Effects of the Intermicellar Exchange on the Size Control of

Langmuir 2001, 17, 7251-7254

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Effects of the Intermicellar Exchange on the Size Control of Nanoparticles Synthesized in Microemulsions S. Quintilla´n,† C. Tojo,*,† M. C. Blanco,‡ and M. A. Lo´pez-Quintela‡ Physical Chemistry Department, Faculty of Sciences, University of Vigo, E-36200 Vigo, Spain, and Physical Chemistry Department, Faculty of Chemistry, University of Santiago de Compostela, E-15706 Santiago de Compostela, Spain Received June 5, 2001. In Final Form: July 31, 2001 The effect of the intermicellar exchange on the size control of nanoparticles synthesized in microemulsions has been studied by computer simulation. The employed algorithm includes a reactant exchange parameter, k, which depends on the surfactant film flexibility and the dimer lifetime. This parameter, k, has a big influence on the final particle size, except in the case that one of the reactants is in a big excess. It has also been proven that a critical value of the reactant exchange parameter exists, which determines the relative weights of the two mechanisms of growth: autocatalysis and ripening. It is then predicted that there is an optimum dimer lifetime for which the smallest particles can be obtained.

Introduction Research in nanocrystalline materials has increased enormously during the past years.1 Nanometer-sized particles find technological applications in many different areas such as catalysis, magnetic recording, highperformance ceramics, and microelectronic components. Synthesis of nanoparticles using microemulsions seems specially suited to tailoring particle properties at the nanolevel. In many of these systems, nanodroplets of the aqueous phase are trapped within aggregates of molecules dispersed in an external oil phase.2,3 The role of microemulsions is to compartmentalize reactants, which are effectively distributed in separate microreactors at the molecular level. Through collisions, the content of the droplets can be exchanged. The surfactant-stabilized cavities provide a cagelike effect that can control nucleation and growth.2,4 The feasibility of the microemulsionbased synthesis method for the production of various colloidal particles has been extensively demonstrated for a number of materials.5-20 As an example, Kurihara et al.21 showed that a great number of particles smaller and more uniform in size are formed in water-in-oil micro† ‡

University of Vigo. University of Santiago de Compostela.

(1) See, for example: Edelstein, A. S., Cammarata, R. C., Eds. Nanomaterials: Synthesis, Properties and Applications; Institute of Physics Publishing: Bristol, 1996. (2) Fendler, J. H. Chem. Rev. 1987, 87, 877. (3) Friberg, S. E., Bothorel, P., Eds. Microemulsion: Structure and Dynamics; CRC Press: Boca Raton, FL, 1987. (4) Robinson, B. H.; Khan-Lodhi, A. N.; Towey, T. In Structure and Reactivity in Reverse Micelles; Pileni, M. P., Ed.; Elsevier: Amsterdam, 1989; p 198. (5) Lo´pez-Quintela, M. A.; Quibe´n, J.; Rivas, J. In Industrial Applications of Microemulsions; Solans, C., Kunieda, H., Eds.; Surfactant Science Series; Marcel Dekker: New York, 1996; p 247-264 (C, L). (6) Lo´pez-Quintela, M. A.; Rivas, J. J. Colloid Interface Sci. 1993, 158, 446. (7) Petit, C.; Lixon, P.; Pileni, M. P. J. Phys. Chem. 1990, 94, 1598. (8) Petit, C.; Lixon, P.; Pileni, M. P. J. Phys. Chem. 1993, 97, 12974. (9) Motte, L.; Petit, C.; Lixon, P.; Boulanger, L.; Pileni, M. P. Langmuir 1992, 8, 1049. (10) Pileni, M. P. J. Chem. Phys. 1993, 97, 6961. (11) Pileni, M. P.; Lisiecki, I.; Motte, L.; Petit, C.; Cizeron, J.; Moumen, N.; Lixon, P. Prog. Colloid Polym. Sci. 1993, 93, 1. (12) Towey, T. F.; Khan-Lodhi, A.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1990, 86, 3757. (13) Kumar, P., Mittal, K. L., Eds. Handbook of Microemulsion Science and Technology; Marcel Dekker: New York, 1999. (14) Arriagada, F. J.; Osseo-Asare, K. Colloids Surf. 1992, 69, 105.

