The nucleation mechanism

In section 14.6.1, we saw that the nucleation process involves two stages, each of them including elementary steps occurring on the whole surface of the sohd. The respective rate will therefore have the same space function. We will examine the type of elementary steps that could describe these two stages. 

The formation of precursors, which are point defects, will take place during various elementary steps occurring at the interface between the initial solid and a surrounding phase. If gases are involved, chemisorption or desorption processes are also occurring at the surface of the solid. 

The formation of an anhydrous salt from its hydrated form will pass via the formation of water vacancies, for example, according to the following process  

This reaction can be split into two steps equivalent to elementary steps  

We see that the two areas where the two steps take place will always be the same size dttring the system evolution, even if these areas vary over time. This is valid for any prectrrsor formation at the surface. 

---

The kinetics of crystal growth has been much studied Refs. 98-102 are representative. Often there is a time lag before crystallization starts, whose parametric dependence may be indicative of the nucleation mechanism. The crystal growth that follows may be controlled by diffusion or by surface or solution chemistry (see also Section XVI-2C). 

Whatever the nucleation mechanism the final particle size of the latex is determined duting Stage I, provided no additional particle nucleation or coalesence occurs ia the later stages. Monomer added duting Stages II and III only serves to increase the size of the existing particles. 

Nucleation and growth of gas hydrate crystals have been investigated with optical methods under different pressures and temperatures. The particle sizes measured during gas hydrate nucleation ranged from 2 to 80 imi [1334,1335]. The nucleation process is nondeterministic, because of a probabilistic element within the nucleation mechanism [1393]. 

The former problem is a general problem not only for polymers but also for any other materials (atomic or low molecular weight systems). Although nucleation is a well-known concept, it has never been confirmed by direct observation due to the low number density of the nuclei to be detected with present experimental techniques, such as small angle X-ray scattering (SAXS). Therefore, one of the most important unresolved problems for basic science is to obtain direct evidence to solve the nucleation mechanism of any material. 

Direct evidence of nucleation during the induction period will also solve a recent argument within the field of polymer science as to whether the mechanism of the induction of polymers is related to the nucleation process or to the phase separation process (including spinodal decomposition). The latter was proposed by Imai et al. based on SAXS observation of so-called cold crystallization from the quenched glass (amorphous state) of polyethylene terephthalate) (PET) [19]. They supposed that the latter mechanism could be expanded to the usual melt crystallization, but there is no experimental support for the supposition. Our results will confirm that the nucleation mechanism is correct, in the case of melt crystallization. 

The model of amyloid fibril formation is a nucleation step followed by growth, where the nucleation mechanism dictates the concentration and time dependence of the aggregation (Harper and Lansbury, 1997 ... 

Phyllosilicates are clay-related compounds with a sheet structure such as talc, mica, kaolin, etc. for which the nucleation mechanism of PET is known to be heterogeneous, although still uncertain. 

For sufficiently large heat flux to mass flow ratios, the nucleation mechanism predominates and the heat transfer becomes independent of the two-phase flow characteristics of the system. Thus at large values of the boiling number, the heat transfer coefficients are virtually independent of the Lockhart-Martinelli parameter, Xn. 

Raeissi et al. [236, 237] showed that temperature, pH, and current density affected the morphology and texture, as well as the nucleation mechanism of the zinc deposits on carbon steel electrode. 

Molecular simulation methods have been applied to investigate the nucleation mechanism of gas hydrates in the bulk water phase (Baez and Clancy, 1994), and more recently at the water-hydrocarbon interface (Radhakrishnan and Trout, 2002 Moon et al., 2003). The recent simulations performed at the water-hydrocarbon interface provide support for a local structuring nucleation hypothesis, rather than the previously described labile cluster model. 

We begin by describing the current understanding of the kinetics of polymerization of classical unsaturated monomers and macromonomers in the disperse systems. In particular, we note the importance of diffusion-controlled reactions of such monomers at high conversions, the nucleation mechanism of particle formation, and the kinetics and kinetic models for radical polymerization in disperse systems. 

