Diffusivity, monodisperse particle

As a rule, short nucleation times are the prerequisite for monodisperse particle formation. A recent mechanistic study showed that when Pt(acac)2 is reduced by alkylalu-minium, virtually all the Pt cluster nuclei appear at the same time and have the same size [86]. The nucleation process quickly consumes enough of the metal atoms formed initially to decrease their concentration below the critical threshold. No new metal cluster nuclei are created in the subsequent diffusion-controlled growth stage. 

Therefore, the most efficient preparation of monodispersed particles can be achieved by regulating the feed rate of reactants (= — dC/dt) as proportional to tm in the case of diffusion-controlled growth and to t1 in the case of reaction-controlled growth, as illustrated in Fig. 4.1.10. 

Thus both the standard deviation o. in particle diameter and diffusion coefficient D can be related to experimental H values. A procedure for obtaining particle information via this route will be detailed in our discussion of monodisperse particle populations. 

Figure 10.3 is a plot of c/c0 versus time, measured at x = HI2 for monodisperse particles having a diameter of 1 xm when H - 2 cm. Note that there is essentially no change in concentration until sometime after 105 s, and then a fairly rapid decrease in concentration takes place. It can be concluded that except for very small particles or very small tubes, pure diffusion will have a small to negligible influence on the concentration changes in an aerosol flowing through a tube. 

Simplifications in kinetic modeling with monodisperse particle sizes and separations, and the detailed characterization offered via [4] more systematic studies of the influence of these parameters can be made, and the associated kinetic modeling is then simplified and becomes more accurate. Furthermore, the active catalyst phase is in direct contact with the reacting gas [e.g., no pore diffusion needs to be accounted for, which simplifies mass transport calculations (when needed)]. 

The intensity fluctuations due to the Brownian motion lake place on a lime scale much faster than conventional photometers or the human eye can detect. The variation in the fluctuating scattered light intensity with time resembles a noise signal that can be analyzed in terms of its correlation function with respect to time. The usual practice is to measure the polarized intensity tiine correlation function that is related to the diffusion coefficient for monodisperse particles as follows... 

The nuclei formed then grow by diffusion. An important condition needed for the formation of monodispersed particles is single act of nucleation, i.e. that no secondary burst of nuclei occurs. For this condition to be fulfilled, the newly formed molecular species of sulfur should be forming at such a rate that their diffusional transport to the already fonned solid particles, rather than secondary acts of nucleation take place. 

Fig. V-34. The influence of diffusion on the Fig. V-35. The effect of diffusion on boundary position during the centrifugation of the shape of sedimentation curves system containing monodispersed particles plotted in c - AR / At coordinates...

C At t = 0 a uniform concentration No of monodisperse particles exists between two horizontal plates separated by a distance h. Assuming that both plates are perfect absorbers of particles and the particles settle with a settling velocity vt, determine the number concentration of particles as a function of time and position. The Brownian diffusivity of the particles is D. 

After fast diffusion of the reducing agent, nucleation occurs in the water droplets where the above-mentioned conditions are satisfied. The nucleus is stabilized by the adsorbed surfactant molecules. The growth of the particles requires an exchange between different water cores. Finally, surfactant-protected monodisperse particles are formed that can be used directly or by being deposited on a support. This study also allowed us to gain some information about the composition of the bimetallic Ni-Co-B particles. 

Another method for determining 5h is to apply dynamic light scattering, referred to as photon correlation spectroscopy (PCS). For this purpose, dilute monodisperse particles must be used. From measurements of the intensity fluctuations of scattered light by the particles as they undergo Brownian diffusion, one can obtain the diffusion coefficient D, which can be used to obtain the hydrodynamic radius by using the Stokes-Einstein equation (equation (20.19)). By measuring D for the particles, both with and without the polymer layer, one can obtain / h and / , respectively. One should make sure that the bare particles are sufficiently stable 8 is then equal to (/ h — / ) ... 

F. 2.8 Impact of diffusion on the concentration profiles in sedimentation experiments for a monodisperse particle system left homogeneous technique, right line-start technique... 

The correlation frmction g q,T) indicates the temporal decay behavior of concentration fluctuations in the fluid as a function of delay time r. In ideal systems (dilute solution, monodisperse particles, ideal Brownian diffusion only), it exhibits a single exponential decay with decay rate r ... 

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