Fractals linear elasticity

Let us fulfill the value theoretical estimation according to the two methods and compare these results with the ones obtained experimentally. The first method simulates interfacial layer in polymer composites as a result of interaction of two fractals— polymer matrix and nanofiller surface [19,20]. In this case, there is a sole linear scale /, which defines these fractals interpenetration distance [21]. As nanofiller elasticity modulus is essentially higher than the corresponding parameter for rubber (in the considered case—in 11 times, see Figure 6.1), then the indicated interaction... 

The elasticity modulus E value decreases at growth (Fig. 4.23). This effect cause (intermolecular bonds strong anharmonicity) is described in detail in Refs. [49, 94, 95], In Fig. 4.24, the dependences of elasticity modulus E on structure fractal dimension are adduced for HDPE and PP, which turned out to be linear and passing through coordinates origin. As it is known [84], the relation between E and is given by the equation ... 

The treatment of an epoxy polymer as a natural nanocomposite or quasi-two-phase system [8] puts in the foregroimd the interaction of such system components, which for nanocomposites is expressed first of all in an interfacial regions formation [2-4]. Let us note that in the reinforcement process (increase in the elasticity modulus of the nanocomposite in comparison with the matrix polymer) interfacial regions play the same role as the nanofiller [2-4], Such a reinforcement mechanism is due to the formation of nanocomposites with inorganic nanofiller [1-A and the structure of natural nanocomposites (linear amorphous polymers) [9] in three-dimensional Euclidean space. Therefore in paper [10] the study of structure formation conditions for crosslinked epoxy polymers, treated as natural nanocomposites, was carried out within the frameworks of fractal analysis. 

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