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
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Research leading to some of the publications listed on this page was
supported by the National Science Foundation through grants
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.
1. J. Erlebacher and D. Margetis (2014),
Mechanism of hollow nanoparticle formation due to shape fluctuations,
Physical Review Letters, Vol. 112, 155505 (5pp).