Designing Bimetallic Nanoparticle Structures Prepared from

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Designing Bimetallic Nanoparticle Structures Prepared from Microemulsions F. Barroso and C. Tojo* Physical Chemistry Department, Faculty of Chemistry, University of Vigo, E-36310 Vigo, Spain ABSTRACT: Computer simulations were performed to study the different structures showed by bimetallic nanoparticles synthesized in microemulsions. The fact that a nucleus evolves to a particle by accumulating new layers implies that the sequence of deposition of the metals determines the final structure. As a result, if one of the metals precipitates before the other, the nanoparticle core is formed by the first metal, and the other metal forms the surrounding shell. The resulting segregation of the metals can be caused not only by a difference in the reduction rates of the metals but also by a difference in the nucleation rates. In agreement with experimental results, we demonstrate that the metal segregation resulting from the different critical nucleus sizes of both metals can be minimized by increasing local concentration inside a droplet. This can be reached simply by using higher concentrations and/or favoring a faster intermicellar exchange, that is, using surfactants with higher flexibility. These results are very promising for the design of the best synthetic conditions to obtain a specific nanoparticle structure.

I. INTRODUCTION The distribution of elemental components in a bimetallic nanoparticle has become not only a matter of fundamental science, but an issue for practical technologies. The presence of the second metal in a bimetallic compound modifies the physical and chemical interactions among various atoms and brings about changes on the structure and surface. This has a strong influence on the optical, magnetic, electronic, and catalytic properties of the nanoparticles. Specifically, in the field of catalysis, the reaction efficiency and selectivity depend on how catalyst constituents are arranged within the first few atomic layers from the surface of a nanoparticle. Catalyst activity is dictated by chemical composition, since the addition of a second metallic element often modifies the pure cluster by affecting both geometrical and electronic properties. Although progress in this field has been impressive in recent years, theoretical studies are scarce, and much has yet to be done in order to obtain better control of the nanostructure of these materials. In bimetallic nanoparticles, the fact that the nucleus evolves to a particle by accumulating new layers implies that the sequence of deposition of the metals determines the final structure. Because controlling metal distribution is crucial for improving the properties of bimetallic particles, it is important to elucidate the mechanism underlying the nucleation and growth of nanoparticles. A priori, the parameter which is considered the key factor to determine the segregation of the two metals in a bimetallic nanoparticle is the difference in the reduction rates of both metal salts. For a bimetallic system prepared by the simultaneous reduction of two metal ions, the ion with higher reduction potential has the priority in reduction: the metal with the faster reduction forms the core; © 2013 American Chemical Society

the other forms the surrounding shell. Therefore, a large difference in the reduction potential usually results in a core− shell structure, and a small difference leads to an alloy one. From experimental1,2 and simulation3 investigations, it is assumed that the difference in reduction potential of two metal ions may be the major factor determining the final structure of the particles. However, this argument cannot explain that metals with similar reduction potential, such as Pt/ Ag,4,5 Pd/Au,6 and Pt/Pd,7−11 have been obtained in a core− shell geometry. Also relevant to the discussion is the observation that clustering always takes a longer time than reduction,12 so many authors consider the chemical reaction as instantaneous. If reductions of the metal ions were instantaneous, the subsequent nucleation process would determine the sequence of deposition of the metals, defining the final structure: if nucleation rates of both metals are very different, the metal with the fastest nucleation rate will give rise to the majority of seeds from which nanoparticles are formed. These seeds will grow giving rise to a monometallic core, on which the slower metal could be deposited. With some reflection, one realizes that bimetallic nanocluster structure should be related to the difference between the nucleation rates of both metals. Wu et al.13 proposed that the number of Pd and Pt atoms required for the formation of nuclei (the critical number) might vary with the composition owing to the different interactions of Pt−Pt, Pd−Pd, and Pd−Pt. Yashima et al.8 found that most Pd particles appeared to be adsorbed on a Pt particle resulting in a core−shell aggregate, but they suggest a more rapid formation Received: May 14, 2013 Revised: June 26, 2013 Published: June 28, 2013 17801

