Langmuir 1997, 13, 4527-4534
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Preparation of Nanoparticles in Microemulsions: A Monte Carlo Study of the Influence of the Synthesis Variables† C. Tojo* Physical Chemistry Department, Faculty of Sciences, University of Vigo, E-36200 Vigo, Spain
M. C. Blanco and M. A. Lo´pez-Quintela Physical Chemistry Department, Faculty of Chemistry, University of Santiago, E-15706 Santiago de Compostela, Spain Received June 21, 1996X Monte Carlo simulations were performed to study the formation of nanoparticles in microemulsions. The influence of the following parameters on particle size distribution (PSD) was investigated: number of reagent molecules per droplet, surfactant film flexibility, droplet size, presence or absence of autocatalysis by the product, and the fraction of bulk volume made up by droplets. It was found that autocatalyzed reactions with high reagent concentrations and low surfactant film flexibility afforded bimodal PSDs. Particle size increased with reagent concentration when this was low, but at higher reagent concentrations it depended chiefly on droplet size. The dependence of PSD on reaction time confirmed the successive occurrence of well-defined nucleation and growth processes. We have compared the simulation results with experimental data taken from different authors and carried out in our laboratory. Good agreement between both kind of results supports the conclusions of this paper.
Introduction Producing small monodisperse particles such as semiconductors, small metallic particles, or ultrahigh molecular weight latexes, has received impressive attention in recent years because several nonconventional physical properties (optic, electric and magnetic) are expected by using such new materials.1-4 Although progress in this field has been extremely important, much has yet to be done in order to understand the properties of monodisperse particles systems and also to obtain better control of the nanostructures of these materials. Microemulsions, among the methods to produce nanomaterials, can be used as nanoreactors to carry out chemical reactions in restricted geometries.5 These microemulsions consist of nanometer-size water droplets which are dispersed in a continuous oil medium and stabilized by surfactant molecules accumulated in the oilwater interface. The main function of the droplet nanoreactor is to provide a compartmentalized medium in order to prevent phase separation of the particles. This technique has undergone fast development in the last few years.5-15 It offers several advantages over other * To whom correspondence should be addressed. † Dedicated to Prof. Wilhelm Knoche (Universita ¨ t Bielefeld, Bielefeld Germany) on the occasion of his 60th birthday. X Abstract published in Advance ACS Abstracts, July 1, 1997. (1) Cahn, R. W. Nature 1992, 359, 591. (2) Hayashi, C. Phys. Today 1987, Dec, 44. (3) Ozin, G. A. Adv. Mater. 1992, 4, 612. (4) Awschalom, D.; DiVincenzo D. Phys. Today 1995, Apr, 43. (5) Fendler, J. H. Chem. Rev. 1987, 87, 877. (6) Wilcoxon, J. P. U.S. Patent 1992, 5,147,841. (7) Nagy, J. B.; Claerbout, A. In Surfactants in Solution; Mittal, K. L., Shah, D. O., Eds.; Plenum Press: New York, 1991; Vol. 11, p 363. (8) Fletcher, D. I.; Howe, A. M.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1987, 83, 985. (9) Pileni, M. P.; Lisiecki, I.; Motte, L.; Petit, C.; Cizeron, J.; Moumen, N.; Lixon, P. Prog. Colloid Polym. Sci. 1993, 93, 1. (10) Towey, T. F.; Khan-Lodhi, A.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1990, 86, 3757. (11) Barnickel, P.; Wokaun, A.; Sager, W.; Eicke, H. F. J. Colloid Interface Sci. 1992, 148, 80. (12) Boutonnet M.; Kizling, J.; Stenius P.; Maire, G. Colloids Surf. 1982, 5, 209. (13) Gobe,M.; Kon-no, K.; Kandori, K.; Kitahara, A. J. Colloid Interface Sci. 1983, 93, 293.
