Smart Control of Monodisperse Stöber Silica Particles: Effect of

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Langmuir 2005, 21, 1516-1523

Smart Control of Monodisperse Sto1 ber Silica Particles: Effect of Reactant Addition Rate on Growth Process K. Nozawa,†,‡,§ H. Gailhanou,†,‡ L. Raison,† P. Panizza,‡ H. Ushiki,§ E. Sellier,| J. P. Delville,‡,# and M. H. Delville*,† Institut de Chimie de la Matie` re Condense´ e de Bordeaux, UPR 9048-CNRS, Universite´ Bordeaux I, 87 Avenue du Dr. A. Schweitzer, 33608 Pessac Cedex, France, Centre de Physique Mole´ culaire Optique et Hertzienne, UMR CNRS 5798, Universite´ Bordeaux I, 351 Cours de la Libe´ ration, 33405 Talence Cedex, France, Laboratory of Molecular Dynamics and Complex Chemical Physics, Department of Environmental and Natural Resource Science, 3-5-8, Saiwai-cho, Tokyo 183-8509, Japan, and Centre de Ressources en Microscopie Electronique et Microanalyse, Universite´ Bordeaux I, 351 Cours de la Libe´ ration, 33405 Talence Cedex, France Received June 10, 2004. In Final Form: October 29, 2004 Control over the synthesis of monodisperse silica particles up to mesoscopic scale is generally made difficult due to intrinsic limitation to submicrometric dimensions and secondary nucleation in seeded experiments. To investigate this issue and overcome these difficulties, we have implemented single step processing by quantifying the effects of the progressive addition of a diluted tetraethyl orthosilicate solution in ethanol on the size and monodispersity of silica particles. Contrary to particles grown in seeded polymerization, monodisperse particles with size up to 2 µm were synthesized. Moreover, the particles exhibit a final diameter (df), which varies with V-1/3 over more than 2 orders of magnitude in rate of addition (V). On the basis of a kinetic study in the presence of addition showing that particle growth is limited by the diffusion of monomer species, we developed a diffusion-limited growth model to theoretically explain the observed df(V) behavior and quantitatively retrieve the measured amplitude and exponent. Using a single parameter procedure, we can therefore predict and generate in the room temperature range, monodisperse particles of a targeted size by simply adjusting the rate of addition.

Introduction Monodisperse colloidal silica particles with uniform size, shape, and composition have wide application not only in the field of physical chemistry dealing with dynamic behavior and stability of particle systems1 but also in industries including pigments, pharmacy,2 photographic emulsions,3 ceramics,4 chromatography,5 catalysts,6 and chemical mechanical polishing.7 Silica particles are also used as stabilizers,8 coatings,9 glazes10 and binders.11 The need for well-defined silica nanoparticles is thus constantly * To whom correspondence may be addressed. Phone: (33) 5 40 00 84 60. Fax: (33) 5 40 00 27 61. E-mail: delville@ icmcb-bordeaux.cnrs.fr. † Institut de Chimie de la Matie ` re Condense´e de Bordeaux, UPR 9048-CNRS, Universite´ Bordeaux I. ‡ Centre de Physique Mole ´ culaire Optique et Hertzienne, UMR CNRS 5798, Universite´ Bordeaux I. § Laboratory of Molecular Dynamics and Complex Chemical Physics, Department of Environmental and Natural Resource Science. | Centre de Ressources en Microscopie Electronique et Microanalyse, Universite´ Bordeaux I. # E-mail: [email protected]. (1) Wiese, G. R.; Healy, T. W. Trans. Faraday Soc. 1970, 66, 490. (2) Paci, A.; Mercier, L.; Bourget, P. J. Pharm. Biomed. Anal. 2003, 30, 1603. (3) Overbeek, J. Th. G. Adv. Colloid Interface Sci. 1982, 15, 251. (4) Sacks, M. D.; Tseng, T. Y. J. Am. Ceram. Soc. 1984, 67, 526. (5) Unger, K. K.; Kumar, D.; Gru¨n, M.; Bu¨chel, G.; Lu¨dtke, S.; Adam, Th.; Schumacher, K.; Renker, S. J. Chromatogr., A 2000, 89, 47. (6) Badly, R. D.; Ford, W. T. J. Org. Chem. 1989, 54, 5347. (7) Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979. (8) Gosa, K. L.; Uricanu, V. Colloids Surf., A 2002, 197, 257. (9) Leder, G.; Ladwig, T.; Valter, V.; Frahn, S.; Meyer, J. Prog. Org. Coatings 2002, 45, 139. (10) Adl, S.; Rahman, I. A. Ceram. Int. 2001, 27, 681. (11) Payne, C. In The Colloid Chemistry of Silica; Bergna, H., Ed.; American Chemical Society: Washington, DC, 1994.

