Oppositely Charged Model Ceramic Colloids: Numerical Predictions

pubs.acs.org/Langmuir © 2010 American Chemical Society

Oppositely Charged Model Ceramic Colloids: Numerical Predictions and Experimental Observations by Confocal Laser Scanning Microscopy M. A. Piechowiak,† A. Videcoq,*,† F. Rossignol,† C. Pagnoux,† C. Carrion,‡ M. Cerbelaud,§ and R. Ferrando§ † SPCTS, UMR 6638, ENSCI, CNRS, Centre Europ
een de la C
eramique, 12 rue Atlantis, 87068 Limoges Cedex, France, ‡Laboratoire d’Immunologie, UMR 6101, Universit
e de Limoges, CNRS, CHU Dupuytren, 87065 Limoges Cedex, France, and §Dipartimento di Fisica dell’Universit a di Genova, via Dodecaneso 33, 16146 Genova, Italy

Received March 13, 2010. Revised Manuscript Received June 3, 2010 Fluorescent silica and alumina-like spherical particles with almost equal sizes are synthesized. Dilute aqueous suspensions are prepared with various ratios of those colloidal particles that exhibit opposite surface charges. These suspensions undergo heteroaggregation for a wide range of compositions. The structure of the formed aggregates is analyzed by means of confocal microscopy. The experimental results are compared to those of Brownian dynamics simulations in which the interactions between colloids are modeled by the DLVO potential. Good agreement between experiments and simulations is obtained.

1. Introduction The study of colloidal phenomena in suspensions is important in many areas of great technological interest, for instance, in several ceramic shaping processes. Because the preparation of suspensions strongly influences the final properties of the product, knowledge and possibly control of the interactions between colloidal particles are of crucial importance. They allow one to determine what kind of aggregates can be formed in the suspensions and what dynamics lead to them. Suspensions composed of a single type of colloid have been intensively studied in recent years.1 In these systems, aggregation can be controlled in several ways, for example, by modifying the suspension pH and the surface chemistry of colloidal particles (by ion or macromolecule adsorption). A large selection of compounds are now available to be used in different ceramic processes.2-6 However, much less is known about aggregation phenomena in suspensions containing oppositely charged colloidal particles (these phenomena are usually known as heteroaggregation), for which early studies can be found in ref 7 and 8. Therefore, predicting and understanding the behavior of these heterogeneous suspensions is presently a very active research field.9 Studies of heteroaggregation have been performed in our laboratory in recent years. Suspensions of alumina and silica oppositely charged colloids of different sizes (with ratios between *To whom correspondence should be addressed. E-mail: arnaud.videcoq@ unilim.fr. (1) Lewis, J. A. J. Am. Ceram. Soc. 2000, 83, 2341–2359. (2) Pringuet, A.; Pagnoux, C.; Videcoq, A.; Baumard, J.-F. Langmuir 2008, 24, 10702–10708. (3) Ben Romdhane, M.; Chartier, T.; Baklouti, S.; Bouaziz, J.; Pagnoux, C.; Baumard, J.-F. J. Eur. Ceram. Soc. 2007, 27, 2687–2695. (4) Penard, A.-L.; Rossignol, F.; Nagaraja, H.; Pagnoux, C.; Chartier, T. J. Eur. Ceram. Soc. 2005, 25, 1109–1118. (5) Boufi, S.; Baklouti, S.; Pagnoux, C.; Baumard, J.-F. J. Eur. Ceram. Soc. 2002, 22, 1493–1500. (6) Hidber, P.; Graule, T.; Gauckler, L. J. Eur. Ceram. Soc. 1997, 17, 239–249. (7) Kitano, H.; Iwai, S.; Ise, N. J. Am. Chem. Soc. 1987, 109, 1867–1868. (8) Kitano, H.; Iwai, S.; Ise, N.; Okubo, T. J. Am. Chem. Soc. 1987, 109, 6641–6644.
(9) L
opez-L
opez, J. M.; Schmitt, A.; Moncho-Jord
a, A.; Hidalgo-Alvarez, R. Soft Matter 2006, 2, 1025–1042. (10) Cerbelaud, M.; Videcoq, A.; Ab
elard, P.; Pagnoux, C.; Rossignol, F.; Ferrando, R. Langmuir 2008, 24, 3001–3008.

