Ostwald ripening
Kelvin's equation describes the relationship between the radius of curvature and the chemical potential between the surface and the inner volume: where
Inferring from Fick’s first law of diffusion, the particles will move from big concentrations, corresponding to areas surrounding small particles, to small concentrations, corresponding to areas surrounding large nanoparticles.
The history of research progress in quantitatively modeling Ostwald ripening is long, with many derivations.
[8] In 1958, Lifshitz and Slyozov[9] performed a mathematical investigation of Ostwald ripening in the case where diffusion of material is the slowest process.
They finally conclude that the average radius of the particles ⟨R⟩, grows as follows: where Note that the quantity ⟨R⟩3 is different from ⟨R3⟩, and that the statement that ⟨R⟩ goes as t1/3 relies on ⟨R⟩0 being zero; but because nucleation is a separate process from growth, this places ⟨R⟩0 outside the bounds of validity of the equation.
[citation needed] Also contained in the Lifshitz and Slyozov derivation is an equation for the size distribution function f(R, t) of particles.
Three years after that Lifshitz and Slyozov published their findings (in Russian, 1958), Carl Wagner performed his own mathematical investigation of Ostwald ripening,[10] examining both systems where diffusion was slow and also where attachment and detachment at the particle surface was slow.
This duplicate derivation went unnoticed for years because the two scientific papers were published on opposite sides of the Iron Curtain in 1961.
Even some systems that undergo spinodal decomposition have been shown to quantitatively obey LSW theory after initial stages of growth.
If the experimental data obeys neither equation, then it is likely that another mechanism is taking place and Ostwald ripening is not occurring.
The rate of this diffusion process is linked to the solubility of the monomer in the continuous (water) phase of the emulsion.
The smaller the pore size, the higher is the supersaturation of the solution required for the crystals to grow.
[15] Another gastronomical example is the ouzo effect, where the droplets in the cloudy microemulsion grow by Ostwald ripening.
In geology, it is the textural coarsening, aging or growth of phenocrysts and crystals in solid rock which is below the solidus temperature.
Limiting Ostwald ripening is fundamental in modern technology for the solution synthesis of quantum dots.
[17] Ostwald ripening is also the key process in the digestion and aging of precipitates, an important step in gravimetric analysis.
Ostwald ripening can also occur in emulsion systems, with molecules diffusing from small droplets to large ones through the continuous phase.
When a miniemulsion is desired, an extremely hydrophobic compound is added to stop this process from taking place.
