Aggregation of fillers

Beside the consideration of the up-cycles in the stretching direction, the model can also describe the down-cycles in the backwards direction. This is depicted in Fig. 47a,b for the case of the S-SBR sample filled with 60 phr N 220. Figure 47a shows an adaptation of the stress-strain curves in the stretching direction with the log-normal cluster size distribution Eq. (55). The depicted down-cycles are simulations obtained by Eq. (49) with the fit parameters from the up-cycles. The difference between up- and down-cycles quantifies the dissipated energy per cycle due to the cyclic breakdown and re-aggregation of filler clusters. The obtained microscopic material parameters for the viscoelastic response of the samples in the quasi-static limit are summarized in Table 4. 

In view of an illustration of the viscoelastic characteristics of the developed model, simulations of uniaxial stress-strain cycles in the small strain regime have been performed for various pre-strains, as depicted in Fig. 47b. Thereby, the material parameters obtained from the adaptation in Fig. 47a (Table 4, sample type C60) have been used. The dashed lines represent the polymer contributions, which include the pre-strain dependent hydrodynamic amplification of the polymer matrix. It becomes clear that in the small and medium strain regime a pronounced filler-induced hysteresis is predicted, due to the cyclic breakdown and re-aggregation of filler clusters. It can considered to be the main mechanism of energy dissipation of filler reinforced rubbers that appears even in the quasi-static limit. In addition, stress softening is present, also at small strains. It leads to the characteristic decline of the polymer contributions with rising pre-strain (dashed lines in... 

Aggregation of filler particles and filler-filler interactions... 

Considerable effort has been spent to explain the effect of reinforcement of elastomers by active fillers. Apparently, several factors contribute to the property improvements for filled elastomers such as, e.g., elastomer-filler and filler-filler interactions, aggregation of filler particles, network structure composed of different types of junctions, an increase of the intrinsic chain deformation in the elastomer matrix compared with that of macroscopic strain and some others factors [39-44]. The author does not pretend to provide a comprehensive explanation of the effect of reinforcement. One way of looking at the reinforcement phenomenon is given below. An attempt is made to find qualitative relations between some mechanical properties of filled PDMS on the one hand and properties of the host matrix, i.e., chain dynamics in the adsorption layer and network structure in the elastomer phase outside the adsorption layer, on the other hand. The influence of filler-filler interactions is also of importance for the improvement of mechanical properties of silicon rubbers (especially at low deformation), but is not included in the present paper. 

In semicrystalline polymers, fillers may act as reinforcement, as well as nucle-ation agents. For example in PP, nanoscale silica fillers may nucleate the crystallization resulting in spherulites that show enrichment in particles in the center of the spherulite (Fig. 3.64). For a quantitative analysis of, e.g., filler sizes and filler size distributions, high resolution imaging is necessary and tip convolution effects [137-140] must be corrected for. The particles shown below are likely aggregates of filler particles considering the mean filler size of 7 nm [136]. 

A fundamental difficulty in the study of the linear viscoelastic behavior of filled rubbers is the secondary aggregation of filler particles, which greatly influences the behavior at small strains, where the response is linear. The effect of this aggregation is overcome at large strains, but now non-linearity and a number of other complications become problems. 

The dispersive (or intensive) mixing involves application of stresses that break domains of the dispersed phase to the desired size. The dispersed phase may be composed of liquid drops, gel particles of the matrix material, aggregates of filler particles, etc. 

This chapter considers a study of two types of composites based on polyhydroxyether and graphite with various amounts of a filler. Using various methods it is possible to estimate the adhesion characteristics and interfacial layer, including its thickness and tensile strength and the interdependence between these values and the adhesion properties. The results were treated on the basis of the theory of irreversible aggregation, cluster theory of the polymer structure and fractal analysis. It was established that all the important characteristics of adhesion, the interfacial layer and mechanical properties are interconnected by the fractal dimensions of the surface of the aggregates of filler particles and of the polymer matrix, whose structure is distorted under the influence of the filler surface. 

A decrease in radius of filler particles in the composite will result in an increased value of stresses needed to initiate the composite failure. Mechanisms of failure in a composite could take place in the polymer matrix by shear yielding and/or crazing, inside the aggregates of filler particles and/or at the interface matrix/filler by mechanism of dewetting. In particulate-filled composites, yielding and crazing do not depend on the work of adhesion between matrix and filler, VFmf, or thermal stresses, but these influence the dewetting phenomenon, considerably, (Eqn. 5) ... 

Spherical Particles Nanofiller with three dimensions in the nanometer regime are the spherical nanofillers obtained by sol-gel process [9, 10]. In sol-gel process the organic/inorganic hybrid material can be formed by the condensation reaction between the functionalized prepolymer and the metal alkoxides, leading to the formation of a chemical bond between the polymer and the inorganic filler. Therefore, the incorporation of filler particles in polymer through the sol-gel process avoids the aggregation of filler. 

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