Volume average diameter

Other possible geometrical diameters can be used to determine the mean particle diameter of a polydisperse system. Examples are the surface average, ds, and volume average diameters, dv where ds is defined as the diameter of a sphere having the same surface area as the particle and dw is the diameter of a sphere having the same volume as the particle. These are given by ... 

The support has an internal pore structure (i.e., pore volume and pore size distribution) that facilitates transport of reactants (products) into (out of) the particle. Low pore volume and small pores limit the accessibility of the internal surface because of increased diffusion resistance. Diffusion of products outward also is decreased, and this may cause product degradation or catalyst fouling within the catalyst particle. As discussed in Sec. 7, the effectiveness factor Tj is the ratio of the actual reaction rate to the rate in the absence of any diffusion limitations. When the rate of reaction greatly exceeds the rate of diffusion, the effectiveness factor is low and the internal volume of the catalyst pellet is not utilized for catalysis. In such cases, expensive catalytic metals are best placed as a shell around the pellet. The rate of diffusion may be increased by optimizing the pore structure to provide larger pores (or macropores) that transport the reactants (products) into (out of) the pellet and smaller pores (micropores) that provide the internal surface area needed for effective catalyst dispersion. Micropores typically have volume-averaged diameters of 50 to... 

The values of these averages can be very different. Typically, the higher the values of n and m are, the larger is the value of the average size. Which one you should use simply depends on the application. When it relates to the surface area (think of emulsion stability, amormt of surfactant needed, energy required to make the emulsion, etc.) then the Sauter diameter is probably the best one. If the application is related to the volume (e.g., amount of oil in the product, material dissolved in the particles), the volume average diameter may be more suitable. 

The number of polymer particles was determined from the monomer conversion Xj and the volume average diameter of the polymer particles dp measured with an electron microscope. 

The particle size of a number of latices were measured using electron microscopy. The size distributions were comparatively narrow, the ratio of volume average diameter to number average di-... 

Figure 2 shows that the maximum polymerization rate and number of particles (calculated from the volume-average diameter Dy) varied... 

Zn(II) was employed as a print molecule because of its strong interaction with the bifunctional monomer, DDDPA. Divinylbenzene, L-glutamic acid dioleylester ribitol and toluene were used as matrix-forming monomer, emulsion stabiliser and diluent, respectively. After polymerisation, the print molecules were removed from the resin, upon which selective recognition sites were formed. The schematic illustration of surface template polymerisation with DDDPA is shown in Scheme 9.8. The Zn(II)-imprinted resins were ground into particles, whose volume-averaged diameters were ca. 40 pm. The yield was ca. 80%. 

The particles may be inhomogeneous. They may be hollow or have a more intricate internal structure. If the inhomogeneity varies among particles, a particle size distribution is insufficient to characterize the dispersion. For instance, the mass average diameter and the volume average diameter may be markedly different this is illustrated by several spray-dried powders, where some of the particles have large vacuoles, while others have not. If the oil droplets in an emulsion are coated with a thick layer of protein, the smallest droplets contain far more protein per unit amount of oil than the largest ones, as illustrated in Table 9.3. 

Most analyses of flocculation kinetics assume a homogeneous suspension (that is, a suspension containing particles of only one size) at the onset of flocculation. To compare such suspensions with the heterogeneous suspensions evaluated here, an influent containing 132 mg/L (50ppm) of particles having the same volume-average diameter (0.688 /xm) as the standard case was assumed. Such a suspension also has the... 

Particle diameters are expressed in terms of averages. The most important averages are the number-average diameter ( ) ), the volume-average diameter (Dv), and the weight-average diameter (D ), all of which may be calculated using ... 

Figure 3.7 Variation in die volume average diameter of the dispersed rubber particles for PA/EP and PA/ EP-MA blends as a function of the mixing time. A (PA6/EP-MA), (PA6/CT) [53]...

Also, Ehas et al. [1] showed that the presence of hydrophilic and hydrophobic silica PP/PS blends was able to reduce the volume average diameter of the PS 3.8 and 2.6 times, respectively. However, they concluded that the stabilization mechanism of PP/PS blend by hydrophobic silica is due to the reduction in the apparent interfacial tension while the hydrophobic silica acted as a rigid layer preventing the coalescence of PS droplets. This was the Palicme s model [88]. 

Evolution of the RIT ratio as a function of time was obtained for a 70/30 PDMS/PIB blend containing different amounts of silica at 20 °C. Silica is an Aerosil Rhodorsil R972, R is the volume average diameter of the PIB droplets, is the apparent interfacial tension of the system [89]. To conclude, it seems that the displacement of the nanoparticles in the melted polymer blends and their localization in the final binary blend influences the compatibilization effect especially because it influences the origin of the droplet size reduction. On the other hand, the understanding of the mechanisms responsible... 

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