12540 DOI: 10.1021/la101027d

diameters of 16 and 1.6) have been prepared and studied.10-12 The aggregation process has also been analyzed with the aid of Brownian dynamics simulations based on the DLVO potential13,14 for the interaction between colloids. These simulations have been able to describe aggregation processes and aggregate shapes in good agreement with experimental observations. The main experimental techniques for characterizing suspensions are sedimentation tests and SEM observations. However, experimental analyses of aggregates in systems that undergo heteroaggregation are difficult because of the fast sedimentation. For this reason, an examination method based on the observation of frozen suspensions using cryo-SEM has been employed.12,15 This method is sufficient to analyze the final aggregates because alumina and silica colloids can be easily identified by their different size and shape, with alumina particles being larger and rather irregular and silica particles being smaller and almost perfectly spherical. In this article, we intend to study heteroaggregation in alumina-silica systems in the case of spherical and equally sized colloids of both types. This case is of interest in ceramic processing because it could lead to the formation of aggregates with a regular distribution of voids and therefore better flow properties. Moreover, it has to be noticed that equally sized colloids with opposite charges can be used as building blocks of colloidal crystals.16 The particles studied in this article can thus be of interest for building colloidal crystals entirely made of ceramic materials. However, commercial alumina particles have irregular shapes. Therefore, a method of producing spherical alumina-like colloids is needed. With this aim, we have chosen to produce monodisperse spherical core-shell particles with a core of silica and a shell (11) Cerbelaud, M.; Videcoq, A.; Ab
elard, P.; Ferrando, R. J. Colloid Interface Sci. 2009, 332, 360–365. (12) Cerbelaud, M.; Videcoq, A.; Ab
elard, P.; Pagnoux, C.; Rossignol, F.; Ferrando, R. Soft Matter 2010, 6, 370–382. (13) Derjaguin, B.; Landau, L. Prog. Surf. Sci. 1993, 43, 30–59. (14) Verwey, E. J. W.; Overbeek, J. T. G. J. Colloid Sci. 1955, 10, 224–225. (15) Garcia-Perez, P.; Pagnoux, C.; Rossignol, F.; Baumard, J.-F. Colloids Surf., A 2006, 281, 58–66. (16) Leunissen, M.; Christova, C.; Hynninen, A.-P.; Royall, C.; Campbell, A.; Imhof, A.; Dijkstra, M.; Van Roij, R.; van Blaaderen, A. Nature 2005, 437, 235– 240.

Published on Web 07/06/2010

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of alumina and to aggregate them with pure monodisperse silica particles. Because both types of particles will have the same shape and very similar sizes, the previously mentioned characterization methods, such as the observation of frozen suspensions using cryo-SEM, turn out to be inefficient. For this reason, we have planed to use confocal microscopy, which is already a powerful tool in many scientific fields from biology to information technology. However, its use in studying colloidal systems is a relatively recent development. Advances in imaging and particle tracking help in understanding colloidal phenomena.17 Among the first studies to look at homogeneous colloids with a confocal microscope were those by Yoshida et al.18 and van Blaaderen and Wiltzius,19 who extended the capability of confocal microscopy to the study of denser systems. To make confocal microscope analysis possible, our particles must be preliminarily functionalized with fluorescent dyes. In parallel with the experiments, the aggregation processes in our system are analyzed by means of Brownian dynamics simulations, using the same kind of modeling that has been successful in describing the aggregation of alumina-silica colloids of different sizes.10-12

2. Experimental System 2.1. Raw Materials. Reagents tetraethyl orthosilicate 99% (TEOS), ammonium hydroxide 28%, and absolute ethanol were purchased from Prolabo VWR (France) for silica particle synthesis. 3-Aminopropyl-triethoxysilane 99% (APS), fluorescein isothiocyanate isomer I 90% (FITC), and rhodamine B isothiocyanate (RBITC) were purchased from Sigma-Aldrich (Germany) and were used to obtain fluorescent particles. To form alumina shells on silica cores, aluminum isopropoxide 98% (AIP) supplied from Acros Organics (Belgium) was used. 2.2. Particle Synthesis. 2.2.1. Synthesis of Fluorescent Silica Particles. Fluorescent silica particles with a core-shell structure were synthesized by a modified St€ ober method in a manner similar to that already reported by van Blaaderen and coworkers20-22 and the research group of Wiesner.23-25 A process consisting of two steps was chosen. First, monodisperse spherical silica cores with a size of 475 nm were synthesized by the modified one-step St€ ober method,26 which is based on the controlled hydrolysis of TEOS in an ethanol/water mixture with ammonia. Concentrations of 0.075 M TEOS, 1.85 M NH3, and 5.55 M H2O were used; then the suspension was stirred overnight at ambient temperature. After the preliminary addition of 6.5
10-6 M organic fluorescent (FITC or RBITC) dyes covalently attached to the (3-aminopropyl)triethoxysilane coupling agent in a seeded suspension, the second step consisted of the controlled growth process of silica shells by the dropwise addition of TEOS. One of the crucial issues in this procedure is to avoid the formation of new secondary particles during the growth process of the shell on the seeds. It is known from both the experimental and theoretical considerations of Chen et al.27 that under given temperatures and concentrations of reactants there exists a critical value of the (17) Rolli
e, S.; Sundmacher, K. Langmuir 2008, 24, 13348–13358. (18) Yoshida, H.; Ito, K.; Ise, N. Phys. Rev. B 1991, 44, 435–438. (19) van Blaaderen, A.; Wiltzius, P. Science 1995, 270, 1177–1179. (20) van Blaaderen, A.; Vrij, A. Langmuir 1992, 8, 2921–2931. (21) van Blaaderen, A. Adv. Mater. 1993, 5, 52–54. (22) Verhaegh, N. A. M.; van Blaaderen, A. Langmuir 1994, 10, 1427–1438. (23) Burns, A.; Ow, H.; Wiesner, U. Chem. Soc. Rev. 2006, 35, 1028–1042. (24) Burns, A.; Sengupta, P.; Zedayko, T.; Baird, B.; Wiesner, U. Small 2006, 2, 723–726. (25) Ow, H.; Larson, D.; Srivastava, M.; Baird, B.; Webb, W.; Wiesner, U. Nano Lett. 2005, 5, 113–117. (26) St€ober, W.; Fink, A.; Bohn, E. J. Colloid Interface Sci. 1968, 26, 62–69. (27) Chen, S.-L.; Dong, P.; Yang, G.-H.; Yang, J.-J. J. Colloid Interface Sci. 1996, 180, 237–241.