emulsions than in homogeneous solutions. Despite the advantages offered by the microemulsion technique, much has yet to be done in order to understand the mechanism of particle formation and also to obtain a better control of its size. To gain more insight into this problem, we carried out computer simulations on the formation of nanoparticles in microemulsions to elucidate the kinetics and mechanism of formation of these particles.22-26 In addition, the influence of different synthesis variables was also studied. The simulation model was successfully applied to explain the experimental results of different reactions in microemulsions.22-25 This work is focused on the study of how the intermicellar exchange process affects the final nanoparticle size. For this purpose, we improve our previously developed simulation algorithm including a reactant exchange parameter that controls the rate of the reactant’s transfer. Simulation Procedure Computer simulation of nanoparticles formation in microemulsions was run to simulate the kinetic course of the reaction. It was developed based on the model previously reported,22,25 which was improved later intro(15) 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 Academic Publishers: Dordrecht, 1990; Vol. 324, p 373. (16) Lo´pez-Quintela, M. A.; Rivas, J. Curr. Opin. Colloid Interface Sci. 1996, 1, 806. (17) Lo´pez-Quintela, M. A.; Quibe´n, J.; Rivas, J. U.S. Patent 4,983,217, 1991; E.C. Patent 370,939, 1993. (18) Monnoyer, Ph.; Fonseca, A.; Nagy, J. B. Colloids Surf. 1995, 100, 233. (19) Bagwe, R. P.; Khilar, K. C. Langmuir 1997, 13, 6432. (20) Bagwe, R. P.; Khilar, K. C. Langmuir 2000, 16, 905. (21) Kurihara, K.; Kizling, J.; Stenius, P.; Fendler, J. H. J. Am. Chem. Soc. 1988, 105, 2574. (22) Tojo, C.; Rivadulla, F.; Blanco, M. C.; Lo´pez-Quintela, M. A. Langmuir 1997, 13, 1970. (23) Tojo, C.; Blanco, M. C.; Lo´pez-Quintela, M. A. Langmuir 1997, 13, 4527. (24) Tojo, C.; Blanco, M. C.; Lo´pez-Quintela, M. A. J. Non-Cryst. Solids 1998, 235-237, 688. (25) Tojo, C.; Blanco, M. C.; Lo´pez-Quintela, M. A. In Non-Crystalline and Nanoscale Materials; Rivas, J., Lo´pez-Quintela, M. A., Eds.; World Scientific Publishing: Singapore, 1998; pp 451-456. (26) Tojo, C.; Blanco, M. C.; Lo´pez-Quintela, M. A. Langmuir 1998, 14, 6835.

10.1021/la0108407 CCC: $20.00 © 2001 American Chemical Society Published on Web 10/13/2001

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ducing very low concentrations.26 The applicability of the developed simulation model was shown by comparison with experimental results.22-26 In this work, the simulation algorithm has been modified to introduce the possibility of interchanging more than one reactant during each collision, to have a better knowledge of the mass transfer process and its influence on the formation of nanoparticles in microemulsions. Motion. Each simulation begins with 1000 microemulsion droplets randomly located on a two-dimensional square lattice. A 10% portion of the space is occupied by droplets. Droplets are allowed to perform random walks to nearest neighbor sites, by choosing at random the direction of motion at each step. The length of each step is constant and equal to one length lattice unit. This random walk is subject to the exclusion principle. Cyclic boundary conditions are enforced at the ends of the lattice. Reactants Distribution. A total of 500 droplets carried cA molecules of A, and 500 droplets carried cB molecules of B, A and B being the reactants. The reactant species were distributed throughout the droplets using a Poisson distribution:

P(n) )

n jn exp(-n j) n!

