Abstract
It is well known today that the melting temperature and the catalytic activation energy of nanoparticles are size-dependent. These properties are here analyzed in a size range between 4 and 100 nm, with a special attention to sizes below 20 nm. Nevertheless, their unique properties are determined not only by their size but also by their shape defined by the relative area of different surface facets. In this paper, the influence of crystal structure and shape of the nanoparticles on the melting and catalytic properties are theoretically investigated. The theory is developed for cubic crystal structures i.e., simple cubic, body centered cubic, and face centered cubic. The following shapes are then considered: tetrahedron, cube, octahedron, decahedron, dodecahedron, rhombic dodecahedron, truncated octahedron, cuboctahedron, and icosahedron. The predictions were compared with available experimental data and molecular dynamics simulation results coming from the literature and relatively good agreement was obtained for gold, silver, nickel, and platinum nanoparticles.
Similar content being viewed by others
References
Abudukelimu G (2009) Thermodynamical approach of phase diagrams of nanosystems: size and shape effects. PhD Thesis in Physics, University of Mons-Hainaut
Andrievski RA (2009) Size-dependent effects in properties of nanostructured materials. Rev Adv Mater Sci 21:107–133
Baletto F, Ferrando R (2005) Structural properties of nanoclusters: energetic, thermodynamic, and kinetic effects. Rev Mod Phys 77:371
Baletto F, Ferrando R, Fortunelli A, Montalenti F, Mottet C (2002) Crossover among structural motifs in transition and noble-metal clusters. J Chem Phys 116:3856
Barnard AS (2010) Modelling of nanoparticles: approaches to morphology and evolution. Rep Prog Phys 73:086502
Barnard AS (2011) Useful equations for modeling the relative stability of common nanoparticle morphologies. Comput Phys Commun 182:11–13
Barnard AS, Chen Y (2011) Kinetic modelling of the shape-dependent evolution of faceted gold nanoparticles. J Mater Chem 21:12239–12245
Barnard AS, Lin XM, Curtiss LA (2005) Equilibrium morphology of face-centered cubic gold nanoparticles >3 nm and the shape changes induced by temperature. J Phys Chem B 109:24465–24472
Barnard AS, Young NP, Kirkland AI, Van Huis MA, Xu H (2009) Nanogold: a quantitative phase map. ACS Nano 3:1431–1436
Burda C, Chen X, Narayanan R, El-Sayed MA (2005) Chemistry and properties of nanocrystals of different shapes. Chem Rev 105:1025–1102
Dash JG (1999) History of the search for continuous melting. Rev Mod Phys 71:1737–1743
Ganguli D (2008) Size effect in melting: a historical overview. Trans Indian Ceram Soc 67:49–62
Gracia-Pinilla MA, Pérez-Tijerina E, Garcia JA, Fernandez-Navarro C, Tlahuice-Flores A, Mejia-Rosales S, Montejano-Carrizales JM, José-Yacaman M (2008) On the structure and properties of silver nanoparticles. J Phys Chem C 112:13492–13498
Guisbiers G (2010) Size-dependent materials properties toward a universal equation. Nanoscale Res Lett 5(7):1132–1136
Guisbiers G (2012) Review on the analytical models describing melting at the nanoscale. J Nanosci Lett 2:8
Guisbiers G, Buchaillot L (2009a) Modeling the melting enthalpy of nanomaterials. J Phys Chem C 113(9):3566–3568
Guisbiers G, Buchaillot L (2009b) Universal size/shape-dependent law for characteristic temperatures. Phys Lett A 374(2):305–308
Guisbiers G, Abudukelimu G, Hourlier D (2011) Size-dependent catalytic and melting properties of platinum-palladium nanoparticles. Nanoscale Res Lett 6:396
Halperin WP (1986) Quantum size effects in metal particles. Rev Mod Phys 58:533
Jiang Q, Lu HM (2008) Size dependent interface energy and its applications. Surf Sci Rep 63:427–464
Kittel C (1995) Introduction to solid state physics, 7th edn. Wiley, New York
Koga K, Sugawara K (2003) Population statistics of gold nanoparticle morphologies: direct determination by HREM observations. Surf Sci 529:23–35
