Skip to main content

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


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.


65.80-g; 82.60.Qr; 64.75.Jk


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

At the nanoscale, the melting temperature T m and melting enthalpy ΔH 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, αshape, is defined as α shape = AD(γ s -γ l )/(V ΔH 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. ΔH 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].

The size-dependent melting temperatures of platinum and palladium are plotted in Figures 1 and 2 respectively. The materials properties of the considered materials are indicated in Table 1. The melting properties for the sphere have been calculated using for the solid surface energy the mean value of experimental data [13]. For the other polyhedra shapes, we have considered the fcc crystal structure of the metals and the respective solid surface energy for each face [14]. Tables 2 and 3 indicate the parameters used for the calculation of the melting properties. Experimentally, the melting of agglomerated Pt nanocrystals (tetrahedrons and cubes) with an average size around approximately 8 nm starts at approximately 900 K [15] in relative good agreement with our theoretical predictions. Molecular dynamics simulations [16] have calculated the size effect on the melting temperature of Pd and found αsphere = 0.95 nm while our theory predicts 1.68 nm.

Figure 1
figure 1

Size-dependent melting temperature of platinum versus the size for different shapes.

Figure 2
figure 2

Size-dependent melting temperature of palladium versus the size for different shapes.

Table 1 Materials properties of platinum and palladium.
Table 2 Solid surface energies for platinum and palladium materials [13].
Table 3 Number of (hkl) faces for each shape.


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

According to the Hume-Rothery's rules, platinum and palladium forms an ideal solution [21]. In this case, considering no surface segregation, the liquidus and solidus curves of bulk and nanostructures are calculated from the following equations [2224]:


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.

The phase diagram of the Pt-Pd alloy is plotted in Figure 3. We note that the lens shape of the phase diagram is conserved at the nanoscale; however, the lens width increases for the shapes characterized by a small melting enthalpy and melting temperature, i.e., exhibiting a strong shape effect. Moreover, the melting temperature increases with the concentration of Pt in agreement with Ref. [25].

Figure 3
figure 3

Phase diagram of the Pt-Pd system for different shapes. Different shapes at a size equal to 4 nm and at the bulk scale. The solid lines indicate the liquidus curves whereas the dashed lines indicate the solidus ones.

In order to predict nanomaterials properties more accurately, we are considering a possible surface segregation which is known as the surface enrichment of one component of a binary alloy. At the nanoscale, surface segregation leads to a new atomic species repartition between the core and the surface. According to Williams and Nason [26], the surface composition of the liquid and solid phase are given by:


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. ΔH vap is the difference between the bulk vaporization enthalpies of the two pure elements, . ΔH 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, ΔH sub = 0 and ΔH 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.

Considering the surface segregation in the Pt-Pd system, we can see in Figure 4 that the lens shape of the surface liquidus/solidus curves is deformed compared to the core. At a given temperature, the liquidus and solidus curves of the surface are enriched in Pd compared to the core; meaning that the surface is depleted of Pt (the higher bond energy element) which is in agreement with experimental observations[2729] and other theoretical calculations[2931]. This is due to the fact that Pd has a lower solid surface energy, a lower cohesive energy compared to Pt and also because diffusion is enhanced at the nanoscale [32].

Figure 4
figure 4

Phase diagram of the Pt-Pd system considering the surface segregation effect. Surface segregation effect at a size equal to 4 nm for a spherical nanoparticle.

Size-dependent catalytic activation energy of Pt-Pd

The catalytic activation energy is the energy quantity that must be overcome in order for a chemical reaction to occur in presence of a catalyst. The low the catalytic activation energy is, the most active the catalyst is. It is thus an important kinetic parameter linked to the chemical activity. Indeed, the catalytic activation energy is a linear function of the work function [3335]. For pure materials, the catalytic activity depends on the fraction of surface atoms on corners and edges while for binary compounds it depends also on the surface segregation. Recently, it has been showed by Lu and Meng in Ref. [36] that the size-dependent catalytic activation energy, 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 [3739]. 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 [3739].