(1)

where P(n) is the probability that a droplet contains n reactants (A or B) whose average occupancy is n j . The j ) 32) in all concentration of A was kept constant (cA ) n simulations. To study the influence of reactant excess x, defined as the ratio between A and B concentrations (x ) cA/cB), the concentration of B has been changed in each simulation (4 e cB ) n j e 32). Time Unit Base. Our time unit base is 1 Monte Carlo step, which is defined as the time taken for all droplets to move in one step into one of their nearest neighbors. Collision. Droplets collide when they occupy contiguous lattice sites, and they can establish a water channel forming a transient dimer, exchanging their contents (reactants and/or products). Exchange of Reactants. Regardless of the presence or absence of product if both colliding droplets carried the same reactant, this reactant is redistributed in accordance with a crude concentration gradient principle: the reactant is transferred from the droplet with more reactants to the droplet with less reactants. In previous research,22-26 we considered that only one molecule of reactant could be interchanged in a single collision. In this work, we improved the simulation algorithm by introducing a new factor, k, which determines how many units of reactant could be transferred during a collision. If the more concentrated droplet carried a quantity of reactants greater than k, only k units of reactant could be interchanged to the droplet containing less reactants. On the contrary, if the quantity of reactants is smaller than k, all reactants are transferred, so that the initially more concentrated water pool became empty after the collision. This new parameter k can be called the reactant exchange parameter. Reaction. When two droplets containing different reactants collide and mass transfer takes place, both reactants locate inside the same water pool. Our simulation is concerned with an instantaneous reaction (A + B f P) in the aqueous core, and hence, the kinetics of the intramicellar reaction is not considered. This approximation is valid when the chemical reaction is very fast as compared to the interdroplet exchange rate. As it is wellknown in most cases, droplet communication is the ratedetermining step in particle formation.12 We can assume

that each collision between reactants gives rise to the formation of products. All units of products inside a single droplet were considered to be aggregated in a single particle (a cluster of P units). These aggregates of P units grow by a different mechanism (see below), giving rise to the observed final particles. Autocatalysis. As the reaction takes place, more droplets could contain products and reactants simultaneously. The interchange of reactants between two colliding droplets in the presence of products allows us to simulate an autocatalytic reaction, which will be catalyzed by the existing P aggregate. To simulate this phenomenon, it is assumed that when one of the droplets is carrying an aggregate, the reaction always proceeds on the aggregate. When both droplets are carrying aggregates, autocatalysis takes place on the bigger one. Therefore, we consider that a larger aggregate has a greater probability of playing as a catalyst because of its bigger surface (autocatalysis). This work is concerned with autocatalytic reactions. The case of no autocatalytic reaction was studied previously.23 Exchange of Products. As the reaction takes place, the exchange of P aggregates becomes more important, because more water pools carry products. At this stage, collisions between two droplets both containing aggregates are the most probable. The interchange of reactants and aggregates during the same collision is allowed. To decide the interchange criteria in this situation, it is important to point out two aspects. A. Surfactant Film Flexibility. The micellar dynamics is affected by the changing length of the oil phase.19,27 To introduce this phenomenon in our simulation, we can relate the flexibility of the surfactant film around the droplets and the ease with which channels communicating colliding droplets can form. Surfactant film flexibility therefore also places a limit on the size of the particles traversing the droplet-droplet channels. The influence of surfactant film flexibility is taken into account by varying a flexibility parameter (f) specifying a maximum particle size for transfer between droplets: P particles with more than f units are not allowed to pass from one droplet to another. In this way, a highly flexible film will allow the interchange of larger aggregates than a rigid film. B. Ripening. The ripening theory assumes that the larger particles will grow by condensation of material, coming from the smaller particles that solubilize more than the large ones. The possibility of ripening has been introduced in the simulation as follows: if a droplet containing an aggregate with a number of i units (Pi) collides with another droplet containing an aggregate with a higher number of P units (Pj), the smaller aggregate can be interchanged during a collision from the initial droplet to the droplet carrying the larger aggregate (Pi + Pj f Pi+j), provided the film flexibility allows this interchange. The simulation also allows modification of the droplet size. We have introduced in the simulation a parameter (q) that restricts the maximum number of products (and therefore the maximum particle size) that can be carried by a droplet. This influence was studied previously,25,26 so that in this work all droplets have the same size in each simulation. Simulation Model It is a well-known experimental result that the intermicellar exchange process has a great influence on the (27) Fletcher, P. D. I.; Robinson, B. H.; Bermejo-Barrera, F.; Oakenfull, D. G. In Microemulsions; Robb, I. D., Ed.; Plenum Press: New York, 1982; p 221.