The nucleation mechanism of dispersion polymerization of low molecular weight monomers in the presence of classical stabilizers was investigated in detail by several groups [2,6,7]. It was, for example, reported that the particle size increased with increasing amount of water in the continuous phase (water/eth-anol), the final latex radius in their dispersion system being inversely proportional to the solubility parameter of the medium [8]. In contrast, Paine et al.[7] reported that the final particle diameter showed a maximum when Hansen polarity and the hydrogen-bonding term in the solubility parameter were close to those of steric stabilizer. 

Goeres, A. Sedlmayr, E. 1991 On the nucleation mechanism of effective fullerite condensation. Chem. Phys. Lett. 184, 310-317. 

What, then, is the nucleation mechanism in the bulk of these viscous molten polymer solutions ... 

These observations suggest that the nucleation mechanism is greatly influenced. 

Reimers and Schork [94, 95] report the use of PMMA to stabihze MM A miniemulsions enough to effect predominant droplet nucleation. Emulsions stabilized against diffusional degradation by incorporating a polymeric costabilizer were produced and polymerized. The presence of large numbers of small droplets shifted the nucleation mechanism from micellar or homogeneous nucleation, to droplet nucleation. Droplet diameters were in the miniemulsion range and reasonably narrowly distributed. On-hne conductance measurements were used to confirm predominant droplet nucleation. The observed reaction rates were dependent on the amount of polymeric costabilizer present. The latexes prepared with polymeric costabilizer had lower polydispersities (1.006) than either latexes prepared from macroemulsions (1.049) or from alkane-stabilized miniemulsions (1.037). 

Wu and Woo [26] compared the isothermal kinetics of sPS/aPS or sPS/PPE melt crystallized blends (T x = 320°C, tmax = 5 min, Tcj = 238-252°C) with those of neat sPS. Crystallization enthalpies, measured by DSC and fitted to the Avrami equation, provided the kinetic rate constant k and the exponent n. The n value found in pure sPS (2.8) points to a homogeneous nucleation and a three-dimensional pattern of the spherulite growth. In sPS/aPS (75 25 wt%) n is similar (2.7), but it decreases with increase in sPS content, whereas in sPS/PPE n is much lower (2.2) and independent of composition. As the shape of spherul-ites does not change with composition, the decrease in n suggests that the addition of aPS or PPE to sPS makes the nucleation mechanism of the latter more heterogeneous. 

This mechanism was modeled with two different techniques, first by Im-bihl et al. (52) with a set of coupled differential equations, and later by Moller et al. (46,48) using a cellular automata technique. Experimental data could be fit relatively well (Fig. 13) with the obvious exception of the discrepancy in the time scales in the differential equation model. The model equations, however, are quite complex because the authors tried to model the nucleation mechanism for the phase transition. Recently the model of... 

According to the nucleation mechanism, the rate of appearance of a new phase must decrease in the following order amorphous phase > liquid crystalline phase > crystalline phase. This can be explained by the fact that for nuclei of the amorphous phase to appear, any fluctuation of particles, whose dimension exceed a certain critical value, is sufficient. At the same time, the nuclei in the liquid crystalline phase appear only at a more strict ordering of molecules, and for the appearance of nuclei of the crystalline phase a still more strict mutual arrangement of molecules is required. 

The concentration threshold above which crystallization is observed at times shorter than the processing time or desired product shelf-life or GI transit time, is determined by the kinetic stability of supersaturated states and is regulated by the nucleation mechanisms and kinetics. Nucleation phenomena are equally important in the control of micrometric properties and in the selective crystallization of a particular polymorph. 

Since secondary nucleation is dominant as soon as nuclei appear, the nucleation mechanisms become virtually impossible to characterize in an industrial operation. In addition, any seeded crystaUization is by definition secondary even though some nuclei may simultaneously form by a primary or other secondary mode mechanism. Therefore, the majority of this discussion will focus on secondary nucleation. 

The nucleation mechanism can be determined by comparing the results to the progressive nucleation model by rewriting equation [4] in terms of the maximum current, imax, and the time at which the maximum current is observed, t,nax ... 

---