Cluster aggregation

Flocculation studies, considering the small-strain mechanical response of the uncross-hnked composites during heat treatment (annealing), demonstrate that a relative movement of the particles takes place that depends on particle size, molar mass of the polymer, as well as polymer-filler and filler-filler interactions (Figure 22.2). This provides strong experimental evidence for a kinetic cluster-cluster aggregation (CCA) mechanism of filler particles in the mbber matrix to form a filler network [24]. 

FIGURE 22.6 Payne effect of butyl composites with various amounts of N330, as indicated (left) [28]. Scaling behavior of the small-strain modulus of the same composites right). The obtained exponent 3.5 confirms the cluster-cluster aggregation model. (From Kliippel, M. and Heinrich, G., Kautschuk, Gummi, Kunststoffe, 58, 217, 2005. With permission.)... 

Biji, V., Barazzouk, S., Thomas, K G., George, M. V. and Kamat, P. V. (2001) Photoinduced electron transfer between 1,2,5-triphenylpyrrolidinofuIlerene cluster aggregates and electron donors. Langmuir, 17, 2930-2936. 

Unlike the simulations which only consider particle-cluster interactions discussed earlier, hierarchical cluster-cluster aggregation (HCCA) allows for the formation of clusters from two clusters of the same size. Clusters formed by this method are not as dense as clusters formed by particle-cluster simulations, because a cluster cannot penetrate into another cluster as far as a single particle can (Fig. 37). The fractal dimension of HCCA clusters varies from 2.0 to 2.3 depending on the model used to generate the structure DLA, RLA, or LTA. For additional details, the reader may consult Meakin (1988). 

Fig. 37. Typical clusters obtained by diffusion-limited aggregation (DLA). Top Two-dimensional diffusion-limited aggregation. Bottom Reaction-limited hierarchical cluster-cluster aggregation (HCCA) (Meakin, 1988 with permission, from the Annual Review of Physical Chemistry, Vol. 39. by Annual Reviews www.Annual/Reviews.org).

In situ SAXS investigations of a variety of sol-gel-derived silicates are consistent with the above predictions. For example, silicate species formed by hydrolysis of TEOS at pH 11.5 and H20/Si = 12, conditions in which we expect monomers to be continually produced by dissolution, are dense, uniform particles with well defined interfaces as determined in SAXS experiments by the Porod slope of -4 (non-fractal) (Brinker, C. J., Hurd, A. J. and Ward, K. D., in press). By comparison, silicate polymers formed by hydrolysis at pH 2 and H20/Si = 5, conditions in which we expect reaction-limited cluster-cluster aggregation with an absence of monomer due to the hydrolytic stability of siloxane bonds, are fractal structures characterized by D - 1.9 (Porod slope — -1.9) (29-30). 

The induction of steric effects by the pore walls was first demonstrated with heterogeneous catalysts, prepared from metal carbonyl clusters such as Rh6(CO)16, Ru3(CO)12, or Ir4(CO)12, which were synthesized in situ after a cation exchange process under CO in the large pores of zeolites such as HY, NaY, or 13X.25,26 The zeolite-entrapped carbonyl clusters are stable towards oxidation-reduction cycles this is in sharp contrast to the behavior of the same clusters supported on non-porous inorganic oxides. At high temperatures these metal carbonyl clusters aggregate to small metal particles, whose size is restricted by the dimensions of the zeolitic framework. Moreover, for a number of reactions, the size of the pores controls the size of the products formed thus a higher selectivity to the lower hydrocarbons has been reported for the Fischer Tropsch reaction. 

A. Hasmy and R. Jullien Sol-Gel Process Simulation by Cluster-Cluster Aggregation. J. Non-Crystalline Solids 186, 352 (1995). 

F. Sciortino and P. Tartaglia Structure Factor Scaling During Irreversible Cluster-Cluster Aggregation. Phys. Rev. Lett 74, 282 (1995). 

In more recent optical extinction measurements on specially filtered samples [60], the weak bump had disappeared. This bump may thus have been due to damaged clusters (see Sect. 3.6) or cluster aggregates which form colloidal inclusions in the sample. The main feature of the UV-visible spectrum of AU55 in solution is then a broad absorption extending across the whole visible region. 

S0rensen ° analysed the In O2 vs. Inx experimentally determined functions at different temperatures. The slope of such curves can be shown to he simply related, by equilibrium equations, to the number of atoms and defects composing a cluster. By this method, clusters and clusters aggregations as given in Table 9 are proposed. 

Transition from non-metallic clusters consisting of only a few atoms to nanosized metallic particles consisting of thousands of atoms and the concomitant conversion from covalent bond to continuous band structures have been the subject of intense scrutiny in both the gas phase and the solid state during the last decade [503-505]. It is only recently that modern-day colloid chemists have launched investigations into the kinetics and mechanisms of duster formation and cluster aggregation in aqueous solutions. Steady-state and pulse-radiolytic techniques have been used primarily to examine the evolution of nanosized metallic particles in metal-ion solutions [506-508]. 

Labile clusters join and grow on the vapor side of the surface until a critical size is achieved. This can occur either by the addition of water and gas molecules to existing cavities, via the joining of cavities along the interface (as indicated in the cluster aggregation mechanism) or both. 

O. Katzenelson, H. Z. Hel-Or, D. Avnir, Chem. Eur. J. 1996, 2, 174-181] and serve for definition of the chirality of large su-pramolecular and macromolecular systems (e.g. chiral clusters, aggregates, polymers, or dendrimers). 

---