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Homogeneous nucleation occurs when small crystalline regions form from structural fluctuations. The growth of these regions depends on a competition between a decrease in bulk energy (which favors growth) and an increase in surface energy (which favors diminution by spontaneous dissolution). Small crystals continually form by fluctuations but then frequently diminish in size due to the high surface energy. Growth becomes energetically favorable only when the clusters reach a critical size. Therefore, clusters must exceed a critical size determined by the competition between the aggregate curvature (Laplace pressure) and the free energy favoring the growth of the new phase. In other words, the nucleus critical size is the minimum size of a stable nucleus, which depends on the specific material. Although condensation processes inside a micelle are heterogeneous and a more complex mechanism of nucleation can be expected, the classical nucleation theory is still the available model. In microemulsions, nucleation requires the simultaneous presence, within a given micelle, of a sufficient number of atoms to reach local saturation, which must overcome the surface energy cost of forming a solid nucleus. This means that, for the nucleation to be effective, one micelle must carry enough material for the nuclei to reach a critical size. Below this size, nuclei are unstable and redissolve. The critical size of the nuclei depends on the reagent concentration and the surface energy of the solid−liquid interface, according to the equation:34

of Pd compared to Pt particles on the basis of the smaller size and amorphous character of the Pd particles. Likewise, Chen et al.14 inferred from XAS data that Pt atoms are partially segregated in the shell region, Pd−Pt alloyed atoms are located in the core, and that Pd atoms act as nuclei. From the discussion above, one can infere that a deeper understanding of the dependence of bimetallic nanoparticle geometry on nucleation rates is of fundamental importance. Previous simulation results showed that the core−shell particles obtained when both reductions take place at the same rate can be explained on the basis of a difference in the nucleation rates of both metals,15 which is directly related to the critical sizes. To design the synthetic route to obtain a nanoparticle with a particular metal distribution, one must keep in mind that the critical numbers of a given pair of metals cannot be modified, but the arrangement of elements depends critically on the preparation method and experimental conditions.2 In relation to the method, a variety of techniques have been used to prepare finely dispersed nanoparticles. One of the most extensively studied ways to obtain nanoparticles is the microemulsion method. From the pioneering research of Boutonnet and her co-workers,16 water-in-oil microemulsions have successfully been employed to produce a variety of nanoparticle shapes and sizes,17−20 including metals,21−23 silica24 and other oxides,22,25 polymers,18,26 semiconductors,27 superconductors,28 and particles with a core−shell structure.29−32 In this technique, small quantities of water are added to a solution of surfactant/oil. The resulting mixture, called water-in-oil microemulsion, consists of nanometer-size water droplets which are dispersed in a continuous oil medium and stabilized by surfactant molecules. The surfactant is accumulated in the oil−water interface; that is, on a microscopic level the surfactant molecules form an interfacial film separating the polar and nonpolar domains. The main function of the droplet nanoreactor is to provide a compartmentalized medium to prevent phase separation of the particles. The common approach used for the synthesis of bimetallic nanoparticles is the one pot method, which involves solubilizing the two metal precursors within the water pools (each metal in one microemulsion) and the addition of a reducing agent solubilized in a third microemulsion. The mixing of the three microemulsions results in the formation of bimetal nanoparticles inside the aqueous nanodroplets. The exchange of the reacting species is believed to occur by direct transfer between the water pools during the collision of the droplets. The exchange process occurs when micelles collide because of the Brownian motion and the attractive forces between micelles. These collisions result in fusion of the micelles, an exchange of the contents inside the droplets, and a redispersion of the micelles. Such dynamic colloidal templates are known to produce particles of low particle size, low polydispersity, and a rather clean surface of nanoparticles than those obtained via normal precipitation in aqueous systems. Nevertheless, it is not known how such templates control the size and shape of the resulting materials, and therefore, this issue still requires further examination. Nucleation is the process by which atoms (or ions) which are free in solution come together to produce a thermodynamically stable cluster. The most widespread modeling approach to study homogeneous nucleation is still the classical nucleation theory.33 Homogeneous nucleation, in which a molecular aggregate of the new phase begins to form within the mother phase, is hindered due to the presence of nucleation barriers.

