Download Cluster Model Interrelation With Modern Physical Concepts by G. V. Kozlov PDF

By G. V. Kozlov

Fractal research offers simply common mathematical description of polymers, i.e. it doesn't determine 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 provides the cluster version of the polymer amorphous country constitution that quantitatively determine its elements.Since those versions contemplate the polymer constitution a little from aspects, they're first-class finishing each other. it's normal wisdom that constructions exhibiting 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 less than, the cluster constitution represents the percolation procedure 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 part of polymers determines fractality in their buildings.

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Dependencies of Lec Lcl (1) and Ltc 0 Ltc (2) (see text for details) on the test temperature for PC [78] Quantitatively, this forecast can be checked by temperature dependence of two relations. The first of them is the relation of chain intersect lengths between e “hookings” Lc (the rubbery state) [81] and between clusters Lcl (the glassy state) t [83]. 45 ( Lc 0 , the rubbery state) and at ν values. The first Clusters as Dissipative Structures ( 33 ) gives results, obtained within the framework of the cluster model [83]; the second one (L 0 L ) - in the framework of the fractal analysis.

Kozlov and G. E. Zaikov it is assumed that at transition to the glassy state νnw does not change. Disadvantages of this interpretation became clear very soon. Actually, if crosslink points of such molecular hookings are considered as the points of topological chain fixation, then the assumption of equality of their frequencies in the rubbery and glassy states is very ambiguous. For example, polymer deformability decrease at transition from the rubbery to the glassy state is known well, but according to the indicated assumption this change must not happen, and for both cases, the stretch rating λ is determined from the known formula [73]: Figure 17.

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 [9]: ϕ cl ~ (1 − K )(Tg − T )βT . m. for three polymers. m. 0 [5], 0 namely, d f value, which is different for different polymers. Obviously, this is the minimum of Df that can be reached for current polymers.

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