increasing, as high-tech industries (e.g., biotechnology/ pharmaceuticals12 or photonics13) provide a tremendous demand for such materials. The preparation of monodisperse silica particles generally proceeds with the hydrolysis and condensation of alkoxysilanes (often tetraethyl orthosilicate (TEOS) [Si(OR)4 with R ) C2H5]) in a mixture of alcohol, water, and ammonia used as a catalyst. Since its discovery by Kolbe,14 many studies have been performed based on this reaction system.15-17 The so-called Sto¨ber synthesis, (the ammonia-catalyzed reaction of TEOS with water in low molecular weight alcohols), is known to produce monodisperse spherical silica nanoparticles. As the maximum particle size achievable with high monodispersity from TEOS seems to be submicrometric in the Sto¨ber synthesis, 18 a great deal of efforts has therefore been devoted to extend this limit up to 2 µm by using different silicon alkoxides and solvent, with a high cost for many of them such as tetrapentyl orthosilicate. Some authors succeeded in the preparation of monodisperse silica particles with sizes above 1 µm in acidic emulsion media.19 (12) Caruso, F.; Caruso, R. A.; Molwald, H. Science 1998, 282, 1111. (13) (a) Xia, Y.; Gates, B.; Ying, Y.; Lu, Y. Adv. Mater. 2000, 12, 693. (b) Sun, H. B.; Song, J.; Matsuo, Y. X. S.; Misawa, H.; Liu G. D. S. J. Opt. Soc. Am. B 2000, 17, 476. (14) Kolbe, G. The Complex Chemical Behavior of Silica. Dissertation, Jena, Germany, 1956. (15) Sto¨ber, W.; Fink, A.; Bohn, E. J. Colloid Interface Sci. 1968, 26, 62. (16) Van Helden, A. K.; Jansen, J. W.; Vrij, A. J. Colloid Interface Sci. 1981, 81, 354. (17) Van Blaaderen, A.; Geest, V. J.; Vrij, A. J. J. Colloid Interface Sci. 1992, 154, 481. (18) Bogush, G. H.; Tracy, M. A.; Zukoski, C. F. J. Non-Cryst. Solids 1988, 104, 95. (19) Esquena, J.; Pons, R.; Azemar, N.; Caelles, J.; Solans, C. Colloids Surf., A 1997, 123-124, 575.

10.1021/la048569r CCC: $30.25 © 2005 American Chemical Society Published on Web 12/18/2004

Synthesis of Monodisperse Silica Particles

In general, the hydrolysis reaction gives the singly hydrolyzed TEOS monomer [(OR)3Si(OH)]

Si(OR)4 + H2O f (OR)3Si(OH) + ROH Subsequently, this intermediate reaction product condenses to eventually form silica according to

(OR)3Si(OH) + H2O f SiO2V + 3ROH This reaction scheme is, of course, a simplification of the very complex condensation processes that lead to the formation of the silica particles. Some of the earliest research on Sto¨ber particles was primarily concerned with empirically predicting the final particle size for a range of the initial reactant concentrations (0.1-0.5 M TEOS, 0.5-17.0 M H2O, and 0.1-3.0 M NH3) that lead to monodisperse colloids, the largest achievable size being 800 nm.15,18 Two models, monomer addition20,21 and controlled aggregation,22 have been proposed to elucidate the chemical and/or physical growth mechanisms of silica. To explain the highly monodisperse nature of these particles, the first authors divided the formation of silica into two events: nucleation and growth. Bogush18,22 and co-workers considered the nucleation and growth of silica particles as an aggregation process of small subparticles several nanometers in size. In contrast, Matsoukas and Gulari20,21 proposed that particle nucleation was the result of the reaction between two hydrolyzed monomers, such that the particles grew only by a molecular addition mechanism.23 More recently, many other investigations have been devoted to the understanding of the particle growth mechanism24-26 including microgravity experiments.27 Important parameters in preparing silica particles seem to be the water and ammonia concentrations. However, depending on the authors, these parameters have an opposite influence on the SiO2 particle size explaining why several groups attempted to rationalize this highly complicated system using experimental design and multivariate analyses.28 As large monodisperse silica particles (typically above 1 µm) are difficult to synthesize according to the Sto¨ber procedure with TEOS,15 some authors preferred to use (20) Matsoukas, T.; Gulari, E. J. Colloid Interface Sci. 1988, 124, 252. (21) (a) Matsoukas, T.; Gulari, E. J. Colloid Interface Sci. 1989, 132, 13. (b) Matsoukas, T.; Gulari, E. J. Colloid Interface Sci. 1991, 145, 557. (22) (a) Bogush, G. H.; Zukoski, C. F. J. Colloid Interface Sci. 1991, 142, 1. (b) Bogush, G. H.; Zukoski, C. F. J. Colloid Interface Sci. 1991, 142, 19. (c) Okudera, H.; Hozumi, A. Thin Solid Films 2003, 434, 62. (23) (a) Kim, K. S.; Kim, J. K.; Kim, W. S. J. Mater. Res. 2001, 16, 545. (b) Chen, S. L.; Dong, P.; Yang, G. H.; Yang, J. J. Ind. Eng. Chem. Res. 1996, 35, 4487. (24) (a) Van Blaaderen, A.; Kentgens, A. P. M. J. Non-Cryst. Solids 1992, 149, 161. (b) Burneau, A.; Humbert, B. Colloids Surf., A 1993, 75, 111. (c) Chen, S. L.; Dong, P.; Yang, G. H.; Yang, J. J. J. Colloid Interface Sci. 1996, 180, 237. (25) (a) Walcarius, A.; Despas, C.; Bessie`re, J. Microporous and Mesoporous Mater. 1998, 23, 309. (b) Brinker, C. J.; Scherer, G. W Sol-Gel Science; Academic Press: San Diego, 1990. (26) (a) Green, D. L.; Lin, J. S.; Lam, Y. F.; Hu, M. Z. C.; Schaefer, D. W.; Harris, M. T. J. Colloid Interface Sci. 2003, 266, 346. (b) Vogelsberger, W.; Seidel, A.; Breyer, T. Langmuir 2002, 18, 3027. (c) Pontoni, D.; Narayanan, T.; Rennie, A. R. Langmuir 2002, 18, 56. (d) Boukari, H.; Lin, J. S.; Harris, M. T. J. Colloid Interface Sci. 1997, 194, 311. (e) Boukari, H.; Long, G. G.; Harris, M. T. J. Colloid Interface Sci. 2000, 229, 129. (f) Boukari, H.; Lin, J. S.; Harris, M. T. Chem. Mater. 1997, 9, 2376. (27) Smith, D. D.; Sibille, L.; Cronise, R. J.; Hunt, A. J.; Oldenburg, S. J.; Wolfe, D.; Halas, N. J. Langmuir 2000, 16, 10055. (28) (a) Lindberg, R.; Sundholm, G.; Pettersen, B.; Sjo¨blom, J.; Friberg, S. E. Colloı¨ds Surf., A 1997, 123-124, 549. (b) Giesche, H. J. Eur. Ceram. Soc. 1994, 14, 189. (c) Dingsoyr, E.; Christy, A. A. Prog. Colloid Polym. Sci. 2000, 116, 67.