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external surface area Sp of the initial seeds that guarantees the growth of monodisperse spheres without secondary nucleation, and this critical value increases linearly with the seed diameter. To choose the right preparation conditions, it is required to take into account the following factors: the generation rate, the specific seed surface area (in a given volume of solution), and also the addition rate of TEOS depending on seed concentration and initial size. There are two similar equations describing the hydrolysis rate that can be used to estimate the generation rate rgen. These equations give rgenGiesche (as proposed by Giesche28) and rgenChen (as proposed by Chen et al.29),


rgenGiesche

rgenChen

 - 3256 K 2:36 exp ½TEOS T ¼ - 1:18 - 0:97 ½NH3  s½H2 O
 - 3067 K ½TEOS 1:246 exp T ¼ s½H2 O - 1:267 ½NH3  - 0:971

ð1Þ

ð2Þ

where square brackets denote the concentration of reagents, T is the temperature (in Kelvin), and K and s indicate Kelvin and seconds, respectively. Our growing suspension included seeds of 475 nm with Sp ≈ 990 cm2/mL, and a TEOS concentration of 0.15 M was used, corresponding to generation rates of 7.25
10-5 and 8.43
10-5 M s-1 as calculated with eqs 1 and 2, respectively. Upon the basis of the experimental results of Chou et al.,30 our operating conditions could guarantee no secondary nucleation. To control the final particle size, we have also to take into account that choosing a value much higher than the critical one will cause a decrease in the final size Lf of grown particles. This is a consequence of the following formula,27
3 Lf ðWs þ WÞ ¼ Ws Ls

ð3Þ

where Ls is the initial size of the seeds, Ws is the weight of SiO2 initially present as seeds, and W is the amount of SiO2 added as a reagent in the form of TEOS. Another important factor in the synthesis is the maximum addition rate of TEOS. In conformity with a calculation method presented by Giesche,28,31 for our growing suspension including seeds of 475 nm and a concentration of 0.26 M, the maximum addition rate of TEOS was estimated to be 0.07 mol/h. Finally, an addition rate RTEOS of 0.05 mol/h was used. As-synthesized powders were afterward centrifugally separated by triple washing in ethanol and were dried overnight at 60 °C (Figure 1a).

2.2.2. Synthesis of a Positively Charged Shell: Aluminalike Particles. The process proposed by Cheng et al.32 was applied to form alumina shells on silica cores. First, a peptization method was used to obtain the Al2O3 sol. Coagulated aluminum monohydroxide (AlOOH) was prepared by adding 10.0 g of aluminum isopropoxide (AIP) to 100 mL of distilled water at 80 °C under vigorous stirring. The pH of the solution was adjusted to 4.0 by adding 1 M nitric acid, and then the solution was continuously stirred for 5 h and cooled to room temperature. Afterwards, 1 g of synthesized FITC-labeled silica particles was dispersed in 40 mL of distilled water via sonication. The pH of the suspension was adjusted to 2.5 by adding 1 M HNO3, and then 4 mL of peptized Al2O3 sol was added. Such a prepared suspension was (28) Giesche, H. J. Eur. Ceram. Soc. 1994, 14, 189–204. (29) Chen, S.-L.; Dong, P.; Yang, G.-H.; Yang, J.-J. Ind. Eng. Chem. Res. 1996, 35, 4487–4493. (30) Chou, K.-S.; Chen, C.-C. Ceram. Int. 2008, 34, 1623–1627. (31) Giesche, H. J. Eur. Ceram. Soc. 1994, 14, 205–214. (32) Cheng, B.; Zhao, L.; Yu, J.; Zhao, X. Mater. Res. Bull. 2008, 43, 714–722.

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Piechowiak et al. 488 nm for FITC- and 543 nm for RBITC-labeled particles, and a lens of 100
/1.4 oil were chosen. Average numbers of neighbors are calculated from plane CLSM images of size 11.25 μm
11.25 μm. Volocity software (PerkinElmer) was used to identify the (x, y) coordinates of particle centers. For each studied composition, several plane CLSM images were analyzed in order to reach a minimum of 3000 identified particles.