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nanoparticle size.8,14,15 For a better understanding of the exchange process, we will focus on two factors that affect the exchange rate: the dimer stability, which depends on the intermicellar attractive potential, and the size of the channel communicating colliding droplets, which depends on the surfactant rigidity. Both factors have a great influence on mass transfer and, consequently, on the exchange rate constant (kex).28,29 The simulation procedure allows us to study the influence of both parameters on the final nanoparticle size. First, we will discuss how the dimer stability is included in the simulation. The larger the dimer stability, the longer two water pools stay together, and more reactants can be transferred during an effective collision. The reactant exchange parameter (k) determines how many units of reactant could be interchanged during a collision. A high value of k would also imply that the droplets have a high tendency to stay together, i.e., the stickiness parameter will be great. Therefore, the reactant exchange parameter (k) increases as the dimer stability increases, and consequently, the rate exchange constant (kex) will increase with k. The second point of interest is the size of the channel that communicates colliding droplets. It is well-known that the intermicellar exchange process includes the opening of the interfacial layer, governed by surfactant film flexibility. A highly flexible film will allow the interchange of larger aggregates of particles than a rigid film. We can include in this picture our film flexibility parameter (f), which limits the size of the particles traversing droplet-droplet channels. As the size of the channel that communicates colliding droplets is proportional to the surfactant film flexibility, the fact that the formation of larger particles is favored by ripening at high f values22,23 implies that the rate will be higher as f increases. Therefore, the effective rate constant (kex) for droplet communication will increase with f. On the other hand, the interdroplet material exchange includes different species: reactants and aggregates of products. Both species can be transferred from one droplet to another if the droplets stay together for enough time and if the size of the channel communicating colliding droplets is large enough. However, the interchange depends on the nature of these species. Because a reactant molecule is smaller than an aggregate, it could be assumed that the main factor that determines the reactant interdroplet transfer would be the dimer stability, and the channel size would not be so important in this case. On the contrary, this size channel would be significant when the interchanged material is a particle constituted by aggregation of some units of products, which have to be transferred as a whole. In our simulation, we can distinguish when the interchanged mass is a reactant and when it is a particle. The parameter k affects only the reactant exchange. In previous studies, it was considered that only one unit of reactant could be transferred during a collision.22-26 With the incorporation of this new parameter k in the algorithm, the interchange of several reactant molecules during a collision is allowed. It can be expected that this multiple interchange will affect the mechanism of nanoparticle formation and therefore the final particle size. Nanoparticle growth can take place via reaction on an existing aggregate (growth by autocatalysis) or via ripening (28) Zana, R.; Lang, J. In Microemulsions: Structure and Dynamics; Frieberg, S. E., Bothorel, P., Eds.; CRC Press: Boca Raton, FL, 1987; p 153. (29) Jain, T. K.; Cassin, G.; Badiali, J. P.; Pileni, M. P. Langmuir 1996, 12, 2408.

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Figure 1. Plot of the average particle size (〈s〉) vs the reactant exchange parameter (k) according to the proposed model. Curve a represents the behavior in a purely ripening process and b in a pure autocatalytic process. Curves f1 and f2 show the previsible behavior for two different film flexibilities: f1 < f2.

(growth by ripening). The influence of k in the autocatalysis process can be described as follows: k quantifies how many reactant molecules will be transferred in each effective collision, and these units will react instantaneously, being the products aggregated to the bigger particle. Consequently, the rate of growth is greatly influenced by the value of k. In addition, we can say that a high value of k implies a fast growth of the biggest aggregates by autocatalysis. Then, when the growth is mainly due to autocatalysis, it is reasonable to assume that an increase of k leads to an increase of the final particle size. On the contrary, growth by ripening does not depend on k because ripening only involves the interchange of aggregates. The general scheme of the described process is represented by the curves a and b in Figure 1, which shows the predicted behavior of particle size vs k. The f parameter determines the interchange of products. According to previous results, growth is preferentially by autocatalysis for low values of f, and growth by ripening is more important for high values of f.26 The minimum value of k is 1, which corresponds to the interchange of one unit of reactant during the collision. Previous studies show that the final particle size and the ripening contribution to the growth become smaller as the film flexibility decreases.26 An increase of k favors autocatalysis. Moreover, the influence of autocatalysis is greater if the film flexibility is smaller. Therefore, the existence of two different behaviors could be expected, depending on the value of k, due to the relative weight of autocatalysis and ripening in the whole growth process. Low values of k give rise to a slow autocatalytic growth, which implies that particles can grow mainly by ripening for any film flexibility. So, ripening contribution is greater as k decreases and larger particles are obtained for lower values of k. Therefore, the model leads to the existence of a minimum value of k (km). When k is smaller than km, ripening is the main contribution to growth. When k is greater than km, nuclei formed during the first stages of the reaction are larger than the interdroplet channel and they cannot be interchanged. Consequently, growth is mainly due to autocatalysis, which is more efficient as k increases and greater particles are formed. In light of these results, one can say that the weight of k and f is opposite, in such a way that the greater the growth by autocatalysis (larger k) the more difficult is the ripening and vice versa. The smallest size is obtained at the minimum, in which k is large enough to hinder the ripening but not so large to make autocatalysis very efficient. On the other hand,

