**2. The model**

*Microemulsion - A Chemical Nanoreactor*

traditional procedures [10, 11].

materials [2, 10, 17, 23–25].

and nanoparticles can be prepared at room temperature. In addition, the confinement of reactants inside micelles induces important changes in reactant concentrations, which strongly affect the reaction rates. Finally, in relation to catalysis, nanoparticles obtained by the microemulsion route present an improved catalytic behavior than particles with the same composition which are synthesized by

A variety of nanomaterials, ranging from metals [12–14], bimetallic structures

Nevertheless, microemulsion route present a challenge due to the difficulty in managing the material intermicellar exchange. As mentioned above, reactants are distributed in separate nanoreactors, so the whole process (chemical reaction, nucleation, and subsequent growth to build up final particles) is conditioned by the material exchange between them. This exchange is mainly dictated by the surfactant, which is located on the interface between water and oil phases. The hydrophilic portion of the surfactant is anchored into water and the lipophilic one into oil, forming a film which surrounds the micelle surface. It is believed that, when a micelle-micelle collision is violent enough, the surfactant film breaks up, allowing the material exchange. As a consequence, the rate of intermicellar exchange controls the reactants encounter and therefore plays a key role in chemical kinetics in microemulsions. The ease with which intermicellar channels are established as well as their size and stability are determined by the microemulsion composition, which

[15–17], other inorganic nanoparticles [18–20], and organic compounds [21, 22], has been prepared by this approach. In the field of catalysis, microemulsion approach was successfully used to prepare different nanostructured catalytic

in turn has been shown to affect final nanoparticle properties [26–28].

In the paper at hand, we are focused on the study of Pt/M (M = Au, Rh) nanoparticles synthesized in microemulsions. Platinum-based nanoparticles (NPs) exhibit remarkable electrocatalytic activity in many important chemical and electrochemical reactions including oxygen reduction reaction (ORR) and direct methanol oxidation [29]. Apart from the inherent chemical and physical properties of the constitutive metals, the catalytic activity, which is one of the more relevant applications of bimetallic nanoparticles, relies notably on the metal distribution, that is, on the intraparticle nanoarrangement [30]. Bimetallic nanoparticles can show four main mixing patterns: (a) core-shell structures, in which one metal forms the core and the second metal covers the first one forming the surrounding shell; (b) mixed structures, which are often called alloys; (c) multilayer structures [31]; and (d) sub-cluster segregated structures, characterized by a small number of heteroatomic bonds [12]. So, the control of bimetallic intrastructure, mainly within the first atomic layers from the surface [25, 32], is key for performance enhancement of bimetallic catalysts. Furthermore, the optimal metal distribution depends on the particular chemical reaction. Au-core/Pt-shell nanocatalyst exhibits an improved activity to catalyze formic acid electro-oxidation [33] or oxygen reduction reaction [34, 35]. On the contrary, an alloyed Pt-Au is better for electro-oxidation of methanol [36]. Therefore, an in-depth study aimed at tailoring well-defined structures

Although the simultaneous reduction of the two metals by the microemulsion route is one of the most common procedures to control the size and composition of bimetallic nanoparticles [24, 37], the prediction of the resulting metal arrangement is complicated, as far as the current state-of-the-art is concerned. As a matter of fact, many studies designed to produce new nanoarrangements via microemulsions come from trial-and-error experiments, mainly due to the high number of involved synthetic variables and to their interaction with the inherent complexity of the reaction media. A robust tool for elucidating the interplay between the different

**60**

will be of great interest.

A model was developed to simulate the kinetic course of the two chemical reductions (see Ref. [38] for details). The reaction medium is a microemulsion, which is described as a set of micelles. The one-pot method is reproduced by mixing equal volumes of three microemulsions, each of which contains one of the three reactants (two metal precursors and the reducing agent R). This pattern of mixing reactants recreates the one-pot method, by which the two metal salts are simultaneously reduced.