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the so-called seed polymerization reaction, which is based on the hydrolysis and condensation of this alkoxide onto preformed silica seeds. They claimed that growth occurs without the formation of a new generation of silica particles.29 However, as illustrated in the following, our experiments (and others30) are clearly at variance with this conclusion beyond a certain particle size. To prevent secondary nucleation effects, the method was extended by coupling seed polymerization to controlled growth reaction in a continuous production process.31,32 Reports on such preparations of silica particles33 qualitatively established the increasing impact of the rate of addition of the TEOS reactant in the reactor vessel on final size and polydispersity of the particles. Consequently, as opposed to the classical Sto¨ber synthesis (also qualified as a batch process34), the use of a so-called semibatch process,33,35 in which one reactant (TEOS/EtOH) is added into a reactor containing the other ones (H2O/NH4OH/ EtOH) at a constant rate, was claimed to give greater control over the resulting particle size, shape, and size distribution. This was illustrated for the synthesis of silica nanoparticles in multivariate analyses at room temperature36 by comparing two runs performed at a rate of addition of the TEOS reactant of 18 mL/min (i.e., almost in batch conditions) and at 0.6 mL/min. Experiments showed that the final particle size is a decreasing function of the addition rate. This was qualitatively explained by a reduction of the nucleation period and better control of the reaction speed because it proceeds in a starved system as reactants are added. However, as large addition rate values were used, the final particle size typically ranged from 60 to 200 nm. It was concluded that the addition rate was the preponderant factor (compared to the temperature, the pH, or the TEOS/H2O ratio) on final size and polydispersity of the particles. In fact, even if a constant addition of reactant proved to be beneficial, up-to-now, no systematic study and no quantitative interpretation of its influence have, so far, been reported. This is the purpose of the present work. We explore the role of the addition rate of one of the reactants in the reaction vessel on the final size and dispersity of the particles. To get significant results, experiments were performed over nearly 3 orders of magnitude in addition rate. Monodisperse particles with sizes up to 2 µm were synthesized. The results of this single step continuous approach are compared with those obtained from the seeded polymerization technique, which also allows for growth of large particles. As we were interested in quantitatively predicting observations, we (29) (a) Chen, S. L.; Dong, P.; Yang, G. H.; Yang, J. J. J. Colloid Interface Sci. 1997, 189, 268. (b) Chen, S. L. Colloids Surf., A 1998, 142, 59. (c) Okubo, T.; Miyamoto, T.; Umemura, K.; Kobayashi, K. Colloid Polym. Sci. 2001, 279, 1236. (30) Chen, S. L.; Dong, P.; Yang, G. H.; Yang, J. J. J. Colloid Interface Sci. 1996, 180, 237. (31) Giesche, H. J. Eur. Ceram. Soc. 1994, 14, 205. (32) (a) Zhang, J. H.; Zhan, P.; Wang, Z. L.; Zhang, W. Y.; Ming, N. B. J. Mater. Res. 2003, 18, 649. (b) Reculusa, S.; Poncet-Legrand, C.; Ravaine, S.; Mingotaud, C.; Duguet, E.; Bourgeat-Lami, E. Chem. Mater. 2002, 14, 2354. (33) (a) Kim, K. D.; Bae, H. J.; Kim, H. T. Colloids Surf., A 2003, 224, 119. (b) Kim, K. D.; Kim, H. T. Colloids Surf., A 2002, 207, 263. (c) Kim, K. D.; Kim, H. T. J. Am. Ceram. Soc. 2002, 85, 1107. (d) Kim, K. D.; Kim, H. T. J. Sol-Gel Sci. Technol. 2002, 25, 183. (e) Kim, K. D.; Kim, H. T. Mater. Lett. 2003, 57, 3211. (34) Fogler, H. S. Elements of Chemical Reaction Engineering: Rate Laws and Stoichiometry; Prentice-Hall: Englewood Cliffs, NJ, 1986; p 59. (35) (a) Park, S. K.; Kim, K. D.; Kim, H. K. J. Ind. Eng. Chem. 2000, 6, 365. (b) Reculusa, S.; Mass, P.; Ravaine, S. J. Colloid Interface Sci. 2004, 279, 471. (36) Park, S. K.; Kim, K. D.; Kim, H. K. Colloids Surf., A 2002, 197, 7.