S0743-7463(96)00620-8 CCC: $14.00
techniques: it is a soft technique, i.e., it does not require extreme temperature or pressure conditions; moreover, it can be used with almost all chemical reactions which have been studied to obtain particles in homogeneous solutions, and it does not require special equipment. An important disadvantage of this technique is that no systematic results have been obtained yet. One of the key objectives for any method of synthesizing nanoparticles is to ensure reproducible control of particle size. Researchers have obtained different results depending on the experimental conditions employed. For example, some authors11,12,16 have found a poor correlation between the final size equilibrium of the particles and the water content of the microemulsion droplets. On the contrary, other researchers15,17-21 have found that the particle size increases with the droplet size for different kind of particles obtained in microemulsions. Thus, it seems fair to say that no definitive conclusions may be established about the control of the particle size. In this work we carried out Monte Carlo simulations to investigate whether these discrepancies may have been due to differences in the other operational conditions used in the various studies. In the case in which chemical reaction is the slowest step, the whole process is governed by the nucleation and growth inside the droplets, and it is very similar to the reaction in bulk. Therefore this simulation procedure is only addressed to study reactions which are controlled by the interdroplet exchange.8 Examples of reactions which can be studied through this simulation model will be discussed later. (14) Kurihara, K.; Kizling, J.; Stenius,P.; Fendler, J. H. J. Am. Chem. Soc. 1983, 105, 2574. (15) Lo´pez-Quintela, M. A.; Rivas, J., J. Colloid Interface Sci. 1993, 158, 446. (16) Khan-Lodhi, A.; Robinson, B. H.; Towey, T.; Hermann, C.; Knoche, W.; Thesing, U. In The Structure, Dynamics and Equilibrium Properties of Colloidal Systems; Bloor, D. M., Wyn-Jones, E., Eds.; NATO ASI Series C, Kluwer Acad. Publ.: Dordrecht, The Netherlands, 1990; Vol. 324. (17) Motte, L.; Lebrun, A.; Pileni, M. P. Prog. Colloid Polym. Sci. 1992, 89, 99. (18) Lianos, P.; Thomas, J. K. Chem.Phys. Lett. 1986, 125, 299 (19) Arriagada, F. J.; Osseo-Asare, K. Colloids Surf. 1992, 69, 105. (20) Petit, C.; Lixon, P.; Pileni, M. P. J. Phys.Chem. 1990, 94, 1598. (21) Petit, C.; Lixon, P.; Pileni, M. P. J. Phys.Chem. 1993, 97, 12974.
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The goal of this work is to test the influence of some of the most important synthesis variables on the final distribution of particle sizes. Specifically, we investigated the dependence of particle size distribution (PSD) on the number of reagent molecules per droplet, surfactant film flexibility, droplet size, the presence or absence of autocatalysis by the product, and the fraction of bulk volume made up by droplets. To verify the validity of the simulation model, we have compared the simulation results with experimental data taken from different authors. Good agreement between both kind of results supports the main conclusions of this paper about the best experimental conditions to get a monodisperse distribution of particle sizes. Simulation Details We considered the case of a reaction in which collision between a reagent A and a reagent B produces a product P with probability 1. All units of P in a single microemulsion droplet were considered to be aggregated in a single particle. Each simulation began with 1000 microemulsion droplets randomly located on a two-dimensional square lattice; the influence of the fraction of bulk volume made up by the droplets (“volume fraction”, φ) was studied by varying the size of the lattice so that φ varied from 5% to 25%. Droplets diffused on the lattice by performing independent random walks to nearest neighbor sites, subject to the exclusion principle (no site was allowed to be occupied by more than one droplet at any one time); cyclic boundary conditions were employed. At the beginning of each simulation, half the 1000 droplets carried c molecules of A and half c molecules of B (100 e c e 1000). All simulations were run for 10 000 Monte Carlo steps (mcs; 1 mcs was defined as the time taken for all droplets to step to a nearest neighbor); in that event, all PSDs became stable after about 2000-8000 mcs, depending on the synthesis variables. Microemulsions are used as microreactors because they can exchange the content of their water pools through a collision process. Although droplet-droplet collisions leading to exchange of droplet contents constitute only about 1/104 of all droplet-droplet collisions in real microemulsions,22 which makes mass transfer the slowest step of a reaction carried out in a microemulsion,10,23 in this work we saved computation time by implementing the transfer of reagents and/or product in all dropletdroplet collisions; in doing so we of course forfeited the possibility of studying the possible influence of the relative diffusion coefficients of the reagents and product. Droplets were deemed to collide whenever they came to occupy contiguous lattice sites, and they can establish a water channel forming a transient dimer.24 At this stage, water cores could exchange their contents. Exchange of contents between two colliding droplets was implemented depending on the nature of the species inside the droplet, as follows (see ref 25 for details): Rule 1. Regardless of the presence or absence of product P, if both droplets carried the same reagent, this reagent was redistributed in accordance with a crude concentration (22) Fletcher, P. D. I.; Robinson, B. H.; Bermejo-Barrera, F.; Oakenfull, D. G. In Microemulsions; Robb, I. D., Ed.; Plenum Press: New York, 1982; pp 221-231. (23) Eicke, H. F.; Shepherd, J. C. W.; Steinmann, A. J. Colloid Interface Sci. 1976, 56, 186. (24) Zana, R.; Lang, J. In Microemulsions; Structure and Dynamics; Frieberg, S. E., Bothorel, P., Eds.; CRC Press, Boca Raton, FL, 1987; p 153. (25) Tojo, C.; Blanco, M. C.; Rivadulla, F.; Lo´pez-Quintela, M. A. Langmuir 1997, 13, 1970.