#### **2.1 Initial reactants concentration**

Reactants are initially distributed throughout micelles using a Poisson distribution, that is, the occupation of all micelles is not similar. In this study, we present results using different values of metal precursors concentration, but keeping a proportion 1:1 of the two metals: 〈cAuCl4 −〉 = 〈cPtCl6 <sup>2</sup>−〉 = 〈c〉 = 2, 16, 32, and 64 metal precursors in each micelle, which corresponds to 0.01, 0.08, 0.16, and 0.40 M, respectively, in a micelle with a radius of 4 nm. Au and Rh precursors (AuCl4 <sup>−</sup> and RhCl6 <sup>3</sup>−) are represented by M+ . Calculations have been made under isolation conditions, that is, reducing agent R is in excess: (〈cR〉 = 10〈cPtCl6 <sup>2</sup>−〉).

#### **2.2 Microemulsion dynamics and time unit**

Micelles move and collide with each other. The intermicellar collision is a key feature in kinetics in microemulsions, because upon collision micelles are able to establish a water channel, which allows the exchange of their contents (metal precursors, reducing agent, metallic atoms, and/or growing particles). The material intermicellar exchange makes possible the reactant encounter inside micelles and, as a consequence, it is determinant of chemical reactions to occur. The intermicellar collision is simulated by choosing a 10% of micelles at random. These selected micelles collide, fuse (allowing material intermicellar exchange), and then redisperse. One Monte Carlo step begins in each intermicellar collision and ends when the quantity of species carried by colliding micelles is revised in agreement to the exchange criteria described below.

#### **2.3 Metal characterization: reduction rate ratio**

The reduction rate of a metal A (vA) can be related to the standard potential (ε 0 A) by means of the Volmer equation:

$$\begin{bmatrix} \boldsymbol{j}\_{\cdot\cdot} - \boldsymbol{v}\_{\cdot\cdot} \boldsymbol{n}\_{\cdot\cdot} \boldsymbol{F} \\ \boldsymbol{j}\_{\cdot\cdot} - \boldsymbol{v}\_{\cdot\cdot} \boldsymbol{n}\_{\cdot\cdot} \boldsymbol{n}\_{\cdot} \end{bmatrix} - \begin{bmatrix} \boldsymbol{n}\_{\cdot\cdot} \boldsymbol{f} \boldsymbol{k}\_{\boldsymbol{n}\boldsymbol{t},\cdot\cdot} \boldsymbol{c}\_{\cdot\cdot\cdot} \boldsymbol{c}\_{\cdot\cdot} \end{bmatrix} \exp - \begin{bmatrix} \boldsymbol{\beta}\_{\cdot\cdot} \boldsymbol{n}\_{\cdot\cdot} \boldsymbol{f} \boldsymbol{c}\_{\cdot\cdot} \\ \boldsymbol{R} \boldsymbol{T} \\ \boldsymbol{n}\_{\cdot\cdot} \boldsymbol{n}\_{\cdot\cdot} \boldsymbol{F} \boldsymbol{c}\_{\cdot\cdot} \end{bmatrix} - \exp \begin{bmatrix} \boldsymbol{\beta}\_{\cdot\cdot} \boldsymbol{n}\_{\cdot\cdot} \boldsymbol{F} \boldsymbol{c}\_{\cdot\cdot} \\ \boldsymbol{R} \boldsymbol{T} \end{bmatrix} \tag{1}$$

where *jA* is the current density, *nA* is the number of electrons, *F* is the Faraday constant, *kred,A* is the chemical rate constant, *βA* is the transfer coefficient, *cO,A* is the concentration of oxidized *A*, *R* is the gas constant, and *T* is temperature. When two metals A and B, initially at the same concentration (*cO,A = cO,B*), are reduced simultaneously to synthesize an A/B bimetallic nanoparticle, this equation can be simplified by assuming the following approximations: the number of electrons (*nA = nB = n*), the transfer coefficients (*βA* =*βA* = *β*), and the chemical rate constants (*kred,A* = *kred,B* = *kred*) are equal. (One must keep in mind that main factor governing reduction rates is by electrochemical potential.) Under this condition, a simple relation between the rates of electron transfer of two species A and B and their standard potentials can be deduced.