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Table 1. Size and Dispersity Evolutions of Silica Particles in Seeded Growth Experiments initial solution

final solution

solvent EtOH (mL)

catalyst 28% NH4OH (mL)

25 mL of S 25 mL of Sa

S Sa Sb

50 175 175

3 12 12

1.5 mL 6.0 mL 6.0 mL

25 mL of Sa 50 mL of Sc

Sc Sd

175 350

12 24

6 × 1 mL/45 min 12 × 1 mL/45 min

Table 2. Experimental Conditions Used for Obtaining Silica Particles under Continuous Addition TEOS (mL) EtOH (mL) NH4OH (mL) rates of addition of TEOS (mL/min) stirring rates (rpm) reaction time after addition (h) reaction temperature (°C)

5 (solution I) 30 (solution I)/50 (solution II) 9.5 (solution II) 0.005-1.0 300-700 12 10-40

performed kinetics experiments to find the mechanisms that govern the growth of silica particles under TEOS addition. This allows us to build a model that predicts the variation of the final particle size versus the addition rate. In view of the quantitative agreement observed between experiments and predictions, our study allows us to deduce the optimal conditions for preparing tailored particles in a single step process by simply controlling one parameter, i.e., the addition rate of one reactant (TEOS/EtOH). Experimental Section Starting Solutions. TEOS (Si(OC2H5)4, 99%, Aldrich Chemical Co.), ethanol (EtOH, J.T. Baker, 99.9% v/v), and ammonia (NH4OH, 28%, Aldrich Chemical Co.) were used as starting materials without any further purification. The solutions were prepared at room temperature under inert atmosphere. An oil bath was used to control the temperature of the reactions with an accuracy of (0.05 °C (LAUDA, E200, ecoline SRE2312). Preparation and Analysis of SiO2 Particles. In the few seeded growth experiments, the preparation of the first seed suspension was performed according to Sto¨ber synthesis.15 After the reaction came to completion (12 h after the addition of TEOS), the resulting solution (S) was used as the first seed solution for a further growth reaction leading to a second generation of seeds Sa. We reiterate the process as long as the new solution was found to be monodisperse by transmission electron microscopy (TEM) measurements, according to details given in Table 1. The desired amounts of TEOS were added, in a single step or by small fractions, over various periods of time, into the seed suspension to give solutions Sb, Sc, and Sd, respectively. The reaction conditions were kept for another 6 h to make sure that

Figure 1. Schematic drawing of the experimental setup used for the controlled particle growth procedure under continuous addition.

reactant TEOS

av diameter (nm) 110 ( 20 220 ( 20 380 ( 20 100 ( 20 470 ( 20 870 ( 10 420 ( 20 200 ( 20

particles reached their final size. The SiO2 dispersions were then transferred out of the reactor, and the powders were washed with ethanol and ultrapure water by repeated centrifugation (at 5000 rpm for 15 min) and further dried at 70 °C for 12 h. In the other set of experiments, the monodispersed spherical silica particles were prepared by the hydrolysis of TEOS according to the following procedure. Two solutions, I (TEOS in ethanol) and II (ammonia in ethanol), were prepared separately. To effectively investigate the rate of addition effect of TEOS in ethanol, the total volumes of solutions I and II as well as the reactant concentrations were kept the same in all the experiment series (Table 2). Solution I was added, via a micro feed pump with chosen constant flow rates, under an argon blanket into a round-bottom flask that contains solution II, under various stirring at controlled temperatures. The whole mixture was allowed to react for 12 h. The schematic diagram of the experiment is shown in Figure 1. Analysis of SiO2 Particles. TEM was performed at room temperature on a JEOL JEM-2000 FX transmission electron microscope, using an accelerating voltage of 200 kV. Scanning electron microscopy (SEM) was performed on a JEOL JSM-840A, scanning electron microscope (diameters of about a hundred particles were used to evaluate the average size and the standard deviation for each sample). Particle sizes were also checked optically using a particle size analyzer, Mastersizer 2000 (Malvern Instruments). For diluted suspensions, measurements were confirmed from the temporal behavior of the angular variation of the correlation function of the scattered field obtained with a homemade dynamic light scattering apparatus using a continuous wave Ar+ laser (wavelength in a vacuum λ0 ) 514 nm) and an ALV5000 correlator.

Results and Discussion Particle Growth via Seeded Experiments. In our objective to produce monodisperse silica particles of various controlled sizes, we first performed experiments based on the seeded growth method from Sto¨ber synthesis, as shown in Table 1. The ratios of added reactants were calculated in order to double the size of the particles from one generation to another according to Van Blaaderen et al.24a,37 Therefore, nanoparticles of 200 nm (Sa) were obtained from silica suspensions of 100 nm seeds (S) (Figure 2a,b). In the same way, nanoparticles of 400 nm (Sb) were grown from the 200 nm particle suspension (Sa). However, as shown in Figure 2c, the nucleation of a second population is observed when the TEOS is added in one step. To avoid this second population, it was necessary to add the TEOS by small fractions over a long period of time (Table 1). As an illustration, results are shown with an addition of 1 mL every 45 min. In this case; highly monodisperse particles (Sc) are formed and no secondary population is observed (see Figure 2d). The same strategy was used to once more double the silica size starting from Sc, the same rate of 1 mL every 45 min was applied (12 times) and led to a polydisperse distribution with three major populations for Sd (Figure 3). (37) Van Blaaderen, A.; Vrij, A. J. J. Colloı¨d Interface Sci. 1993, 156, 1.

Synthesis of Monodisperse Silica Particles

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Figure 3. Transmission electron micrograph of silica particles showing the limits of the seeded method. The seed solution is the one presented in Figure 2d. The fractional addition of TEOS used in this case leads to three major populations (P1, P2, P3).

Figure 2. Transmission electron micrographs of silica particles illustrating the particle size obtained via the seeded technique: (a) starting solution (S); (b) doubling of the particle size in a single step (Sa); (c) starting from Sa, attempt of doubling the particle size for a single addition of TEOS, formation of a second population of particles; (d) starting from Sa, doubling of the particle size by fractional addition of TEOS (see details in Table 1).