3. Simulation Method and Interaction Model Figure 1. Schemes of the particle internal composition: (a) silica

(average size of 585 nm and zeta potential of -52 mV at pH 5.5), (b) alumina-like (average size of 620 nm and a zeta potential of 20 mV at pH 5.5). (The complete characterization of particle size and zeta potential as a function of pH is reported in section 4.1).

stirred for 30 min, the pH was adjusted again to 6.5 by adding a 2 M NH4OH solution, and the mixed suspension was stirred for 3 h. The resulting powder was then centrifugally separated with triple washing in water and dried overnight at 60 °C (Figure 1b). 2.2.3. Suspension Preparation. A series of mixed suspensions of positively charged alumina-like FITC-labeled particles and negatively charged silica RBITC-labeled particles were prepared with a total solid loading fixed at 3 vol %. Powders were added to deionized water, and suspensions were submitted to ultrasonic treatment. Suspensions were identified by the mass ratio R of negative silica particles mSiO2 with respect to the total mass of solid (mAl2O3þ mSiO2): R ¼

mSiO2 mAl2 O3 þ mSiO2

ð4Þ

The following values of R were studied: 0, 0.16, 0.31, 0.48, 0.65, 0.82, and 1.00. The pH of all suspensions was adjusted to 5.5 by adding 0.25 M HCl. 2.3. Characterization Methods. The size distribution of synthesized particles in suspension (3 vol %) was determined by laser granulometry with a Mastersizer 2000 (Malvern Instruments, U.K.). Before the measurements, the suspensions were deagglomerated by applying ultrasonic treatment. The powder density was measured with a Micromeritics AccuPyc 1330 helium pycnometer. The particle shape, homogeneity, and size were observed using a Hitachi S 2500 scanning electron microscope. The zeta potential of the particles as a function of pH was measured with a Zetasizer Nano ZS90 (Malvern Instruments, U.K.) equipped with an MPT-2 autotitrator. The equipment uses a combination of laser Doppler velocimetry and phase analysis light scattering to measure the particle electrophoretic mobility. The zeta potential is related to the electrophoretic mobility by the Henry equation, which applies, in the case of our suspensions, within the Smoluchowski approximation. Strongly diluted aqueous suspensions of 0.002 vol % prepared from a mother suspension were measured and titrated with a 0.05 M HCl solution. The fluorescence emission of labeled particles was recorded with a Cary Eclipse fluorescence spectrophotometer (Varian) at an excitation wavelength of 260 nm. The agglomeration of the alumina-like/silica mixed systems was studied by carrying out sedimentation experiments as a function of the mass ratio R. Immediately after preparation, the samples were allowed to settle in closed tubes for a total of 1 month. After that time, a clear supernatant was observed and the height of the cake was measured. Fluorescently labeled particles made it possible to observe the suspension structure using confocal laser scanning microscopy (CLSM) at a resolution sufficient to see elementary particles in the bulk of the suspension.22 Therefore, suspensions were placed in optical cells and allowed to settle before an observation was made. An LSM 510 META laser scanning microscope (Zeiss, Germany) comprising one 30 mW argon and two helium-neon lasers was used. Double-channel mode, with excitation wavelengths of 12542 DOI: 10.1021/la101027d

3.1. Simulation Method. The system is simulated using the technique already described in refs 12 and 33, namely, Brownian dynamics.34,35 The solvent is treated implicitly in the simulations, and its effects on the solute are represented by a combination of random forces and frictional terms. The motion of particle i with a mass mi and velocity vi is thus described by the Langevin equation: mi

X dvi ðtÞ Fij frij ðtÞg þ Γi ðtÞ ¼ - ζi vi ðtÞ þ dt j

ð5Þ

On the right-hand side of eq 5, the first term is the frictional one given by the Stokes’ law, where the friction coefficient ζi = 6πηai depends on the solvent viscosity η and on the particle radius ai. The second term represents the interaction forces originated by all other particles on particle i. It depends on the interparticle distances rij, and the pairwise additivity of two-body interactions is assumed. These forces are derived from interaction potentials (Fij = -rUij) that will be presented in section 3.2. The third term Γi(t) represents a stochastic force that models collisions between colloidal particles and solvent molecules. The coupled system of eq 5 can be solved only numerically, using a constant time step of δt. To integrate the set of eq 5, we have chosen a time step of 2
10-7 s, which is much longer than velocity relaxation time τv = mi/ζi (≈ 5
10-8 s), and we have neglected the inertia term on left-hand side of the equation. This leads to the following firstorder differential equation33 dri ðtÞ 1X 1 ¼ Fij frij ðtÞg þ Γi ðtÞ dt ζi j ζi

