Nucleation of particles

Nucleation of particles in a very short time foUowed by growth without supersaturation yields monodispersed coUoidal oxide particles that resist agglomeration (9,10). A large range of coUoidal powders having controUed size and morphologies have been produced using these concepts (3,14). 

In precipitation reactions, powder characteristics depend on the speed of the nucleation of particles and their growth due to the mass flow to the surfaces. In freeze drying and spray drying, powder characteristics primarily depend on the size of droplets, which in turn is determined by the parameters of a nozzle and characteristics of the flow of a carrier gas. Both these methods enable one to obtain powders with very high surface area. 

Solid state reactions are also very common in producing oxide materials and are based on thermal treatment of solid oxides, hydroxides and metal salts (carbonates, oxalates, nitrates, sulphates, acetates, etc.) which decompose and react forming target products and evolving gaseous products. Solid-state chemistry states that, like in the case of precipitation, powder characteristics depend on the speed of the nucleation of particles and their growth however, these processes in solids are much slower than in liquids. 

It appears that the increase in particle density is exponential and that the best conditions are reached at 323 K, where a great number of small particles are produced per surface unit. However, at 353 K large agglomerates are produced by accretion of 10-50 nm particles, which is consistent with homogeneous nucleation of particles in the gas phase. 

Although Eq. 27 appears to be the most likely initiation reaction, we cannot rule out a process in which water vapor and DMTC react, based on the ab initio results described in Sect. 4.6. If this does occur, however, it apparently does not lead to homogeneous nucleation of particles, since anecdotal evidence from the glass industry indicates that DMTC and water vapor can be premixed prior APCVD of tin oxide without substantial buildup of solids in delivery lines. Perhaps this is due to significant kinetic barriers to the decomposition of the tin-water complexes that initially form, so that further gas-phase reaction does not occur until the reactants enter the heated boundary layer above the substrate. 

In accordance with the Smith-Ewart theory, the nucleation of particles takes place solely in the monomer-swollen micelles which are transformed into polymer particles [16]. This mechanism is applicable for hydrophobic (macro)mon-omers (see Scheme 2). The initiation of emulsion polymerization is a two-step process. It starts in water with the primary free radicals derived from the water-soluble initiator. The second step occurs in the monomer (macromonomer)-swollen micelles by entered oligomeric radicals. 

The boundary condition for this equation results for the nucleation of particles of size Lq and is defined as... 

Here we see an exponential size distribution is predicted by the population balance. (B(Lq) is also the birth term due to nucleation of particles of size Lq. It could also be used in the population balance substituting for B directly, but this approach requires a LaPlace transform solution, which also results in equation (3.14).) Many inorganic precipitations operate in this way with small supersaturation that is, nearly all the mass is precipitated in one pass through the precipitation. This equation for a well-mixed constant volume aystallizer will be discussed in further detail in Chapter 6. 

We hav shown that with the use of a mixed surfactant system in styrene emulsion polymerization, the composition of the mixed surfactant has an effect on the rate of polymerization, the number of particles formed and the particle size distribution. We have also shown that a change in the ratio, r of the two surfactants in the mixture results in a considerable change in the micellar weight of the resultant mixed micelles. We have thus proposed and proven that the efficiency of nucleation of particles (even when the same number of micelles is used in the experiment) is dependent on the size of the mixed micelle, and that there is an optimum size at which the polymerization rate is the fastest and the particle size distribution is the narrowest. 

Chemical reactions occurring in the gas-phase can be more or less important in CVD, depending on the system, and can often be analyzed in detail. Gas-phase reactions are more likely to be important with the use of high temperatures and high total reactor pressures, but less likely to be important at low reactor pressures. Many CVD systems are operated in ways that minimize gas-phase reactions in order to avoid particle formation that could interfere with the desired film deposition. Note that the absence of homogeneous nucleation of particles is not synonymous with the absence of gas-phase chemical reactions. In contrast, other CVD systems utilize gas-phase reactions to convert reactant molecules that are relatively unreactive at the surface into more reactive species. Examples where this strategy is used include the combustion CVD processes discussed in Chapter 4 and plasma-enhanced CVD processes. 

In addition to process time and uniformity, other factors must be considered in selecting optimal conditions. As in any CVD process, a specific temperature range will usually be required to obtain a desired morphology of the deposited material. Specific process conditions may also be required either to induce or to inhibit certain gas-phase reactions, such as those involved in the production of necessary deposition precursors or those leading to undesirable gas-phase nucleation of particles. Here, we will present an optimization approach that can be used to maximize deposition rates subject to any of these constraints. 

In addition to the practical interest, the process presents challenges encouraging further fundamental exploration. A thorough study not reported here, has been performed on the mechanism and kinetics of the polymerization of acrylamide in AOT/water/toluene microemulsions (Carver, M.T.r Dreyer, U. Knoesel, R. Candau, F. Fitch, R.M. J. Polym. Sci. Polym. Chem. Ed., in press. Carver, M.T. Candau, F. Fitch, R.M. J. Polym. Sci. Polym. Chem. Ed., in press). The termination reaction of the polymerization was found to be first order in radical concentration, i.e. a monoradical reaction instead of the classical biradical reaction. Another major conclusion was that the nucleation of particles is continuous all throughout the polymerization in contrast to conventional emulsion polymerization where particle nucleation only occurs in the very early stages of polymerization. These studies deserve further investigations and should be extended to other systems in order to confirm the unique character of the process. 

We now know that emulsion polymerization is not just another polymer synthesis method and that the complexity of the interactions, whether chemical or physical, must he considered before any control is possiUe over the outcome of the reaction. The creation and nucleation of particles, for example, is not necessarily and simply explained by the presence or or absence of micelles, but needs the understanding of interactions of all the ingredients present. Variables such as hydrophilic and hydrophobic associations or repulsions, polarity of the monomers, chemical structure of the surfactants, have to lx taken into account. 

Fig. 3 Granule growth mechanisms (A) agglomerate formation by nucleation of particles (B) agglomerate growth by coalescence (C) layering of a binder-coated granule and (D) layering of a partially filled binder droplet. (From Ref John Wiley and Sons, Inc.)...

The rate of nucleation of particles or clusters of size x can be written as the product of the number of clusters of size x and the probability that another molecule gets to the interface by overcoming kinetic barriers which provide an activation energy barrier, Ag. This latter term includes viscosity and diffusion effects of the bulk liquid medium as well as solvent association reactions that deplete monomers. Ifx is the critical size then the nucleation rate, Jx is... 

Since mass is conserved during transport, the continuous contribution Gp is due to mass transfer from the fiuid to the solid phase. Likewise, the discontinuous term 5m might appear due to nucleation of particles with nonzero mass from the fluid phase. For systems with no mass transfer between the disperse and continuous phases, the right-hand side of Eq. (4.64) will be null. 

As the gas is cooled, it becomes supersaturated, leading to the nucleation of particles. This nucleation is a result of molecules colliding and agglomerating until a critical nucleus size is reached and a panicle is formed. As these particles move down, the supersaturated gas molecules conden.se on the particles causing them to grow in size and then to flocculate. In the development on the CD-ROM. w c will model the formation and growth of aluminum nanoparticles in an, AFPR. 

Let us now examine how the nucleation of particles occurs during the initial stages of a solid state reaction. In general, the rate of solid state nucleation is similar to the classical rate of chemical reaction, and is given by ... 

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