Multiphasic size-dependent growth dynamics of nanoparticle ensembles

Abstract

Colloidal nanoparticles are of great interest in modern science and industry. However, the thermodynamic mechanism and dynamics of nanoparticle growth have yet to be understood. Addressing these issues, we tracked hundreds of in-situ growth trajectories of a nanoparticle ensemble using liquid-phase TEM and found that the nanoparticle growth, including coalescence, exhibits nanoparticle size-dependent multiphasic dynamics, unexplainable by current theories. Motivated by this finding, we developed a model and theory for an ensemble of growing nanoparticles, providing a unified, quantitative understanding of the time-dependent mean and fluctuation of nanoparticle size and size-dependent growth rate profiles across various nanoparticle systems and experimental conditions. Our work reveals that the chemical potential in a small nanoparticle strongly deviates from the Gibbs–Thomson equation, shedding light on how it governs the size-dependent growth dynamics of nanoparticles. Copyright © 2025 the Author(s).