Multiphasic growth dynamics of nanoparticle ensembles

Colloidal nanoparticles are of great interest in modern science and industry, yet the thermodynamic origin of nanoparticle formation remains a mystery and nanoparticle growth frequently exhibits nonclassical dynamics. Here, we tracked hundreds of in-situ growth trajectories of a nanoparticle ensemble using an advanced liquid-phase-TEM, and discovered that nanoparticle growth, including coalescence, exhibits monomer supply rate dependent multiphasic dynamics, unexplainable by current theories. Motivated by this finding, we developed a realistic model and statistical theories of growing nanoparticles, providing a unified, quantitative understanding of the mean and fluctuation of nanoparticle size and size-dependent growth rate across various nanoparticle systems and experimental conditions. Our work reveals that the chemical potential in a nanoparticle has a finite maximum at a critical size and exhibits a nonclassical dependence on nanoparticle size. This clear discrepancy from the classical nucleation theory (CNT) results from the strongly non-extensive free energy originating from nanoparticle motion, configurational degeneracy, and edge interaction, which were neglected in the CNT. We also uncover how this chemical potential in a nanoparticle governs formation and growth dynamics of an ensemble of nanoparticles, together with the time-dependent monomer concentration in solution.