$$\log\frac{\mathbf{v}\_4}{\mathbf{v}\_N} \quad \frac{1}{2.3} \frac{\int nF(\mathbf{c}\_5 \quad \mathbf{c}\_4)}{RT} \tag{2}$$

This equation supports the rule according to which the higher the difference between the standard potentials of the two metals, the higher the ratio between both reduction rates is.

#### *2.3.1 Au/Pt nanoparticles*

On the basis of Eq. (2), to simulate the reduction rate of Au/Pt nanoparticles, the standard reduction potential must be taken into account. When the Au precursor is AuCl4 <sup>−</sup>, the standard reduction potential is ε 0 (AuCl4 <sup>−</sup>) = 0.926 V, which is higher than that of Pt precursor ε 0 (PtCl6 <sup>2</sup><sup>−</sup> = 0.742 V). This results in a faster formation rate of Au particles. In fact, Au is reduced so quickly that kinetics cannot be studied by conventional methods, so stopped flow techniques were needed [39]. The color change occurs instantaneously, so Au reduction was simulated as fast as possible, that is, 100% of Au precursors located in colliding micelles react to produce Au atoms, whenever the amount of reducing agent was enough. The reduction rate parameter of a metal A (vA) is the percentage of reactants inside colliding micelles which are reduced during a collision to give rise to products (A atoms). Regarding to Pt, its reduction rate was successfully simulated by using vPt = 10%, that is, only a 10% of Pt precursor reacts in each collision (vPt = 10%) [40]. In this way, Au/Pt nanoparticle formation is simulated by a reduction rate ratio vAu/vPt = 100/10 = 10, that is, Au reduction is 10 times faster than Pt.

The two reductions can take place simultaneously within the same micelle. The metal precursors and/or reducing agent that did not react remain behind in the micelle and will be exchanged or react later.

#### *2.3.2 Pt/Rh nanoparticles*

In order to research the influence of another metal in the pair Pt/M on Pt reduction, a metal whose reduction rate would be 10 times slower than Pt was chosen. In this manner, the reduction rate ratio is the same as used to simulate Au/Pt nanoparticles, so the possible differences in the kinetic behavior and the final metal distributions cannot be supported by the difference between the standard potentials. Therefore, the reduction rate of Pt is the same as that of Au/Pt pair (vPt = 10%), but now Pt is the faster metal. Taking into account the standard reduction potential of RhCl6 <sup>3</sup><sup>−</sup>, ε 0 (RhCl6 <sup>3</sup><sup>−</sup>) = 0.44 V, this Rh precursor is a good candidate to be simulated as vRh = 1% (only a 1% of RhCl6 <sup>3</sup><sup>−</sup> located in the colliding micelles will be reduced (vPt/vRh = 10/1 = 10)).

The number of each species located within each micelle is adjusted at each step in agreement with the possibility of chemical reduction and the intermicellar

**63**

playing as catalyst.

*Microemulsions as Nanoreactors to Obtain Bimetallic Nanoparticles*

exchange criteria (see below). As the metallic atoms are produced in each micelle, they are assumed to be deposited on nanoparticle seed. That is, unlike for reactants, which are isolated within the micelle, all metal atoms inside a micelle are aggregated forming a growing nanoparticle. In order to calculate the metal distribution in the final bimetallic nanoparticle, the sequence of metals which are reduced is moni-

Two different intermicellar exchange criteria are implemented depending on the nature of exchanged species. Metal precursor, reducing agent, and free metal atoms are isolated species, which will be redistributed between two colliding micelles in accordance with the concentration gradient principle: they are transferred from the more to the less occupied micelle. The exchange parameter *kex* quantifies the maximum amount of isolated species that can be exchanged during an intermicellar

the reducing agent R can be located within the same micelle. At this stage, chemical

