Growth particle

Particle growth occurs throughout Intervals 1,2 and 3. The kinetics are mainly controlled by the distribution and exchange of radicals over the various phases and cannot be oversimplified. Models are numerous but well described in excellent reviews (Ugelstad et al, 1976 Hansen et al, 1982 Gilbert et al, 1983, 1995). The basic rate equation for homogeneous batch free-radical polymerisation is  

Np changes throughout Interval 1. In Interval 2, the presence of monomer droplets keeps [M]p approximately constant, and Np is also constant. In Interval 3, Np remains constant while [M]p decreases as determined by simple mass conservation from the behaviour of Rp. 

The value of kp can be determined by pulsed-laser polymerisation (PLP) (Olaj Bitai, 1987 Coote et al, 1996 van Herk 2000). A list of reliable values of kp determined by this method is given in Appendix I. The number of particles, Np, is determined from particle size (Chapter 8) and conversion, through Equation 3.1. 

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By carefully controlling the precipitation reaction we can significantly increase a precipitate s average particle size. Precipitation consists of two distinct events nu-cleation, or the initial formation of smaller stable particles of precipitate, and the subsequent growth of these particles. Larger particles form when the rate of particle growth exceeds the rate of nucleation. 

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 As additional precipitant is created, nucleation is eventually superseded by particle growth.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. 

An expression for the number of particles formed during Stage I was developed, assuming micellar entry as the formation mechanism (13), where k is a constant varying from 0.37 to 0.53 depending on the relative rates of radical adsorption in micelles and polymer particles, r is the rate of radical generation, m is the rate of particle growth, is the surface area covered by one surfactant molecule, and S is the total concentration of soap molecules. 

B. Honigmann and D. Horn, Particle Growth in Suspensions, Academic Press, Inc., New York, 1973. 

Fig. 11. Effects of pH in the colloidal siUca-water system (1), where A represents the point of zero charge regions B, C, and D correspond to metastable gels, rapid aggregation, and particle growth, respectively. Positive and negative correspond to the charges on the surface of the siUca particle.

A kinetic model for the particle growth stage for continuous-addition emulsion polymerization has been proposed (35). Below the monomer... 

In drying solutions or slurries of solutions, the location of the feed-injection nozzle (spray nozzle) has a great effecl on the size of particle formed in the bed. Also of importance are the operating temperature, relative humidity of the off gas, and gas velocity. Particle growth can occur as agglomeration or as an onion sldnuing. ... 

Visibility is also affected by alteration of particle size due to hydroscopic particle growth, which is a function of relative humidity. In Los Angeles, California, the air, principally of marine origin, has numerous sea salt particles. Visibility is noticeably reduced when humidity exceeds about 67%. In a study of visibility related to both relative humidity and origin of... 

Particle growth Increase in particle size due to hydration. 

In the MSMPR crystallizer at steady state, the increase of particle number density brought about by particle growth and agglomeration is compensated by withdrawal of the product from the crystallizer. 

J. Soderlund, L. B. Kiss, G. A. Niklasson, C. G. Granqvist. Lognormal size distributions in particle growth processes without coagulation. Phys Rev Lett 0 2386, 1998. 

The water solubilities of the functional comonomers are reasonably high since they are usually polar compounds. Therefore, the initiation in the water phase may be too rapid when the initiator or the comonomer concentration is high. In such a case, the particle growth stage cannot be suppressed by the diffusion capture mechanism and the solution or dispersion polymerization of the functional comonomer within water phase may accompany the emulsion copolymerization reaction. This leads to the formation of polymeric products in the form of particle, aggregate, or soluble polymer with different compositions and molecular weights. The yield for the incorporation of functional comonomer into the uniform polymeric particles may be low since some of the functional comonomer may polymerize by an undesired mechanism. 

If particle growth rate is known, as a function of particle size, the size distribution can be calculated from Equation 8. 

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