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Monte Carlo Simulation of the Size and Composition of Bimetallic Nanoparticles Synthesized in Water in Oil Microemulsions Daniel G. Angelescu,*,† Luis M. Magno,‡ and Cosima Stubenrauch‡,§ Institute of Physical Chemistry, I. G. Murgulescu Romanian Academy, 060021 Bucharest, Romania, School of Chemical and Bioprocess Engineering, UniVersity College Dublin, Belfield, Dublin 4, Ireland, and Institut fu¨r Physikalische Chemie, UniVersita¨t Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany ReceiVed: August 19, 2010; ReVised Manuscript ReceiVed: October 20, 2010
Structural features of bimetallic nanoparticles synthesized in w/o microemulsion have been examined by using a coarse model solved by Monte Carlo simulations. The microemulsion was modeled as spherical droplets containing either two metal salts or reducing agent, and the processes occurring during the collision of the droplets and leading to nucleation and growth of the bimetallic nanoparticles were determined by a set of variables. The bimetallic nanoparticle structure is mainly determined by the difference in the reduction rates of the two metal ions and the excess of reducing agent. An intermetallic structure is always obtained when both reduction reactions take place at about the same rate. When the metal ions have very different reduction potentials, a core-shell to intermetallic structure transition is found at increasing the excess of the reducing agent. An enhancement of the intermetallic structure at the expense of the core-shell, one can be obtained either by decreasing the concentration of both metal salts or by increasing the interdroplet exchange rates. Predictions of the Monte Carlo simulations at large differences in the reduction rates of both metal ions compare well with the experimental data on the size and structure of PtBi nanoparticles, leading to prediction of the experimental conditions for designing specific bimetallic structures. 1. Introduction Great interest has recently been devoted to bimetallic nanoparticles because of their perspectives in applications such as catalysis1,2 and optoelectronic devices.3,4 The presence of the second metal in a bimetallic compound is of primary importance as it modifies the physical and chemical interactions among various atoms and brings about changes on the structure and surface, thus generating new properties of the bimetallic materials. Controlling the structures of the bimetallic nanoparticles-in the form of either core-shell nanostructures or (dis)ordered alloys-is crucial to improving their properties.5,6 Different methods and approaches have been used for synthesizing bimetallic nanoparticles, for example, single spontaneous deposition,7,8 thermal annealing,9,10 sputtering,11 and solvochemical reduction.12-14 An alternative method making it possible to control the size and composition of bimetallic nanoparticles is the microemulsion route. Boutonnet et al. showed that metallic nanoparticles can be obtained by mixing two water-in-oil (w/o) microemulsions of equal structure, one containing one or more metal salts and the other containing a strong reducing agent.15,16 By exchanging the droplets contents via a fusion-fission mechanism, the reduction reaction between the reactants is enabled and the nanoparticles start to grow. The microemulsion route allows better control over the size of the bimetallic particles because they are formed at low temperatures, whereas the other methods usually require higher temperatures where large particles are inherently formed. Moreover, the microemulsion method is believed to be capable of providing some control over the * To whom correspondence should be addressed. † I. G. Murgulescu Romanian Academy. ‡ University College Dublin. § Universita¨t Stuttgart.
composition of the nanoparticle via the initial ratio of the metal precursor concentrations in the water droplets.17,18 Intermetallic nanoparticles have been reported mainly for metals with similar reduction potential, such as PtAg,19 PtAu,20 and PtPd,21,22 whereas core-shell structures are expected when the difference in the reduction potential of the two metal salts becomes important. On the other hand, the preparation conditions also play an important role in defining the preferred bimetallic structures. Hence, both AgAu nanoalloy23 and AgAu core-shell particles have been synthesized via the microemulsion route. In the latter case, the core consists of Au and the shell of Ag.24 As regards electrocatalysis, one of the challenges is to obtain ordered intermetallic phases via metal salts, which have very different reduction potentials, as is the case for the compounds PtBi and PtPb.25,26 It has recently been shown that not only Pt nanoparticles but also intermetallic PtPb and PtBi nanoparticles can indeed be synthesized via microemulsions and that it is even possible to control their size and composition.27-31 We are convinced that the development of the microemulsion route as well as a thorough understanding of the formation mechanism of bimetallic nanoparticles is crucial to controlling the nanoparticle size and structure. As many parameters have to be taken into account for controlling the properties of bimetallic nanoparticles, the identification of the important ones should be carried out by computer simulations. Over the past few years, several models of monometallic nanoparticle growth have been developed,30,32-34 and in several cases, the simulation results have been directly compared with experimental results.30,33,35,36 The present work focuses on Monte Carlo simulations for investigating the properties of the bimetallic nanoparticles obtained via the microemulsion route. On the basis of the modeled mechanism for the bimetallic nanoparticle formation, we will attempt to elucidate the role of the reduction rate of the
10.1021/jp107863y 2010 American Chemical Society Published on Web 11/23/2010
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njk(i, 0) ) min[njk*(i), njk(i)] where i ) A1, A2
two metal ions as well as of the interdroplet material exchange on the size and structure of the resulting nanoparticles. 2. Model and Particle Characterization 2.1. Model. The system modeling the nanoparticle synthesis via microemulsion route is similar to that previously reported by Lo´pez-Quintela et al.32,34,37-42 and related to the models developed by Bandyopadhyaya et al.33,35,43-45 and Kumar et al.46 The microemulsion structure is assumed as spherical water droplets dispersed in a continuous oil phase. The nanoparticle precursors are distributed among the droplets as follows: The two metal ions, A1 and A2, are initially located in the droplets of one microemulsion, whereas the reducing agent B is found in the droplets of a second microemulsion. Droplets are all randomly placed in the 3D simulation box, and the periodical boundary conditions are applied in x-, y-, and z-directions (the box is multiplied in all three directions). The mean number of each precursor per droplet is referred to as nreact(i), where i represents A1, A2, or B, and the precursors are distributed among the droplets according to a Poisson distribution as
njk(B)
and
)
∑ l)1
4.