From the size-dependent Pt-Pd phase diagram, the melting temperature of the alloy can be deduced. Equation 6 describes the melting temperature of the bulk Pt-Pd while Equations 7 and 8 describe the nanoscaled melting temperature of a non-segregated and segregated spherical nanoparticle (with a diameter equal to 4 nm), respectively.


where 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.

Figure 5
figure 5

Composition dependency of the catalytic activation energy for a spherical nanoparticle of Pt-Pd. Nanoparticle of Pt-Pd with a size equal to 4 nm.


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.


  1. Maye MM, Kariuki NN, Luo J, Han L, Njoki P, Wang L, Lin Y, Naslund HR, Zhong CJ: Electrocatalytic reduction of oxygen: gold and gold-platinum nanoparticle catalysts prepared by two phase protocol. Gold Bulletin 2004, 37: 217. 10.1007/BF03215216

    Article  Google Scholar 

  2. Deng L, Hu W, Deng H, Xiao S: Surface segregation and structural features of bi-metallic Au-Pt nanoparticles. Journal of Physical Chemistry C 2010, 114: 11026. 10.1021/jp100194p

    Article  Google Scholar 

  3. Sealy C: The problem with platinum. Materials Today 2008, 11: 65–68. 10.1016/S1369-7021(08)70254-2

    Article  Google Scholar 

  4. Tao F, Grass ME, Zhang Y, Butcher DR, Renzas JR, Liu Z, Chung JY, Mun BS, Salmeron M, Samorjai GA: Reaction-driven restructuring of Rh-Pd and Pt-Pd core-shell nanoparticles. Science 2008, 322: 932–934. 10.1126/science.1164170

    Article  Google Scholar 

  5. Guisbiers G, Buchaillot L: Universal size/shape-dependent law for characteristic temperatures. Physics Letters A 2009, 374: 305–308. 10.1016/j.physleta.2009.10.054

    Article  Google Scholar 

  6. Guisbiers G: Size-dependent materials properties towards a universal equation. Nanoscale Research Letters 2010, 5: 1132–1136. 10.1007/s11671-010-9614-1

    Article  Google Scholar 

  7. Barnard AS: Using theory and modelling to investigate shape at the nanoscale. Journal of Materials Chemistry 2006, 16: 813–815. 10.1039/b513095f

    Article  Google Scholar 

  8. Yacaman MJ, Ascencio JA, Liu HB, Gardea-Torresdey J: Structure shape and stability of nanometric sized particles. Journal of Vacuum Science & Technology B 2001, 19: 1091–1103. 10.1116/1.1387089

    Article  Google Scholar 

  9. Guisbiers G, Buchaillot L: Modeling the melting enthalpy of nanomaterials. Journal of Physical Chemistry C 2009, 113: 3566. 10.1021/jp809338t

    Article  Google Scholar 

  10. Liang LH, Zhao M, Jiang Q: Melting enthalpy depression of nanocrystals based on surface effect. Journal of Materials Science Letters 2002, 21: 1843–1845. 10.1023/A:1021532311219

    Article  Google Scholar 

  11. Lu HM, Jiang Q: Size-dependent surface energies of nanocrystals. Journal of Physical Chemistry B 2004, 108: 5617–5619. 10.1021/jp0366264

    Article  Google Scholar 

  12. Barnard AS, Zapol P: A model for the phase stability of arbitrary nanoparticles as a function of size and shape. Journal of Chemical Physics 2004, 121: 4276. 10.1063/1.1775770

    Article  Google Scholar 

  13. Vitos L, Ruban AV, Skriver HL, Kollar J: The surface energy of metals. Surface Science 1998, 411: 186–202. 10.1016/S0039-6028(98)00363-X

    Article  Google Scholar 

  14. Abudukelimu G: Thermodynamical approach of phase diagrams of nanosystems: size and shape effects. In Ph D thesis. University of Mons-Hainaut; 2009.

