Random aggregates

Fibril aggregates randomly entangled were sulfonated at 300°C by reacting with sulfuric acid containing 20% SO3 by Fisher et al. (5). 

The model system is used to determine the dependence of the projected area and the envelope radius on the given parameters. It is easy to show and see that both scale with the radius of the primary particles. It is therefore possible to transfer the results obtained for a given primary-particle radius to other radii. In the calculations presented here, the value of the particle radius was 10 run. Since the algorithm generates aggregates randomly, there exists substantial fluctuation in the values determined for the projected area and the envelope radius. As in the case of real experiments, it is... 

Scanning TEM shows that semicrystalline Zn-EMAA neutralized between 17% and 78% contains nearly monodisperse spherical aggregates randomly distributed in the polymer matrix (Fig. The... 

Provided a large difference in molecular weight between the block copolymer and the matrix, we have to take into account that the relative ratio between the segments in the block copolymer plays an important role in the final morphology. As depicted in Fig. 5.16, typically, for AB block copolymers with similar volumes of block A and B we observe the formation of a lamellar phase that turns into a so-called onion ring pattern when blended with a A homopolymer. On the contrary, asymmetric block copolymers with larger A block tend to produce micellar aggregates randomly distributed in the homopolymer phase. 

Posner clusters i.e., Cag(P04)6), with sizes close to 0.8 nm, are present in supersaturated and metastable CaP solutions claimed to simulate the electrolyte portion of blood plasma, as experimentally proved by Oyane etal. using dynamic light scattering [49]. Directly quoting from the work of Posner [50, 51], in the process of AGP formation in solution, Ca9(P04)6 clusters form first (with the experimental support to this provided by the later work of Oyane et al. [49]) and then are aggregated randomly to produce the larger spherical particles with the inter-duster space filled with water. The solution of Table 1 shall have the similar Posner dusters prior to its in sfru precipitation of AGP when it is warmed up. 

Others (Roelfstra (11)) used a numerical approach, designing a finite element mesh which represents a certain volume of material, with its constitutive elements (cement paste and aggregates randomly distributed) and have studied the behaviour of such a structure. 

Two point defects may aggregate to give a defect pair (such as when the two vacanc that constitute a Schottky defect come from neighbouring sites). Ousters of defects ( also form. These defect clusters may ultimately give rise to a new periodic structure oi an extended defect such as a dislocation. Increasing disorder may alternatively give j to a random, amorphous solid. As the properties of a material may be dramatically alte by the presence of defects it is obviously of great interest to be able to imderstand th relationships and ultimately predict them. However, we will restrict our discussion small concentrations of defects. 

We assume that at the grain boundaries aggregates, that are responsible of the radiative emission, are randomly oriented and therefore giving rise to isotropic emission. 

As has been described in Chapter 4, random copolymers of styrene (St) and 2-(acrylamido)-2-methylpropanesulfonic acid (AMPS) form a micelle-like microphase structure in aqueous solution [29]. The intramolecular hydrophobic aggregation of the St residues occurs when the St content in the copolymer is higher than ca. 50 mol%. When a small mole fraction of the phenanthrene (Phen) residues is covalently incorporated into such an amphiphilic polyelectrolyte, the Phen residues are hydrophobically encapsulated in the aggregate of the St residues. This kind of polymer system (poly(A/St/Phen), 29) can be prepared by free radical ter-polymerization of AMPS, St, and a small mole fraction of 9-vinylphenanthrene [119]. 

Fig. 2. (continued)—(d) an aggregate of microcrystallites whose long axes are parallel, but randomly oriented (left), diffracts to produce a series of layer lines (right) and (e) a polycrystalline and preferentially oriented specimen (left) diffracts to give Bragg reflections on layer lines (right). The meridional reflection on the fourth layer line indicates 4-fold helix symmetry. 

By relating the endpoint of crushed DBF absorption to the void space within and between equivalent spheres of aggregates, and assuming the spheres to be packed at random, Wang et al. obtained the following equation for the effective volume fraction of carbon black ... 

---