As the reductions take place, metal atoms are produced within micelles. It is assumed that metal atoms are deposited on nanoparticle seed, so all metal atoms inside a micelle are considered to be aggregated forming a growing nanoparticle. The larger size of a growing nanoparticle leads to a second interdroplet exchange protocol. It is assumed that the exchange of growing particles is restricted by the size of the channel connecting colliding micelles. The ease with which this channel can be established as well as the channel size is mainly determined by the flexibility of the surfactant film. The flexibility parameter (*f*) specifies the maximum particle size for transfer between micelles. The exchange criterium of growing particles also takes into account Ostwald ripening, which assumes that larger particles grow by condensation of material, coming from the smaller ones that solubilize more readily than larger ones. This feature is included in the model by considering that if both colliding micelles carry a growing particle, the smaller one is exchanged towards the micelle carrying the larger one, whenever the channel size would be large enough. As the synthesis advances, micelles can contain simultaneously reactants and growing particles. In this situation, autocatalysis can take place. Thus, if one of the colliding micelles is carrying a growing particle, the reaction always proceeds on it. If both colliding micelles contain particles, reaction takes place in the micelle containing the larger one, because it has a larger surface, so a higher probability of

Based on these simple criteria for material interdroplet exchange, surfactant film flexibility can be characterized as follows. There are two main requirements for material intermicellar exchange to occur: the size of the channel connecting colliding micelles must be large enough and the dimer formed by colliding micelles must be stable, that is, they must remain together long enough. Isolated species (reactants and free metals) traverse the intermicellar channel one by one, so one can assume that the key factor determining their exchange is the dimer stability. That is, when the two micelles stay together longer (higher dimer stability), a larger quantity of species can be exchanged. Channel size would not be relevant in this case. Based on this, *kex*, which quantifies how many units of isolated species can be exchanged during a collision, is related to the dimer stability. Conversely, when the transferred material is a particle constituted by aggregation of metal atoms, which travels through the channel as a whole, channel size becomes decisive. This kind of material exchange will be restricted by the intermicellar channel size (*f* parameter). From this picture, the flexibility of the surfactant film is simulated by means of these two parameters, *kex* (dimer stability) and *f* (intermicellar channel size).

<sup>2</sup>− and/or M+

) and

**2.4 Microemulsion characterization: intermicellar exchange criteria**

collision. As a result of this redistribution, the metal salts (PtCl6

reduction can occur at a rate which depends on the nature of the metal.

*DOI: http://dx.doi.org/10.5772/intechopen.80549*

tored in each micelle as a function of time.

#### *Microemulsions as Nanoreactors to Obtain Bimetallic Nanoparticles DOI: http://dx.doi.org/10.5772/intechopen.80549*

*Microemulsion - A Chemical Nanoreactor*

potentials can be deduced.

both reduction rates is.

*2.3.1 Au/Pt nanoparticles*

than that of Pt precursor ε

*2.3.2 Pt/Rh nanoparticles*

<sup>−</sup>, the standard reduction potential is ε

0 (PtCl6

that is, Au reduction is 10 times faster than Pt.

micelle and will be exchanged or react later.

is AuCl4

where *jA* is the current density, *nA* is the number of electrons, *F* is the Faraday constant, *kred,A* is the chemical rate constant, *βA* is the transfer coefficient, *cO,A* is the concentration of oxidized *A*, *R* is the gas constant, and *T* is temperature. When two metals A and B, initially at the same concentration (*cO,A = cO,B*), are reduced simultaneously to synthesize an A/B bimetallic nanoparticle, this equation can be simplified by assuming the following approximations: the number of electrons (*nA = nB = n*), the transfer coefficients (*βA* =*βA* = *β*), and the chemical rate constants (*kred,A* = *kred,B* = *kred*) are equal. (One must keep in mind that main factor governing reduction rates is by electrochemical potential.) Under this condition, a simple relation between the rates of electron transfer of two species A and B and their standard