nreact(i)n(i) P[n(i)] ) exp[-nreact(i)], i ) A1, A2, or B n(i)!
(1) where P[n(i)] is the probability that a droplet contains n(i) reactants. The simulation algorithm involves the droplets that are subjected to random translational displacement. They have an exclusion volume so that the trial movements resulting in droplet overlapping are excluded. Nonetheless, the corresponding reactants are allowed to be exchanged, reduced metal(s) are allowed to form, and bimetallic particles are allowed to grow during the overlapping process. The rules that model those processes are presented in the following. 1. The species existing in the droplets are (a) metal ions A1 and A2, (b) reducing agent B, (c) atoms of the reduced metals A1(0) and A2(0), and (d) nucleus (seed) of the reduced metals A1,m(0)A2,n(0), where m and n stand for the number of atoms of each reduced metal in the nucleus. 2. When the two colliding droplets carry components that do not react with each other [metal ion(s), reduced metal atoms, reducing agent, or ion(s) + reduced metal(s) atoms, reducing agent + reduced metal(s) atoms], species will be moved from a droplet containing a higher number to the droplets containing a lower number of species according to the concentration gradient. The atoms exchange process is controlled by the variable kex(i). At kex(i) ) 0, no exchange of i type atom occurs, whereas at kex(i) ) 1.0, the exchange evens out the concentration in the two droplets. For example, kex(i) ) 0.8 means that 80% of the atom concentration difference between the two droplets is evened out during the collision event. 3. Provided that the colliding droplets carry reacting species, the ions are reduced according to the variable Vr(i) (with i corresponding to metal ions A1 and A2), which represents the probability of obtaining one reduced metal atom from each pair metal ion-reducing agent molecule available in the colliding droplets. Hence, the fastest reaction corresponds to Vr(i) ) 1.0, that is, metal ions are reduced to the largest possible extent, while at Vr(i) < 1.0, only parts are reduced. Thus, one considers the number of reduced atoms in two droplets j and k upon collision, njk(i,0), to be represented by
njk*(i)
5.
6.
7.
(2)
{
1, Vr(i) < ξ 0, Vr(i) > ξ
njk(i) represents the number of metal ions of type i and njk(B) the number of reducing agent molecules in the two droplets. The pair metal ion-reducing agent molecule produces a reduced metal atom of type i if Vr(i) is smaller than ξ, where ξ is a random number between 0 and 1. When both reducing reactions are possible, the metal ion type is decided randomly before the reduction of each atom. The resulting reduced atoms A1(0) and A2(0) are subjected to rules 4, 5, and 6, whereas the remaining nonreacted molecules are not allowed to exchange according to rule 2. The variable critical nucleus, ncrit, defines the number of reduced atoms that may irreversibly form a stable nucleus. The formed nuclei may contain atoms of either one or of both metals, and the model assumed that the critical value ncrit of the nucleus A1,m(0)A2,n(0) is independent of the nucleus composition, that is, the m, n atom numbers. If the critical size ncrit is not exceeded, the nucleus is considered to be “unstable” and breaks up spontaneously to produce atoms. If there are no nuclei in the colliding droplets, the reduced atoms are interchanged with the exchange rate kexprod(i) and according to rule 2. At njk(i,0) > ncrit, the nuclei are seen as seed nuclei, which are capable of growth by autocatalysis or coarsening (see rules 5, 6, and 7). Coarsening is a reduction in the number of particles and a corresponding increase of their mean size. The two possible pathways for coarsening are either Ostwald ripening, i.e. growth of larger particles on the expense of smaller ones by transport of material, or Smoluchowski ripening, i.e. diffusion-mediated coagulation of particles. In the present case it is difficult to tell which of the two is the dominant process as the solubility of individual metal atoms in the oil phase is not known (Ostwald ripening would only be possible if they were soluble). When nuclei are present and at njk(i,0) < ncrit, a process known as autocatalysis37 or coalescence45 may occur. According to this process, the reduced atoms are assigned to the largest existent nucleus irrespective of the atom metal type. At njk(i,0) > ncrit and in the absence of any pre-existent nuclei, a new nucleus is formed. If there are already nuclei in colliding droplets, the