These results strongly suggest that a systematic approach of the role of the addition rate of the TEOS reactant is necessary to bring new insight on the conditions necessary to confidently control the particle size over a large variation. Such an approach will help define the appropriate requirements to produce a direct synthesis of large monodisperse particles without using any seeds and time-consuming multistep reaction scheme. Addition Rate Effect on Final Particle Size. Experiments were performed at controlled temperature with a systematic molar ratio for TEOS/NH3/H2O of 1/6.3/ 15.2, which is an overall ratio since TEOS is added dropwise via a micro feed pump and therefore in very small quantities as compared to water and ammonia amounts. To determine the relevant mechanisms leading to the final particle size, we first checked whether the stirring speed could play a role for a given rate of addition of TEOS. In a second step, we analyzed by kinetic measurements, the particle growth rate under controlled continuous addition. The kinetic evolution of the particle size is susceptible to provide important information about the involved growth mechanism. Finally, we investigated the influence of the variation of the rate of addition of the TEOS reagent within the reactor on the final size of the particles. Effect of Stirring Speed on Final Particle Size. We performed a set of experiments for a TEOS addition rate of 0.1 mL/min at T ) 20 °C with stirring speeds varying between 300 and 700 rpm. Using dynamic light

scattering (see below), we found a mean particle diameter 950 ( 20 nm for the whole set of attempts even for the extreme values (300 and 700 rpm). Despite a ratio larger than 2 between these extremes, the reproducibility of the result is not surprising since the associated hydrodynamic Peclet number, Pe, which compares the particle advection versus the solute diffusion in a reactor,38 is much smaller than unity in both cases. Indeed, by definition, one has Pe ) Ωr2/Dm, where Ω, r, and Dm are respectively the angular velocity associated to the stirring, the particle radius, and the molecular diffusion coefficient of the solute within the mixture. Using the ethanol viscosity η ) 1.2 × 10-3 Pa‚s at T ) 20 °C as it constitutes the major part of the solvent phase and a typical solute size ∼2 Å, we find Dm ) 10-9 m2/s. On the other hand, the angular velocity Ω varies over more than a factor of 2 from 5 Hz (at 300 rpm) to 12 Hz (at 700 rpm). Then, as experiments lead to a final particle size rf ≈ 500 nm, we finally find 10-3 e Pe e 3 × 10-3. Consequently, for classical stirring velocities, the particle growth is totally dominated by diffusion and hydrodynamic effects can thus be discarded. This point is clearly illustrated by the particle growth law presented below because flow effects are known to accelerate the kinetics compared to diffusion or reaction-limited growth.38 Particle Growth: Theoretical Background. As in any growth process performed when all the reactants are added simultaneously, the particle size strongly depends on the coarsening mechanism39 because the reactant must be transported to the interface, generally by diffusion, and then incorporated into the particle by interface interaction. If the monomer incorporation (the diffusion) is the fastest process, then the growth is limited by diffusion (the interface kinetic). In theses conditions, the growth rate dr/dt of a spherical particle of radius r can be described by a general expression, which includes both bulk diffusion and interface reactions40 (38) Baumberger, T.; Perrot, F.; Beysens, D. Phys. Rev. A 1992, 46, 7636. (39) Marqusee, J. A.; Ross, J. J. Chem. Phys. 1983, 79, 373. (40) (a) Leubner, I. H.; Jagannathan, R.; Wey, J. S. Photogr. Sci. Eng. 1980, 24, 268. (b) Leubner, I. H. J. Imaging Sci. 1985, 29, 219. (c) Leubner, I. H. J. Phys. Chem. 1987, 91, 6069.

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(C(t) - Ceq(r)) dr ) Ki dt 1 + r

Nozawa et al.

(1)

where C(t) is the concentration at a given time, t, and Ceq(r) is the equilibrium concentration around the particle. Ki is the rate constant for the surface integration of monomer, and -1 is a screening length that compares bulk diffusion to surface integration effect;  is defined by

 ) Ki/(DmVM)

(2)

where VM is the molar volume of the precipitate. On the other hand, Ceq(r) is given by the Gibbs-Thomson relation

Ceq(r) ) CS exp(R/r) ≈ CS(1 + R/r)

(3)

CS represents the bulk solubility and R is a capillary length

R)2

γVM RT

(4)

γ is the liquid/particle interfacial surface energy and R is the universal gas constant. Consequently, by defining the supersaturation S as S(t) ) (C(t) - CS)/CS, the general expression of the particle growth rate becomes

dr KiCSR (1 - rC/r) ) dt rC 1 + r

(5)

where rC ) R/S represents the critical radius above which a particle spontaneously grows and below which it dissolves. The transition between the interface kinetic limited and the diffusion-limited growth is controlled by the product r, i.e., from r , 1 to r . 1. This means that growth is usually limited by the monomer incorporation at the particle surface at an early stage and eventually becomes diffusion-limited at large particle radius. Equation 5 shows that the particle growth is strongly dependent on the temporal behavior of the supersaturation S. The kinetics of precipitation can be divided in four main stages.41 If initially the system is at equilibrium, then spontaneous nucleation occurs as soon as the supersaturation S reaches its critical value SC. Particles are formed, and growth will compete with nucleation until S reaches a maximum. Then, S starts to decrease and drops below SC. After this nucleation regime, a transient period appears where S continues to decrease to reach a quasi-steady state corresponding to the so-called free-growth regime. Finally, due to the mass conservation, this free-growth regime cannot survive indefinitely, and growth switches to the well-known Ostwald ripening where S starts to decrease again toward its asymptotic value S ) 0. To retrieve the particle growth law in the free-growth regime, we assume a constant supersaturation S. In the interface kinetic limited case (r , 1), eq 5 reduces to

(

)

rC dr KiCSR ) 1dt rC r

(6)

Integration of eq 6 for r/rC . 1 shows that the particle size increases linearly with time during the free-growth regime. This r ∼ t regime is then followed by the Ostwald ripening regime where mass conservation leads to a slowing down characterized by r ∼ t1/2.39 (41) Lamer, V. K.; Dinegar, R. H. J. Am. Chem. Soc. 1950, 72, 4847.