This equation supports the rule according to which the higher the difference between the standard potentials of the two metals, the higher the ratio between

On the basis of Eq. (2), to simulate the reduction rate of Au/Pt nanoparticles, the standard reduction potential must be taken into account. When the Au precursor

rate of Au particles. In fact, Au is reduced so quickly that kinetics cannot be studied by conventional methods, so stopped flow techniques were needed [39]. The color change occurs instantaneously, so Au reduction was simulated as fast as possible, that is, 100% of Au precursors located in colliding micelles react to produce Au atoms, whenever the amount of reducing agent was enough. The reduction rate parameter of a metal A (vA) is the percentage of reactants inside colliding micelles which are reduced during a collision to give rise to products (A atoms). Regarding to Pt, its reduction rate was successfully simulated by using vPt = 10%, that is, only a 10% of Pt precursor reacts in each collision (vPt = 10%) [40]. In this way, Au/Pt nanoparticle formation is simulated by a reduction rate ratio vAu/vPt = 100/10 = 10,

The two reductions can take place simultaneously within the same micelle. The metal precursors and/or reducing agent that did not react remain behind in the

In order to research the influence of another metal in the pair Pt/M on Pt reduction, a metal whose reduction rate would be 10 times slower than Pt was chosen. In this manner, the reduction rate ratio is the same as used to simulate Au/Pt nanoparticles, so the possible differences in the kinetic behavior and the final metal distributions cannot be supported by the difference between the standard potentials. Therefore, the reduction rate of Pt is the same as that of Au/Pt pair (vPt = 10%), but now Pt is the faster metal. Taking into account the standard reduction potential of

The number of each species located within each micelle is adjusted at each step in agreement with the possibility of chemical reduction and the intermicellar

<sup>3</sup><sup>−</sup>) = 0.44 V, this Rh precursor is a good candidate to be simulated

<sup>3</sup><sup>−</sup> located in the colliding micelles will be reduced

0 (AuCl4

<sup>2</sup><sup>−</sup> = 0.742 V). This results in a faster formation

(2)

<sup>−</sup>) = 0.926 V, which is higher

**62**

RhCl6

<sup>3</sup><sup>−</sup>, ε 0 (RhCl6

(vPt/vRh = 10/1 = 10)).

as vRh = 1% (only a 1% of RhCl6

exchange criteria (see below). As the metallic atoms are produced in each micelle, they are assumed to be deposited on nanoparticle seed. That is, unlike for reactants, which are isolated within the micelle, all metal atoms inside a micelle are aggregated forming a growing nanoparticle. In order to calculate the metal distribution in the final bimetallic nanoparticle, the sequence of metals which are reduced is monitored in each micelle as a function of time.

## **2.4 Microemulsion characterization: intermicellar exchange criteria**

Two different intermicellar exchange criteria are implemented depending on the nature of exchanged species. Metal precursor, reducing agent, and free metal atoms are isolated species, which will be redistributed between two colliding micelles in accordance with the concentration gradient principle: they are transferred from the more to the less occupied micelle. The exchange parameter *kex* quantifies the maximum amount of isolated species that can be exchanged during an intermicellar collision. As a result of this redistribution, the metal salts (PtCl6 <sup>2</sup>− and/or M+ ) and the reducing agent R can be located within the same micelle. At this stage, chemical reduction can occur at a rate which depends on the nature of the metal.

