Ramified clusters

Radical initiator 127 Ramified clusters 219 Random walk 191, 214, 263 Random phase approximation (RPA) 191-226, 245, 271, 274, 284, 286, 290 Reprotonation 95 Reptation model 202, 204 Rheology 280... 

Flocculated powders have ramified clusters, which do not stack well in the green form which is then not dense enough. A sintered alumina ceramic will not become fully dense after sintering if it starts out from a green form made near the isoelectric pH. 

Fig. 3c, the behavior is very different. There is no longer any clear-cut distinction between the droplet interior and its interface, and the amplitude of the whole order parameter variation across the droplet vanishes as V ms Physically, such a droplet profile can be interpreted as the spherical average of a ramified cluster, unlike the compact droplet assumed in Eq. (15) and found for near l/ coex (Fig. 3b). Actually, the free energy cost to form such a droplet also is rather small, one finds AF ( ms li sp) oc r (V sp ...

A specific class of dimeric alkoxides is represented by the cluster derivatives of Mo and W in lower oxidation states studied during the 2 last decades by Chisholm et al. The derivatives of Mo (II) and (HI) as well as W(TTT) with bulky or ramified radicals (sec-, tert-, neo-R, C6H3R2-2,6) form ethane-like molecules with multiple M-M bonds. In contrast to the abovementioned aggregates, they do not contain any bridging groups, for example, (RO)3Mo=Mo(OR)3,where R=CH2Bu . The length of a metal-metal bond is a... 

By contrast at low TPAOH content the lower availability of OH favors large and ramified oligomers, surrounding the TPA solvated clusters. The dimension of TPA clusters seems independent on the TPAOH amount, indeed the pore diameter decreases when the amount of TPAOH increases. 

Another consequence of the phase term (Equation 14.B7) is that if qa< 1, the fields from the scattering elements add coherently. For an object in three dimensions this coherent addition occurs for all three dimensions, and the three dimensions add coherently. Thus, the scattered field will be proportional to the amount of matter in the object, which proportional to the volume V of a dense particle or the number of monomers per cluster, N, of a ramified object. Since intensity is the field squared, we obtain or dependencies. 

In CCA, monomers are depleted at an early stage of the growth process, so further growth must occur exclusively between clusters. Strong mutual screening of cluster interiors leads to ramified objects characterized by a mass fractal dimension D 2 (Porod slope P —2). As shown in Figure 6 for the two-step acid-catalyzed sample, Porod slopes of —2 are generally observed for silicate sols prepared from alkoxides under acid-... 

When p is nonzero, there are clusters of liquidlike cells, each one of which has at least z liquidlike neighbors. It is well known that in such situations there is a critical concentration above which there exists an infinite cluster. Thus for p>p, there is an infinite, connected liquidlike cluster, and we can consider the material within it to be liquid. For pliquidlike clusters exist, which might imply a glass phase because the fluidity would be reduced. However, percolation theory tells us that just above p the infinite cluster is very stringy or ramified so that bulk liquid properties are not fully developed. 

When silica is prepared by acidification of water glass (alkali solution of silica), polycondensation reactions occur between dissolved oligomeric silica species, resulting in (sub)colloidal particles [1]. These primary particles combine to very ramified aggregates, a process described by diffusion or reaction limited cluster-cluster aggregation with power-law dependent density (fractals) [2,3]. After gelation the fractal structure is still preserved at sub-micrometer scale, while at larger scale Euclidean behaviour is observed. 

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