autocatalysis also occurs, which means that the pre-existent nucleus increases at the expense of the formation of new nuclei. The autocatalysis does not take into account the type of the reduced atoms so that the reduced atoms A1(0) may bind to the a nucleus containing A2(0) atoms and vice versa. The nuclei are exchanged by the process referred to as coagulation45 or Ostwald ripening.37 The two nuclei in the colliding droplets give rise to a single nucleus when the smaller nucleus contains less than f reduced atoms. We thus define the condition under which the smaller nucleus can pass the channel, which connects the colliding droplets. Exchanging bigger nuclei would require wider channels, which, in turn, should be reflected in a more flexible surfactant film at the oil-water interface. Thus, one can argue that the parameter f is related to the surfactant film flexibility (the larger f the more flexible
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the film). Again, the parameter f does not take into account the nucleus composition. The simulations were performed using a Monte Carlo/molecular dynamics/Brownian dynamics simulation package.47 2.2. Characterization of Bimetallic Particles. The outcome of the MC simulations is given by three parameters that describe the properties of the nanoparticles. (a) The size distribution function, P(d), describes the distribution of the nanoparticle diameters. The diameters are calculated on the assumption that the nanoparticles are spherical and that their densities are the same as in the bulk crystalline phase. Thus, the particle diameter is evaluated according to
dj )
3
∑
6 N (i)V(i) π i)1,2 j
(3)
where Nj(i) stands for the number of atoms of type 1 and 2 per nucleus j and V(i) for the atomic volume of the two reduced metals. (b) The composition distribution function, P(w), describes the distribution of the composition. The composition is given by the weight of one of the reduced metals in the nucleus, that is
wj )
Hj )
{
∑ l
|[
1 H Nj(1) + Nj(2) j
size of the simulation box (nm) radius of the droplet (nm) number of droplets containing the two metal salts and reducing agent, respectively critical nucleus ncrit atomic volume V(A1), V(A2) (nm3)
139 × 139 × 139 2a 5000, 5000 10 0.0155b
a
Volume fraction of droplets in simulation box is 0.123 and thus larger than in the experimental systems; the simulation outcome did not depend on the droplet density, and the large volume fraction was chosen to save computational time. b Corresponds to Pt atomic volume.
At this point, it is noteworthy that the h parameter does not allow distinguishing an onionlike structure from a typical core-shell structure (one core surrounded by a single shell), in both cases, one obtains a h value of 1.0. We stress also that the coarsened model does not aim at simulating the crystal nucleation, and thus, the parameter h does not provide any information about whether the homogeneous intermetallic structure are chemically ordered or disordered phases. The values of the parameters used for the simulations are summarized in Table 1. 3. Results
Nj(1) Nj(1) + Nj(2)
(4)
(c) The homogeneity distribution function, P(h), where h is defined as
hj )
TABLE 1: General Data of the Model Used in MC Simulations
(5a)
|
Nj,l+1(1) - Nj,l(1)] - [Nj,l+1(2) - Nj,l(2)] ,
nucleus formation and autocatalysis Hj + Hk, Ostwald ripening, nucleus k adheres to nucleus j
(5b)
In eq 5b, l stands for the growth step (other than coarsening) and Nj,l(i) is the number of reduced metal atoms i in the droplet j at the growth step l. In the case of coarsening, the homogeneity parameter of the condensing nuclei is transferred to the growing nucleus. Nj(i) in eq 5a represents the number of reduced atoms i in the droplet j for the nucleus attaining the largest possible size (the nucleus does not grow anymore either by autocatalysis or coarsening). In other words, the homogeneity hj of a nucleus j is the sum over the growing steps of the excess of metal atoms, which is subsequently normalized to the final number of both metals atoms in the nucleus j. Thus, one obtains hj ) 0 for a homogeneous intermetallic structure where both atom types contribute equally to each growing step, while hj reaches 1 for a core-shell structure where the binding of the second metal type atoms starts after the growth of the nuclei of the first metal type has ceased. The quantity h can be used to assess qualitatively the extent to which the nanoparticles have either a homogeneous or a core-shell structure.
