Study of nanoparticle stability

In many situations of experimental and industrial interest, nanoparticles with specific properties need to be synthesized. An emerging physical problem is to predict how the shape evolution and fluctuations of such particles are influenced by constituent material parameters and temperature. The fluctuations can be a consequence of: random initial data (preparation of shapes that are randomly distributed in the lab setting); and the effect of random noise by the environment. Mathematically, this problem motivates the use of stochastic tools in free boundary settings.

I have been addressing questions arising in this context in collaboration with Prof. J. D. Erlebacher at the Materials Science & Engineering Dept., Johns Hopkins U. Our approach is primarily analytical, driven by experimental issues.

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Research leading to some of the publications listed on this page was supported by the National Science Foundation through grants DMS-0847587 (2009-14) and DMR-0520471 (2007-09).

Topics and papers:

  • The relevance of the room-temperature Kirkendall effect in explaining the formation of hollow nanoparticles: Derivation of shape fluctuation modes of slightly perturbed spherical particle; description of shape fluctuation statistics via the Gibbs distribution for initial shape; and comparison to experimental observations regarding time of formation.

    Related papers:

    1. J. Erlebacher and D. Margetis (2014), Mechanism of hollow nanoparticle formation due to shape fluctuations, Physical Review Letters, Vol. 112, 155505 (5pp).