A La Mer diagram plots the concentration of growth species against time. Label the equilibrium solubility and a higher effective nucleation threshold . Generate growth species until the concentration briefly exceeds ; a short burst nucleation interval then creates seeds. Consumption brings the concentration below while leaving it above , allowing existing particles to grow without substantial continuing nucleation. Rapid mixing, a short seed-formation interval and a common growth period help produce a narrow particle size distribution. Suppress secondary nucleation and aggregation, then quench or consume the remaining growth species when the desired size is reached. The threshold is an operational kinetic scale, not a sharp new equilibrium phase boundary.
Reducing the solid-liquid interfacial tension lowers the classical barrier, which scales as at fixed supersaturation. More seeds can then form at a smaller supersaturation; at fixed total precipitated mass, more seeds generally mean a smaller mean final particle size. A narrower distribution is not guaranteed: if nucleation continues throughout growth, particles have different ages and the distribution can broaden. A brief well-separated burst and uniform subsequent growth are the controlling requirements, not low interfacial tension alone. The historical model concerns separated nucleation/growth in sulfur hydrosols, rather than a universal demonstrated mechanism for every nanoparticle synthesis.[ref]
Theory, Production and Mechanism of Formation of Monodispersed Hydrosols by Victor K. La Mer and Robert H. Dinegar. JACS 72 (1950), pp.4847–4854, model and monodisperse-hydrosol preparation