M3 Ostwald Ripening

Topic

The curvature of each small particle within this nanoparticle suspension—which is far more pronounced than that of any large particle in the same suspension—increases the particle's solubility according to the Kelvin equation. This equation describes how a surface with greater curvature raises the surface energy per atom; this additional surface energy causes the material of the small particle to dissolve more readily into the surrounding solution than the material of a much less curved, large particle of the same type. The fact that the particle is smaller, and thus possesses even greater curvature, results in higher solubility, again in accordance with the Kelvin equation.

This disparity in solubility—where small particles are more soluble than large ones within the same suspension—drives a dissolution-reprecipitation process between them: material preferentially dissolving from the more soluble small particles becomes available in the solution to reprecipitate onto the less soluble large particles. Consequently, the large particles grow at the expense of the small particles, which in turn shrink further. A greater difference in solubility between the small and large particles accelerates this dissolution-reprecipitation process, causing the large particles to grow more rapidly at the expense of the small ones. Thus, this model—characterized by small-particle curvature and the dissolution-reprecipitation process that initiated the system—kinetically describes (via the Lifshitz-Slyozov-Wagner law) how the mean radius of the nanoparticle suspension evolves over time as the dissolution-reprecipitation process proceeds. Specifically, this Ostwald ripening causes large particles in the suspension to grow at the expense of smaller ones, thereby broadening the size distribution—a distribution that had previously been narrowed through the temporal separation of explosive nucleation and diffusion-controlled growth (as described by another model in this set). Allowing this Ostwald ripening to continue beyond the initial bottom-up synthesis causes the monodispersity achieved through "size focusing" to be progressively lost, moving in the exact opposite direction of the outcome that model sought to achieve.

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