Journal of Nanoparticle Research

, Volume 13, Issue 11, pp 6059–6067 | Cite as

Thermodynamics and molecular dynamics investigation of a possible new critical size for surface and inner cohesive energy of Al nanoparticles

  • Amir Chamaani
  • Ehsan Marzbanrad
  • Mohammad Reza Rahimipour
  • Maziar S. Yaghmaee
  • Alireza Aghaei
  • Reza Darvishi Kamachali
  • Yashar Behnamian
Special Issue: Nanostructured Materials 2010

Abstract

In this study, the authors first review the previously developed, thermodynamics-based theory for size dependency of the cohesion energy of free-standing spherically shaped Al nanoparticles. Then, this model is extrapolated to the cubic and truncated octahedron Al nanoparticle shapes. A series of computations for Al nanoparticles with these two new shapes are presented for particles in the range of 1–100 nm. The thermodynamics computational results reveal that there is a second critical size around 1.62 and 1 nm for cubes and truncated octahedrons, respectively. Below this critical size, particles behave as if they consisted only of surface-energy-state atoms. A molecular dynamics simulation is used to verify this second critical size for Al nanoparticles in the range of 1–5 nm. MD simulation for cube and truncated octahedron shapes shows the second critical point to be around 1.63 and 1.14 nm, respectively. According to the modeling and simulation results, this second critical size seems to be a material property characteristic rather than a shape-dependent feature.

Keywords

Modeling Al nanoparticle Thermodynamics Molecular dynamics simulation Critical size 