Koga K, Ikeshoji T, Sugawara K (2004) Size- and temperature-dependent structural transitions in gold nanoparticles. Phys Rev Lett 92:115507
Lu HM, Jiang Q (2004) Size-dependent surface energies of nanocrystals. J Phys Chem B 108:5617–5619
Lu HM, Meng XK (2010) Theoretical model to calculate catalytic activation energies of platinum nanoparticles of different sizes and shapes. J Phys Chem C 114:1534–1538
Lu HM, Li PY, Cao ZH, Meng XK (2009) Size-, shape-, and dimensionality-dependent melting temperatures of nanocrystals. J Phys Chem C 113:7598–7602
Martienssen W, Warlimont H (2005) Springer handbook of condensed matter and materials data. Springer, Berlin
Mei QS, Lu K (2007) Melting and superheating of crystalline solids: from bulk to nanocrystals. Prog Mater Sci 52:1175–1262
Nanda KK (2009) Size-dependent melting of nanoparticles: 100 years of thermodynamic model. Pramana J Phys 72:617–628
Niu W, Zheng S, Wang D, Liu X, Li H, Han S, Chen J, Tang Z, Xu G (2009) Selective synthesis of single-crystalline rhombic dodecahedral, octahedral, and cubic gold nanocrystals. J Am Chem Soc 131:697–703
Pawlow P (1909) Z Phys Chem 65:1
Qi WH, Wang MP (2004) Size and shape dependent melting temperature of metallic nanoparticles. Mater Chem Phys 88:280–284
Qi WH, Wang MP (2005) Size and shape dependent lattice parameters of metallic nanoparticles. J Nanopart Res 7:51–57
Qi WH, Wang MP, Su YC (2002) Size effect on the lattice parameters of nanoparticles. J Mater Sci Lett 21:877–878
Roduner E (2006) Size matters: why nanomaterials are different. Chem Soc Rev 35:583–592
Safaei A, Shandiz MA, Sanjabi S, Barber ZH (2008) Modeling the melting temperature of nanoparticles by an analytical approach. J Phys Chem C 112:99–105
Sun CQ (2007) Size dependence of nanostructures: impact of bond order deficiency. Prog Solid State Chem 35(1):1–159
Sun Y, Xia Y (2002) Shape-controlled synthesis of gold and silver nanoparticles. Science 298:2176–2179
Sun CQ, Tay BK, Zeng XT, Li S, Chen TP, Zhou J, Bai HL, Jiang EY (2002) Bond-order-bond-length-bond-strength (bond-OLS) correlation mechanism for the shape-and-size dependence of a nanosolid. J Phys Condens Matter 14(34):7781–7795
Tao AR, Habas S, Yang P (2008) Shape control of colloidal metal nanocrystals. Small 4:310–325
Tjong SC, Chen H (2004) Nanocrystalline materials and coatings. Mater Sci Eng R 45:1–88
Vitos L, Ruban AV, Skriver HL, Kollar J (1998) The surface energy of metals. Surf Sci 411(1–2):186–202
Wang ZL (ed) (2000) Characterization of nanophase materials. Wiley-VCH, Weinheim
Wang Y, Teitel S, Dellago C (2004) Melting and equilibrium shape of icosahedral gold nanoparticles. Chem Phys Lett 394:257–261
Wautelet M (1998) On the shape dependence of the melting temperature of small particles. Phys Lett A 246(3–4):341–342
Wautelet M (2005) On the melting of polyhedral elemental nanosolids. Eur Phys J Appl Phys 29(1):51–54
Wautelet M, Duvivier D (2007) The characteristic dimensions of the nanoworld. Eur J Phys 28(5):953–959
Xiong S, Qi W, Cheng Y, Huang B, Wang M, Li Y (2011a) Modeling size effects on the surface free energy of metallic nanoparticles and nanocavities. Phys Chem Chem Phys 13:10648–10651
Xiong S, Qi W, Cheng Y, Huang B, Wang M, Li Y (2011b) Universal relation for size dependent thermodynamic properties of metallic nanoparticles. Phys Chem Chem Phys 13:10652–10660
Yacaman MJ, Ascencio JA, Liu HB, Gardea-Torresdey J (2001a) Structure shape and stability of nanometric sized particles. J Vac Sci Technol B 19(4):1091–1103
Yacaman MJ, Marin-Almazo M, Ascencio JA (2001b) High resolution TEM studies on palladium nanoparticles. J Mol Catal A 173:61–74
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guisbiers, G., Abudukelimu, G. Influence of nanomorphology on the melting and catalytic properties of convex polyhedral nanoparticles. J Nanopart Res 15, 1431 (2013). https://doi.org/10.1007/s11051-013-1431-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11051-013-1431-x