nucleation alone. In 1950, Viktor LaMer used CNT as the nucleation basis for his model of nanoparticle growth. There are three portions to the LaMer model: 1. Rapid increase in the concentration of free monomers in solution, 2. fast nucleation of the monomer characterized by explosive growth of particles, 3. Growth of particles controlled by diffusion of the monomer. This model describes that the growth on the nucleus is spontaneous but limited by diffusion of the precursor to the nuclei surface. The LaMer model has not been able to explain the kinetics of nucleation in any modern system. Ostwald ripening Ostwald ripening is a process typically avoided in nanoparticle synthesis as it is known to negatively impact the functionality of nanoparticles. In this process, large particles grow at the expense of the smaller particles due to diffusion of disperse phase molecules through the continuous phase. Two-step mechanism – autocatalysis model In 1997, Finke and Watzky proposed a new kinetic model for the nucleation and growth of nanoparticles. This 2-step model suggested that constant slow nucleation (occurring far from supersaturation) is followed by autocatalytic growth where dispersity of nanoparticles is largely determined. This F-W (Finke-Watzky) 2-step model provides a firmer mechanistic basis for the design of nanoparticles with a focus on size, shape, and dispersity control. The model was later expanded to a 3-step and two 4-step models between 2004-2008. Here, an additional step was included to account for small particle aggregation, where two smaller particles could aggregate to form a larger particle. Next, a fourth step (another autocatalytic step) was added to account for a small particle agglomerating with a larger particle. Finally in 2014, an alternative fourth step was considered that accounted for a atomistic surface growth on a large particle. Modeling nucleation in nanoparticles Recent work has begun to look at modeling the early stages of nucleation as well as the rates associated with nucleation through multiscale computational modeling. This includes exploration into an improved kinetic rate equation model as well as density function studies using the phase-field crystal model. Measuring the rate of nucleation The classical nucleation theory explains that the nucleation rate will correspond to the driving force One method for measuring the nucleation rate is through the induction time method. This process uses the stochastic nature of nucleation and determines the rate of nucleation by analysis of the time between constant supersaturation and when crystals