    Google Scholar 

  15. Wang ZL, Petroski JM, Green TC, El-Sayed MA: Shape Transformation and Surface Melting of Cubic and Tetrahedral Platinum Nanocrystals. Journal of Physical Chemistry B 1998, 102: 6145–6151. 10.1021/jp981594j

    Article  Google Scholar 

  16. Miao L, Bhethanabotla VR, Joseph B: Melting of Pd clusters and nanowires: a comparison study using molecular dynamics simulation. Physical Review B 2005, 72: 134109.

    Article  Google Scholar 

  17. Montejano-Carrizales JM, Rodriguez-Lopez JL, Pal U, Miki-Yoshida M, José-Yacaman M: The completion of the platonic atomic polyhedra: The dodecahedron. Small 2006, 2: 351–355. 10.1002/smll.200500362

    Article  Google Scholar 

  18. Xiong Y, Xia Y: Shape-controlled synthesis of metal nanostructures: the case of palladium. Advanced Materials 2007, 19: 3385–3391. 10.1002/adma.200701301

    Article  Google Scholar 

  19. Cheong S, Watt JD, Tilley RD: Shape control of platinum and palladium nanoparticles for catalysis. Nanoscale 2010, 2: 2045–2053. 10.1039/c0nr00276c

    Article  Google Scholar 

  20. Vollath D, Fischer FD: Structural fluctuations in nanoparticles. Journal of Nanoparticle Research 2009, 11: 433–439. 10.1007/s11051-007-9326-3

    Article  Google Scholar 

  21. Kittel C: Introduction to solid state physics. 7th edition. New York: Wiley; 1995.

    Google Scholar 

  22. Guisbiers G, Wautelet M, Buchaillot L: Phase diagrams and optical properties of phosphide, arsenide, and antimonide binary and ternary III-V nanoalloys. Physical Review B 2009, 79: 155426.

    Article  Google Scholar 

  23. Guisbiers G, Liu D, Jiang Q, Buchaillot L: Theoretical predictions of wurtzite III-nitrides nano-materials properties. Physical Chemistry Chemical Physics 2010, 12: 7203.

    Article  Google Scholar 

  24. Guisbiers G, Abudukelimu G, Wautelet M, Buchaillot L: Size, shape, composition, and segregation tuning of InGaAs thermo-optical properties. Journal of Physical Chemistry C 2008, 112: 17889–17892. 10.1021/jp805760h

    Article  Google Scholar 

  25. Sankaranarayanan SKRS, Bhethanabotla VR, Joseph B: Molecular dynamics simulation study of the melting of Pd-Pt nanoclusters. Physical Review B 2005, 71: 195415.

    Article  Google Scholar 

  26. Williams FL, Nason D: Binary alloy surface compositions from bulk alloy thermodynamic data. Surface Science 1974, 45: 377–408. 10.1016/0039-6028(74)90177-0

    Article  Google Scholar 

  27. Renouprez AJ, Rousset JL, Cadrot AM, Soldo Y, Stievano L: Structure and catalytic activity of palladium-platinum aggregates obtained by laser vaporisation of bulk alloys. Journal of Alloys and Compounds 2001, 328: 50. 10.1016/S0925-8388(01)01346-9

    Article  Google Scholar 

  28. Rousset JL, Cadrot AM, Cadete Santos Aires FJ, Renouprez A, Mélinon P, Perez A, Pellarin M, Vialle JL, Broyer M: Study of bimetallic Pd-Pt clusters in both free and supported phases. Journal of Chemical Physics 1995, 102: 8574–8585. 10.1063/1.468847

    Article  Google Scholar 

  29. Ferrando R, Jellinek J, Johnston RL: Nanoalloys: From Theory to Applications of Alloy Clusters and Nanoparticles. Chemical Reviews 2008, 108: 845–910. 10.1021/cr040090g

    Article  Google Scholar 

  30. Massen C, Mortimer-Jones TV, Johnston RL: Geometries and segregation properties of platinum-palladium nanoalloy clusters. Journal of the Chemical Society, Dalton Transactions 2002, 4375–4388.

