Particle growth limits

An increase in the time required to form a visible precipitate under conditions of low RSS is a consequence of both a slow rate of nucleation and a steady decrease in RSS as the precipitate forms. One solution to the latter problem is to chemically generate the precipitant in solution as the product of a slow chemical reaction. This maintains the RSS at an effectively constant level. The precipitate initially forms under conditions of low RSS, leading to the nucleation of a limited number of particles. As additional precipitant is created, nucleation is eventually superseded by particle growth. This process is called homogeneous precipitation. ... 

Since polymer swelling is poor and the aqueous solubiUty of acrylonitrile is relatively high, the tendency for radical capture is limited. Consequentiy, the rate of particle nucleation is high throughout the course of the polymerization, and particle growth occurs predominantiy by a process of agglomeration of primary particles. Unlike emulsion particles of a readily swollen polymer, such as polystyrene, the acrylonitrile aqueous dispersion polymer particles are massive agglomerates of primary particles which are approximately 100 nm in diameter. 

While the model was in general agreement with the limited experimental data published on bulk PVC particle size distribution, there is still no generally applicable theory describing particle growth and flocculation in the presences of mechanical agitation for precipitation polymerizations. 

A log normal distribution will give a straight line when plotted on this ti pe of paper. This means that the PSD is not limited, i.e.- aU sizes of particles are present from - to +°°. However, if the PSD is growth-limited, it will readily apparent from the graph. Ostwald ripening, a mechanism where large... 

This similar methods involves UV light irradiation, with light intensity, stirring speed, suspension volume and temperature influencing particle growth. Fig. 6.5. Shorter irradiation times can be used to limit the amount of particle deposition. Photo-deposited samples do not require calcination hence there is little chance of particle agglomeration. 

Similar to transparent titanium dioxide microparticles of zinc oxide are manufactured by using sol/gel processes or precipitation in the presence of protective colloids to limit particle growth [5.288],... 

In later experiments, Izumi et al. (47, 48) examined aerosol formation during photooxidation of a variety of hydrocarbons in an evacuable smog chamber. No seed particles were used in these experiments, but good estimates of the yield of aerosol from photochemical oxidation of the hydrocarbon precursors were obtained by using EAA data. In some cases, the volumetric yield was found to decrease with decreasing precursor concentration (Figure 4), so the finite vapor pressure of the reaction products limited nucleation, particle growth, or both. 

In the following, this model is used to analyze the kinetics for the two cases where the particle growth is either diffusion- or source-limited. Each of the two cases yields a different growth law for the particles in the distribution. 

Source-Limited Coarsening. During source-limited coarsening, the interfaces surrounding the particles behave as poor sources and sinks, and the coarsening rate then depends upon the rate at which the diffusion fluxes between the particles can be created or destroyed (accommodated) at the particle interfaces. In a simple model, the same assumptions can be made about the source action at the particles as those that led to Eq. 13.24. The rate of particle growth can then be written... 

Stability of Ct//3 Interface during Diffusion-Limited Particle Growth... 

In some cases, particularly in the growth of aerosol particles, the assumption of equilibrium at the interface must be modified. Frisch and Collins (F8) consider the diffusion equation, neglecting the convective term, and the form of the boundary condition when the diffusional jump length (mean free path) becomes comparable to the radius of the particle. One limiting case is the boundary condition proposed by Smoluchowski (S7), C(R, t) = 0, which presumes that all molecules colliding with the interface are absorbed there (equivalent to zero vapor pressure). A more realistic boundary condition for the case when the diffusion jump length, (z) R, has been shown by Collins and Kimball (Cll) and Collins (CIO) to be... 

The mechanism of particle growth in the course of hydrolysis and condensation of Ti, Zr, and Ta alkoxides has been frequently discussed. Nevertheless, the discussion so far remains open. Ring suggested a diffusion-limited model for growth of particles [484, 1357] other authors, however, assume a growth mechanism limited by reaction on the surface of the growing species [1228, 708, 477]. 

Microemulsion is used as a special microreactor to limit the nano-sized particles growth. The shape of the microreactor depends on reaction conditions [9]. This method increases the homogeneity of the chemical composition at nano-level and facilitates the preparation of nano-particles with comparatively equal sizes [11]. The specific properties of the nano-particles make them suitable for microelectronics, ceramics, catalysis, medicine, cosmetics, as piezoelectric materials, conductors, etc. 

Solid silica spheres are prepared by the Stober8 method. This involves the condensation of TEOS in alcoholic solution of water and ammonia. The mechanism of this synthesis was elucidated by Van Blaaderen et al.20,21 The particle growth is rate-limited by the production of hydrolysed monomer molecules. It involves a surface condensation of monomers and oligomers, while aggregation of particles is only occurring in the early stages of the condensation. 

The applicability of Maxwell s equation is limited in describing particle growth or depletion by mass transfer. Strictly speaking, mass transfer to a small droplet cannot be a steady process because the radius changes, causing a change in the transfer rate. However, when the difference between vapor concentration far from the droplet and at the droplet surface is small, the transport rate given by Maxwell s equation holds at any instant. That is, the diffusional transport process proceeds as a quasi-stationary process. 

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