# Size-dependent catalytic and melting properties of platinum-palladium nanoparticles

- Grégory Guisbiers
^{1}Email author, - Gulmira Abudukelimu
^{2}and - Djamila Hourlier
^{3}

**6**:396

**DOI: **10.1186/1556-276X-6-396

© Guisbiers et al; licensee Springer. 2011

**Received: **11 March 2011

**Accepted: **26 May 2011

**Published: **26 May 2011

## Abstract

While nanocatalysis is a very active field, there have been very few studies in the size/shape-dependent catalytic properties of transition metals from a thermodynamical approach. Transition metal nanoparticles are very attractive due their high surface to volume ratio and their high surface energy. In particular, in this paper we focus on the Pt-Pd catalyst which is an important system in catalysis. The melting temperature, melting enthalpy, and catalytic activation energy were found to decrease with size. The face centered cubic crystal structure of platinum and palladium has been considered in the model. The shape stability has been discussed. The phase diagram of different polyhedral shapes has been plotted and the surface segregation has been considered. The model predicts a nanoparticle core rich in Pt surrounded by a layer enriched in Pd. The Pd segregation at the surface strongly modifies the catalytic activation energy compared to the non-segregated nanoparticle. The predictions were compared with the available experimental data in the literature.

### PACS

65.80-g; 82.60.Qr; 64.75.Jk

## Introduction

Bimetallic nanoparticles exhibit unusual physicochemical properties different from those of the bulk material or their individual constituents [1, 2]. They are very used in catalysis, fuel cells, and hydrogen storage. These unusual properties are determined by their size, shape, and composition. When considering metallic catalysts, platinum is a standard material but this material is most expensive than gold [3]. Therefore, to reduce the amount of platinum and then the cost of the application, one possible way is to use an alloy of platinum with another metal. In the present study, the chosen alloy is the binary Pt-Pd system [4] that we propose to theoretically study from a thermodynamic approach [5, 6], as well as its pure components. It has been shown previously [5, 6] that thermodynamics may provide useful insights in nanotechnology where the size of the considered nanoparticles is higher than approximately 4 nm. Within this approach, the size and shape effects on the melting temperature, melting enthalpy, phase diagram, and catalytic activation energy of this system are investigated.

As face-centered cubic (fcc) metals, Pt and Pd can exhibit a variety of geometrical shapes. Therefore, to address the shape effect on the materials properties of these metals at the nanoscale [7, 8], the following shapes have been considered: sphere, tetrahedron, cube, octahedron, decahedron, dodecahedron, truncated octahedron, cuboctahedron, and icosahedron.

### Size-dependent melting properties of Pt and Pd

*T*

_{ m }and melting enthalpy Δ

*H*

_{ m }, for free-standing nanostructures can be expressed as function of their bulk corresponding property, the size of the structure and one shape parameter [9].

where the shape parameter, α_{shape}, is defined as *α*
_{shape} = *AD*(*γ*
_{
s
}-*γ*
_{
l
})/(*V* Δ*H*
_{
m, ∞}); *D* being the size of the structure (*i.e.* for a sphere, *D* is the diameter), *A* (meter squared) and *V* (cubic meter) are the surface area and volume of the nanostructure, respectively. Δ*H*
_{
m,∞
}is the bulk melting enthalpy (Joule per cubic meter), whereas *γ*
_{
l
}and *γ*
_{
s
}are the surface energy in the liquid and solid phases (Joule per square meter), respectively. *γ*
_{
l
}and *γ*
_{
s
}are considered size independent. This is justified by the fact that the size effect on the surface energies is less than 4% for sizes higher than 4 nm [10, 11]. Indeed, below this size, edges, and corners of the structures begin to play a significant role in the surface energy [12].

_{sphere}= 0.95

*nm*while our theory predicts 1.68 nm.

Materials properties of platinum and palladium.

Solid surface energies for platinum and palladium materials [13].

Faces | Platinum | Palladium |
---|---|---|

| 2.299 | 1.920 |

| 2.734 | 2.326 |

| 2.819 | 2.225 |

Number of (hkl) faces for each shape.