To investigate the main factors that determine the size and structure (composition and homogeneity) of bimetallic nanoparticles, the influence of five different parameters was studied. The results will be presented and discussed in the following. 3.1. Effect of the Reaction Rate. When the microemulsion water droplets contain two metal ions, the obvious key parameter controlling the nanoparticle composition and homogeneity is the rate of the chemical reduction, which reflects the different reduction potentials of the metal salts. Simulations were carried out using a constant and high reduction rate of the first metal ion, Vr(A1) ) 1.0, and different reduction rates of the second metal ion, Vr(A2). The effect of decreasing Vr(A2) from 1.0 to 0.05 is illustrated in Figure 1. The results are presented as contour plots of the distribution functions of the composition w and homogeneity h. When both reduction rates are equal and attained the highest possible value, that is, Vr(A1) ) Vr(A2) ) 1.0, h is close to 0 (see Figure 1a), which means that an intermetallic structure is obtained. At the same time, most of the nanoparticles consisted of a 1:1 metal mixture (w ) 0.5). Note that there are some particles that have a less pronounced intermetallic structure (h > 0.2) despite the fact that both metal ions were allowed to be reduced at the same rate. This is due to the fact that the metal ions were distributed among the droplets according to the Poisson distribution. Lower values of homogeneity h are expected when the metal salts and the reducing agent are evenly distributed in the droplets prior to the start of the synthesis. On decreasing the reaction rate Vr(A2) down to 0.5 (Figure 1b), a pronounced change in the nanoparticle structure is observed. First, the h parameter increased to around 0.4, which means that the nanoparticles are no longer intermetallics but rather mixtures of disordered and core-shell structures. As regards the composition, one sees that most particles still contain the same amount of both metals. However, the increase of the h value is accompanied with a broader distribution of the nanoparticle composition (larger range of w values). Furthermore, the particle densities found at h > 0.8 and w < 0.2 can be attributed to nanoparticles containing almost
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Figure 1. Contour plot of the distribution functions of the composition w and homogeneity h of bimetallic nanoparticles obtained at the reaction rates of Vr(A1) ) 1.0 and Vr(A2) ) 1.0 (a), 0.5 (b), 0.2 (c), and 0.05 (d). The mean numbers of metal salts and reducing agent molecules per droplet are nreact(A1) ) nreact(A2) ) nreact(B)/2.0 ) 50, and ncrit ) 10, f ) 15, and kex ) kexprod ) 1.0. Color code: high number of particles (blue), intermediate number of particles (red), and zero number of particles (white).
exclusively the metal with the faster reduction rate. Decreasing the reduction rate even further (Figures 1c), one observes an additional further increase of the h parameter, which can be understood as a progressive replacement of the intermetallic with the core-shell structure. The results also show that nanoparticles become more and more polydisperse in terms of composition w if the slowest reaction rate decreases. The densities found at the composition w < 0.3 or w > 0.7 indicate that there are nanoparticles that contained preponderantly either the metal with the fastest reduction rate or that with the slowest reduction rate. When Vr(A1) ) 1 and Vr(A2) ) 0.05 (Figure 1d), a h value of 0.9 is obtained, which corresponds to a core-shell structure. This result demonstrates that the reduction of the A2 metal ion mainly takes place after completion of the A1 reduction. Nevertheless, these A2 atoms rather bind to the pre-existent nucleus containing the reduced A1 atoms via autocatalysis than form new nuclei because the w composition lies mainly between 0.4 and 0.6, similarly to the cases when 1.0 < Vr(A2) < 0.05. It is worth mentioning that the particles shown in Figure 1 had a mean particle size of 1.4 ( 0.2 nm independent of the reaction rate Vr(A2). This is most likely due to the fact that nreact > ncrit and nreact > f. Under the first restriction (nreact > ncrit), a large number of seed nuclei are formed regardless of the reaction rate Vr(A2) because there are enough A1 reactant atoms in the droplets to nucleate after reduction. Once these initial nuclei are formed, the second condition (nreact > f) causes a growth via autocatalysis of either A1 or A2 atoms to dominate over coarsening. At nreact < ncrit, we would expect the formation of fewer seed nuclei. When nreact(A1) ) nreact(A2) ) nreact(B)/2.0 ) 7, that is, nreact < ncrit, while all other parameters were kept constant, we found that the seed nuclei grew at the same extent so that the mean particle size was ∼1.2 nm when Vr(A2) decreased from 1.0 to 0.05 (see Figure S1 in the Supporting Information). For nreact < f, we again expect the reaction rate Vr(A2) to have a
negligible effect on the particle size as, in this case, the coarsening is the main growth process and the mean diameter of the nanoparticles is determined by the value of f. 3.2. Effect of the Reducing Agent Concentration. As the formation of reduced metal atoms depends not only on the reduction rate but also on the concentration of the reducing agent (see eq 2), we investigated how this concentration influences the simulation results. For that purpose, three different ratios of number of the reducing agent molecules and number of the metal ions, that is, nreact(B)/[nreact(A1) + nreact(A2)], were investigated, namely, 1, 3, and 6. The influence of this ratio was investigated at three different reduction rates Vr(A2), namely, 0.5, 0.2, and 0.05. The rest of the parameters were fixed at Vr(A2) ) 1.0, nreact(A1) ) nreact(A2) ) 50, ncrit ) 10, f ) 15, and kex ) kexprod ) 1.0. Figure 2 shows the resulting contour plots of the distribution functions of the composition w and homogeneity h of the bimetallic nanoparticles (note that Figure 2a.i-c.i is the same as Figure 1b-d, respectively). The main conclusion that can be drawn from Figure 2 is that an increase of the concentration of the reducing agent leads to a decrease of the h value. In other words, the higher the concentration of the reducing agent, the more the formation of an intermetallic structure is favored. However, the slower the reaction rate Vr(A2), the more excess of the reducing agent is required for the formation of a pure intermetallic structure, that is, h ∼ 0. As can be seen in Figure 2, for Vr(A2) ) 0.5, the disordered structure was already formed at nreact(B)/[nreact(A1) + nreact(A2)] ) 3 (Figure 2a), while at the slower reduction rate of Vr(A2) ) 0.2, a 6-fold excess of the reducing agent was needed to obtain h ∼ 0 (Figure 2b). For the slowest reduction rate investigated, that is, for Vr(A2) ) 0.05, an intermetallic structure was not obtained with a 6-fold excess, which means that an even larger excess is required to obtain a pure intermetallic structure (Figure 2c).
