Particle-cluster aggregation mechanism

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]. 

In contrast, the three- or two-dimensional morphologies of colloidal aggregates via Brownian particle trajectories show a fractal-like structure. One of the most prominent features of the surface deposits formed by the diffusion-limited aggregation mechanism is the formation of isolated treelike clusters (9). In our experiments, the surface morphology of the silica-coated polyethylene composite prepared by... 

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]. 

For Q<0, this distribution function is peaked around a maximum cluster size (2Q/(2Q-1))< >, where < > is the mean cluster size. 2Q=a+df1 is a parameter describing details of the aggregation mechanism, where a1 is an exponent considering the dependency of the diffusion constant A of the clusters on its particle number, i.e., A NAa. This exponent is in general not very well known. In a simple approach, the particles in the cluster can assumed to diffusion independent from each other, as, e.g., in the Rouse model of linear polymer chains. Then, the diffusion constant varies inversely with the number of particles in the cluster (A Na-1), implying 2Q=-0.44 for CCA-clusters with characteristic fractal dimension d =l.8. 

The CCA-model considers the filler network as a result of kinetically cluster-cluster-aggregation, where the size of the fractal network heterogeneity is given by a space-filling condition for the filler clusters [60,63,64,92]. We will summarize the basic assumptions of this approach and extend it by adding additional considerations as well as experimental results. Thereby, we will apply the CCA-model to rubber composites filled with carbon black as well as polymeric filler particles (microgels) of spherical shape and almost mono-disperse size distribution that allow for a better understanding of the mechanisms of rubber reinforcement. 

The macroscopic properties of liquid suspensions of fumed powders of silica, alumina etc. are not only affected by the size and structure of primary particles and aggregates, which are determined by the particle synthesis, but as well by the size and structure of agglomerates or mesoscopic clusters, which are determined by the particle-particle interactions, hence by a variety of product- and process-specific factors like the suspending medium, solutes, the solid concentration, or the employed mechanical stress. However, it is still unclear how these secondary and tertiary particle structures can be adequately characterized, and we are a long way from calculating product properties from them [1,2]. 

At the synthesis beginning solution contains only monomer, which within the frameworks of irreversible aggregation models can be considered as particles, uniting later in a cluster (macromolecular coil). As it is known [21], within the frameworks of the indicated models such mechanism is called mechanism particle-cluster and aggregates with fractal dimension 2.5 is the result of its action. Besides, the value Cj was calculated according to the Eq. (18) with the following parameters using t = 0.5 min, i3r=4.8 mol/l s and Q=8.3><10-3. 

In Fig. 29, the dependences of D on reaction duration t for DMDAACh polymerization at both indicated above conditions are adduced. As one can see, the two dependences Dj(t) are similar qualitatively and their distinction consists of only in more slow reaction realization for DMDAACh-1 (the kinetic parameters for DMDAACh synthesis adduced conditions differ on about two orders [1]). Let us note, that for DMDAACh-2 the aggregation mechanism change is observed twice within the range of t < 2 min mechanism particle-cluster is changed by diffusion-limited mechanism cluster-cluster and within the range of t = 5-10 min opposite change occurs [21]. It is important to note, that the last mechanisms change occitrs at constant initial monomers concentration c and practically constant value MM [1]. 

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