ΔGnucl = Sγ + V ΔGcryst

(1)

where S and V are the surface and volume of the nucleus, γ the interfacial energy, and ΔG cryst is the free energy of crystallization. ΔGcryst depends on the reactant concentration and becomes negative as saturation is reached. Due to the very small size of micelles, local concentrations can be very high, favoring nucleation. Moreover, the interfacial energy is lowered by the adsorption of surfactant to the nuclei; that is, nucleation can be induced at the droplet interface by using surfactants/ cosurfactants that promote nucleation.35 From this picture, Ritcey et al.36 propose that reverse micelles constitute environments in which critical nucleus size is smaller than that associated with precipitation in simple aqueous solutions. Within micelles, stable nuclei composed of as few as 2−4 metal ions have been proposed for Ni2B37 and CdS,38 respectively. In line with our ongoing effort to evaluate the formation mechanism of simple39,40 and bimetallic3,15 nanoparticles in microemulsions, we have aimed here to investigate how to minimize the effects of critical size on metal segregation. The multitude of process parameters controlling the reactant exchange, particle formation, and growth during the fusion− fission process was taken into account in Monte Carlo computer simulations. Good agreement between experimental and simulation results3,41 supports the validity of the simulation model. As said above, the composition, morphology, and electronic structure of bimetallic nanoparticles are markedly affected by the preparation method and experimental conditions. For one particular preparation method (microemulsion route), and for one particular bimetallic particle (characterized by the critical numbers and reduction rates), the only way to manipulate metal distribution is varying the synthesis conditions. With the final goal of tuning the conditions for synthesizing specific bimetallic structures, we studied whether the difference in critical nucleus numbers of the metals can be attenuated by changing synthesis parameters such as reactant concentration and microemulsion composition. 17802

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micelles chosen randomly are allowed to collide (due to Brownian motion), fuse, and redisperse. Upon collision they can establish a water channel forming a transient dimer (fusion), exchanging their contents (reactants, products, and/or growing particles). Both ways of simulating the motion and collision lead to exactly the same results.42 The second method was used to simulate bimetallic nanoparticle synthesis because it is less time-consuming. 2.4. Time Unit Base. Initially, the time unit base was one Monte Carlo step, defined as the time taken for all droplets to move one step into one of their nearest neighbors. Droplets collided when they occupied contiguous lattice sites, allowing material exchange. In the present version, in each step, 10% of droplets are randomly chosen to collide, allowing material exchange. One Monte Carlo step is completed when the composition of colliding droplets is revised after collision according to the criteria described below. 2.5. Intermicellar Exchange Criteria of Reactants. When the two colliding droplets are carrying the same reactant, this reactant is redistributed in accordance with a concentration gradient principle: the reactant (metal salt or reducing agent) is transferred from the droplet with more reactants to the droplet with less reactants. The parameter kex,A determines how many units of reactant A+ could be transferred during a collision. If the more concentrated droplet carries a quantity of molecules greater than kex,A, a maximum number kex,A units of reactant A+ is exchanged to the less concentrated droplet. If the number of molecules to transfer is smaller than kex, concentrations inside both colliding droplets will be the same after collision. In order to take into account the material nature, size, and electric charge, the algorithm can distinguish a different value for each kind of reactant (kex,A, kex,B, and kex,R). In this paper we present results using kex,A = kex,B = kex,R = kex. 2.6. Chemical Reduction Rates. When two droplets containing different reactants collide and mass transfer takes place, both kinds of reactants can be located inside the same micelle, and the chemical reaction is possible. To include different reaction rates, only a percentage of v of reactants inside the colliding droplets gives rise to products. The fastest reaction corresponds to v = 1 (100% reactants transform in products); that is, an instantaneous reaction is considered. The chemical reaction rate is simulated by decreasing the value of v. The coexistence of reactant molecules (both metal salts and/or reductor) inside the same micelle is allowed, so the reactants which did not react remain in the water-pool, and will be transferred or will react in a posterior collision. Because a bimetallic nanoparticle is composed by two different metals, which reduction can occur at different rates, two different reaction rate parameters have to be considered. The reduction of the metal salt A+ to obtain metal A (A+ + R → A) is called vA, vA being the percentage of metal precursor A+ inside the colliding droplets which gives rise to metal atoms A. Likewise, the reduction of the metal salt B+ (B+ + R → B) is determined by vB. Because the chemical reaction rate strongly affects the nucleation rate43 and can interfere in the interpretation of the critical nucleus influence, in this study we monitored results considering both reduction rates equal and instantaneous (vA = vB = 1). This approximation is valid when the chemical reaction is very fast as compared to the interdroplet exchange. As it is well-known, in most cases droplet communication is the rate-determining step in particle formation.44

