LaMer model
The LaMer model , which was developed by the American chemist Victor LaMer (1895–1966), explains the growth of nanoparticles using a kinetic approach. Originally, LaMer was the first to describe the production of monodisperse sulfur brines. The model is used today for the growth of a wide variety of nanoparticles. Since the production of nanoparticles of the same size is a constant challenge in colloid chemistry , the importance of the model lies in the qualitative description of the necessary conditions under which monodisperse nanoparticles can arise. In addition, diffusion coefficients can be determined quantitatively with the help of the mathematical formulation of the model.
The LaMer model is explained in a simplified manner using the dilution method. Sulfur is soluble in ethanol , but insoluble in water. If water is slowly added to a sulfur-in-ethanol solution, the solubility of the sulfur in the ethanol / water mixture decreases as the proportion of water increases. After the saturation concentration has been reached, the absence of nucleation nuclei leads to oversaturation . Only when a critical concentration is exceeded does the sulfur spontaneously nucleate to form nanoparticles. The nucleation rate is then so great that nuclei of the same size are formed everywhere in the solution. This leads to a partial reduction in the supersaturation until the nucleation rate drops back to zero. The remaining supersaturation is reduced by diffusion of the sulfur to the germs with the enlargement of the nanoparticles. It should be noted that homogeneous mixing of the components is always assumed so that supersaturation does not take place locally.
Monodisperse nucleation nuclei are formed with this method because approx. 10%… 20% oversaturation lead to nucleation. If, on the other hand, a high level of supersaturation is caused by quickly adding a large amount of water to a sulfur-in-ethanol solution, many germs of different sizes can arise, which leads to the formation of a polydisperse, so-called sulfur milk.
LaMer also achieved supersaturation through the reaction 2Na 2 S 2 O 3 + 2HCl → 2HSO 3 - + S 2 + 4Na + + 2Cl - in water. In a certain concentration range of the starting materials, the formation of sulfur is so slow that the critical supersaturation concentration is slowly reached and monodisperse nanoparticles result. At high initial concentrations, on the other hand, the rapid supersaturation above the critical concentration leads to the formation of polydisperse particles. In other systems, a distinction must also be made between binodal and spinodal segregation. In the latter, phase separation can take place without nucleation, which can also lead to a polydisperse product.
The phases of saturation → supersaturation → critical supersaturation → fast nucleation → partial reduction of supersaturation down to nucleation rate zero → reduction of supersaturation by diffusion have been mathematically described by LaMer.
literature
- Victor K. LaMer, Robert H. Dinegar, "Theory, Production and Mechanism of Formation of Monodispersed Hydrosols", Journal of the American Chemical Society 72 (11) (1950) 4847-4854.