Effect of coalescence energy release on the temporal shape evolution of nanoparticles

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Abstract
The driving force for coalescence of two nanoparticles is the reduction in free energy through a reduction in surface area. The resulting particle also has a lower total potential energy, which through conservation of energy can lead to a significant increase in particle temperature. In a growth process particle heating competes with heat transfer to the cooler carrier gas. In this paper we develop a model that illustrates that this temperature increase can be extremely important and should be accounted for when modeling collision/coalescence processes. Our calculations indicate that the heat release associated with particle coalescence may reduce the coalescence time by as much as a few orders of magnitude. This is especially true for the final stages of exponential surface area decay toward sphericity, which becomes much faster and qualitatively explains the fact that primary particles of only a few nanometers in diameter are of spherical shape. We develop in this analysis a dimensionless “coalescence heating number,” which can be used to assess if the exothermic nature of coalescence should be accounted for under a given set of conditions. We also show that a simple coalescence model, which includes the temperature effect, closely follows our prior molecular dynamics calculations for silicon nanoparticles sintering. This analysis also explains a set of experimental results for alumina nanoparticle production, previously unexplainable by classical methods. Finally, we see that lower gas pressures result in lower gas-phase heat transfer, which in turn results in larger primary particles.