By G. V. Kozlov
Fractal research supplies simply normal mathematical description of polymers, i.e. it doesn't establish structural devices (elements), from which any actual polymer is shaped. actual description of thermodynamically non-equilibrium polymer constitution within the framework of the neighborhood order rules offers the cluster version of the polymer amorphous nation constitution that quantitatively establish its elements.Since those versions think of the polymer constitution a bit of from aspects, they're very good finishing each other. it's common wisdom that buildings showing fractal behaviour on small size scale and being homogeneous on huge size scale are named homogeneous fractals. those fractals are percolation clusters on the percolation threshold. As proven under, the cluster constitution represents the percolation method and, because of the above-said, the homogeneous fractal. to place it in a different way, the presence of the neighborhood order within the condensed section of polymers determines fractality in their constructions.
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Extra info for Cluster Model Interrelation With Modern Physical Concepts
Thus shorter length of the chain “rigidity segment”, lst, in the glassy state is caused by conformational restructurings typical of this state . For amorphous-crystalline polymers, reduced relative part of clusters, ϕ clr , is used. It characterizes this parameter in relation to the entire volume of the polymer, but not its amorphous phase exclusively [123, 124]: ϕ clr = ϕ cl 1− K , (80) where K is the crystallinity degree. 72) can be reduced to the form as follows : ϕ cl ~ (1 − K )(Tg − T )βT .
Clearly the correlation between ωD and V in double logarithmic coordinates The Cluster Model and the Anharmonicity Concept 43 is well approximated by a linear correlation. In accordance with the equation (61), this means that γD constancy in the considered temperature interval (293 – 453 K for PAr and 293 – 433 K for PSF). 75 for PSF) are close to the ones previously obtained for polymers of this type . Figure 23. Variation of the Debye frequency, ωD, with the specific volume, V, present in double logarithmic coordinates for PAr (1) and PSF (2)  Figure 24.
E. decrease of Lc) in accordance with the equation (56) in the glassy state rather than in the rubbery state even at invariable D. This effect is intensified by the appropriate decrease of D that follows even from the well known fact as follows: the decrease of molecular mobility in the polymer glassy state , and is proved experimentally . Thus the fractal analysis suggested enables forecast of the topological chain fixation point number increase at T < Tg, suggested before [75, 83]. Figure 19.