaction between the oppositely charged alumina and silica particles, both contributions to the DLVO potential are attractive, leading to a strong attraction between alumina and silica particles. 3.1.1. Short-Distance Approximation. As shown in Figure 3, the DLVO potential becomes infinitely attractive at short interparticle distances as a result of the divergence of the van der Waals contribution. The divergence is not physical and would lead to overlapping between the particles in numerical simulations (described in the next section), unless some hard-sphere-like term is included to avoid it. For this reason, we decided to cut the DLVO potential at a center-to-center distance of rij ) rs. The value of rs depends on the type of interaction (alumina-alumina, alumina-silica, or silica-silica), as explained in the following text. To avoid the particles penetrating each other, we replace the DLVO interaction at short distance by a constant repulsive force, whose strength is sufficiently high to avoid the particles penetrating each other by more than approximately 10%. Other methods to avoid overlapping between the particles have been tried. The one used by Hu¨tter25 that mimics soft bonds between particles close to each other is very difficult to implement in this system because of the large size difference between the particles. The silica-silica interaction remains repulsive up to very short surface-to-surface separation distances (∼1.5 nm), as shown in Figure 3b. Although the repulsion barrier is not very high (60kBT), and a simulation carried out with only alumina particles and with the same solid volume fraction does not show aggregation between the particles. Our simulations show that the silica-covered alumina particles attract each other with sufficient strength to cause steady aggregation. Now we focus on the case in which a small amount of silica is added to the suspension, showing both in experiment and simulations that this is sufficient to cause agglomeration. Let us consider the mass ratio r ) 1.1. Simulations have been carried out with a total number of particles of N ) 2744, with N1 ) 33 alumina particles and N2 ) 2711 silica particles. Figure 7 shows two examples of agglomerates obtained in the simula-

Heteroaggregation between Al2O3 and SiO2 Particles

Langmuir, Vol. 24, No. 7, 2008 3007

Figure 8. Snapshot from a simulation for a mass ratio of r ) 1.1 with N ) 2744 particles after 0.1 s. The whole simulation box is shown. Because of periodic boundary conditions, we actually observe the same tetrahedron-like cluster in the four corners of the picture. The representation employs a depth cueing method that makes the deep particles less visible than the nearest ones.

Figure 7. (a) Snapshot of two agglomerates formed in the simulation with a mass ratio of r ) 1.1 (t ) 0.1 s). In the bottom picture, the agglomerate is a chain of six alumina particles. The representation employs a depth cueing method that makes the deep particles less visible than the nearest ones. (b) Cryo-FEGSEM picture showing alumina particles surrounded by silica particles for a mass ratio of r ) 1.1.17

tions, together with an experimental image. Figure 8 shows an image of the simulated system taken after 0.1 s, a time that is comparable to the fast onset of flocculation in experiments. Both images prove that this amount of silica causes agglomeration. Very interestingly, in the experimental and the simulation images we observe aggregates with few silica nanoparticles between the alumina particles. The simulation time scale is sufficient for following only the initial stages of the experimental agglomeration process. However, within this time scale, the simulations show that agglomeration develops in two stages: (a) a fast initial stage, which is completed on a scale of about 0.02 s, in which the silica nanoparticles adsorb on isolated alumina particles and reach stationary coverage (Figure 6) and (b) a slower agglomeration process, which begins on the scale of 0.1 s, in which the silica-covered alumina particles can meet, feel a rather short-range effective attraction, and begin to form aggregates. Stage b is possible, in the case of r ) 1.1, because of a rather subtle effect involving the different attraction and repulsion strengths between the particles, which can be explained as follows. Consider, for example, two alumina particles. As seen in Figure 3a, these particles will feel quite a strong repulsion when approaching each other and will not come into contact because

there is a high barrier (about 60kBT) to overcome. Now insert a few silica particles in between these two alumina particles. When the latter are sufficiently close, the silica particles will form a ring between them. Each silica particle within the ring is adsorbed on both alumina particles. If there is a sufficient number of silica particles, then the ring causes the aggregation of the two alumina particles, even though the latter could not come into contact. Therefore, the agglomeration of silica-covered alumina particles is not related to a depletion effect.31 This picture is supported by the experimental results. In fact, silica particles coadsorbed between two alumina particles are evident in the experimental image of Figure 7b. Taking into account the aggregation scenario depicted above, it is interesting to compare the behavior of our alumina-silica system with that of silica-zirconia, which has been experimentally studied by Tohver et al.5 and simulated by Liu and Luijten.10 In silica-zirconia, large silica particles are assumed to have zero surface potential, and the much smaller (by a factor of 100) zirconia particles are strongly charged so that they can induce local charging in silica, which causes a silica-zirconia attraction. For this reason, Liu and Luijten used the same model (HHF approximation, eq 5) for the electrostatic interaction between zirconia and silica, as in our case for alumina and silica. However, from eq 5, comparing the interaction parameters for silica-zirconia and alumina-silica, it follows that there are important differences that make the effect of adding zirconia to silica completely different from the effect of adding silica to alumina. The range of the silica-zirconia attraction is on the order of 1 nm,10 whereas the range of alumina-silica attraction in our case is on the order of 10 nm. Moreover, silica particles in silica-zirconia have a radius of 300 nm, which is even larger than the radius of our alumina particles. Therefore, silica-zirconia attraction is extremely short-ranged compared to the size of silica particles so that coadsorption of a zirconia nanoparticle on two adjacent silica particles is extremely unlikely. This forbids the agglomeration mechanism that we find in alumina-silica in which the coadsorption of silica and the formation of a silica ring between alumina particles play essential roles. (31) Asakura, S.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255-1256. (32) Humphrey, W.; Dalke, A.; Schulten, K. J. Mol. Graphics 1996, 14, 3338.