ð6Þ

where ri is the position of particle i. Indeed, δt must also be chosen small enough to ensure that interaction forces do not change significantly during one integration step. For the numerical integration of eq 6, we used the “white noise” algorithm developed by Mannella and Palleschi36 and limited it to first order in δt, leading to the following integration scheme sffiffiffiffiffiffiffiffiffiffiffiffi 2kB T 1X ri ðt þ δtÞ ¼ ri ðtÞ þ Fij frij ðtÞgδt ð7Þ ðδtÞ1=2 Yi þ ζi ζi j where kB is the Boltzmann constant and T is the temperature. Yi denotes uncorrelated Gaussian-distributed random numbers with an average of zero and a standard deviation of 1. 3.2. DLVO Potential. To describe the interaction between the colloids, we use an application of DLVO theory to heteroaggregation.10-12,37 The interaction is the sum of two contriand the butions: attraction due to van der Waals forces UvdW ij (33) Videcoq, A.; Han, M.; Ab
elard, P.; Pagnoux, C.; Rossignol, F.; Ferrando, R. Physica A 2007, 374, 507–516. (34) Ermark, D. L. J. Chem. Phys. 1975, 62, 4189–4196. (35) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: Oxford, U.K., 1987. (36) Mannella, R.; Palleschi, V. Phys. Rev. A 1989, 40, 3381–3386. (37) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. Particle Deposition and Aggregation: Measurement, Modelling, and Simulation; Butterworth-Heinemann: Oxford, 1995.

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electrostatic double-layer interaction Uelij due to the surface charges of the colloids: UijDLVO ¼ UijvdW þ Uijel

ð8Þ

The van der Waals term is given by38 UijvdW ðrij Þ

" Aij 2ai aj 2ai aj ¼ þ 6 rij 2 - ðai þ aj Þ2 rij 2 - ðai - aj Þ2 !# rij 2 - ðai þ aj Þ2 þ ln rij 2 - ðai - aj Þ2

ð9Þ

where Aij is the Hamaker constant that depends on the polarizability of particles i and j and on the solvent itself. The values chosen for our aqueous system were A11 = 4.76
10-20 J, A22 = 4.6
10-21 J, and A12 = (A11A22)1/2 = 1.48
10-20 J for aluminalike/alumina-like, silica/silica, and silica/alumina-like interactions, respectively.39 For the electrostatic term, we use the HoggHealy-Fuerstenau (HHF) equation40 under the condition of constant surface potential ai aj ðψ 2 þ ψj 2 Þ ai þ aj i 2 3 ! - Khij 2ψi ψj 1 þ e 2Kh ij 5 þ lnð1 - e
4 2 ln Þ ψi þ ψj 2 1 - e - Khij

Uijel ðrij Þ ¼ πε

ð10Þ where ε = ε0εr is the dielectric constant of the solvent (for water, εr = 81), ψi is the surface potential of particle i, hij = rij - (ai þ aj) is the surface-to-surface separation distance, and κ is the inverse Debye screening length, which is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2e2 z2 NA I K ¼ εkB T

ð11Þ

for a symmetric z - z electrolyte, with z being the counterion valence. NA is the Avogadro’s number, e is the elementary electronic charge, and I is the ionic concentration. κ = 108 m-1 was used in our simulations. The zeta potential values measured experimentally at pH 5.5 are taken for the particle surface potential: ψ1 = 20 mV for alumina-like particles and ψ2 = -52 mV for silica particles. The DLVO potential is plotted in Figure 2. The interaction is repulsive between identical particles and attractive between oppositely charged particles. As shown in Figure 2, the DLVO potential goes to infinity at short interparticle distances as a result of the divergence of the van der Waals contribution. This divergence would lead to particles overlapping in simulations; therefore, we modify the interaction potential at short distances, as explained and discussed in detail in refs 10-12. In the following text, we recall the main points of that modification. We cut the DLVO potential at a center-to-center distance of rij = rs, which depends on the type of interaction. We replace the DLVO interaction at short distance by a constant repulsive force with a strength that is sufficiently high to avoid particle (38) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: London, 1991; Vol. 1. (39) Bergstr€om, L. Adv. Colloid Interface Sci. 1997, 70, 125–168. (40) Hogg, R.; Healy, T.; Fuerstenau, D. J. Chem. Soc., Faraday Trans. 1 1966, 62, 1638–1651.