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Figure 2. Contour plot of the distribution functions of the composition w and homogeneity h of bimetallic nanoparticles obtained at the reaction rates of Vr(A1) ) 1.0 and Vr(A2) ) 0.5 (a), 0.2 (b), and 0.05 (c). The mean number of reducing agent molecules per droplet was nreact(B) ) 100 (i), 300 (ii), and 600 (iii). The other parameters are the same as in Figure 1. Color code: high number of particles (blue), intermediate number of particles (red), and zero number of particles (white).
As to the corresponding nanoparticle sizes, similar mean particle diameters were found independent of the amount of the reducing agent. The mean diameter of the particles displayed in Figure 2 was 1.4 nm. We noted that an enhanced probability of nanoparticles having this size was obtained when nreact(B) ensured that the pure intermetallic structure was obtained, that is, h ∼ 0 (Figure S2 in the Supporting Information). On the other hand, when the reducing agent was in excess and the intermetallic structure was not yet reached, the particle size distribution could be well fitted by a Gaussian distribution (see for comparison Figure S2a.i,b.i-ii,c.i-ii,d.i-iv in the Supporting Information and Figure 2a.i,b.i-ii,c.i-iii). One can therefore conclude that an increase of nreact(B) does not only favor the formation of the disordered structure but also decreases the particle polydispersity. Note that the latter phenomenon was also found for monometallic nanoparticles, as can be seen in Figure S2a in the Supporting Information (for the sake of clarity, it has to be mentioned that in Figure S2a the results for same reaction rates, that is, Vr(A1) ) Vr(A2) ) 1.0, are shown, which can be interpreted as formation of monometallic nanoparticles). This feature is in line with Schmidt et al.48 who reported the addition of the metal salt containing microemulsion to the one
that contains the reducing agent leads to a much narrower size distribution as compared to the opposite mixing protocol. To explain the results concerning the particle size distribution found when both metal salts are reduced with similar priorities, we have to keep in mind that there are two competing processes that mainly reduce the number of the reacting species (A1, A2, and B) in the droplets, namely, (i) the reduction of metal ions and formation of seed nuclei at nreact > ncrit and (ii) the exchange of the droplet content with droplets that do not contain metal salts or reduced atoms anymore. When the reducing agent is in excess, the droplets do not get depleted in the reducing agent during these two processes. As a consequence, the collision of droplets containing reacting species in the absence of any preexistent nuclei would give rise to the formation of a new seed nucleus (provided that overall number of the reacting metal ions in the colliding droplets is still larger than ncrit) rather than to a metal ion redistribution between droplets. In other words, the excess of reducing agent enhances the formation of seed nuclei that subsequently grow mainly by autocatalysis. When nreact , f, the number of nuclei at early stages of the synthesis becomes less important as coarsening is the main growth mechanism and consequently similar polydispersity in size is expected inde-
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Figure 3. Contour plot of the distribution functions of the composition w and homogeneity h of bimetallic nanoparticles obtained at the reaction rates of Vr(A1) ) 1.0 and Vr(A2) ) 0.2. The mean numbers of metal salts and reducing agent molecules per droplet are nreact(A1) ) nreact(A2) ) nreact(B)/2.0 ) 7 (a) and nreact(A1) ) nreact(A2) ) nreact(B)/2.0 ) 50 (b); ncrit ) 10, f ) 15, and kex ) kexprod ) 1.0. Color code: high number of particles (blue), intermediate number of particles (red), and zero number of particles (white).