On the other hand, growth limited by diffusion presents different kinetic behaviors. In this case (r . 1), eq 5 becomes

dr DmVMCSR (1 - rC/r) ) dt r/rC r 2

(7)

C

For r/rC . 1, eq 7 shows that the diffusion-limited freegrowth is characterized by a first behavior r ∼ t followed by an r ∼ t1/2 regime.38,42 These regimes are also followed by the Ostwald ripening which is described by r ∼ t1/3.39,43 Finally, the particle number remains constant in the free growth regime,44 whatever the mechanism that governs the growth, either interface kinetic or diffusion limited. While these growth mechanisms were successfully investigated in experiments involving phase transition in fluid media,39 their extension to inorganic colloid dispersions is much more recent. At first, an extensive study17 showed that silica beads grow by the incorporation of hydrolyzed monomers instead of aggregation of smaller particles. Observation of this mechanism supports the fact that classical ripening theories should also apply to growth of inorganic colloids. It has effectively been demonstrated that late stage growth of Sto¨ber particles was limited by diffusion. Using small-angle X-ray scattering, Pontoni et al.26c have investigated the early stage growth of silica particles and found an r ∼ t regime followed by the behavior r ∼ t1/2. These authors also showed that the particle number as well as their mass density remains nearly constant over the investigated reaction time, in agreement with the predictions deduced from the classical ripening theories.44 However, while saturation in growth is observed at the late stage, the transition toward the Ostwald ripening regime, characterized by a r ∼ t1/3 behavior, is not clearly evidenced. This regime has nevertheless been observed by Oskam et al.,45 during the coarsening of other types of metal oxide nanoparticles (i.e., zinc and titanium oxide particles). Particle Growth in the Presence of the Progressive Addition of One Reactant. Since our main motivation is to analyze the influence of one of the reactants addition on Sto¨ber type silica particle growth, we extende Pontoni’s investigation to a study of the coarsening while specifically controlling the rate of addition of the TEOS reactant in the solution. The kinetic evolution of the particle size in a typical experiment carried out at 20 °C and for a rate of addition of TEOS of V ) 0.125 mL/min is presented in Figure 4. The particle growth was characterized according to the following procedure. During the TEOS addition, we extracted 1 or 2 drops of solution at regular time intervals and quickly dilute it in 10 mL of alcohol in order to instantaneously quench the reaction. Then, for each sample, we deduced the mean particle size by dynamic light scattering. To increase accuracy, the correlation function was measured by varying the scattering angle θ every 5° between 0 and 90°. Assuming that growing particles behave as Rayleigh scatterers, the relaxation time τθ associated to the temporal behavior of the correlation function is given by (τθ)-1 ) 2Dpq2, where Dp is the mass diffusion of the particles and q ) 4πn/λ0 sin(θ/ 2) the modulus of the transfer wave vector (n is the index (42) Cumming, A.; Wiltzius, P.; Bates, F. S. Phys. Rev. Lett. 1990, 65, 863. (43) Perrot, F.; Guenoun, P.; Baumberger, T.; Beysens, D.; Garrabos, Y.; Le Neindre, B. Phys. Rev. Lett. 1994, 73, 688. (44) Tokuyama, M.; Enomoto, Y. Phys. Rev. Lett. 1992, 69, 312. (45) Oskam, G.; Hu, Z.; Lee Penn, R.; Pesika, N.; Searson, P. C. Phys. Rev. E 2002, 66, 011403.

Synthesis of Monodisperse Silica Particles

Langmuir, Vol. 21, No. 4, 2005 1521

Figure 4. Growth law of silica particles performed at 20 °C and for a rate of addition of TEOS of 0.125 mL/mn. The line is a guide for the eyes. Inset: overview of the early stage growth. A regime r ∼ t1/2 is clearly evidenced. The arrow indicates the end of the TEOS addition.

of refraction of the solvent, here mainly ethanol). Then, by fitting the linear behavior of (τθ)-1 versus q2, we obtain a reliable value of Dp and thus of r. The inset in Figure 4, clearly shows that the growth regime corresponds to an r ∼ t1/2 behavior when applying a progressive TEOS addition (the temporal exponent measured in Figure 4 is 0.53 ( 0.03). Bearing in mind that the supersaturation reaches a constant value during the TEOS addition, the observed particle growth necessarily corresponds to the free-growth regime; the particle growth had already switched from interface (r , 1) to diffusion limited (r . 1) at the beginning of the investigated temporal window. Indeed, for reaction-driven growth, we would instead observe an r ∼ t free-growth regime, as a law r ∼ t1/2 can only appear at the end of the growth during Ostwald ripening,39 i.e., well after the end of the addition of TEOS. In these experiments, the diffusive origin of the growth is also confirmed by the effective persistence of the r ∼ t1/2 regime after the end of the addition. Finally, as in Pontoni’s experiments,26c we do not clearly identify the Ostwald ripening regime r ∼ t1/3 between the free-growth regime and the saturation to the final particle size. Effect of the Rate of Addition on the Final Size of the Particles. Comforted by the results presented in Figure 4, we then undertook a systematic study of the impact of the rate of addition of TEOS on the final size of the particles. The SEM pictures presented in Figure 5 show the final size of silica particles obtained in strictly identical conditions at 25 °C except for the addition rates of TEOS that were 0.005, 0.05, and 0.5 mL/min. They illustrate the simplicity as well as the strength of the method. First, the particle size is an obviously decreasing function of the addition rate of TEOS. Then, the particle size can clearly be monitored over a large range by playing with the addition rate (typically a factor of 5 over 2 orders of magnitude in addition rate). This approach leads in one step and without renucleation to particle size larger than those obtained in the seeded process (Table 1). Finally, the particle distribution in the three different experiments appears to be highly monodisperse with a standard deviation varying from 5% to 2% with decreasing rate of addition. To analyze the influence of different independent parameters, we investigated the evolution of the final particle size versus