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gradient principle: specifically, one reagent was transferred from the droplet with more reagents to the droplet with fewer. Rule 2. If one droplet carried A and the other B and neither carried any P, then reaction between one reagent A and one reagent B produced one unit of P in the droplet with fewer reagents (again in accordance with the concentration gradient principle). Rule 3. If both the droplets carried particles of P, Ostwald ripening was enforced: the smaller particle (the one with fewer units) was transferred to the same droplet as the larger, subject only to the film flexibility and droplet size conditions specified below (rules 5 and 6). Rule 4. If one droplet carried A and the other B, and one or both of the droplets also carried particles of P, then one of the following alternative procedures was implemented. Rule 4a. Autocatalysis by P. Some reactions are catalyzed by the existing nucleus. To simulate autocatalysis of the reaction by P, reaction between one reagent A and one reagent B produced one unit P in the droplet with the larger existing P particle (subject to rule 5 below). In this way we consider that the larger nucleus had a bigger probability of playing as a catalyst because of its bigger surface. Rule 4b. No autocatalysis. In this case, the unit P produced by the reaction was placed in the droplet with fewer reagents, as in rule 2 (subject to rule 5). Rule 5. The influence of droplet size was investigated by varying a size parameter q specifying the maximum permitted particle size, i.e. the maximum number of P units allowed in any single droplet. It should be noted that, as was experimentally observed,26-30 the final size of the particles may be slightly bigger or smaller than the droplet size, depending on the flexibility of the surfactant film and/or the surfactant adsorption. Rule 6. The ease with which channels can form to communicate colliding water droplets and the size of these channels are governed by the flexibility of the surfactant film around the droplets, which therefore also places a limit on the size of the particles traversing the dropletdroplet channels. The influence of surfactant film flexibility was investigated by varying a flexibility parameter f specifying a maximum particle size for transfer between droplets: P particles with more than f units were not allowed to pass from one droplet to another. Rule 7. To save computation time, empty droplets were removed from the simulation. By means of this simulation procedure, we have monitored several experimental conditions by varying the film flexibility (f), the concentration of reactants (c), the size of the droplet (q), and the volume fraction of droplets (φ), for autocatalytic and noncatalytic reactions. In each case, we have calculated the distribution of particle sizes at the end of the reaction in order to study the influence of each variable on the particles growth. Results and Discussion In agreement with experimental observations,11,20 both unimodal and bimodal PSDs were obtained, as well as (26) Monnoyer, Ph.; Fonseca, A.; Nagy, J. B. Colloids Surf. 1995, 100, 233. (27) Lufimpadio, N.; Nagy, J. B.; Derouane, E. G. In Surfactants in Solution; Mittal, D., Lindman, B., Eds.; Plenum Press: New York, 1983; Vol. 3, p 1483. (28) Ravet, I.; Lufimpadio, N.; Gourgue, A.; Nagy, J. B. Acta Chim. Hung. 1985, 119, 155. (29) Boutonnet, M.; Kizling, J.; Touronde, R.; Marie, G.; Stenius, P. Appl. Catal. 1986, 20, 163. (30) Nagy, J.; Gourgue, A.; Derouane, E. G. Stud. Surf. Sci. Catal. 1991, 16, 193.
