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Nanoparticle Growth via the Precipitation Method

  • V. Cregan
  • T. G. Myers
  • S. L. Mitchell
  • H. Ribera
  • M. C. Schwarzwälder
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

We consider a model for the evolution of a system of nanoparticles in solution via the processes of size focusing and Ostwald ripening. The model consists of a diffusion equation for the concentration of the solution, a Stefan-type condition to track the particle-liquid interfaces and a time-dependent expression for the bulk concentration obtained via mass conservation. Based on a small dimensionless parameter we propose a pseudo-steady state model, which is solved numerically to obtain the average particle radius and standard deviation. The results are shown to be in good agreement with experimental data for cadmium selenide nanoparticles.

Notes

Acknowledgements

V. Cregan, H. Ribera and M.C. Schwarzwälder were supported by “la Caixa” foundation grant. T. Myers acknowledges the support of a Ministerio de Ciencia e Innovación Grant MTM2011-23789. S.L. Mitchell acknowledges the support of the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie) funded by the Science Foundation Ireland grant 12/IA/1683.

References

  1. 1.
    Clark, M.D., Kumar, S.K., Owen, J.S., Chan, E.M.: Nano Lett. 11(5), 1976–1980 (2011)CrossRefGoogle Scholar
  2. 2.
    La Mer, V.K.: Ind. Eng. Chem. 44(6), 1270–1277 (1952)Google Scholar
  3. 3.
    Mantzaris, N.V.: Chem. Eng. Sci. 60(17), 4749–4770 (2005)Google Scholar
  4. 4.
    Peng, X., Wickham, J., Alivisatos, A.P.: J. Am. Chem. Soc. 120(21), 5343–5344 (1998)CrossRefGoogle Scholar
  5. 5.
    Peng, Z.A., Peng, Z.: J. Am. Chem. Soc. 123(7), 1389–1395 (2001)Google Scholar
  6. 6.
    Sugimoto, T.: Adv. Colloid Interface Sci. 28, 65–108 (1987)CrossRefGoogle Scholar
  7. 7.
    Talapin, D.V., Rogach, A.L., Haase, M., Weller, H.: J. Phys. Chem. B 105(49), 12278–12285 (2001)CrossRefGoogle Scholar
  8. 8.
    Viswanatha, R., Sarma, D.D.: Growth of nanocrystals in solution. In: Nanomaterials Chemistry: Recent Developments and New Directions, pp. 139–170. Wiley Online Library, Hoboken (2007)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • V. Cregan
    • 1
  • T. G. Myers
    • 1
  • S. L. Mitchell
    • 2
  • H. Ribera
    • 1
  • M. C. Schwarzwälder
    • 1
  1. 1.Centre de Recerca MatemàticaBarcelonaSpain
  2. 2.Mathematics Applications Consortium for Science and IndustryUniversity of LimerickCo. LimerickIreland

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