In this paper we give a computer simulation perspective, performing a comprehensive analysis of the structural effects of synthesis conditions.

II. MODEL AND SIMULATION METHOD A Monte Carlo computer simulation was run to simulate the kinetic course of the reaction. 2.1. Microemulsion Droplets. The microemulsion structure is represented as a set of droplets randomly located on a three-dimensional lattice, which can move and collide with each other. Periodical boundary conditions are enforced at the end of the lattice. Each simulation begins with a random distribution of three sets of microemulsion droplets. The onepot method is simulated by mixing equal volumes of three microemulsions, containing the metal salt A+, the metal salt B+, and the reductor R, respectively. Thus the simulation is initialized with a given total number of droplets N: N = N (A+) + N (B+) + N (R)

(2)

where N(i) are the number of droplets carrying reactant i (i = A+, B+, R). In this study a φ = 10% portion of the space is occupied by droplets. 2.2. Initial Reactant Distribution. The number of reactant species is distributed throughout the droplets using a Poisson distribution: The number of each reagent per droplet is referred to as ni, where i represents one of the metal salts or the reducing agent. P(ni) =

⟨ni⟩ni exp( −⟨ni⟩) ni!

i = A+, B+, or R

(3)

where P(ni) is the probability that a droplet contains ni reactants (A+, B+, or R) whose average occupancy is ⟨ni⟩. In this study we present results using ⟨c⟩ units of each kind of reactant inside the droplets, that is, [A+] = [B+] = ⟨c⟩ = 4, 32, or 128 metal ions in a droplet, which corresponds to 0.02 M, 0.16 M, and 0.64 M, respectively. Molar concentrations were calculated using the droplet radius r of a 75% isooctane/20% tergitol/5% water microemulsion (r = 4 nm, obtained by DLS). From this radius, and assuming spherical shape (Vdroplet = 4πr3/ 3), the molar concentration of a droplet containing four atoms is calculated from ⟨c⟩ = 4 ×

atoms 1 × droplet Vdroplet(L·droplet−1)

1 = 0.02 M NAv(atoms· mol−1)

(4)

where NAv is the Avogadro’s number. The reducing agent concentration ⟨cR⟩ was always double that of the metal precursors. 2.3. Motion and Collision. In the previous algorithm used to simulate the preparation of simple nanoparticles (nonbimetallic), droplets were allowed to perform random walks to nearest neighbor sites by choosing at random the direction of the motion at each step.39,40 The length of each step was constant and equal to one length lattice unit. This random walk was subject to the exclusion principle so that the trial movements resulting in droplet overlapping are excluded. Cyclic boundary conditions are enforced at the ends of the lattice. Droplets collided when they occupied contiguous lattice sites. To save computation time, the model was improved by simulating the movement and collisions as follows: Two 17803

