Nucleation-precipitation model

Crystal syntheses do not differ, in their essence, from classical chemical experiments in which molecules are modelled, synthetic routes devised, products characterized and their properties evaluated. However, this typical chemical approach needs, in a sense, to be repeated twice first, in order to prepare the building blocks (whether molecules or ions), and then to arrange the building blocks in a desired way via nucleation, precipitation and crystallization to attain and/or control crystal properties. Obviously, crystallization invariably implies the need to characterize the solid product, often in the form of a polycrystalline powder, for which routine analytical and spectroscopic laboratory tools are much less useful than in the case of solution chemistry. 

The instantaneous nucleation-growth-precipitation model [39] assumes that the film is formed directly on the substrate, without previous dissolution however, it was observed that active dissolution of the metal occurs. Therefore, Equations 8.11 through 8.13 were examined and rewritten considering metal dissolution, that is, terms corresponding to dissolution were added to the mathematical expressions ... 

Downstream of the reactor section the polyethylene-ethylene solution is expanded to a lower pressure, typically to about 350 bar. Because the solvent power of supercritical ethylene is lowered during the pressure reduction, the polyethylene formed in the reactor nucleates, precipitates from solution, and is collected in the separator. Note that this separation step is exactly analogous to the separation of naphthalene in the model extraction/separation process described in chapter 6. The low-pressure ethylene from the polyethylene separator is recompressed and recycled to the reactor. Interestingly, high-pressure ethylene is both the reactant and the solvent for the product in this process. 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

Donnet, M., Jongen, N., Lemaitre, J., Bowen, P. and Hofmann, H., 1999. Better control of nucleation and phase purity using a new segmented flow tubular reactor Model system Precipitation of calcium oxalate. In 14th International Symposium on Industrial Crystallization. Cambridge, U.K., September 12-16, Institution of Chemical Engineers, CD ROM, pp. 1-13. 

We might take a purist s approach and attempt to use kinetic theory to describe the dissolution and precipitation of each mineral that might appear in the calculation. Such an approach, although appealing and conceptually correct, is seldom practical. The database required to support the calculation would have to include rate laws for every possible reaction mechanism for each of perhaps hundreds of minerals. Even unstable minerals that can be neglected in equilibrium models would have to be included in the database, since they might well form in a kinetic model (see Section 26.4, Ostwald s Step Rule). If we are to allow new minerals to form, furthermore, it will be necessary to describe how quickly each mineral can nucleate on each possible substrate. 

Adsorption and Precipitation vs heterogeneous Nucleation and Surface Precipitation. There is not only a continuum between surface complexation (adsorption) and precipitation, but there is also obiously a continuum from heterogeneous nucleation to surface precipitation. The two models are two limiting cases for the initiation of precipitation. In the heterogeneous nucleation model, the interface is fixed and no mixing of ions occurs across the interface. As a consequence precipi-... 

The geochemical fate of most reactive substances (trace metals, pollutants) is controlled by the reaction of solutes with solid surfaces. Simple chemical models for the residence time of reactive elements in oceans, lakes, sediment, and soil systems are based on the partitioning of chemical species between the aqueous solution and the particle surface. The rates of processes involved in precipitation (heterogeneous nucleation, crystal growth) and dissolution of mineral phases, of importance in the weathering of rocks, in the formation of soils, and sediment diagenesis, are critically dependent on surface species and their structural identity. 

Large concentrations of Fe + develop in the soil solution in the weeks following flooding, often several mM or tens of mM (Figure 4.5). Calculations with chemical equilibrium models show that the ion activity products of pure ferrous hydroxides, carbonates and other minerals are often exceeded 100-fold (Neue and Bloom, 1989). Evidently precipitation of these minerals is inhibited, probably as a result of adsorption of foreign solutes, such as dissolved organic matter and phosphate ions, onto nucleation sites (Section 3.7). However, once a sufficient supersaturation has been reached there is a rapid precipitation of amorphous solid phases, which may later re-order to more crystalline forms. Only a small part of the Fe(II) formed in reduction remains in solution the bulk is sorbed in exchangeable forms or, eventually, precipitated. 

An extensive formulation of classical and nonclassical models for homogeneous nucleation, as well as experimental tests of their validity, have been carried out for the Co-Cu precipitation system in which coherent Co-rich nuclei form [15]. 

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