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Figure 1. (A) Broad unimodal distribution of particle sizes, corresponding to a film of flexibility f ) 30 (particles of less than 30 units can be exchanged), φ ) 10%, c ) 500 reagents per droplet, time ) 5000 Monte Carlo steps (mcs), and autocatalytic case. The line is simply a guide to the eye. (B) Quasi-monodisperse unimodal distribution of particle sizes, corresponding to a film of flexibility f ) 5 (particles of less than 5 units can be exchanged), φ ) 10%, c ) 500 reagents per droplet, time ) 5000 Monte Carlo steps (mcs), and no autocatalytic case. The line is simply a guide to the eye. Table 1. Influence of Autocatalysis on the Final Distribution of Particle Size (q ) 5000) conditions
autocatalysis, bimodal
no catalysis, unimodal
f
φ
c
〈s1〉
σ1/〈s1〉
〈s2〉
σ2/〈s2〉
〈s2〉/〈s1〉
〈s〉
σ/〈s〉
0 5 5
10 10 10
500 500 1000
49.3 127.9 142.0
0.85 0.63 0.69
454.9 467.3 909.6
0.18 0.18 0.17
9.23 3.65 6.41
250.1 304.3 589.2
0.14 0.27 0.20
Figure 2. Bimodal distribution of particle sizes, corresponding to a film of flexibility f ) 2 (nuclei of less than 2 units can be exchanged), φ ) 10%, c ) 500 reagents per droplet, time ) 5000 Monte Carlo steps (mcs), and autocatalytic case. The line is simply a guide to the eye.
intermediate asymmetric unimodal PSDs (Figures 1 and 2). The shape of the PSD depends on the simulation conditions. In particular, bimodal distributions only arise in the autocatalytic regime; Table 1, in which 〈s〉 and σ indicate the mean and standard deviation of a given PSD peak (with subscripts identifying the two peaks of a bimodal distribution), lists three sets of conditions in which the appearance of a bimodal or unimodal distribution depends solely on whether the autocatalytic reaction rule 4a or the nonautocatalytic rule 4b was employed. If it is accepted that autocatalysis by an aggregated product will have a greater effect for slow reactions than for fast reactions, then these results are in keeping with the
experimental results of Petit et al.31 who found that the PSD of silver particles prepared in microemulsions was bimodal when NaBH4 was used as the reducing agent (a slow reaction) but unimodal when N2H4 was used (a fast reaction). Influence of Flexibility. For fixed c (500 molecules per droplet), φ (10%) and q (5000), increasing the film flexibility variable f from 0 to 30 under the autocatalytic regime gives rise to a transition from a bimodal to a unimodal PSD (Table 2). Above the transition point, mean particle size increases with f, and below the transition point the mean size of the particles belonging to the smaller-particle peak, 〈s1〉, likewise increases with f. However, when the concentration is small, the distribution is always unimodal, independently of the film flexibility. By using different surfactants and/or oils (different values of parameter f), the particle size can be modified, obtaining a broader unimodal distribution and a bigger mean size when the flexibility of the film is greater. Moreover, the polydispersity of particle sizes becomes bigger as the flexibility increases (see Table 2). Therefore, the monodispersity strongly depends on the surfactant and oil used. These results are in keeping with the experimental results of Petit et al.31 They studied the synthesis of silver nanoclusters in AOT reverse micelles, using different alkanes (isooctane and cyclohexane). The intermicellar exchange processes were governed by attractive interactions between droplets. It is known that bulk solvent plays an important role in the intermicellar potential. As a matter of fact, the use of cyclohexane compared to isooctane as bulk solvent induces a decrease in the interaction potential which decreases the intermicellar exchange rate constant by a factor of 10.10 By using cyclohexane as bulk solvent, electron micrographs reveal a decrease in the size, polydispersity, and number of silver particles compared to that obtained with isooctane (see (31) Petit, C.; Lixon, P.; Pileni, M. P. J. Phys. Chem. 1993, 97, 12977.