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2.7. Critical Nucleation Sizes. According to La Mer’s homogeneous nucleation and growth model,45 there will be a critical nucleus size which is characteristic of the specific material considered. The nucleus critical size represents the minimum size of a stable nucleus. Particles larger than the critical nucleus will inevitably continue to grow, but when the nucleus is smaller than the critical size, spontaneous dissolution can occur. This process is introduced in the simulation by including a parameter n* (the critical nucleus size), as follows: if the number of reduction products (A or B metals) inside the same droplet is smaller than n*, they are considered free inside the droplet, so they can be interchanged one by one during a posterior collision, this interchange being governed by the kex,P parameter defined below. On the contrary, if the number of reduced metal atoms inside one droplet is equal or greater than n*, they come together forming a stable growing nucleus. This nucleus can only be transferred between droplets as a whole, being this exchange limited by the size of the intermicellar channel (f parameter, see below). Considering the formation of a nucleus, the total Gibbs energy might vary with the compositions due to the different interactions of metal−metal (A−A, B−B, and A−B). So the two different metals (A and B) composing a bimetallic nanoparticle can require for the formation of a nucleus a different minimum number of atoms. To characterize two different metals, the algorithm distinguishes two different critical nucleation numbers (nA* and nB*). Likewise, heterogeneous nucleation (nucleus composed by two different metals) is also considered, by means of the nAB* parameter, defined as the minimum number of metal products (A or B) inside the same droplet needed to form a heterogeneous nucleus capable of further growth. On the basis that cohesive energies of the atoms within nanoparticles and small clusters are composition-, site-, and structure-dependent,46,47 one can assume that critical size can be different in homogeneous and heterogeneous nucleus. As an example, nAB* = 4 means that A3B, A2B2, or AB3 clusters are considered as a nucleus, but this does not imply that A4 or B4 also become a nucleus, because homogeneous nucleation obeys to nA* or nB*, which are not necessary equal than nAB*. Thus, in the absence of any pre-existing nuclei, if the number of reduced atoms verifies one of the following conditions:

results using the same value for all free units (reactants and metal products): kex,P = kex. Thus, the exchange criteria for reactants (A+, B+, R) and nonaggregated products (A, B) can be mathematically described as follows: If nbj (i) > nbk (i), then nja(i) = njb(i) − l nka(i) = nkb(i) − l ⎡ n b( i ) − n b( i ) ⎤ j k l = min⎢ , kex ⎥ ⎢⎣ ⎥⎦ 2

with i = A+, B+, R, A, B, and j, k as the index for the colliding droplets. The superscripts b and a describe micelle contents before and after collision, respectively. Whenever a metal atom is exchanged to a droplet carrying a nucleus, this atom is added to the nucleus, giving rise to a growing particle (metal aggregate). 2.9. Autocatalysis. As the synthesis advances, more micelles contain reactants, and metals aggregate simultaneously. The exchange of reactants between two colliding droplets in the presence of a growing nucleus allows us to simulate an autocatalytic reaction on the growing nanoparticle surface. Heterogeneous catalysis commonly depends on the adsorption of a reactant on to the surface of a metal. The reaction rate is expected to increase as the extent of surface coverage increases; that is, the larger the surface area, the faster the reaction. To simulate this phenomenon, it is assumed that, when one of the droplets is carrying an aggregate, the reaction always proceeds on the aggregate because of its catalytic role. In addition, the reaction rate will be double when it is smaller than one. In the case that both colliding droplets are carrying aggregates, autocatalysis takes place on the bigger one. In this way, it is assumed that a larger particle has a greater probability of playing as a catalyst because of its larger surface. Reaction in the absence of autocatalysis was studied previously.39 This work is concerned with autocatalytic reactions. 2.10. Intermicellar Exchange Criteria of Growing Particles. Collisions between two droplets both containing growing particles are most probable as the synthesis advances. The exchange of reactants, free metal atoms, and growing particles during the same collision is allowed. To explain the exchange criteria of growing particles (metals aggregates), two aspects must be taken into account: 2.10.1. Surfactant Film Flexibility. The intermicellar dynamics strongly depend on microemulsion composition (surfactant, length of the oil phase, cosurfactant).48−54 Specifically, the elasticity of the film, which determines the material interdroplet exchange, varies with the surfactant, the presence of additives, and the length of the oil phase.48,49,53,54 A basic property of a surfactant film, called flexibility, is its ability to depart from the optimal curvature. Surfactants can be flexible or rigid, depending on the strength of the interactions at both sides of the interface. These interactions determine the material intermicellar exchange process, because it implies the opening of the interfacial layer: The rate of communication between droplets is very fast,55 and the exchange can only take place when an energetic collision between two droplets is able to establish a water channel between the droplets,55 forming a transient droplet dimer.56 The dimer formation requires a change in the curvature of the surfactant film,56,57 so it is

nj(A) ≥ nA* nj(B) ≥ nB* * nj(A) + nj(B) ≥ nAB

(6)