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Figure 2. DLVO interaction potentials UDLVO as a function of ij

dimensionless center-to-center separation distance rij/(ai þ aj). UDLVO alumina-like/alumina-like (---), UDLVO silica/silica ( 3 3 3 ), 11 22 and UDLVO alumina-like/silica (-) interactions. 12

interpenetration. Consequently, we cut the alumina-like/aluminalike and silica/silica DLVO potentials at their maxima (occurring for interparticle distances of =1.013
2a1 and =1.002
2a2, respectively). For the alumina-like/silica interaction, we have chosen to cut the DLVO potential at a constant well depth of Ew = -14kBT. This choice of Ew ensures good agreement between experiment and simulation in the previously studied cases, as discussed in refs 10-12. Indeed, in the case of similarly sized particles, which corresponds to the present situation, we have checked that the simulation results are weakly sensitive to the value of Ew, provided that -20kBT e Ew e -12kBT.12 In the case of highly size-asymmetric particles, the adsorption of small silica particles on alumina particles that are 16 times larger was experimentally measured and compared to simulations. The best agreement between experiments and simulations was found for -16kBT e Ew e -14kBT.11 Our choice of Hamaker constants is also worth discussing. The van der Waals interactions involving alumina-like particles are calculated using the Hamaker constant of pure alumina. This is an approximation because alumina-like particles have an important silica core. By assuming pairwise additivity, one can evaluate these interactions more precisely. Indeed, they can be expressed as the sum of contributions from solid spherical particles.41 Even if the alumina shell is thin (17 nm), choosing the Hamaker constant of pure alumina for the aluminalike particles leads to a good approximation because silica has a much smaller Hamaker constant. For the alumina-like/silica interaction, the approximation is very good (the maximum correction to the DLVO potential is about 0.5kBT ) because the van der Waals attraction is much lower than the electrostatic attraction. For the alumina-like/alumina-like interaction, the more accurate calculation gives rise to a slightly more repulsive DLVO potential (with a barrier that is 6kBT higher than the one shown in Figure 2). However, we do not expect significant changes concerning the results shown in the next section. Moreover, this reinforces our assumption that consists of replacing the alumina-like/alumina-like DLVO potential by a constant repulsive force at a short distance. Simulations are performed in a cubic cell with periodic boundary conditions and particles are initially placed at random, nonoverlapping positions. In all simulations, the number of particles was N = 3240, the viscosity of water was η = 10-3 Pa s, the particle volume fraction was φ = 0.03, and the temperature of the system was fixed at T = 293 K. (41) Viravathana, P.; Marr, D. J. Colloid Interface Sci. 2000, 221, 301–307.

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Figure 3. (a) Size distribution, (b) ζ potential as a function of pH, and (c) fluorescence spectra of labeled alumina-like particles (;), labeled silica particles (---), and cores ( 3 3 3 ).

Figure 4. SEM images of (a) silica and (b, c) alumina-like labeled powders.

It is to be noticed that we neglect the partial solubility of the oxide particles because we analyze the early stages of the aggregation process that take place in a few tens of seconds after the mixing of the two kinds of particles in suspension.

4. Results and Discussion 4.1. Synthesized Particles. Synthesized core-shell particles exhibit a very homogeneous morphology in term of shape and size. The size distributions of cores as well as of both kinds of particles (Figure 3a) are narrow and centered at 475, 585, and 620 nm for cores, labeled silica, and labeled alumina-like particles, respectively. The natural pH of the alumina-like suspension (3 vol %) is 7.5, and that of the silica suspension is 8.9. The zeta potential of labeled alumina-like particles (-) and labeled silica particles (---) in an aqueous suspension is reported as a function of pH in Figure 3b. We point out that the zeta potential of silica is negative over a wide range of pH, whereas the zeta potential of particles with the alumina shell is entirely positive in the pH range considered. Therefore, we succeeded in changing the surface properties of silica particles by an alumina shell and obtaining two populations of oppositely charged colloids. In addition we used two different types of fluorescent dyes in order to distinguish the two types of particles by their different emission spectra with the confocal microscope. Figure 3c reports the fluorescence spectra obtained for an excitation length of 260 nm. Alumina-like particles, labeled by fluorescein, show a green emission with the maximum at λmaxAl O ≈ 520 nm whereas silica particles, dyed by rhodamine B, show a red emission with the maximum at λmaxSiO ≈ 580 nm. Figure 4 shows SEM images of powders revealing their perfect isodiametric spherical shape. Using the helium pycnometer, the mass densities obtained for the particles are FSiO2 = 2.23 g/cm3 (silica) and FAl2O3 = 2.45 g/ cm3 (alumina-like). This last value is in good agreement with the theoretical density of a 585 nm silica sphere (whose density is 2

2

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3

Table 1. Number Ratio between Silica and Alumina-like Particles, Height of the Sedimentation Cake (h), and Powder Volume Fraction in the Sediment (OS, Given as a Percentage) as a Function of Different Compositions R R

0

0.16

0.31

0.48

0.65

0.82

1

nSiO2/nAl2O3 h (mm) ( 0.1 mm φS (%)

