Growth rate particle

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

Nucleation and particle growth rates related to relative supersaturation. 

However, care must be taken to ensure that seed nuclei are present on which condensation can occur. If a very clean system is used in which nuclei are not present, spontaneous nucleation may occur this process is such that nuclei do not appear uniformly either in space or in time, and the initial particle growth rate depends on the degree of supersaturation. As a result, a polydisperse aerosol is produced under these conditions. 

Reaction Rate. The reaction rate can be defined i n different ways. One can distinguish between the hydrolysis and the condensation reaction, or one could simply relate the reaction rate to the particle growth rate. Depending on the technique applied, the various relations are determined. This section now focuses on the reaction rate as determined from the particle growth. 

For the experiments, various test conditions were selected for reaction temperature, initial Cu concentration, and length of reaction and crystallization periods. In some tests a seed solution was used to determine if it improved particle growth rate. The conditions evaluated are listed below ... 

Figure 15.3 Particle growth rate vs. particle size in Eq. 15.13. /1 and fi represent the growth rate for two different particle-size distributions, such that (R)2 = 1.5(/ )i.

It is clear from Eq. 1 that the monomer concentration in a polymer particle is one of the three key factors that control the particle growth rate, and accordingly, the rate of polymerization. In emulsion polymerization, the course of emulsion polymerization is usually divided into three stages, namely. Intervals I, II and III. In Intervals I and II of emulsion homopolymerization, the monomer concentration in the polymer particles is assumed to be approximately constant. In Interval III, it decreases with reaction time. Two methods are now used to predict the monomer concentration in the polymer particles in emulsion homopolymerization empirical and thermodynamic methods. 

Figure 5. Variation of In (particle growth rate) versus reciproeal of temperature.

Furthermore, they studied the effect of radical desorption from the polymer particles on the particle number formed in Internal I of emulsion polymerization, using above equations, and showed that radical desorption leads to an increase in the number of particles. The reason fw this is that (I) The desorbed radicals reenter the micelles and take part in particle nu-cleation (2) Radical desorption decreases the particle growth rate and hence, results in a decrease in the rate of micelle consumption. This also increases the chance of radical entry into the micelles. They also showed that radical desorption brought about the change in the orders of particle number with respect to emulsifier and initiator according to the following relationship ... 

S6). It depended on the variation of the number of latex particles formed iV with temperature. Unfortunately, they have overlooked the fact that the particle growth rate fi which appears to the power —f in the Smith-Ewart expression for the number of latex particles formed coitains the propa gation rate constant which is temperature dependent. It has also recently been realized that another factor on which JV depends, the area occupied by a surfactant molecule at the polymer-water interface Og, is also temperature dependent- Dunn et al. (1981) observed that the temperature dependence of N in the thermal polymerization of styrene differed from different emulsifiers. It seems unlikely that the differences ran be wholly explained by differing enthalpies of adsorption of the emulsifiers and, if not, this observation implies that the energy of activation for thermal initiation of styrene in emulsion depends on the emulsifier used. Participation of emulsifiers in thermal initiation (and probsbly also in initiation by oil-soluble initiators) is most probably attributable to transfer to emulsifier and desorption of the emulsifier radical frcan the micelle x>r latex particle into the aqueous phase the rates of these processes are likely to differ with the emulsifier. 

The rate of growth of particles depends on the concentration of the reagents in the particles, radicals and monomer, and on the propagation rate constant. The gel effect, which causes the termination rate constant to be lower at higher conversions, can cause higher free radical concentrations in the particles and thus higher particle growth rates. This effect also contributes to conversion oscillations. 

Figure 10.6 Particle growth rates between the fourth and (il th size distribution measurements for the data of Fig. 10.5. The solid line i.s a lea.st-squarc best lit of the diffusional growth law. moditied to include mean free path effects (10.21) and the Kelvin effect (10.24). The intercept on the size axis is the average critical size, d. ...

In the equations below, for simplicity, we will assume that the particle-growth rate Gl is size-independent so that Gl. = Gl. However, in general, the functional dependence of Gl on size must be provided by the modeler in order to apply Eq. (2.19). 

If we now combine our expressions (4) and (6) for the isolated particle growth rate, (7) for the coalescence rate and (8), the mass balance and integrate from some initial time t0 when NQ particles are present, we arrive at the analytical results ... 

AgCl nanoparticles have been synthesised by using a water/cyclohexane/polyoxyethylene (6) nonylphenyl ether (NP-6) microemulsion wherein AgN03 and KC1 solutions were added and mixed [66]. The particle growth rate and the final particle size at a given co were... 

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