pendent of the initial reducing agent concentration (see for comparison Figures S2a.iii and S3 in the Supporting Information). 3.3. Effect of the Metal Salt Concentration. Figure 3 displays the influence of the metal salt concentration on the nanoparticle formation. The chosen parameters are (a) nreact(A1) ) nreact(A2) ) nreact(B)/2.0 ) 7 and (b) nreact(A1) ) nreact(A2) ) nreact(B)/2.0 ) 50. The other parameters were fixed at Vr(A1) ) 1.0, Vr(A2) ) 0.2, ncrit ) 10, f ) 15, and kex ) kexprod ) 1.0. It is seen that the formation of a richer core-shell structure (higher h) exhibiting a larger heterogeneity (wider w distribution) is favored when the mean number of metal salt ions per droplet nreact increases. This behavior can be explained by the fact that the initial number of seed nuclei depends on the relation between nreact and ncrit. Thus, lower numbers of these nuclei are expected at nreact < ncrit (Figure 3a) as compared with the case when nreact . ncrit (Figure 3b). The subsequent autocatalytic growth involving both metals within the same growth step would take place to a greater extent at lower numbers of seed nuclei and thus would favor an intermetallic (low h values) rather than a core-shell (high h values) structure. 3.4. Effect of the Exchange Rate. The exchange rate of the reduced metal atoms or the metal ions is related to the surfactant film flexibility. When the stabilizing surfactant layer is rigid, the channel opening between the colliding droplets is narrow and the diffusion of the water-soluble species is supposedly hindered. As a consequence, not only are the atoms not evened out between the two droplets but also the coarsening is restricted to small nuclei. To gain some insight into the influence of these two processes, namely, atom exchange and coarsening, on the nanoparticle structure, they are addressed separately. When the exchange rate is reduced, the way that the metal ion reduction is defined (eq 2) implies that the reduction rate Vr has to be reduced accordingly. Figure 4 shows the contour plot of the distribution functions of the composition w and homogeneity h of bimetallic particles obtained at two exchange rates and two reduction rate ratios. For two cases, atom migration is allowed to the full extent, that is, kex ) kexprod ) 1.0 and Vr(A1) ) Vr(A2) ) 1.0 or Vr(A1) ) 5 × Vr(A2) ) 1.0, while for the other two cases the atom exchange is reduced down to a half, that is, kex ) kexprod ) 0.5 and Vr(A1) ) Vr(A2) ) 0.5 or Vr(A1) ) 5 × Vr(A2) ) 0.5. The rest of the parameters are kept constant, that is, nreact(A1) ) nreact(A2) ) nreact(B)/2.0 ) 50, f ) 15, and ncrit ) 10. The contour plot shows a weak increase of the h value, that is, a more pronounced core-shell structure, at decreasing the exchange rates and constant ratio of the two reaction rates. A more pronounced
increase of the h value with decreasing the exchange rates was obtained at Vr(A1) ) 5 × Vr(A2) in the presence of a large excess of the reducing agent (Figure 5). As regards the nanoparticle composition, the distribution width was independent of the exchange rates, while it dependedsas expectedson the ratio of the reduction rates Vr(A1)/Vr(A2). Despite the fact that the homogeneity h was modified by the exchange rates under certain circumstances, the mean size of all particles presented in Figures 4 and 5 was 1.4 ( 0.2 nm. 3.5. Effect of the Value of the f Parameter. As we mentioned in the previous section, the film flexibility is important for the reactant exchange in the reaction and nucleation stages and for the coarsening during the subsequent growth stage. In this section, the effect of the latter process on the bimetallic nanoparticle structure is addressed. Figure 6 shows the distribution functions P(w) and P(h) for bimetallic particles obtained at three different f values. The rest of the parameters are nreact(A1) ) nreact(A2) ) nreact(B)/2.0 ) 50, kex ) kexprod ) 1.0, Vr(A1) ) 5, Vr(A2) ) 1.0, and ncrit ) 10. One can see that the nanoparticle’s homogeneity h does not depend on the f value. This is simply due to the way in which the h parameter was defined (see eq 5) since the homogeneity h of a bigger nucleus obtained by merging two nuclei via coarsening is in fact the sum of the h parameters of the two initial nuclei. As a consequence, the homogeneity is actually given during the initial nucleation and the subsequent autocatalysis growth. On the other hand, the polydispersity of the composition becomes smaller as the f value increases. This originates from the fact that larger f values result in bigger particles with a narrower size distribution, which leads to a smearing out of the particle composition. 4. Comparison with Experimental Results The model proposed for the investigation of the formation and growth of bimetallic nanoparticles synthesized via microemulsions is supported when one compares the experiment and simulation of PtBi nanoparticle synthesis. While the two metal ions are solubilized in the same microemulsion, their different standard reduction potentials (PtCl62-/PtCl42- ) +0.68 V, PtCl42-/Pt ) +0.76 V, and Bi3+/Bi ) +0.22 V) result in different priorities as regards the reduction reaction. We have shown recently that the PtBi bimetallic structure can be altered by varying the amount of the reducing agent.27 It was found that only pure or oxidized Pt particles plus pure or oxidized Bi particles were obtained at molar ratio of NaBH4/(PtCl62 + Bi3+) ) 6.1, whereas a single, chemically order intermetallic phase of PtBi was found at NaBH4/(PtCl62 + Bi3+) ) 12.3.
