Primary particles, definition

Although, the true density of solid phase p=m/Vp (e.g., g/cm3) is defined by an atomic-molecular structure (/ ), it has become fundamental to the definition of many texture parameters. In the case of porous solids, the volume of solid phase Vp is equal to the volume of all nonporous components (particles, fibers, etc.) of a PS. That is, Vp excludes all pores that may be present in the particles and the interparticular space. The PS shown in Figure 9.17a is formed from nonporous particles that form porous aggregates, which, in turn, form a macroscopic granule of a catalyst. In this case, the volume Vp is equal to the total volume of all nonporous primary particles, and the free volume between and inside the aggregates (secondary particles) is not included. 

This moment is equal to the total number of floccules per unit volume, and Eq. 6.13a shows that it must always decline with increasing time if kmn > 0. The first moment M, is equal to the total number of primary particles "per unit volume, which should be constant according to the definition of the flocculation process and to Eq. 6.12 dM,/dt = 0.15 The number-average size is the ratio of M, to M0 16... 

Such a different conclusion can be understood by considering the difficulties connected to the experimental determination and the definition of Thiele modulus parameters, such as So and D. According to Chien, S means the catalyst primary particle size with a value of about 10 cm for a-TiCIj instead, in the Multigrain model, Sp seems to correspond to the size of the whole catalyst granule. 

In the previous paragraphs, carbon nanofillers such as nanotubes and graphite nanoparticles were examined. An intriguing carbon nanofiller is undoubtedly nano-CB. A preliminary crucial aspect is to define the meaning of nano-CB. By considering the diameter of primary particle, most carbon blacks could be classified as nano-CB, " as it is shown in Table 2.7. In fact, as mentioned in the Introduction, according to the acknowledged definition, a nanoparticle should have at least one dimension of the order of 100 nm or less . However, it was... 

Crystallite. The distinction between a crystal and a crystallite is subjective, and there does not appear to be a quantitative definition that differentiates one from the other. A crystallite is generally understood to be a microscopic crystal. It usually exists as one of many similar particles that adhere loosely to one another, being separated by grain boundaries. A crystallite is therefore a primary particle of a poly crystalline (or microcrystalline) solid, which is often referred to as a powder. 

While there is no precise definition, nano-fillers can be considered as particles which, when dispersed in polymers, are very small in at least one dimension. This concept is pushed quite far in some of the literature, with particles of up to at least a hundred nanometers being described as nano-particles. A reasonable working definition would seem to be that at least one dimension of the effective particle, when dispersed in a polymer matrix, should be no more than 20 nm, or 200 A. As a result, the specific surface area, which plays a significant role in the effects observed, will be at least 150 m /g. The term effective particle is used to eliminate fillers, such as carbon blacks, where the primary particle could be in the specified range, but are strongly aggregated into larger structures, that become the effective particles. 

In constant plan (flat-bottom) clarifiers the upflow velocity should be uniform at all levels and the floe blanket (fluidized bed) should have a uniform concentration and uniform particle size. In expanding upflow clarifiers (conical, or hopper-bottom) the lower levels should have greater upflow velocities and, therefore, lower floe volume concentrations or particles. In practice, such expanding upflow is highly unstable and massive vertical eddies cause recirculation, with almost uniform concentrations and particle sizes throughout the fluidized bed. A definite zone of separation forms at the surface with a clean water zone above it, relatively free from primary particles and floes. 

In a publication firom 1920, Staudinger coined the name Makromolekiile and in 1922 he generated the correct definition of macromolecules, stating For such colloid particles, in which the molecule is identical with the primary particle, and in which the individual atoms of this colloid molecule are linked together by covalent bonds, we propose for better definition the name macromolecule. ... 

Figure 2 shows examples of dimensionless total potential energy of a spherical cluster, Mt/wo, versus the number of primary particles, N, at a fixed value of a (aluo = 2) and different values of b/uo- The clusters are definitely stable at Mt < 0. At relatively small charge Z of the primary particles, the curve m, goes through the maximum (see, inset in Fig. 2) at ... 

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