A Model for Nanoparticle Melting with a Newton Cooling Condition and Size-Dependent Latent Heat

Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

In this paper we study the melting of a spherical nanoparticle. To match with experimental data, the model includes several new features such as size-dependent latent heat and a cooling boundary condition at the boundary. Melt temperature variation and density change are also included. A novel form of Stefan condition is used to determine the position of the melt front. Results show that melting times can be significantly faster than those predicted by previous theoretical models, primarily due to the latent heat variation.

Notes

Acknowledgements

The authors acknowledge that the research leading to these results has received funding from “la Caixa” Foundation. TM acknowledges financial support from the Ministerio de Ciencia e Innovación grant MTM2014-56218.

References

  1. 1.
    Alexiades, V., Solomon, A.D.: Mathematical Modeling of Melting and Freezing Processes. Hemisphere, Washington, DC (1992)Google Scholar
  2. 2.
    Bachels, T., Güntherodt, H.-J., Schäfer, R.: Melting of isolated tin nanoparticles. Phys. Rev. Lett. 85, 1250–1253 (2000)CrossRefGoogle Scholar
  3. 3.
    Back, J.M.: Stefan problems for melting nanoscaled particles. Ph.D. thesis, U. Queensland (2014). http://eprints.qut.edu.au/79905/1/Julian_Back_Thesis.pdf
  4. 4.
    Buffat, P., Borel, J.-P.: Size effect on the melting temperature of gold particles. Phys. Rev. A 13, 2287–2298 (1976)CrossRefGoogle Scholar
  5. 5.
    Ercolessi, F., Andreoni, W., Tosatti, E.: Melting of small gold particles: mechanism and size effects. Phys. Rev. Lett. 66, 911–914 (1991)CrossRefGoogle Scholar
  6. 6.
    Font, F., Myers, T.G., Mitchell, S.L.: A mathematical model for nanoparticle melting with density change. Microfluid. Nanofluid. 18, 233–243 (2014)CrossRefGoogle Scholar
  7. 7.
    Jiang, H., Moon, K.-S., Dong, H., Hua, F., Wong, C.: Size-dependent melting properties of tin nanoparticles. Chem. Phys. Lett. 429, 492–496 (2006)CrossRefGoogle Scholar
  8. 8.
    Lai, S., Guo, J., Petrova, V., Ramanath, G., Allen, L.: Size-dependent melting properties of small tin particles: nanocalorimetric measurements. Phys. Rev. Lett. 77, 99–102 (1996)CrossRefGoogle Scholar
  9. 9.
    Myers, T.G.: Mathematical modelling of phase change at the nanoscale. Int. Commun. Heat Mass Transfer 76, 59–62 (2016)CrossRefGoogle Scholar
  10. 10.
    Ribera, H., Myers, T.G.: A mathematical model for nanoparticle melting with size-dependent latent heat and melt temperature. Microfluid. Nanofluid. 20(11), 147 (2016)CrossRefGoogle Scholar
  11. 11.
    Shin, J.-H., Deinert, M.R.: A model for the latent heat of melting in free standing metal nanoparticles. J. Chem. Phys. 140, 164707 (2014)CrossRefGoogle Scholar
  12. 12.
    Sun, J., Simon, S.: The melting behavior of aluminum nanoparticles. Thermochim. Acta 463, 32–40 (2007)CrossRefGoogle Scholar
  13. 13.
    Tolman, R.C.: The effect of droplet size on surface tension. J. Chem. Phys. 17, 333 (1949)CrossRefGoogle Scholar
  14. 14.
    Xiong, S., Qi, W., Cheng, Y., Huang, B., Wang, M., Li, Y.: Universal relation for size dependent thermodynamic properties of metallic nanoparticles. Phys. Chem. Chem. Phys. 13, 10652–10660 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Centre de Recerca MatemàticaBarcelonaSpain

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