Figure 5. Scanning electron micrographs of silica particles obtained at 25 °C over 2 orders of magnitude in addition rates of TEOS: (a) 0.005 mL/min (1820 nm, standard deviation 2%); (b) 0.05 mL/min (1330 nm, standard deviation 3%), 0.5 mL/min (635 nm, standard deviation 5%).

addition rate of TEOS for three temperatures centered on ambient temperature (10, 25, and 40 °C). The corresponding evolutions are shown in Figure 6. To increase the accuracy of the measurements, particle diameters were characterized by three different techniques, SEM, dynamic light scattering, and a Malvern particle size analyzer. As illustrated in Figure 6, the results given by the three techniques are in very good agreement with each other. The general trend confirms that the final particle diameter, df, decreases with the rate of addition (V), whatever the temperature. From a quantitative point of view, a power law fit of the data sets shows that the general behavior df ∼ V-1/3 emerges. Power law fits give, (a) df ) 0.38 V-0.32 for T ) 10 °C, (b) df ) 0.39 V-0.32 for T ) 25 °C, and (c) df ) 0.29

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Nozawa et al.

is the significant increase in duration of the free-growth regime due to a constant supersaturation resulting from the equilibrium between reactant addition and particle growth. This is clearly illustrated in Figure 4 in which the r ∼ t1/2 regime is observed over a much larger time period than that measured by Pontoni et al. when all the reactants are added in a single step. Since the main effect of addition is to increase the duration of the free growth regime, the number density of particles should then be time independent, as predicted52 and observed26c in the absence of addition. Different models of jet precipitation47,53,54 based on particle growth limited by diffusion, also retrieve this expectation and show that the particle number N versus addition rate behaves as

N)β

Figure 6. Evolution of the particle diameter with the rate of addition of TEOS at (a) 10 °C, (b) 25 °C, and (c) 40 °C determined by (4) scanning electron microscopy, (O) dynamic light scattering, and (0) particle size analyzer.

V-0.31 for T ) 40 °C when df is expressed in micrometers and V in mL/min; error on df is less than 5%. Contrary to the strong dependence on addition rate, these results also show that temperature variations have almost no influence on the particle final size over the investigated range. This result is at variance with experiments performed without TEOS addition.46 To understand the very simple scaling measured as well as its robustness, we developed an analogy between the growth of Sto¨ber type spherical silica particles with a controlled addition rate of TEOS and the formation of photographic colloids, typically silver halide crystals, in controlled jet precipitation (see for instance Leubner’s review47). Indeed, as it is necessary to control the final crystal size with an error smaller than 5% in order to get reliable photographic emulsions, numerous methods have been implemented including semibatch crystallization,48,49 and it appeared that an interesting way to achieve this goal was the use of the jet precipitation technique.50,51 It consists of introducing one of the reactants at a carefully controlled rate over a defined period into a stirred solution. In these conditions, the kinetics of precipitation can still be divided in four stages.47 The main difference with those presented above for growth under a single step addition (46) Tan, C. G.; Bowen, B. D.; Epstein, N. J. Colloid Interface Sci. 1987, 118, 290. (47) Leubner, I. H. Curr. Opin. Colloid Interface Sci. 2000, 5, 151. (48) Tavare, N. S.; Garside, J. Chem. Eng. Sci. 1993, 48, 475. (49) Torbacke, M.; Rasmuson, A. C. Chem. Eng. Sci. 2001, 56, 2459. (50) Sta´vek, J.; Sı´pek, M.; Hirasawa, I.; Toyokura, K. Chem. Mater. 1992, 4, 545. (51) Zhong, Q.; Matijevic´, E. J. Mater. Chem. 1996, 6, 443.

VRT 8πDmγVM2CS

(8)

where β is a numeric factor depending on the chosen model. This prediction for free-growth limited by diffusion, particularly the behavior of N vs addition rate, V, was experimentally verified in double-jet precipitation (zinc oxide colloids,51 silver halides40,47,53). However, when addition stops, as in our experiments, we could imagine that the constant character of N should break down due to the change in growth conditions. Owing to Ostwald ripening, we would expect a continuous reduction of N by particle coalescence and evaporation, as predicted39 and observed in liquid-phase transitions43 or some metal oxide colloids.45 However, since the seminal Sto¨ber investigation,15 this scheme has never been observed when experiments involve growth of silica particles. A monodisperse assembly of silica particles is often found at the end of the coarsening, a point that makes those particles so attractive but still misses a quantitative explanation.55 This nonexpected late stage growth behavior is also kinetically illustrated in both Pontoni’s investigation26c and Figure 4, in the absence and the presence of TEOS addition, where the r ∼ t1/3 regime that characterizes Ostwald ripening is clearly absent. This result could be explained by the fact that the experimental conditions of the reaction (especially in terms of the pH of the solution) are not strong enough to allow silica dissolution.7 Consequently, both cross-related aspects, monodisperse particle assembly and lack of observable Ostwald ripening, strongly suggest that the constant number of particles during the freegrowth regime N is preserved until the end of the coarsening and thus corresponds to the final particle number. By use of mass conservation, this particle number N is then related to the final radius rf by