(5)

the atoms come together and they are seen as seed nuclei, which are capable of growth by autocatalysis or ripening (see later). 2.8. Intermicellar Exchange Criteria of Free Metal Atoms. If the number of metals inside the same water pool does not reach the critical nucleus size value, they remain free (nonaggregated) inside the micelle. During a posterior collision these free metals can be exchanged one by one. The product exchange parameter (k ex,P ) governs this exchange, by quantifying how many atoms of product (A or B metal) can be transferred during an intermicellar collision. Likewise, the characteristics of each metal can allow passing the interdroplet channel easier or more difficult, so the interdroplet exchange parameter could be different. In this study we only present 17804

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with λeff being an efficiency factor taking into account only successful exchanges (which depends on film flexibility f), N0 the initial number of droplets, and V the volume.71 The encounter rate constant, ken, can be estimated by the Smoluchowski equation,

energetically unfavorable. In the formulation of microemulsions, where the free energy cost for creating the interfacial area has to be compensated by a large entropic term, a flexible surfactant allowing curvature fluctuations is required.58,59 Surfactants which strongly adsorb at interfaces and efficiently lower the interfacial tension have a very hydrophobic part (long alkyl chain) and a very hydrophilic headgroup;60 they are rigid surfactants. To introduce this phenomenon in the simulation, we 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: particles composed by 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 metal aggregates than a rigid film. 2.10.2. Ripening. A particular coarsening process which has to be considered is Ostwald ripening. The particle size changes by solubilization and condensation of material. Ostwald ripening assumes that the largest particles will grow by condensation of material, coming from the smallest particles that solubilize more readily than larger ones. The possibility of ripening has been introduced in the simulation as follows: if a droplet containing i units of product (Pi, being P one of the two reduced metals) collides with another droplet with a higher number of P units (Pj), the smaller aggregate can be exchanged during a collision from the initial droplet to the droplet carrying the larger one (Pi + Pj → Pi+j). This mass transfer is only allowed if the channel size f is greater or equal to Pi+j. This criterion is only dependent on the aggregate size; that is, it does not take into account the composition (A or B metals). 2.11. Droplet Size. The growth of nanoparticle via coagulation may be limited by the size of the drops because a substantial amount of energy would be required to increase the drop size, as the surfactant film covering the drop has a finite bending modulus. When the microemulsion technique was introduced, it was thought that this would allow particle size to be controlled just by controlling the droplet size. However, several different types of behavior have been observed when the droplet size increases: increasing of particle size,61−63 bimodal distributions,64,65 and essentially no control by droplet size.66,67 Droplet size is simulated by a parameter which restricts the maximum number of products which can be carried by a droplet. This influence was studied previously,68 so in this work droplets do not restrict nanoparticle growth. 2.12. Modeling Material Interdroplet Exchange. For a better understanding of the surfactant role on the nanoparticle synthesis in microemulsions, we will focus our attention on two factors determined by the surfactant: 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.69 The droplet exchange constant kex is related to the collision or encounter rate constant (ken) of equally sized droplets due to Brownian motion.50,70,71 This correlation is given by

kex = λ eff ken

N0 V

ken =

8kBT = 16πNAvDr 3η

(8)

where kB is the Boltzmann constant, T is the absolute temperature, η is the viscosity of the medium, NAv is the Avogadro’s number, D is the diffusion coefficient, and r is the droplet’s radius. So, the collision rate is directly related to temperature. As an example, for microemulsion droplets at 25 °C moving in a typical oil, like n-heptane, ken ≈ 1010 M−1 s−1.51 The collision can be followed by another process in which the droplets fuse together, giving rise to a transient dimer, which allows material exchange. As said above, dimer formation is a slow process because it needs the opening of the micellar walls and the inversion of the surfactant film curvature. The interface rigidity was dependent upon the nature of the surfactant and oil as well as temperature;72 that is, the temperature dependence of microemulsions arises from the temperature sensitivity of the preferred monolayer curvature.73 As a consequence, the transient dimer has a T-dependent lifetime, which can be evaluated according to:74 τen = k −en−1 = 4r 2/6D = 4πNAvηr 3/RT