References

  1. Allen MP, Tildesley DJ (1992) Computer simulation of liquids. Clarendon, OxfordGoogle Scholar
  2. Antony Jobin K, Vasa Nilesh J, Chakravarthy SR, Sarathi R (2010) Understanding the mechanism of nano-aluminum particle formation by wire explosion process using optical emission technique. J Quant Spectrosc Radiat Transfer 111:2509–2516CrossRefGoogle Scholar
  3. Barin I (ed) (1993) Thermodynamical data of pure substances. VCH Verlagsgesellschaft mbH, WeinheimGoogle Scholar
  4. Bhatt Divesh et al (2006) Critical properties of aluminum. J Am Chem Soc 128:4224–4225CrossRefGoogle Scholar
  5. Chen B, Penwell D, Benedetti LR, Jeanloz R, Kruger MB (2002) Particle-size effect on the compressibility of nanocrystalline alumina. Phys Rev B 66:144101CrossRefGoogle Scholar
  6. Ding F, Bolton K, Ros`en A (2004) Iron-carbide cluster thermal dynamics for catalyzed carbon nanotube growth. J Vac Sci Technol A 22:1471–1476CrossRefGoogle Scholar
  7. Ercolessi F, Adams JB (1994) Interatomic potentials from first-principles calculations: the force-matching method. Europhys Lett 26:584–588CrossRefGoogle Scholar
  8. Ercolessi F, Parrinello M, Tosatti E (1988) Simulation of gold in the glue model. Phil Magaz A 58:213–226CrossRefGoogle Scholar
  9. Haile JM (1992) Molecular dynamics simulation: elementary method. John Wiley & Sons, New YorkGoogle Scholar
  10. Iida T, Guthrie RIL (1993) The physical properties of liquid metals. Clarendon, OxfordGoogle Scholar
  11. Jiang Q, Li JC, Chi BQ (2002) Size-dependent cohesive energy of nanocrystals. Chem Phys Lett 366:551CrossRefGoogle Scholar
  12. Kaptay G, Bader E, Bolyan L (2000) Interfacial forces and energies relevant to production of metal matrix composites. Mater Sci Forum 329–330:151–156CrossRefGoogle Scholar
  13. Kaptay G, Csicsovszki G, Yaghmaee MS (2003) An absolute scale for the cohesion energy of pure metals. Mater Sci Forum 414–415:235–240CrossRefGoogle Scholar
  14. Kim HK, Huh SH, Park JW et al (2002) The cluster size dependence of thermal stabilities of both molybdenum and tungsten nanoclusters. Chem Phys Lett 354(1–2):165–172CrossRefGoogle Scholar
  15. Li H, Zhao M, Jiang Q (2009) Cohesive energy of clusters referenced by Wulff construction. J Phys Chem C 113:7594–7597CrossRefGoogle Scholar
  16. Nanda KK, Sahu SN, Behera SN (2002) Liquid-drop model for the size-dependent melting of low-dimensional systems. Phys Rev A 66:013208CrossRefGoogle Scholar
  17. Qi WH, Lee ST (2009) Core–shell structures of silicon nanoparticles and nanowires with free and hydrogenated surface. Chem Phys Lett 483:247–249CrossRefGoogle Scholar
  18. Qi WH, Wang MP (2002) Size effect on the cohesive energy of nanoparticle. J Mater Sci Lett 21:1743–1745CrossRefGoogle Scholar
  19. Qi WH, Wang MP, Xu GY (2003) The particle size dependence of cohesive energy of metallic nanoparticles. Chem Phys Lett 372:632–634CrossRefGoogle Scholar
  20. Qi WH, Wang MP, Zhou M, Hu WY (2005) Surface-area-difference model for thermodynamic properties of metallic nanocrystals. J Phys D Appl Phys 38:1429–1436CrossRefGoogle Scholar
  21. Qi WH, Huang B, Wang MP (2009a) Bond-length and -energy variation of small gold nanoparticles. J Comput Theor Nanosci 6:635–639CrossRefGoogle Scholar
  22. Qi WH, Huang B, Wang MP (2009b) Structure of unsupported small palladium nanoparticles. Nanoscale Res Lett 4:269–273CrossRefGoogle Scholar
  23. Shao X, Wu X, Cai W (2010) Growth pattern of truncated octahedron in AlN (N ≤ 310) clusters. J Phys Chem A 114:29–36CrossRefGoogle Scholar
  24. Sun Ch Q, Wang Y, Tay BK, Li S, Huang H, Zhang YB (2002) Correlation between the melting point of a nanosolid and the cohesive energy of a surface atom. J Phys Chem B 106:10701–10705CrossRefGoogle Scholar
  25. Varnavski Oleg et al (2010) Critical size for the observation of quantum confinement in optically excited gold clusters. J Am Chem Soc 132:16–17CrossRefGoogle Scholar
  26. Xie D, Wang MP, Qi WH (2004) A simplified model to calculate the surface-to-volume atomic ratio dependent cohesive energy of nanocrystals. J Phys Condens Matter 16:L401–L405CrossRefGoogle Scholar
  27. Yaghmaee MS, Shokri B (2007) Effect of size on bulk and surface cohesion energy of metallic nano-particles. Smart Mater Struct 16:349–354CrossRefGoogle Scholar
  28. Yaghmaee MS, Shokri B, Rahimipour MR (2009) Size dependence surface activity of metallic nanoparticles. Plasma Processes Polym 6:S876–S882CrossRefGoogle Scholar
  29. Zhang H, Penn RL, Hamers RJ, Banfield JF (1999) Enhanced adsorption of molecules on surfaces of nanocrystalline particles. J Phys Chem B 103:4656–4662CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Amir Chamaani
    • 1
  • Ehsan Marzbanrad
    • 1
  • Mohammad Reza Rahimipour
    • 1
  • Maziar S. Yaghmaee
    • 1
  • Alireza Aghaei
    • 1
  • Reza Darvishi Kamachali
    • 2
  • Yashar Behnamian
    • 3
  1. 1.Department of CeramicMaterials and Energy Research CenterTehranIran
  2. 2.ICAMS, Ruhr-University BochumBochumGermany
  3. 3.Department of Chemical and Materials EngineeringUniversity of AlbertaEdmontonCanada

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