Shape | Number of (111) faces | Number of (100) faces | Number of (110) faces |
---|---|---|---|

Tetrahedron | 4 | 0 | 0 |

Cube | 0 | 6 | 0 |

Octahedron | 8 | 0 | 0 |

Decahedron | 10 | 0 | 0 |

Dodecahedron | 12 | 0 | 0 |

Truncated octahedron | 8 | 6 | 0 |

Cuboctahedron | 8 | 6 | 0 |

Icosahedron | 20 | 0 | 0 |

## Discussion

At the nanoscale, the shape which exhibits the highest melting temperature is the one which minimizes the most the Gibbs' free energy (*G* = *H - TS*); and is then the favored one. From Figures 1 and 2, the four most-stable shapes among the ones considered are the dodecahedron, truncated octahedron, icosahedron, and the cuboctahedron. Experimentally, truncated octahedron and cuboctahedron are observed for platinum nanoparticles [8] whereas icosahedron, decahedron, truncated octahedron and cuboctahedron are observed for palladium nanoparticles [8]. Therefore, our predictions are in relative good agreement with the observations for palladium and platinum except that dodecahedron and icosahedron are not observed for platinum. Other theoretical calculations confirmed that the dodecahedron is a stable shape for palladium [17]. More generally, according to Yacaman *et al.*[8], the most often observed shapes at the nanoscale are the cuboctahedron, icosahedron, and the decahedron.

Furthermore, care has to be taken when we compare theoretical results with experimental ones due those materials properties depend on the synthesis process [18, 19]. And then predicted properties from thermodynamics may differ from the experimentally observed if the synthesis process is not running under thermodynamical equilibrium. Moreover, thermal fluctuations are often observed in nanoparticles [20] meaning that the shape stability is much more complicated than just a minimisation of the *A/V* ratio with faces exhibiting the lowest surface energy.

### Nano-phase diagram of Pt-Pd

where *x*
_{solidus} (*x*
_{liquidus}) is the composition in the solid (liquid) phase at a given *T*, respectively.
is the size-dependent melting temperature of the element *i*.
is the size-dependent melting enthalpy of the element *i*.

*i.e.*, exhibiting a strong shape effect. Moreover, the melting temperature increases with the concentration of Pt in agreement with Ref. [25].

where *z*
_{1} is the first nearest neighbor atoms; *z*
_{1ν
}is the number of first nearest atoms above the same plane (vertical direction). In the case of face-centered cubic (fcc) crystal structure of Pt and Pd materials, we have *z*
_{1} = 12, *z*
_{1ν
}= 4 for (100) faces and three for (111) faces. Δ*H*
_{vap} is the difference between the bulk vaporization enthalpies of the two pure elements,
. Δ*H*
_{sub} is the difference between the bulk sublimation enthalpies of the two pure elements,
. Element *A* is chosen to be the one with the highest sublimation and vaporization enthalpies. If the two components are identical, Δ*H*
_{sub} = 0 and Δ*H*
_{vap} = 0, there is no segregation and we retrieve Equation 3. *x*
_{solidus} and *x*
_{liquidus} are obtained from solving Equation 3. Assuming an ideal solution, only the first surface layer will be different from the core composition.

### Size-dependent catalytic activation energy of Pt-Pd

*E*

_{ca}could be obtained from the following relation:

Therefore, it means that the size-dependent catalytic activation energy decreases with size.

To compare with experimental results, the ratio of the catalytic activation energies between tetrahedral (*D* = 4.8 nm) and spherical (*D* = 4.9 nm) pure platinum nanoparticles has been determined around 0.66 in excellent agreement with the experimental value of 0.62 ± 0.06 announced by Narayanan and El-Sayed [37–39]. Moreover, the ratio of the catalytic activation energies between cubic (*D* = 7.1 nm) and spherical (*D* = 4.9 nm) pure platinum nanoparticles is around 1.01 in relative good agreement with the experimental value of 1.17 ± 0.12 [37–39].

*x*represents the alloy composition. For a spherical Pt-Pd nanoparticle with a diameter equal to 4 nm, by combining Equations 5-8,

*E*

_{ca}seems to evolve quadratically with the composition when the segregation is not considered; which is not the case when the segregation is considered (Figure 5). For the segregated Pt-Pd nanoparticle, a maximum in the catalytic activation energy is reached around 16% of Pt composition.

## Conclusions

In conclusion, it has been shown that thermodynamics can still provide useful insights in nanoscience and more specifically in catalysis. The future development of catalysts and fuel cells is dependent upon our ability to control the size, shape, and surface chemistry of individual nanoparticles. Future theoretical work will have to consider the environment in which the particles are synthesized as well as the preparation method because these parameters can have a great influence on the shape stability and on the catalytic properties.

## Declarations

### Acknowledgements

G. Guisbiers would like to thank the Belgian Federal Science Policy Office (BELSPO) through the "Mandats de retour" action for their financial support.

## Authors’ Affiliations

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