Nucleation model, heterogeneous

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-... 

Solution. A simple model can be constructed based on the idea that the nucleation is heterogeneous and that the heterogeneous nucleation sites (i.e., the particles), are being neutralized as nucleation and growth proceed. Once a nucleation event has occurred at a given particle, the solid will grow and envelop the particle, and it is unlikely that an additional nucleation event will occur there. After the incubation period has passed. Eq. 19.17 may be written for heterogeneous nucleation in the form... 

The homogeneous nucleation of martensite in typical solids is too slow by many orders of magnitude to account for observed results. Calculations of typical values of AQc using the classical nucleation model of Section 19.1.4 (see Exercise 19.3) yield values greatly exceeding 76 kT. Furthermore, nearly all martensitic transformations commence at very sparsely distributed sites. Small-particle experiments [14] have yielded typical nucleation densities on the order of one nucleation event per 50 pm diameter Fe-Ni alloy powder particle.3 Thus, nucleation of martensite is believed to occur at a small number of especially potent heterogeneous nucleation sites. 

Cavitation in the rubber particles of PS/high-impact PS (HIPS) was also identified as a heterogeneous nucleation site, using batch-foam processing [15, 16]. The experimentally observed cell densities as a function of the temperature, the rubber (HIPS) concentration, the rubber particle size, and saturation pressure were found to be in good agreement with the proposed nucleation model. Similar nucleation mechanisms of elastomeric particles were claimed for acrylic and di-olefinic latex particles in various thermoplastics [17, 18]. 

Classical nucleation theory uses macroscopic properties characteristic of bulk phases, like free energies and surface tensions, for the description of small clusters These macroscopic concepts may lack physical significance for typical nucleus sizes of often a few atoms as found from experimental studies of heterogeneous nucleation. This has prompted the development of microscopic models of the kinetics of nucleation in terms of atomic interactions, attachment and detachment frequencies to clusters composed of a few atoms and with different structural configurations, as part of a general nucleation theory based on the steady state nucleation model [6]. The size of the critical nucleus follows straightforwardly in the atomistic description from the logarithmic relation between the steady state nucleation rate and the overpotential. It has been shown that at small supersaturations, the atomistic description corresponds to that of the classical theory of nucleation [7]. 

We can anticipate that the highly defective lattice and heterogeneities within which the transformations are nucleated and grow will play a dominant role. We expect that nucleation will occur at localized defect sites. If the nucleation site density is high (which we expect) the bulk sample will transform rapidly. Furthermore, as Dremin and Breusov have pointed out [68D01], the relative material motion of lattice defects and nucleation sites provides an environment in which material is mechanically forced to the nucleus at high velocity. Such behavior was termed a roller model and is depicted in Fig. 2.14. In these catastrophic shock situations, the transformation kinetics and perhaps structure must be controlled by the defective solid considerations. In this case perhaps the best published succinct statement... 

Figure 22 Schematic representation of proposed models for the fibril formation in the cases of pH 3.3 and 7.5. (A) hCT monomers in solution (B) a homogeneous association to form the a-helical bundle (micelle) (C) a homogeneous nucleation process to form the P-sheet and heterogeneous association process (D) a heterogeneous fibrillation process to grow a large fibril, a-helix, antiparallel p-sheet, and parallel p-sheet forms are shown by a box, drawn by dark grey and grey, respectively. From Ref. 163 with permission.

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. 

Ramesh, N. S., Rasmussen, D. H., and Campbell, G. A., The Heterogeneous Nucleation of Microcellular Foams Assisted by the Survival of Microvoids in Polymers Containing Low Glass Transition Particles. Part 1 Mathematical Modeling and Numerical Simulation, Polym. Eng. ScL, 34, 1685 (1994)... 

In zone B, despite a reproductibility probably modified by heterogenous nucleation phenomena in these weakly supersaturated solutions, agreement of the model has been checked on the above... 

In CVD processes, due to the simultaneous presence of gaseous and solid phases, models should consider heterogeneous nucleation (defined as nucleation at an interface) rather than homogeneous nucleation (defined as nucleation in an indefinite point of a fluid matrix). Nevertheless, the complexity of the factors involved in heterogeneous nucleation leads us to first examine the more simple homogeneous nucleation. 

Liger-Belair, G., Voisin, C., and Jeandet, P. (2005b). Modeling non-classical heterogeneous bubble nucleation from cellulose fibers Applications to bubbling in carbonated beverages. /. Phys. Chem. B 109,14573-14580. 

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