3008 Langmuir, Vol. 24, No. 7, 2008

Cerbelaud et al.

system constituted of equally sized, oppositely charged polystyrene spheres. In the system studied here, in spite of the high size asymmetry between the two components, we still have the short-range attraction between alumina and silica particles and the longer-range repulsion between alumina particles. This might explain the chainlike structures that we observe.

5. Conclusions

Figure 9. Snapshot from a simulation for a mass ratio of r ) 0.2 after 0.1 s.

An important issue that arises is the minimum quantity of silica required to induce flocculation. Experimentally, we find that r ) 0.2 (corresponding to number ratio rn ) 15) is sufficient to cause flocculation. We have asked if our model is able to reproduce agglomeration for such a low r value, finding a positive answer, as can be seen in Figure 9. For r ) 0.2, the charge compensation assumption would decrease the surface potential of alumina from only 45 to 43 mV, and it would give no reason for the suspension flocculation. Thus, charge compensation cannot explain either the adsorption data (as shown in the previous section) or the flocculation of the suspension for the small quantities of added silica. We note that the agglomeration mechanism of alumina particles discussed in this section specifically applies to very small amounts of added silica (r ) 0.2-1.1). In this range of added silica, the pH still corresponds to a high surface charge of alumina (g30 mV) (Table 1). Therefore, the colloidal stability of the alumina system is not affected by the pH change but rather by the effect of added silica nanoparticles. Finally, let us discuss the properties of the sediment with respect to the factors concerning sediment height h and powder volume fraction in the sediment φS (which is simply inversely proportional to the sediment height). The data are reported in Table 3. We note that the cakes obtained for r > 0, whose heights are in the range of 60-70 mm (compared with 26 mm without silica), must correspond to very porous networks of agglomerated particles. The formation of chainlike aggregates (as shown in Figure 7a) in the early stage of aggregation could explain such an open structure in the final cake. The observation of such elongated shapes is typical of a system where reorganization is very slow. Moreover, chainlike aggregates have already been observed in systems where there is a short-range attraction and a long-range repulsion. For example, Kim et al.8 reported on the numerical and experimental observation of linear chains in a

A dilute colloidal system consisting of two kinds of inorganic particles, alumina and silica, with a large size difference has been investigated experimentally and by means of Brownian dynamics simulations. The interactions between the particles have been described by the DLVO theory with realistic parameters estimated from experimental measurements, such as the Debye length and the surface potential of the particles. The classical Brownian dynamics algorithm has been adapted to properly account for the motions of both particles that take place on very distinct time scales. The conditions of heteroaggregation have been explored. It is found that, in the first stage of the aggregation process, the silica nanoparticles adsorb on the alumina submicrometer particles. This adsorption stage is followed by aggregation between alumina particles surrounded by small silica particles under conditions where the repulsion between isolated alumina particles is fairly strong. Therefore, we find that an attractive effective interaction, which is mediated through the silica nanoparticles, arises between alumina particles. Both experiments and simulations have shown that a very small amount of added silica can destabilize the alumina suspension, causing the formation of aggregates. The adsorption of silica nanoparticles on alumina particles has been investigated in detail, and we find that silica particles can cover the alumina surface up to saturation at a value that is much smaller than the close-packing coverage. Very good agreement has been found between experimental and simulation results about the quantity of silica adsorbed on alumina. This shows that the present model, which is based on two-body interactions described by the DLVO theory but including all of them, is appropriate. This kind of modeling thus looks promising for predicting the behavior of such multicomponent systems. As a further development of this work, we think that it would be interesting to analyze in more detail the shape of the aggregates that are formed in this kind of binary mixture with oppositely charged and highly size-asymmetric components, at the initial stage of the aggregation process before precipitation. This will be the subject of further simulation studies. Acknowledgment. We acknowledge a fellowship from the Programme VINCI 2006 de l’Universite´ Franco-Italienne on the subject “Etude fondamentale de la structuration de suspensions colloidales”. Figures 5, 7a, 8, and 9 have been obtained by VMD, a molecular graphics program originally designed for the interactive visualization and analyses of biological materials, developed by the Theoretical Biophysics Group in the Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign.32 LA702104U