Particulate aggregate network, structural

Parameter that provides a mathematical description of the fractal structure of a polymer network, an aggregated particulate sol, or of the particles that comprise them. 

The calculated dimensions D, based on the aforementioned method, are adduced in Table 6.2. The values for the studied nanocomposites are varied within the range of 1.10-1.36, i.e., they characterize more or less branched linear formations ( chains ) of nanofiller particles (aggregates of particles) in elastomeric nanocomposite structure. Let us remind that for particulate-filled composites polyhydroxyether/graphite, the value changes within the range of 2.30-2.80 [4, 10], i.e., for these materials filler particles network is a bulk object, but not a linear one [36]. 

Up to now we considered pol5meric fiiactals behavior in Euclidean spaces only (for the most often realized in practice case fractals structure formation can occur in fractal spaces as well (fractal lattices in case of computer simulation), that influences essentially on polymeric fractals dimension value. This problem represents not only purely theoretical interest, but gives important practical applications. So, in case of polymer composites it has been shown [45] that particles (aggregates of particles) of filler form bulk network, having fractal dimension, changing within the wide enough limits. In its turn, this network defines composite polymer matrix structure, characterized by its fractal dimension polymer material properties. And on the contrary, the absence in particulate-filled polymer nanocomposites of such network results in polymer matrix structure invariability at nanofiller contents variation and its fractal dimension remains constant and equal to this parameter for matrix polymer [46]. 

The formation of a particulate network with fractal structure has been reported, which suggests a reaction-limited cluster aggregation (RLCA) mechanism [34]. RLCA requires moderate repulsions to exist between the partides (Le., an energy barrier has to be overcome to permit a cluster-forming collision between particles). Since in ILs the classical electrostatic repukion should be annihilated, the alternate cation-anion layers patterning at the surface of the particles, which is induced by solvation, is thought to provide an effective repulsive barrier. 

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