    Google Scholar 

  31. Luyten J, Creemers C: Surface segregation in ternary Pt-Pd-Rh alloys studied with Monte Carlo simulations and the modified embedded atom method. Surface Science 2008, 602: 2491–2495. 10.1016/j.susc.2008.05.024

    Article  Google Scholar 

  32. Guisbiers G, Buchaillot L: Size and shape effects on creep and diffusion at the nanoscale. Nanotechnology 2008, 19: 435701. 10.1088/0957-4484/19/43/435701

    Article  Google Scholar 

  33. Vayenas CG, Bebelis S, Pliangos C, Brosda S, Tsiplakides D: Electrochemical activation of catalysis. New York: Kluwer Academic; 2001.

    Google Scholar 

  34. Kemball C: Catalysis on evaporated metal films. I. The efficiency of different metals for the reaction between ammonia and deuterium. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 1952, 214: 413–426. 10.1098/rspa.1952.0177

    Article  Google Scholar 

  35. Vayenas CG, Ladas S, Bebelis S, Yentekakis IV, Neophytides S, Yi J, Karavasilis C, Pliangos C: Electrochemical promotion in catalysis: non-faradaic electrochemical modification of catalytic activity. Electrochimica Acta 1994, 39: 1849–1855. 10.1016/0013-4686(94)85174-3

    Article  Google Scholar 

  36. Lu HM, Meng XK: Theoretical model to calculate catalytic activation energies of platinum nanoparticles of different sizes and shapes. Journal of Physical Chemistry C 2010, 114: 1534–1538. 10.1021/jp9106475

    Article  Google Scholar 

  37. Narayanan R, El-Sayed MA: Shape-dependent catalytic activity of platinum nanoparticles in colloidal solution. Nano Letters 2004, 4: 1343. 10.1021/nl0495256

    Article  Google Scholar 

  38. Narayanan R, El-Sayed MA: Catalysis with transition metal nanoparticles in colloidal solution: nanoparticle shape dependence and stability. Journal of Physical Chemistry B 2005, 109: 12663–12676. 10.1021/jp051066p

    Article  Google Scholar 

  39. Narayanan R, El-Sayed MA: Some aspects of colloidal nanoparticle stability, catalytic activity, and recycling potential. Topics in Catalysis 2008, 47: 15–21. 10.1007/s11244-007-9029-0

    Article  Google Scholar 

  40. Martienssen W, Warlimont H: Springer Handbook of Condensed Matter and Materials Data. Berlin: Springer; 2005.

    Book  Google Scholar 

  41. Arblaster JW: Vapour pressure equations for the platinum group elements. Platinum Metals Review 2007, 51: 130–135. 10.1595/147106707X213830

    Article  Google Scholar 

Download references


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

Author information

Authors and Affiliations


Corresponding author

Correspondence to Grégory Guisbiers.

Additional information

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

GG carried out the calculations on the size and shape effects on the melting temperature, phase diagrams and catalytic activation energy; drafted the manuscript. GA carried out the calculations on the phase diagrams (shape effect) in collaboration with GG. DH carried out the calculations on the phase diagrams (segregation effect) in collaboration with GG. All authors read and approved the final manuscript.

Authors’ original submitted files for images

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Guisbiers, G., Abudukelimu, G. & Hourlier, D. Size-dependent catalytic and melting properties of platinum-palladium nanoparticles. Nanoscale Res Lett 6, 396 (2011).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


  • Melting Enthalpy
  • Shape Effect
  • Surface Segregation
  • Vaporization Enthalpy
  • Shape Stability