Local order regions

For small particles supported on thin films of amorphous or microcrystalline materials it is not easy to determine whether there is any consistent correlation between the particle orientation and the orientation of the adjacent locally ordered region of the substrate. For some samples of Pt and Pd on gamma-alumina, for example, nanodiffraction shows that the support films have regions of local ordering of extent 2 to 5 nm. Patterns from the metal particles often contain spots from the alumina which appear to be consistently related to the metal diffraction spots. 

However, serious drawbacks of model 3 are that (i) the proportion r of the rotators should be fitted that is, it is not determined from physical considerations and (ii) the depth of the well, in which a polar particle moves, is considered to be infinite. Both drawbacks were removed in VIG (p. 305, 326, 465) and in Ref. 3, where it was assumed that (a) The potential is zero on the bottom of the well (/(()) = 0 at [ fi < 0 < P], where an angle 0 is a deflection of a dipole from the symmetry axis of a cone, (b) Outside the well the depth of the rectangular well is assumed to be constant (and finite) U(Q) = Uq at [— ti/2 < 0 < ti/2]. Actually, two such wells with oppositely directed symmetry axes were supposed to arise in the circle, so that the resulting dipole moment of a local-order region is equal to zero (as well as the total electric moment in any sample of an isotropic medium). 

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] ... 

It is shown, that the stracture formation of nanocomposites based on the polypropylene takes in Euclidean space with dimension interfacial areas and crystalline P-phase. This model allows qrrantitative description of nanocomposites properties. 

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. ... 

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. 

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] ... 

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] ... 

As it has been noted above, in the indicated compositions solid-phase extrusion process the sharp drop of (p, (from 0.26 up to -0.05) within the range of A, = 1 3 is observed, that results to corresponding increase from 2.63 up to -2.87 [5]. As it is known [12], between the parameters J and (p the intercommunication exists, expressed by the Eq. (1.12). In Fig. 14.1 the dependences, calculated according to the Eqs. (1.9) and (1.12) eomparison is shown. As one can see, the good conformity between them is observed, that confirms the made above conclusion - local order regions deeay (9 decrease) in solid-phase extrusion process is the d growth eause [11]. 

The local order region, consisting of several densely packed collinear segments of various polymer chains (for more details see chapter one) according to a signs number should be attributed to the nanoparticles (nanoclusters) [9] ... 

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. 

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