As the reductions take place, metal atoms are produced within micelles. It is assumed that metal atoms are deposited on nanoparticle seed, so all metal atoms inside a micelle are considered to be aggregated forming a growing nanoparticle. The larger size of a growing nanoparticle leads to a second interdroplet exchange protocol. It is assumed that the exchange of growing particles is restricted by the size of the channel connecting colliding micelles. The ease with which this channel can be established as well as the channel size is mainly determined by the flexibility of the surfactant film. The flexibility parameter (*f*) specifies the maximum particle size for transfer between micelles. The exchange criterium of growing particles also takes into account Ostwald ripening, which assumes that larger particles grow by condensation of material, coming from the smaller ones that solubilize more readily than larger ones. This feature is included in the model by considering that if both colliding micelles carry a growing particle, the smaller one is exchanged towards the micelle carrying the larger one, whenever the channel size would be large enough.

As the synthesis advances, micelles can contain simultaneously reactants and growing particles. In this situation, autocatalysis can take place. Thus, if one of the colliding micelles is carrying a growing particle, the reaction always proceeds on it. If both colliding micelles contain particles, reaction takes place in the micelle containing the larger one, because it has a larger surface, so a higher probability of playing as catalyst.

Based on these simple criteria for material interdroplet exchange, surfactant film flexibility can be characterized as follows. There are two main requirements for material intermicellar exchange to occur: the size of the channel connecting colliding micelles must be large enough and the dimer formed by colliding micelles must be stable, that is, they must remain together long enough. Isolated species (reactants and free metals) traverse the intermicellar channel one by one, so one can assume that the key factor determining their exchange is the dimer stability. That is, when the two micelles stay together longer (higher dimer stability), a larger quantity of species can be exchanged. Channel size would not be relevant in this case. Based on this, *kex*, which quantifies how many units of isolated species can be exchanged during a collision, is related to the dimer stability. Conversely, when the transferred material is a particle constituted by aggregation of metal atoms, which travels through the channel as a whole, channel size becomes decisive. This kind of material exchange will be restricted by the intermicellar channel size (*f* parameter). From this picture, the flexibility of the surfactant film is simulated by means of these two parameters, *kex* (dimer stability) and *f* (intermicellar channel size).

A rigid film, such as AOT/n-heptane/water microemulsion, was successfully reproduced considering a channel size *f* = 5, associated to *kex* = 1 free atoms exchanged during a collision [26]. In case of flexible film, both factors rise together, because a more flexible film produces more stable dimer and larger channel size, allowing a quicker exchange of isolated species as well as an exchange of larger particles [41]. That is, a flexible film is associated to a faster material intermicellar exchange rate. A more flexible microemulsion, such as 75% Isooctane/20% Tergitol/5% water microemulsion, was successful compared to simulation data using the values *f* = 30, *kex* = 5 [42].

### **2.5 Description of the metal distribution in the bimetallic nanoparticle**

The composition of each nanoparticle is revised at each step and monitored as a function of time. When all metal precursors were reduced and the content of all micelles remains constant over time, nanoparticle synthesis is considered to be finished. At this stage, the sequence of metal deposition of each particle (which is stored as a function of time) is stabilized. One simulation run produces a set of micelles, each one of them can carry one particle with different composition or be empty. At the end of each run, the averaged nanoparticle is calculated. Finally, results are averaged over 1000 runs.

The intrastructure of each particle is calculated by analyzing the sequence in which the two metals are deposited on the nanoparticle surface. So that, each sequence is arranged in 10 concentric layers, assuming that final nanoparticle is spherical. Then, the averaged percentage of each metal is calculated layer by layer. The final bimetallic distribution is represented by histograms, in which the layer composition is described by a color grading, as stated in the following pattern: Au, Pt, and Rh are represented by red, blue, and green, respectively. As the proportion of pure metal in the layer is higher, the color becomes lighter. In order to illustrate the heterogeneity of nanoparticle composition, the number of particles with a given percentage of the faster reduction metal (Au in Au/Pt and Pt in Pt/Rh nanoparticles) in each of 10 layers is also represented in the histograms. This analysis is reproduced layer by layer, from the beginning of the synthesis (inner layer or core) to the end (outer layer or surface). To simplify, the metal distribution is also shown by means of concentric spheres, whose thickness is proportional to the number of layers with the same composition, keeping the same color pattern.
