Advertisement

Mathematical Modelling of Nanocrystal Growth

  • Claudia FanelliEmail author
  • Timothy G. Myers
  • Vincent Cregan
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)

Abstract

We will describe a model for the process of synthesizing nanoparticles of a specific size from a liquid solution. Initially, we will consider a single particle model that accounts for monomer diffusion in solution around the particle and kinetic reactions at the particle surface. For the far-field bulk concentration, a mass conservation expression is used. Based on a small dimensionless parameter, we propose a pseudo-steady state approximation to the model. The model is then extended to a system of N particles. Numerical solutions for the time-dependent average particle radius compared against experimental data are shown to have excellent agreement.

References

  1. 1.
    Bastús, N.G., Comenge, J., Puntes, V.: Kinetically controlled seeded growth synthesis of citrate-stabilized gold nanoparticles of up to 200 nm: size focusing versus Ostwald ripening. Langmuir 27(17), 11098–11105 (2011)CrossRefGoogle Scholar
  2. 2.
    Bullen, C.R., Mulvaney, P.: Nucleation and growth kinetics of CdSe nanocrystals in octadecene. Nano Lett. 4(12), 2303–2307 (2004)CrossRefGoogle Scholar
  3. 3.
    Chuang, X., Hongxun, H., Wei, C. and Jingkang, W.: Crystallization kinetics of CdSe nanocrystals synthesized via the TOPTOPOHDA route. J. Cryst. Growth 310(15), 3504–3507 (2008)CrossRefGoogle Scholar
  4. 4.
    La Mer, V.K., Dinegar, R.: Theory, production and mechanism of formation of monodispersed hydrosols. J. Am. Chem. Soc. 72(11), 4847–4854 (1950)CrossRefGoogle Scholar
  5. 5.
    Mantzaris, N.V.: Liquid-phase synthesis of nanoparticles: particle size distribution dynamics and control. Chem. Eng. Sci. 60(17), 4749–4770 (2005)CrossRefGoogle Scholar
  6. 6.
    Myers, T.G., Fanelli, C.: On the incorrect use and interpretation of the model for colloidal, spherical crystal growth. J. Colloid Interface Sci. 536, 98–104 (2019)CrossRefGoogle Scholar
  7. 7.
    Pan, B., He, R., Gao, F., Cui, D., Zhang, Y.: Study on growth kinetics of CdSe nanocrystals in oleic acid/dodecylamine. J. Cryst. Growth 286(2), 318–323 (2006)CrossRefGoogle Scholar
  8. 8.
    Peng, X., Wickham, J., Alivisatos, A.P.: Kinetics of II–VI and III–V colloidal semiconductor nanocrystal growth:“focusing” of size distributions. J. Am. Chem. Soc. 120(21), 5343–5344 (1998)CrossRefGoogle Scholar
  9. 9.
    Su, H., Dixon, J.D., Wang, A.Y., Low, J., Xu, J., Wang, J.: Study on growth kinetics of CdSe nanocrystals with a new model. Nanoscale Res. Lett. 5(5), 823–828 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Claudia Fanelli
    • 1
    • 2
    Email author
  • Timothy G. Myers
    • 1
    • 2
  • Vincent Cregan
    • 3
  1. 1.Centre de Recerca Matemàtica/BGSMathBarcelonaSpain
  2. 2.Universitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.MACSI/PMTCUniversity of LimerickLimerickIreland

Personalised recommendations