0 9.8 25.6

0.25 18.5 13.5

0.59 39.2 6.4

1.21 40.8 6.1

2.43 35.8 7.0

5.96 12.8 19.6

6.8 36.8

about 2.2 g/cm3), covered with a 17-nm-thick shell consisting of alumina (whose density is about 4.0 g/cm3): FAl2O3,th=(2.2aSiO23 þ 4(aAl2O33 - aSiO23))/aAl2O33. In the following text, we analyze suspensions where both kinds of particles are mixed and the composition is expressed by the mass ratio R (eq 4). According to the sizes and mass densities of the two kinds of synthesized particles, the suspension composition may also be described by the number ratio nSiO2/nAl2O3 between silica and alumina-like particles. This number ratio is given in Table 1. 4.2. Characterization of Mixed Systems in Experiments and Simulations. The occurrence of opposite zeta potentials induces heteroaggregation as expected. The pH of the mixed suspensions is adjusted to 5.5, a value for which both kinds of particles present relatively high absolute values of the zeta potential: 20 and -52 mV for alumina-like and silica particles, respectively (Figure 3b). As in our previous study,12 the first way in which we characterize the heteroaggregation phenomena is the sedimentation test for different compositions R. In Figure 5, we show sediments obtained after 1 month. The heights of sedimentation cakes and the powder volume fraction in the sediments are given in Table 1. Samples with insignificant aggregation lead to compact cakes, exhibiting the lowest porosity. The observed more compact cake of the pure silica suspension (φS=36.8 vol %) compared to that of the alumina-like suspension (φS = 25.6 vol %) is closely connected to a higher absolute value of the zeta potential, Langmuir 2010, 26(15), 12540–12547

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Figure 5. Images of sedimented suspensions (3 vol %) of mixedlabeled alumina-like and silica particles as a function of different compositions R after 1 month.

and it conducts to a stronger interparticle repulsion that hinders their homoaggregation. High sediment is proof of aggregation and internal sediment porosity. Mixed systems of particles are strongly destabilized, showing higher cakes. The powder volume fraction in the sediment decreases as the mass ratio R increases, reaching a minimum compactness for R = 0.48 (φS = 6.1 vol %). Above R = 0.48, the cake compactness increases for systems comprising a majority of silica particles. Few groups have reported on the observation of colloidal suspensions by confocal laser scanning microscopy (CLSM).16,42-44 Compared to the present system, the particle diameter is usually larger, greater than 1 μm. Our first observations carried out by CLSM give satisfying and qualitatively good results. The problem of particle distinction inside an aggregate is indeed solved by our particles’ fluorescent labeling. Figure 6a,b shows CLSM images of mixed suspensions for different compositions. The resolution of CLSM allows us to observe the entire aggregates easily as well as to get some information about their internal structure. Green and red are the colors of alumina-like and silica particles, respectively. Aggregation is observed in all mixed samples. Depending on the suspension composition, aggregates of different average size are formed. In agreement with the results of the sedimentation tests, smaller aggregates are formed for compositions corresponding to mass ratios in which one of the particle types is present in a clear majority (R = 0.16 and 0.82, maximum size less than 5 μm). Intermediate compositions lead to the formation of aggregates with a much larger average size (R = 0.31, 0.48, and 0.65, maximum size greater than 10 μm). Figure 6c reports simulation snapshots corresponding to the same compositions. Experimental and simulated aggregates show a striking similarity in terms of intermixing. At this point, it is worth noting that the initial ultrasonic treatment is necessary in order to disperse the particles. We mimic this situation in the simulations by initially placing the particles randomly. Then, we notice that heteroaggregation ensures a good intermixing of both kinds of particles inside aggregates. This is pointed out in both experiments and simulations. An interesting feature can be observed in aggregates for R = 0.16 and 0.82. In these cases, the particles that are in the minority form the inner part of the aggregates, being surrounded by particles of the other type (Figure 7). In suspensions that consist of oppositely charged latex particles, Leunissen et al. have observed a local crystallization of particles.16,43,44 Here, we have not observed such a crystallization within the aggregates. This can be attributed to the low value of the Debye screening (42) Gilchrist, J. F.; Chan, A. T.; Weeks, E. R.; Lewis, J. A. Langmuir 2005, 721, 11040–11047. (43) Sanz, E.; Leunissen, M. E.; Fortini, A.; van Blaaderen, A.; Dijkstra, M. J. Phys. Chem. B 2008, 112, 10861–10872. (44) Sanz, E.; Valeriani, C.; Vissers, T.; Fortini, A.; Leunissen, M. E.; van Blaaderen, A.; Frenkel, D.; Dijkstra, M. J. Phys.: Condens. Matter 2008, 20, 494247.

