Local order regions clusters

Let s consider structural aspect of t50 change due to introduction Z. As it is known [3, 15], for compositions HDPE+Z is observed the extreme rise of relative fraction of local order regions (clusters) cpci, that results to decrease of fractal dimension of structure df according to the equation [15] ... 

Then the relative fraction of local order regions (clusters) cp< / have been estimated with the aid of the equation [7] ... 

In Fig. 1.4, the dependences v j(7) for polycarbonate (PC) and polyarylate (PAr) are adduced. These dependences show v, reduction at T growth, that assumes local order regions (clusters) thermofluctuational nature. Besides, on the indicated dependences two characteristic temperatures are found easily. The first from them, glass transition temperature F, defines clusters fixll decay (see also Fig. 1.1), the second corresponds to the fold on curves v j(7) and settles down on about 50 K lower T. ... 

Hence, the adduced above results shown that the main factor, influencing on molecular mobility level in HDPE noncrystalline regions, is these regions structure, characterized by fractal dimension or relative fraction of local order regions (clusters) (p j. Definite influence is exercised by molecular characteristics, especially if to take into account, that between and (p, on the one hand, and S and C, on the other hand, the close intercommunication exists (see, for the example, the Eqs. (1.11) and (1.12)). As consequence, the equations using, taking into account their structural state, will be correct for polymers dimension estimation [38]. 

In the model [98] it has been assiuned, that nucleus domain with size u is formed in defect-free part of semicrystalline polymer, that is, in crystallite. Within the frameworks of model [1] and in respect to these polymers amorphous phase structure such region is loosely packed matrix, surrounding a local order region (cluster), whose structure is close enough to defect-free polymer structure, postulated by the Flory felt model [16, 17]. In such treatment the value u can be determined as follows [43] ... 

Proceeding from the said above and analyzing values of polymers limiting strains, one can obtain the information about local order regions type in amorphous and semicrystalline polymers. The fulfilled by the authors of Ref [36] calculations have show that the most probable type of local nanostructures in amorphous polymer matrix is an analog of crystallite with stretched chains, that is, cluster. 

The authors of Ref [19] used the stated above treatment of polymers cold flow with application of Witten-Sander model of diffusion-limited aggregation [20] on the example of PC. As it has been shown in Refs. [21, 22], PC structure can be simulated as totality of Witten-Sander clusters (WS clusters) large number. These clusters have compact central part, which in the model [18, 23] is associated with notion cluster. Further to prevent misunderstandings the term cluster will be understood exactly as a compact local order region. At translational motion of such compact region in viscous medium molecular friction coefficient of each cluster, a particle, having radius a, is determined as follows [24] ... 

The density of a physical entanglement cluster network, the nodes of which are local order regions, is calculated according to Equation 1.11 and the molecular weight M i of the chain part between clusters according to Equation 1.3. 

At the formation of the structure of crosslinked polymers one can observe the formation of dissipative structures (DS) of two levels - micro- and macro-DS. Micro-DS are local order domains (clusters) and their formation is due to the high viscosity of the reactive medium in the gelation period. As it is known [47], this results in turbulence of viscous media and subsequent formation of ordered regions. 

Tinte et al.54 have carried out molecular dynamic simulations of first-principles based effective Hamiltonian for PSN under pressure and of PMN at ambient pressure that clearly exhibit a relaxor state in the paraelectric phase. Analysis of the short-to-medium range polar order allows them to locate Burns temperature Tb. Burns temperature is identified as the temperature below which dynamic nanoscale polar clusters form. Below TB, the relaxor state characterized by enhanced short-to-medium range polar order (PNR) pinned to nanoscale chemically ordered regions. The calculated temperature-pressure phase diagram of PSN demonstrates that the stability of the relaxor state depends on a delicate balance between the energetics that stabilize normal ferroelectricity and the average strength of quenched "random" local fields. 

It is worth mentioning that the influence of the regions of local order, i.e., clusters, on the orientation behaviour of amorphous polymers has been discussed previously [14,15]. 

The stractural mechanism of polymer nano composites filled with organoclay on supra segmental level was offered. Within the frameworks of these mechanism nanocomposites elasticity modulus is defined by local order domains (nano clusters) sizes similarly to natural nano composites (polymers). Densely packed interfacial regions formation in nano composites at nano filler introduction is the physical basis of nano clusters size decreasing. 

Earlier within the frameworks of local order concepts it has been shown that temperature T is associated with segmental mobility releasing in polymer loosely packet regions. This means, that within the frameworks of cluster model can be associated with loosely packed matrix devitrification. The dependences F(T) for the same polymers have a similar form (Fig. 1.5). 

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