Topological fixation points

Thus, the stated above results demonstrated, that fractal analysis application for polymers fracture process description allowed to give more general fracture concept, than a dilation one. Let us note, that the dilaton model equations are still applicable in this more general case, at any rate formally. The fractal concept of polymers fracture includes dilaton theory as an individual case for nonfractal (Euclidean) parts of chains between topological fixation points, characterized by the excited states delocalization. The offered concept allows to revise the main factors role in nonoriented polymers fracture process. Local anharmonicity ofintraand intermolecular bonds, local mechanical overloads on bonds and chains molecular mobility are such factors in the first place [9, 10]. 

Therefore, within the frameworks of fractal analysis an increase in network density with reduction in chain statistical flexibility was obtained. The increase in the number of topological fixation points of macromolecules in the glassy state in comparison with the high-elastic state can be predicted by using fractal analysis methods [29,61]. 

The fractal dimension D of the chain part between its topological fixation points (entanglements, clusters, crosslinking nodes) is the most important structural parameter, checking molecular mobility and deformability of polymers. Two of the main factors, due to application of dimension D, are its clearly defined variation limits (1 < D < 2) and the dependence on polymer supersegmental (supermolecular) structure. Let us especially note that all fractal relationships contain, at any rate, two variables. 

---