From Atoms to Nanoparticles
Nanoparticle synthesis begins when dissolved precursors reach a supersaturation threshold, triggering the spontaneous formation of solid nuclei from solution. This nucleation event is governed by classical nucleation theory: the competition between the favorable volume free energy of the new phase and the unfavorable surface energy of creating a new interface. Only clusters that exceed the critical radius survive and grow.
The LaMer Burst Nucleation Model
Victor LaMer's 1950 model explains how monodisperse nanoparticles form. Monomers accumulate until supersaturation crosses a nucleation threshold, triggering a burst of nucleus formation that rapidly depletes monomers. Once supersaturation drops below the nucleation threshold, no new nuclei form and existing particles grow uniformly by diffusion — separating nucleation from growth in time produces remarkably uniform size distributions.
Critical Radius and the Energy Barrier
The critical nucleus radius r* marks the tipping point: clusters smaller than r* are unstable and dissolve, while larger clusters grow spontaneously. The nucleation barrier ΔG* depends on the cube of the surface energy divided by the square of the supersaturation driving force. High supersaturation or low surface energy lowers this barrier, promoting rapid nucleation of many small nuclei rather than slow growth of a few large ones.
Ostwald Ripening and Size Control
After initial growth, Ostwald ripening reshapes the size distribution. Smaller particles have higher surface curvature and thus higher chemical potential — they slowly dissolve while larger particles grow. This thermodynamic coarsening process narrows the relative size distribution but increases the mean diameter over time. Controlling ripening through temperature, capping agents, and reaction quenching is central to precision nanoparticle manufacturing.