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Figure 3. (A) Simulation results for c ) 100 and different values of f, autocatalytic case. (B) Size distribution of silver particles synthesized in isooctane and cyclohexane (data obtained from ref 31). The lines are simply a guide to the eye. Table 2. Influence of Flexibility on the Final Distribution of Particle Size (Autocatalytic Case; q ) 5000) conditions
bimodal
unimodal
f
φ
c
〈s1〉
σ1/〈s1〉
〈s2〉
σ2/〈s2〉
〈s2〉/〈s1〉
0 2 5 15 30 0 2 5 15 30
10 10 10 10 10 10 10 10 10 10
500 500 500 500 500 100 100 100 100 100
49.3 66.1 127.9
0.85 0.78 0.63
454.9 447.8 467.3
0.18 0.20 0.18
9.23 6.77 3.65
Figure 3). It should be noticed that no change in micellar size has been observed by SAXS. Hence, at a given water content, the decrease of the intermicellar exchange rate constant induces a decrease in particle size. The number of silver metallic particles obtained is lower than that observed by using isooctane as bulk solvent, indicating a diminution in the reduction yield. This is confirmed by a decrease in the 250-nm absorbance when using cyclohexane instead of isooctane. We can explain these results on the basis of our simulations (see Table 2). The interdroplet rate exchange in cyclohexane is lower than that in isooctane.8 The natural droplet curvature in cyclohexane is similar to the actual droplet curvature, because of the hard-sphere interactions. On the other hand, the natural droplet curvature in isooctane is smaller than the actual droplet curvature, because of the attractive interactions. This means that the film flexibility in cyclohexane is smaller than that in isooctane, as can be observed in Figure 3, which shows the agreement between
〈s〉
σ/〈s〉
422.3 587.2 57.0 64.3 79.7 120 184
0.43 0.41 0.67 0.63 0.53 0.44 0.42
experimental and simulation results. It is worth noticing that the rate constant for droplet communication that depends on the film flexibility has not been explicitly introduced in our simulation. However, the fact that larger particles are favored by ripening at high f values implies that the rate will be quicker as f increases, and therefore, the effective rate constant for droplet communication will be greater.25 Influence of Concentration. For fixed f (5), φ (10%), and q (5000), increasing initial reagent concentration c from 100 to 1000 under the autocatalytic regime brought about a transition from a unimodal to a bimodal PSD (Table 3). Below the transition point, mean particle size increased with c, and above the transition point 〈s2〉 likewise increased with c. Experimentally, increasing reagent concentration has been found by several authors to increase particle size.7,9,17,26,31 The bimodality we have found by simulation at high concentrations has been also found by Monnoyer et al.26 They studied the formation
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Figure 4. (A) Size distributions (number of particles vs diameter of particles (Amstrong) of the AgBr particles (data obtained from ref 26). (B) Size distributions obtained from simulation (f ) 5, q ) 500, autocatalytic case). Table 3. Influence of Concentration on the Distribution of Particle Size (Autocatalytic Case; q ) 5000) conditions
bimodal
f
φ
c
5 5 5 5 5
10 10 10 10 10
100 200 500 800 1000
〈s1〉
127.9 134.0 142.0
σ1/〈s1〉
0.63 0.67 0.69
of silver bromide particles, mixing two microemulsions containing the precursors salts AgNO3 and KBr (the concentrations of KBr were always 3% higher than those of AgNO3, i.e. cA ≈ cB). Microemulsions of AOT, n-heptane, and water were employed. They found that the particles were all spherical in shape and that their mean size increased as a function of initial AgNO3 concentration (see Figure 4A). All size distribution histograms presented a population of very small size AgBr particles (30 Å). When the concentration of reactants was increased it changed from an unimodal to a bimodal size distribution. A further increase of the concentration leads to a separation of the two mean sizes. Figure 4A shows the experimental results of Monnoyer et al.26 using microemulsions of R ) 12.5, where R ) [H2O]/[AOT], and Figure 4B shows our simulation data using different concentrations. It must be emphasized the consistency between our simulation data and the experimental results. Figure 5 shows the mean size variation as a function of concentration. Symbols represent the experimental data from Monnoyer et al.,26 for AgBr particles prepared from a microemulsions of R ) 12.5. Lines are plotting the simulation results (synthesis conditions: f (5), q (500), autocatalytic reaction). It must be noted that Monnoyer et al.26 thought that very small monodisperse parasitic particles of the first mode could be associated with colloidal metallic silver particles from the aqueous solution of silver nitrate used to prepare the microemulsion of AgNO3. Even though they have carried out EDAX measurements to validate their hypothesis, no definitive conclusion was reached. In order to check further appearance of bimodality at high concentrations, we have prepared Pt particles in water/Brij30/n-heptane microemulsions using different precursor concentrations. Typical photomicrographs of
〈s2〉
467.3 722.8 909.6
unimodal σ2/〈s2〉
0.18 0.18 0.17
〈s2〉/〈s1〉
〈s〉
σ/〈s〉
79.7 137.3
0.53 0.56
3.65 5.39 6.41
Figure 5. Particle size vs concentration. Symbols: experimental data for the synthesis of AgBr in AOT/n-heptane/water, R ) 12.5 (data obtained from ref 26). Lines: simulation results (f ) 5, q ) 500, autocatalytic case).
