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Nanoparticle Growth via the Precipitation Method

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Progress in Industrial Mathematics at ECMI 2016 (ECMI 2016)

Part of the book series: Mathematics in Industry ((TECMI,volume 26))

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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.

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References

  1. Clark, M.D., Kumar, S.K., Owen, J.S., Chan, E.M.: Nano Lett. 11(5), 1976–1980 (2011)

    Article  Google Scholar 

  2. La Mer, V.K.: Ind. Eng. Chem. 44(6), 1270–1277 (1952)

    Google Scholar 

  3. Mantzaris, N.V.: Chem. Eng. Sci. 60(17), 4749–4770 (2005)

    Google Scholar 

  4. Peng, X., Wickham, J., Alivisatos, A.P.: J. Am. Chem. Soc. 120(21), 5343–5344 (1998)

    Article  Google Scholar 

  5. Peng, Z.A., Peng, Z.: J. Am. Chem. Soc. 123(7), 1389–1395 (2001)

    Google Scholar 

  6. Sugimoto, T.: Adv. Colloid Interface Sci. 28, 65–108 (1987)

    Article  Google Scholar 

  7. Talapin, D.V., Rogach, A.L., Haase, M., Weller, H.: J. Phys. Chem. B 105(49), 12278–12285 (2001)

    Article  Google Scholar 

  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 

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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.

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Authors and Affiliations

  1. Centre de Recerca Matemàtica, Campus UAB Edifici C, Bellaterra, 08193, Barcelona, Spain

    V. Cregan, T. G. Myers, H. Ribera & M. C. Schwarzwälder

  2. Mathematics Applications Consortium for Science and Industry, University of Limerick, Sreelane, Castletroy, Co. Limerick, Ireland

    S. L. Mitchell

Authors
  1. V. Cregan
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  2. T. G. Myers
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  3. S. L. Mitchell
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  4. H. Ribera
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  5. M. C. Schwarzwälder
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Corresponding author

Correspondence to V. Cregan .

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Editors and Affiliations

  1. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Peregrina Quintela

  2. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Patricia Barral

  3. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Dolores Gómez

  4. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Francisco J. Pena

  5. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Jerónimo Rodríguez

  6. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Pilar Salgado

  7. Department of Applied Mathematics, University of Santiago de Compostela, Lugo, Spain, Spain

    Miguel E. Vázquez-Méndez

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Cregan, V., Myers, T.G., Mitchell, S.L., Ribera, H., Schwarzwälder, M.C. (2017). Nanoparticle Growth via the Precipitation Method. In: Quintela, P., et al. Progress in Industrial Mathematics at ECMI 2016. ECMI 2016. Mathematics in Industry(), vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-63082-3_56

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