= Solution
A <La Mer diagram> plots the <concentration> of growth species against time. Label the equilibrium <solubility> $C_s$ and a higher effective <nucleation> threshold $C_n$. Generate growth species until the <concentration> briefly exceeds $C_n$; a short <burst nucleation> interval then creates seeds. Consumption brings the <concentration> below $C_n$ while leaving it above $C_s$, 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 $\gamma^3$ at fixed <supersaturation>. More seeds can then form at a smaller <supersaturation>; at fixed total precipitated <mass>, more seeds generally mean a \b[smaller mean final particle size]. A \b[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.<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]{ref}
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