platinum particles and their corresponding histograms are shown in Figure 6. They clearly show the appearance of bimodality at high concentration. Therefore, according to our results, we think that the first mode obtained from Monnoyer et al.26 is mainly due to very small AgBr particles. Influence of Volume Fraction of Droplets. For fixed f (5), c (500), and q (5000), increasing the volume
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Figure 6. Electron microscopy of Pt particles synthesized in Brij30/n-heptane/water microemulsions (top) and their corresponding histograms (bottom): (A) c ) 0.025 M, R ) 1.2; (B) c ) 0.2 M, R ) 3.88. Table 4. Influence of Volume Fraction of Droplets on the Final Distribution of Particle Size (Autocatalytic Case; q ) 5000) conditions
bimodal
f
φ
c
〈s1〉
σ1/〈s1〉
〈s2〉
σ2/〈s2〉
〈s2〉/〈s1〉
5 5 5 5 5
5 10 15 20 25
500 500 500 500 500
99.4 127.9 137.7 151.9 143.2
0.84 0.63 0.55 0.50 0.57
403.0 467.3 476.8 466.3 491.8
0.16 0.18 0.18 0.19 0.16
4.05 3.65 3.46 3.07 3.44
fraction parameter φ under the autocatalytic regime had little effect on the final PSD (Table 4). Influence of the Droplet Size. Assuming simple geometrical arguments, the size of the droplet is expected to be proportional to the mole ratio [H2O]/[surfactant]. This have been experimentally confirmed by techniques such as small-angle neutron scattering,32 ultracentrifugation,33 and time-resolved fluorescence quenching.34 (32) Kotlarchyk, M.; Chen, S. H.; Huang, J. S.; Kim, M. W. Phys. Rev. A 1984, 29, 2054.
Thus, the size of the water cores can be changed simply by changing the water/surfactant ratio, and the compartmentalized water droplets of different sizes can be used then to have control on the particle growth. For fixed φ (10%), the results of increasing the droplet size variable q from a lower limit of 80 or 300 to an upper limit of 5000 under the autocatalytic regime are listed in Table 5 for four extreme combinations of f (5 or 30) and c (100 or 500). The final PSD was unimodal for the high f, high c and low f, low c combinations, but bimodal for the combination of low f and high c. In agreement with experimental results,15-17 particle size was controlled by droplet size in the small droplet range (where increasing q increased 〈s〉 or 〈s2〉 and decreased 〈s1〉), but not in the large droplet range, where reagent concentration c appears to be the controlling factor. Note the high monodispersity of the larger-particle peak obtained with the combination of low f, low q, and high c. (33) Robinson, B. H.; Steytler, D. C.; Tack, R. D. J. Chem. Soc., Faraday Trans. 1 1979, 75, 481. (34) Bridge, N. J.; Fletcher, P. D. I. J. Chem. Soc., Faraday Trans. 1 1983, 79, 2161.
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Figure 7. Particle size vs droplet size. (A) Symbols show CdS particles in AOT/n-heptane/water, c ) 1 × 10-4 M (data obtained from ref 16); lines show simulation results (c ) 100, f ) 5, autocatalysis). (B) Symbols show AgBr particles in AOT/n-heptane/water, c ) 0.250 M (data obtained from ref 26); lines show simulation results (c ) 500, f ) 5, autocatalysis). Table 5. Influence of the Droplet Size on the Final Distribution of Particle Size (Autocatalytic Case; φ ) 10%) conditions
Figure 8. Time course of the number of droplets carrying particles with between 100 and 150 units (continuous line) and the number of droplets carrying particles with between 500 and 550 units (dashed line) in an autocatalytic reaction with f ) 5 (nuclei of less than 5 units can be exchanged), φ ) 10%, c ) 500 reagents per droplet, and q ) 5000.