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Figure 4. Contour plot of the distribution functions of the composition w and homogeneity h [P(w), P(h)] of bimetallic nanoparticles obtained at the exchange rates of kex ) kexprod ) 1.0 (left) and kex ) kexprod ) 0.5 (right); the reaction rates were Vr(A1) ) Vr(A2) ) 1.0 (a.i), Vr(A1) ) Vr(A2) ) 0.5 (a.ii), Vr(A1) ) 5 × Vr(A2) ) 1.0 (b.i), and Vr(A1) ) 5 × Vr(A2) ) 0.5 (b.ii); nreact(A1) ) nreact(A2) ) nreact(B)/2.0 ) 50, ncrit ) 10, and f ) 15.
Figure 5. Contour plot of the distribution functions of the composition w and homogeneity h [P(w), P(h)] of bimetallic nanoparticles obtained at Vr(A1) ) 5 × Vr(A2) ) 1.0, kex ) kexprod ) 1.0 (a) and Vr(A1) ) 5 × Vr(A2) ) 0.5, kex ) kexprod ) 0.5 (b). The mean numbers of metal salts and reducing agent molecules per droplet are nreact(A1) ) nreact(A2) ) nreact(B)/6.0 ) 50. Furthermore, it holds ncrit ) 10 and f ) 15. Color code: high number of particles (blue), intermediate number of particles (red), and zero number of particles (white).
Table 2 shows a comparison between the experimental results and the Monte Carlo simulation. Agreement between simulation and experiment was attained for a ratio of the reduction rate of Vr(Pt)/Vr(Bi) ) 0.2 and a flexibility parameter of f ) 1000. The large film flexibility was needed to simulate the particle size distribution with good accuracy. The ratio Vr(Pt)/Vr(Bi) ) 0.2 led to a nanoparticle homogeneity of h ) 0.7 at a molar ratio of NaBH4/(PtCl62 + Bi3+) ) 0.57. Increasing this molar ratio up to 7.5 led to a steady decrease of the h value down to 0.1, which suggests the formation of an intermetallic structure of the bimetallic nanoparticles. We should stress that the amount of reducing agent needed to reach an intermetallic phase of two metals exhibiting different reduction potential could not be predicted although both experimental and simulation data demonstrated that a transition from a core-shell to an intermetallic structure occurs with increasing the excess of the reducing agent. First, this is caused by the fact that the stoichiometry of the
reduction reaction was discarded in the model as it is known only for Pt ions. Second, the relationship between the homogeneity h and the two structures given by TEM analysis, namely, intermetallic or core-shell structure, is not obvious. Note that the value of the parameter h varies continuously between 0 (disordered structure) and 1 (core-shell structure), while TEM provides the structures that are actually formed. In spite of this shortcoming, the model is considered appropriate in terms of analyzing and predicting bimetallic structures originating from metal ions with large differences in the standard reduction potential and obtained via microemulsion route. For example, the model may be used to simulate the Pt-Cu intermetallic structure (difference in standard reduction potentials of 0.4 V), which was obtained via the microemulsion route with an excess of hydrazine.49 One important conclusion that can be drawn from the agreement between simulation and experimental data is the fact that not only the reduction rate but also the relative concentration
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Figure 6. Contour plot of the distribution functions of the composition w and homogeneity h [P(w), P(h)] of bimetallic nanoparticles obtained at f ) 0 (a), 15 (b), and 250 (c); nreact(A1) ) nreact(A2) ) nreact(B)/6.0 ) 50, Vr(A1) ) 5, Vr(A2) ) 1.0, kex ) kexprod ) 1.0, and ncrit ) 10. Color code: high number of particles (blue), intermediate number of particles (red), and zero number of particles (white).
TABLE 2: Experimental and Simulated Characteristics of the Experimental PtBi Bimetallic Nanoparticles Prepared via Microemulsion Route27 particle characterization particle diameter
structure
metal precursorsa
reducing agent
TEM experiments (nm)
MC simulationb (nm)
TEM, HRTEM, and EDX experiments
13 mM H2PtCl6:13 mM Bi(NO3)3
160 mM NaBH4
4.5 ( 1.5
4.2 ( 0.5
13 mM H2PtCl6:13 mM Bi(NO3)3
320 mM NaBH4
4.5 ( 1.5
4.2 ( 0.5
Bare and core-shell Pt, Bi nanoparticles PtBi intermetallic
c
MC simulation PtBi core shellc PtBi intermetallicd
a Ratio of the standard reduction potential (PtCl42- f Pt)/(Bi3+ f Bi) ) 0.28. b Ratio of the reduction rate Vr(PtCl42-)/Vr(Bi3+) ) 0.2. Molar ratio NaBH4/[H2PtCl6 + Bi(NO3)3] ) 0.57. d Molar ratio NaBH4/[H2PtCl6 + Bi(NO3)3] ) 7.5.
