Structure of polymer networks as a percolation system

Fractial parameterization of the structure of filled polymers

“…Since Df -___ C| [38], an increase in Df means a change in statistical stiffness of the chain. In addition, the quantity Df characterizes the size distribution of microcavities in the fluctuational free volume [39], which also changes upon introduction of a filler.…”

“…Equation (5) assumes that any increase in d m with increasing volume content of the filler, ~p, leads to a decrease in the relative content of clusters, ~c~, and hence, to a decrease in the degree of local order of the structure of the polymer matrix. Moreover, a rise in d m means that the distance between the clusters increases or, in other words, the coefficient of self-similarity of the structure, A i, increases [38],…”

“…In addition, the quantity Df characterizes the size distribution of microcavities in the fluctuational free volume [39], which also changes upon introduction of a filler. Consequently, the term "disturbance" of the structure describes a wide spectrum of changes on the molecular, topological, and submolecular levels of the structure.…”

“…(2),)for PHE specimens, from which it follows that the increase in D n is responsible for the growth in D r or the intensification of energy excitation in sparsely packed regions of the polymer matrix. The increase in Dr, in turn, affects both the structural [38] and mechanical [8] characteristics of the polymer matrix.…”

“…The first of them, the dimension D r of localization regions of the excess energy [44], determines the degree of energy excitation in the sparsely packed polymer matrix within the framework of the cluster model [39] and is defined as…”