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length in our system (l D = 1/κ = 0.033
ai). This length is directly related to the range of electrostatic interactions. In ref 43, the authors explain that they observe crystallization for l D = 1
a (with a being the radius of the particles) but not for shorterranged interactions (e.g., l D = 0.33
a, which is still 10 times larger than in our case). An analysis of the aggregates obtained in the simulations shows that the number of aggregates in the simulation box decreases as a function of time (Figure 8a). In the first seconds of the simulations, for intermediate compositions of R = (0.31 - 0.65), many aggregates are created (∼600) but a smaller number of them are formed for R = 0.16 (∼480) and R = 0.82 (∼400). In each system, the number of aggregates then decreases to values not greater than 200. The average size of aggregates (Figure 8b) differs depending on the composition. The smallest aggregates are observed for R = 0.82, where each aggregate possesses approximately 15 particles on average after a simulated time span of 10 s. It must be noticed that, in agreement with the sedimentation tests of Figure 5, that aggregates corresponding to R = 0.82 are predicted to be smaller than those obtained with R = 0.16 (Figure 8b). However, the largest aggregates (average number of particles ∼23) are formed for R = 0.31 and 0.48. The percentage of isolated colloidal particles (Figure 8c) for systems with a majority of one kind of particle remains at an appreciable value (15 and 8% for R = 0.82 and 0.16, respecively) even after a simulated time span of 10 s. For the systems with more balanced composition, we observe almost no free particles. These results are due to the fact that particles in the minority are readily covered by majority particles and form small aggregates that become strongly repulsive toward the remaining isolated majority particles and toward other aggregates.12 For this reason, we expect that if we could continue the simulations over much longer times then the coalescence of aggregates would stop in the case of R = 0.82 and 0.16 but would continue for cases of intermediate composition up to the formation of large aggregates. The indication of the formation of large aggregates only for the intermediate compositions is indeed clear in the experimental CLSM images in Figure 6. For each composition, the average number of neighbors as a function of time for each kind of particle is calculated from simulation data (Figure 9). We notice a fast increase of the number of neighbors in each system until reaching nearly saturation. An average number of neighbors is also calculated from plane CLSM images. The same kind of 2D calculation is performed from simulation data by dividing the simulation box into slices of thickness 650 nm, which corresponds to the microscope optical slice, and averaging over all slices. Both results are shown in Figure 10. Good agreement is obtained between experimental and simulation results. This quantitative characterization shows that particles in the minority have many more neighbors of the other kind than neighbors of the same kind. This is in agreement with a heteroaggregation process characterized by an attraction between different kinds of particles and a repulsion between identical particles. The greatest number of neighbors is obtained for minority particles at extreme compositions (see R = 0.82 in Figures 9a and 10 and R = 0.16 in Figures 9b and 10). Concerning calculations of neighbors of the same particle type, silica particles have in general a smaller number of neighbors of the same type (Figures 9d and 10) than alumina-like particles (Figures 9c and 10) because alumina-like particles are less repulsive than silica ones. We notice that this difference is exaggerated in the simulations by considering the Hamaker constant of pure alumina, which slightly overestimates the attraction between alumina-like particles (section 3.2). This allows us to conclude DOI: 10.1021/la101027d

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Figure 6. (a, b) Confocal laser scanning microscopy images of alumina-like/silica suspensions (3 vol %) and (c) simulation snapshots (at 10 s) as a function of the mass ratio R.

Figure 7. Internal structure of aggregates observed in suspensions with the majority of one type of particle: simulation snapshots for (a) R = 0.16 and (c) R = 0.82 and CLSM images for (b) R = 0.16 and (d) R = 0.82.

Figure 8. Analysis of aggregation kinetics from simulation data: (a) number of aggregates, (b) mean number of particles per aggregate, and (c) percentage of free particles as a function of time.

Figure 9. Average number of neighbors (analysis from simulation data) for (a) alumina-like among silica, (b) silica among alumina-like, (c) alumina-like among alumina-like, and (d) silica among silica particles as a function of time. 12546 DOI: 10.1021/la101027d

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Figure 10. Calculation of the average number of neighbors in 2D slices from (a) CLSM images and (b) simulation data.

that, as a result of the interactions, alumina-like particles undergo an easier aggregation process.

5. Conclusions Dilute suspensions of spherical, almost monodisperse silica and alumina-like fluorescent particles have been prepared and characterized. It has been shown that, for a wide range of compositions, these suspensions undergo steady aggregation and flocculation because of the opposite charges present on the surface of the two types of particles. The structure of the aggregates has then been analyzed by confocal microscopy, which has allowed a direct visualization of the size and internal structure of the aggregates, with a clear distinction between silica and alumina-like particles. In parallel, a model of the system, based on the DLVO interactions between colloids, has been developed and studied by Brownian dynamics in order to analyze the mechanisms by (45) Humphrey, W.; Dalke, A.; Schulten, K. J. Mol. Graphics 1996, 14, 33–38.

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which aggregation occurs. The results of the model and the features observed experimentally show similar trends in terms of size, number, and internal structure of the aggregates. These features include a larger size of the aggregates formed in the case of intermediate compositions and an enrichment of the aggregate surface by the majority component, with the minority component being mostly confined to the inner part. Acknowledgment. We acknowledge financial support from the R
egion Limousin and from the Programme VINCI 2008 de l’Universit
e Franco-Italienne on the subject “mise en forme de c
eramiques nanostructur
ees par voie colloı¨ dale”. Simulation snapshots in Figures 6 and 7 have been obtained by VMD, a molecular graphics program originally designed for the interactive visualization and analysis 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.45

DOI: 10.1021/la101027d

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