(9)

Also for droplets of radius r = 5 nm at 25 °C moving in nheptane, τen ≈ 0.15 μs. All parameters in eqs 7, 8, and 9 are constants for a given microemulsion at room temperature. The dimer stability is included in the simulation as follows: The larger the dimer stability, the longer two water pools stay together, and more material can be transferred during a collision. The exchange parameter kex determines how many units of reactant and/or nonaggregated products could be interchanged during a collision. A high value of kex would also imply that the droplets have a high tendency to stay together. Therefore, the exchange parameter kex increases as the dimer stability increases and consequently the rate of intemicellar exchange. In relation to the size of the channel communicating colliding droplets, it should be noted 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 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 which 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 values39 implies that the rate will be higher as f increases. Therefore, the effective rate constant for droplet communication will increase with f. In the model the f parameter is related to channel size:70 a value f = 30 would imply a “permeation channel” (the minimum section inside the fused dimer) of approximately 6−10 Å, assuming that 30 metal atoms are aggregated in a spherical shape. For f = 5 one can obtain a permeation channel of about 1−2 Å. From an experimental point of view, it is interesting to note that good agreement between simulation and experimental results was obtained when a rigid microemulsion, such as AOT/n-heptane/water, is related to f = 5, kex = 1 parameters.39 Likewise, results obtained

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Figure 1. Number of particles versus the percentage of one of the products (A), from the nanoparticle core to the outside (layer by layer) using two different values of the critical nucleus number of the metal with a faster nucleation (n*A), and keeping constant the critical nucleus number of the slower nucleation metal (n*B = 9) and the heterogeneous nucleation (n*AB = 4). Synthesis conditions: reactant concentration ⟨cA⟩ = ⟨cB⟩ = 4, ⟨cR⟩ = 8, film flexibility f = 5, kex = 1, no restriction by droplet size, instantaneous reduction rates. (A) n*A = 1; (B) n*A = 3.

predesigned structure, we study how the metals segregation in a bimetallic nanoparticle due to a difference in critical nucleus numbers can be modified by changing reactant concentration and surfactant flexibility. With that purpose in mind, the effect of a difference in nucleation rates on the bimetallic nanoparticle structure was studied in the first place. Effect of Critical Size Difference on Nanoparticle Structure. A small value of the critical nucleus size implies that a high number of nucleus seeds appear quickly; that is, the nucleation rate is faster as the critical nucleus is smaller.15,41 Therefore, the metal with a higher nucleation rate will give rise to the majority of seeds from which nanoparticles will be formed. These seeds will grow giving rise to a monometallic core, on which the slower metal is deposited. As a consequence, the bimetallic nanocluster structure is directly related to the difference between the nucleation rates of both metals: a large difference in the nucleation rates of the two metals results mainly in a core−shell structure, and a small difference in the nucleation rates leads to an alloy one, as can be observed in Figure 1. This Figure shows simulation results using different combinations of values of the critical nucleus numbers and keeping the other synthesis variables constant (reactant concentration, surfactant flexibility, droplet size). To isolate the influence of critical sizes, reduction rates of the metals are kept equal and instantaneous (vA = vB = 1, that is, 100% of reactants inside the colliding droplets gives rise to products). To describe the structure, the sequence of metal deposition of each nanoparticle is stored and divided in 10 concentric layers. The histograms showed in Figure 1 show the average composition layer by layer. Likewise, the number of particles containing different percentages of one of the metals (A) is monitored from the nanoparticle core to the outside. From these figures one can observe how the average composition varies from the beginning of the synthesis (core, inner layer) to the end (shell, outer layer). Considering the heterogeneous nucleation as the faster process does not present structural interest, because if mixing is favored from the beginning, an alloy structure will be obtained under all experimental conditions. The homogeneous nucleation is favored if one the metals exhibits a faster nucleation than the other (n*A < n*B) and the heterogeneous nucleation (n*A