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Figure 2. Simulation results showing the average particle size (〈s〉) vs reactant exchange parameter (k) for different values of reactant excess (x) and using two different film flexibilities: f ) 5 in panel A, and f ) 15 in panel B. Lines are only a guide to the eye.

it could be expected that the minimum will appear at higher values of k when the film flexibility increases because the autocatalytic contribution is smaller. Results and Discussion Figure 2 shows the change of the nanoparticle size with k obtained by simulation, using different surfactants (different f values) and different concentration ratios (x). One can observe that the largest particles are obtained using flexible films, which is attributed to a larger efficiency of surfactant to allow the growth of particles via ripening.23 On the other hand, and according to experimental results,15 nanoparticle size decreases for any value of surfactant film flexibility as the excess of one of the reactants increases. First, the influence of concentration ratio x on final particle size is discussed. In all cases, a tendency to a constant size when x is larger can be observed. This could be explained by taking into account that the limitant

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reactant concentration has a great influence on the final size of the nanoparticles: although it is allowed to exchange k units of one reactant during a single collision, only the real amount of the other reactant inside the colliding droplet will react to products. This means that for x > 1, one of the reactants is exhausted very early, so the reaction, and consequently the autocatalytic growth, is more difficult.26 In these cases, growth has to be mainly due to ripening, which is not affected by k, as can be observed in Figure 2 for x ) 4. This result supports the proposed model (see curve a in Figure 1). However, for x ) 1, both mechanisms (autocatalysis and ripening) take place, each being more or less important depending on the values of k and f, as we have discussed in the previous section. A second point of interest is the existence of a minimum obtained from our simulation results (Figure 2), which agrees with the expected behavior from the model (Figure 1). The displacement of this minimum to higher values of k when f increases can also be observed, due to the effective increase of the autocatalytic weight. For k < km, ripening is the most important way of growth because for small values of k only few reactants are transferred in each collision, and consequently, the autocatalysis contribution is not much. For k > km, autocatalysis is favored for any value of film flexibility. Therefore, our results allow us to separate both contributions, autocatalysis and ripening, to the whole growth process. From a practical point of view, it would be necessary to achieve the optimum combination of the channel size and the dimer stability (f and k parameters) in order to get small sizes. On this basis, we can predict that for a given surfactant (film flexibility fixed), there exists a determined value of k (i.e., a determined value of the dimer lifetime) that leads to the smallest particles. As a particular example, it is known that in AOT microemulsions, the increase of temperature gives rise to an increase of the dimer stability.30 Therefore, we can predict that larger particles will be obtained at high and low temperatures and that the smallest particles will be obtained using an intermediate temperature. Conclusions For chemical reactions very fast as compared to the interdroplet exchange rate, a model including the reactant exchange parameter k has been developed in order to explain the relative influence of the two mechanisms of growth on the final particle size. Consistency between the simulation results and the model supports the obtained conclusions. It has been shown that the nanoparticle size does not depend on k when the concentration excess is high enough and the ripening is responsible for this behavior. When there is not reactant excess (x ) 1), final nanoparticle size is hardly affected by k and f. In addition, it has been found that each value of f corresponds to an optimum value of k (km); that is, there exists for each surfactant a determined value of k that leads to the smallest particle size. LA0108407 (30) Fletcher, P. D. I.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1 1987, 83, 985.