To illustrate the dependence of particle size on the water content R, Figure 7A shows the dependence of particle size on R at low concentrations, comparing experimental and simulation results. In this case, we have studied the results of Khan-Lodhi et al.16 They have prepared CdS microparticles by mixing sodium sulfide and cadmium nitrate solubilized in two AOT/n-heptane microemulsions. The concentration of both reactants was 1 × 10-4 M. Symbols in Figure 7A show the effect of water droplet size on CdS microparticle size. Because AOT/n-heptane/water microemulsions seems to correspond to a film flexibility value f (5) (see above), we have used this value in the simulation. Line in Figure 7A shows the simulation results (autocatalytic reaction, f (5), c (100). One can see a very good agreement between our results and the experimental ones. Figure 7B represents the experimental results from Monnoyer et al.,26 using a high value of concentration (c ) 0.250 M) and different R values. Lines show simulation
bimodal
f
q
c
〈s1〉
σ1/〈s1〉
〈s2〉
5 5 5 5 5 30 30 30 30 30 5 5 5 5 5 30 30 30 30 30
300 400 500 800 5000 300 400 500 800 5000 80 100 200 500 5000 80 100 200 500 5000
500 500 500 500 500 500 500 500 500 500 100 100 100 100 100 100 100 100 100 100
152.3 133.1 128.1 127.9 127.9
0.35 0.59 0.61 0.63 0.63
271.4 370.7 439.9 464.3 467.3
unimodal
σ2/〈s2〉 〈s2〉/〈s1〉 0.04 0.04 0.11 0.18 0.18
〈s〉
σ/〈s〉
260.0 336.0 377.4 564.2 587.2 59.9 65.7 79.2 79.7 79.7 76.3 94.1 156 183 184
0.17 0.24 0.36 0.39 0.41 0.35 0.41 0.52 0.53 0.53 0.07 0.11 0.34 0.42 0.42
1.78 2.79 3.43 3.63 3.65
results for an autocatalytic reaction with c (500) and f (5). The size of the smallest particles remains almost constant, and this is consistent with experimental results. However, the size of the biggest particles diminishes as R increases, although the general behavior is that the size increases as R9,16,31 increases. This particle decrease observed in AgBr particles could be due to the adsorption of the surfactant onto the particle,35 which produces a particle size diminution. This mechanism becomes more probable as R becomes bigger. Therefore, as R increases, the particle size increases if adsorption does not take place. When adsorption takes place, the particle size diminishes as R increases. Both effects are opposite in such a way that the size increases or decreases depending on the predominance of the adsorption over the fact that a big droplet can carry more particles than a small droplet. Nucleation and Growth Processes. Figure 8 shows, for a simulation performed under the autocatalytic regime with f (5), φ (10%), c (500) and q (5000), the time dependence of the number of product particles sized 100(35) Pileni, M. P. Adv. Colloid Interface Sci. 1993, 46, 139.
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150 and the number of product particles sized 500-550 (approximately the final size of the biggest particles). This figure shows that under these conditions the particle formation comprises two quite well-defined processes: the rapid formation of a large number of small particles (nucleation) and the subsequent slower growth of these nuclei (see ref 25 for details). Similar dynamics have been deduced by Lo´pez-Quintela et al.15 from time-resolved small-angle X-ray scattering measurements of iron particles prepared in AOT microemulsions. The nucleation maximum has also been detected spectrophotometrically, and the time at which it occurred was used to estimate the agglomeration number of the nuclei assuming a droplet-communication-controlled Smoluchowski mechanism.8,10,20 The lag before the appearance of large particles has also been observed experimentally.10 Conclusions The above results suggest that microemulsion droplet size controls the size of particles only in the lower size range, at least when the reaction producing the particles is autocatalyzed by the product. When droplet size is not the limiting factor, particle size increases with surfactant film flexibility (which depends on both the surfactant and the oil used, among other factors) as well as with the reagent concentration. Furthermore, film flexibility and reagent concentration also determine whether an auto-
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catalyzed reaction will afford a unimodal or a bimodal PSD: bimodal distributions are afforded by the combination of high reagent concentration and low film flexibility. To obtain small particles with a unimodal PSD, a low reagent concentration should be used (for the smallest particles, film flexibility and droplet size should also be low); to obtain larger particles with a unimodal PSD, higher reagent concentrations can be used with highflexibility films. Alternatively, it may be more desirable to use high reagent concentration, low film flexibility, and small droplet size to obtain a bimodal PSD with a very monodisperse large-particle peak and then separate the two sizes classes by ultracentrifugation, liquid chromatography, or some other suitable separation technique. Consistency between experimental and simulation results, using different synthesis conditions, show the validity of the simulation model used in this study. Although in the simulations carried out in this work we have used a simple model of reactions in microemulsions, they appear to be able to explain the size distributions of nanoparticle synthesized in these nanostructured media. Acknowledgment. The authors are grateful for the financial support of the Regional Government of Galicia (Projects XUGA9320903B95 and XUGA34701A95). LA9606207