N

4 πr 3 ) nSiO2VM 3 f

(9)

where nSiO2 is the mole number of silica corresponding to the volume of added TEOS. By combining eq 8 and eq 9, we finally find the expected relation between the final particle radius and the addition rate

df ) 2rf ) 2

[

]

6DmγnSiO2VM3CS βRT

1/3

V-1/3

(10)

Consequently, our analogy with jet precipitation leads to the behavior rf ∼ V-1/3, in very good agreement with (52) Tokuyama, M.; Enomoto, Y. Phys. Rev. Lett. 1992, 69, 312. (53) Sugimoto, T. J. Colloid Interface Sci. 1992, 150, 208. (54) Chong, J. J. Imaging Sci. Technol. 1995, 39, 120. (55) Matijevic´, E. J. Langmuir 1994, 10, 8.

Synthesis of Monodisperse Silica Particles

measurements. To compare the measured amplitude factor between df and V -1/3 with its predicted value, we used the following data. From literature,7 we find that γ ) 46 erg/ cm2 and Cs ) 2 × 10-6 mol/cm3 for 6 e pH e 10, at room temperature. Assuming a particle density of 1.8 g/cm3, corresponding to the typical density of Sto¨ber particles,7 we deduce VM ) 33.3 cm3. Moreover, as we added 5 mL of TEOS (molar mass 208 g and density 0.934 g/cm3) within the reactor, the corresponding mole number of silica is nSiO2 ) 2.25 × 10-2 mol. Finally, considering the different existing jet precipitation models, one has53 1 e β e 3; note that this dispersion in β values has only a weak influence on the final results due to the one-third power appearing in the amplitude factor of eq 10. Consequently, when df and V are respectively expressed in micrometers and cm3/min, we find 0.3 e 2[6DmγnSiO2VM3Cs/(βRT))]1/3 e 0.43, in excellent agreement with the measured values (0.3-0.4). Conclusion A Sto¨ber-like synthesis of silica particles was performed in which the control of the addition rate of one of the reactant (TEOS) was the main varying parameter. This investigation was motivated by the necessity to obtain the synthesis of low cost reproducible mesoscopic monodisperse silica particles (i.e., of diameter typically larger than 1 µm) based on the standard Sto¨ber method. The method presented here fulfills this requirement since it strongly lowers the time spent to increase particle size by using the seeded method which also implies much more manipulation as well as dilution of starting solution at each step. The cost is also decreased in terms of reactants consumption and solvent recycling. Furthermore this method allows the use of classical EtOH and Si(OEt)4 even when sizes as big as 2 µm are targeted. It is therefore cheaper than the classical Sto¨ber method, which uses more expensive reactants, such as pentyl ester silicon derivative, and often exhibits a wider size distribution. Besides the use of seeds to induce further growth which, as illustrated in the first part of our investigation, eventually leads to the nucleation of new generations of particles, we rationalize here a method which totally circumvents this renucleation. Indeed, our systematic study of the impact of the rate of addition on the final size of the particles for three temperatures (10, 25, and 40 °C) shows that the particle size decreases as the rate of addition increases whatever the temperature, according to a very simple power law. As a corollary, this means that one can work at any temperature fulfilling the condition of nonevaporation of reactant. Moreover, monodispersity in particle distribution is always observed (from 5% down to 2%). Finally, the production of the desired size particle is performed in one step, instead of several ones as in seeded experiments, just by adjusting the addition rate. These two last points are of very practical

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importance in the sense that particle manipulation is no more required and the time consumption is strongly reduced within the processing, as already mentioned. To quantify these results, we first analyze the particle growth rate maintaining a specific addition rate of the reactant. These measurements reveal that growth of silica particles is limited by diffusion, as already demonstrated when all the reactants are added in a single step. Considering this property and using an analogy with crystal formation in jet precipitation, we build a growth model that takes the addition rate into consideration. As for the free-growth regime in classical phase transitions, we show that the particle number remains constant during the addition. The main advantage of this model is to demonstrate that the particle number is directly proportional to the addition rate and to give an expression for the proportionality constant. Using this approach and taking into account the mass conservation, we retrieve the observed power law for the variation of the final particle radius versus addition rate. The amplitude of the predicted power law, associated to the proportionality constant between particle number and addition rate, was also confronted in experiments. We found very good quantitative agreement between theory and experiments. Even if data are missing for a quantitative comparison, particularly the mole number of silica corresponding to the volume of added TEOS, we also find good qualitative agreement with the two experiments performed at 0.6 and 18 mL/min,36 since (i) a decrease in particle size was observed for increasing addition rates and (ii) the addition rate was considered as the dominant factor on final size and polydispersity of the particles, as compared to the temperature for instance. Therefore, the agreement observed between our measurements with results obtained at large addition rates for synthesis of nanoparticles36 illustrates over almost 4 orders of magnitude in addition rate (from V ) 5 × 10-3 to 18 mL/min) how monodisperse silica particles can be synthesized using a single step process with size ranging from a few tens of nanometers to a few micrometers. Consequently, the simplicity of this method opens new prospects in the synthesis of silica particles and offers a flexible level of particle size reproducibility that could be very appealing for nanoscopic to mesoscopic particle assembling (photonics, chromatography). Acknowledgment. The authors want to thank Dr. S. Reculusa for helpful discussions and A. S. Beaumont and C. Sableaux for some experimental work. Note Added after ASAP Publication. References 32b and 35b and the Acknowledgment paragraph were omitted in the version published ASAP December 18, 2004; the corrected version was published ASAP January 18, 2005. LA048569R