of metal salt and reducing agent in colliding droplets has to be taken into account for modeling the metal atom formation. If one assumes the reduction of metal ions in eq 2 is alternatively given as njk(i,0) ) min{int[Vr(i)njk(i)],nij(B)}, we found occurring at increasing the reducing agent concentration only a marginal decrease in the h value instead of the core-shell (h ∼ 1) to intermetallic (h ∼ 0) structure transition. The different outcomes provided by the two approaches of the reduction of the metal ions can be explained by the fact that eq 2 allows the metal with the slowest reduction rate to be reduced with a varying priority depending on the excess of the reducing agent in the colliding droplets. When the difference in the reaction rate Vr(A1) - Vr(A2) is large and the metal reduction is given by njk(i,0) ) min{int[Vr(i)njk(i)],nij(B)}, the formation and growth of the nuclei containing the metal with the fastest reduction rate occur prior to the reduction and nucleation of the metal with the slowest reduction rate, leading thus to nanoparticles whose core is predominantly composed of the metal with the fastest reduction rate. It is noteworthy that the transition from a core-shell to a disordered structure was found by Tojo et al.42 when the surfactant film flexibility, that is, the f value, increased. It was
stated that a more flexible film resulted in a better mixing of the two metals, a quicker exchange of reactants and a quicker exchange of larger nuclei, which, in turn, favors the growth by coarsening. However, it was claimed that tuning of the bimetallic structure (either core-shell or intermetallic) simply by changing the film flexibility was limited to the cases where the difference in the reaction rate Vr(A1) - Vr(A2) was small; otherwise, the nanoparticle structure continues to be a core-shell one. At first sight, it seems that these conclusions are in contrast to our simulations data as we reported in section 3.5 that the nanoparticle homogeneity, h, is independent of the film flexibility, f. Nonetheless, we stress that a more flexible film implies a faster exchange of species during droplet-droplet collision, that is, larger kex and kexprod exchange rates, which, in turn, might lead to a decrease of the h value under certain circumstances, as seen in Figure 5. 5. Conclusions Monte Carlo simulations have been employed to determine the mean structure and size of bimetallic nanoparticles synthesized by mixing two w/o microemulsions. The water droplets
Monte Carlo Simulation Bimetallic Nanoparticles of one microemulsion contained both metal salt precursors and the droplets of the other the reducing agent. Droplets were modeled as spheres, which are free to move randomly, and the reactant exchange, nucleation, and growth of the resulting bimetallic nanoparticles during the droplet-droplet collisions were handled using appropriate rules. It was shown that the mechanism used for the metal reduction led to experimentally validated simulation results. An intermetallic structure is always obtained when the ratio of the reduction rate of two metal ions is close to one (both reduction reactions take place at about the same rate). When the metal ions have very different reduction potentials, as is the case with Pt and Bi ions, the nanoparticles can have either a core-shell or an intermetallic structure, depending on the reducing agent concentration. Experimental data on the structure of PtBi bimetallic nanoparticles, which were obtained with increasing excess of the reducing agent,27 are fairly reasonably predicted by the Monte Carlo simulations carried out in the study at hand. The simulations predicted that a continuous transition from a core-shell to a disordered structure takes place with increasing excess of the reducing agent. The simulation results also suggest that an improvement of the bimetallic structure, in the sense that the content of the disordered structure is enhanced at the expense of the core-shell one, may be realized by decreasing the concentration of the metal ions per droplets. On the other hand, the agreement of the experimental and simulated particle size distribution implies that the mean particle size is determined by the film flexibility rather than by the metal ion concentrations. The combination of these two findings allows us to tune the experimental conditions for designing specific bimetallic structures at similar nanoparticle mean size. We did not find the nanoparticle structure to be strongly dependent on surfactant film flexibility. A more flexible film, which implied more pronounced coarsening and atom exchange effect, resulted in an improved bimetallic nanoparticle composition and had a weak impact onto the bimetallic nanoparticle homogeneity. The latter feature occurred when the reduction rates were different and the reducing agent was in excess. Further insights into the interplay between the bimetallic structure and the composition of the microemulsion can be gained from kinetics studies, which will be dealt with in future investigations. Acknowledgment. Per Linse is gratefully acknowledged for the access to Lunarc and Fkem1 clusters that allowed the Monte Carlo simulations. Supporting Information Available: Figures of normalized diameter distributions of the bimetallic nanoparticles. This material is available free of charge via the Internet at http:// pubs.acs.org. Glossary A 1, A 2 A1(0), A2(0) B nreact(i), i ) A1, A2 nreact(B) kex(i), i ) A1, A2, B
metal ions reduced metal atoms reducing agent molecules mean number of metal ions of type i per microemulsion droplet prior to synthesis mean number of reducing agent molecules per microemulsion droplet prior to synthesis exchange parameter for the metal ions and reducing agent molecules during droplet-droplet collision
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