Network structure carbon-black-filled

The morphology of the agglomerates has been problematic, although some forms of network-like structures have been assumed on the basis of percolation behavior of conductivity and some mechanical properties, e.g., the Payne effect. These network stmctures are assumed to be determining the electrical and mechanical properties of the carbon-black-filled vulcanizates. In tire industries also, it plays an important role for the macroscopic properties of soft nano-composites, e.g., tear. 

Figure 10.10 Schematic representation of the physical network structure in a carbon-black-filled elastomer [62]. The symbol - indicates elastomer - carbon black adsorption junctions. The length scales in this figure and the EPDM/carbon black volume ratio are fictional. For simplicity, none of the contacting carbon black aggregates, which form agglomerates, have been included...

As in carbon-black-filled EPDM and NR rubbers, the physical network in silica-filled PDMS has a bimodal structure [61]. A loosely bound PDMS fraction has a high density of adsorption junctions and topological constraints. Extractable or free rubber does virtually not interact with the silica particles. It was found that the density of adsorption junctions and the strength of the adsorption interaction, which depends largely on the temperature and the type of silica surface, largely determine the modulus of elasticity and ultimate stress-strain properties of filled silicon rubbers [113]. 

This behavior can be understood if a superimposed kinetic aggregation process of primary carbon black aggregates in the rubber matrix is considered that alters the local structure of the percolation network. A corresponding model for the percolation behavior of carbon black filled rubbers that includes kinetic aggregation effects is developed in [22], where the filler concentrations and c are replaced by effective concentrations. In a simplified approach, not considering dispersion effects, the effective filler concentration is given by ... 

Equation (70) predicts a power law behavior G cp3-5 for the elastic modulus. Thereby, the exponent (3 + d ) / (3 - df) 3.5 reflects the characteristic structure of the fractal heterogeneity of the filler network, i.e., the CCA-clusters. The predicted power law behavior at higher filler concentrations is confirmed by the experimental results shown in Fig. 15, where the small strain storage modulus of a variety of carbon black filled rubbers is plotted against carbon black loading in a double logarithmic manner. It also agrees with older experimental data obtained by Payne [1] as shown in [63,64]. 

D-TEM gave 3D images of nano-filler dispersion in NR, which clearly indicated aggregates and agglomerates of carbon black leading to a kind of network structure in NR vulcanizates. That is, filled rubbers may have double networks, one of rubber by covalent bonding and the other of nanofiller by physical interaction. The revealed 3D network structure was in conformity with many physical properties, e.g., percolation behavior of electron conductivity. 

Equations 22.3-22.14 represent the simplest formulation of filled phantom polymer networks. Clearly, specific features of the fractal filler structures of carbon black, etc., are totally neglected. However, the model uses chain variables R(i) directly. It assumes the chains are Gaussian the cross-links and filler particles are placed in position randomly and instantaneously and are thereafter permanent. Additionally, constraints arising from entanglements and packing effects can be introduced using the mean field approach of harmonic tube constraints [15]. 

The results obtained for unvulcanised EPDM and NR filled with carbon black provide convincing evidence that the physical network has a bimodal structure [62, 79]. Two types of EPDM chains and/or chain fragments with widely differing densities of EPDM-carbon black adsorption junctions are present in the rubbery matrix outside the EPDM-carbon black interface (tightly bound rubber) (Figure 10.11) [62],... 

H NMR transverse magnetisation relaxation experiments have been used to characterise the interactions between NR, isoprene rubber, BR, EPDM and polyethylacrylate rubbers with hydrophilic silica and silicas modified with coupling agents [124-129]. These studies showed that the physical interactions and the structures of the physical networks in rubbers filled with carbon black and rubbers filled with silicas are very similar. In both cases the principal mechanism behind the formation of the bound rubber is physical adsorption of rubber molecules onto the filler surface. 

Filled rubbers form a complex network of cross-linked chains connected to surface-active particles such as carbon black or amorphous silica (see Carbon Black). Here we will only indicate the structural features of importance in unfilled cross-linked elastomers. Two breakdown mechanisms are conceivable the initiation and growth of a cavity in a moderately strained matrix and the accelerating, cooperative rupture of interconnected, highly loaded network chains. The second mechanism is more important imder conditions, which permit the largest breaking elongation Xbmax to be attained (29). In that case, the quantity >-bmax is expected to be proportional to the inverse square root of the cross-link density Vg in fact, an increase of A,bmax with to is found experimentally for a... 

Fig. 4 Dynamic storage (upper panel) and loss (lower panel) moduli of single network (XR = 1, filled symbols) and double networks [XR=1.34 (open triangle)-, XR=1.67 (open circle) XR = 2.00 (inverted triangle)], measured using torsional shear of ring samples at 10 Hz and 30 °C. The plateau in G is due to flocculated filler, the disruption of which at higher strain gives rise to the maximum in G". The magnitude of these two characteristic features is smaller, reflecting less carbon black agglomeration, in the double networks. The structure in the loss moduli data below ca. 0.1% strain is an instrumental artifact [34]...

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