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Functional Polymer Blends and Nanocomposites: A Practical by Gennady E. Zaikov, Liliya I. Bazylyak, A. K. Haghi PDF

By Gennady E. Zaikov, Liliya I. Bazylyak, A. K. Haghi

ISBN-10: 1926895894

ISBN-13: 9781926895895

This ebook info unique, theoretical, and demanding experimental effects that use non-routine methodologies usually unusual to so much readers. it's also papers on novel purposes of extra known experimental ideas and analyses of composite difficulties. The publication offers finished insurance at the most recent advancements of analysis within the ever-expanding quarter of composite fabrics and their purposes to huge clinical fields spanning physics, chemistry, biology, fabrics, and more.

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Extra info for Functional Polymer Blends and Nanocomposites: A Practical Engineering Approach

Example text

Let’s separate from them any undefined star, and in it – any undefined pair of rays, forming the linear chain by 2N length. Its phantom Gaussian walks are ordered to the same distribution law (Eq. 13) with the same normalization condition (Eq. 10). However, the probability ω (z ) of the msN differed links distribution upon Z identical cells at the condition, that in every cell there is not more than one link, will be determined by a new expression: ω ( z) = Z! 1 1 ( )msN (1 − )Z −msN (88) (Z − msN)!

Taking into account the fractal properties of polymer chain and assuming that a set of traps in its conformational volume is a fractal as well, we obtain the expression similar to Eq. (54): { ψ(t) = g exp −t τ p (ρm / ρ0 )ξ } 1/ ξ (55) where τ p is characteristic time of chain propagation act, ρ m and ρ 0 are monomer and traps concentrations in the macroradical’s conformational volume, respectively. According to the derivation of Eq. (55) (56) where d f = ( d + 2) 3 and d L are fractal dimensions of the conformational volume of macroradical and a set of traps in it.

Ni − si ) / 2)! (13) i i i i i i The condition of the absence of self-intersection trajectories of walks requires from the point of view of the links of star per cells distribution that in every cell of the lattice space should be exist not more than one link of a star. The links of a polymeric chain are continuous; they cannot be separated one from other and located upon the cells into the undefined order. Therefore, the number of a links in a chain is its essential distinctive feature. The links of the different rays are also distinguishable.

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Functional Polymer Blends and Nanocomposites: A Practical Engineering Approach by Gennady E. Zaikov, Liliya I. Bazylyak, A. K. Haghi

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