Nanoclusters fractal dimension

The main stmcture parameter of cluster model-nanoclusters relative fraction (p, which is polymers structure order parameter in strict physical sense of this tern, can be calculated according to the Eq. (1.11). In its turn, the polymer structure fractal dimension value is determined according to the Eqs. (1.9) and (2.20). 

The first from the indicated points was considered in detail above. The authors of Refs. [20,21] showed that nanoclusters surface fractal dimension changes within the range of 2.15 2.85 that is their well developed surface sign. And at last, let us consider quantum (wave) aspect of nanoclusters nature on the example of PC [22]. Structural levels hierarchy formation and development scenario in this case can be presented with the aid of iterated process [23] ... 

FIGURE 15.19 The dependence of parameter on nanoclusters surface fractal dimension J /orPC[50],... 

The authors of Ref [48] showed that the interfacial adhesion level for composites polyhydroxyether/graphite was raised at the decrease of polymer matrix and filler particles surface fractal dimensions difference. The similar approach was used by the authors of Ref [50], who calculated nanoclusters... 

Bashorov, M. T., Kozlov, G. V, Shustov, G. B., Mikitaev, A. K. (2009). The Estimation of Fractal Dimension of Nanoclusters Surface in Polymers. Izvestiya Vuzov, Severo-Kavkazsk region, estestv. Nauki, (N6), 44-46. 

Figure 9.1 Comparison of the fractal dimensions of a loosely packed matrix dj and a space in which a nanocluster structure is formed, for epoxy polymers EP-1 (1) EP-1-200 (2) EP-2 (3) and EP-2-200 (4) [10]...

Nanoclusters do not possess three-dimensional symmetry and it was shown [17] that statistical segments in them could be displaced by each relatively an other lengthwise, which assumes their rough surface. This roughness degree, which can be estimated with the aid of the surface fractal dimension J affects the contact on the nanocluster... 

Figure 9.6 The dependence of the surface fractal dimension of nanoclusters on the number of segments in one nanocluster n. The designations are the same as in...

Thus, the simple method of estimation of the surface fractal dimension d of nanoclusters for the structure of crosslinked epoxy polymers, which are considered as natural nanocomposites, was offered. The lower boundary of 2.55 indicates that packing of nanoclusters is less dense in comparison with an ideal one, for which surf expected. Unlike inorganic nanofiller nanoparticles, nanoclusters in... 

As it is known [6], within the frameworks of fractal analysis the molecular mobility level can be described with the aid of the fractal dimension of the chain part between nanoclusters D p, which changes within the limits of 1... 

It has been shown earlier [67] that index P is a function of the molecular mobility level, characterised by the fractal dimension of a chain part between nanoclusters. At = 1 the indicated part is fully stretched between nanoclusters, its molecular mobility is suppressed and P, = p. At = 2 the molecular mobility is the greatest, which is typical for the rubber-like state of polymers [6]. Calculation of the dimension D, can be carried out with the help of Equation 6.22. 

Nanoclusters formation synergetics is directly connected with the studied polymers structure macroscopic characteristics. As it has been noted above, the fractal structure, characterized by the dimension is formed as a result of nanoclusters reformations. In Fig. 15.7 the dependence for the considered polymers is adduced, from which increase at A. growth follows. This means, that the increasing of possible reformations number m, resulting to Aj reduction (Fig. 15.6), defines the growth of segments number in nanoclusters, the latter relative fraction cp j enhancement and, as consequence, d reduction [3-5]. 

In Figure 9.1 the comparison of dimensions and for the studied EP is adduced. Their good correspondence indicates unequivocally that their loosely packed matrix, which serves simultaneously as a natural nanocomposite matrix, is the fractal space where the nanocluster structure of epoxy polymers is formed. Since for linear amorphous polymers = 3 [9], i.e., their nanostructure formation is realised in three-dimensional Euclidean space, then the conclusion that chemical crosslinking network availability in the considered EP serves as the indicated distinction cause is obvious enough. In Figure 9.2 the dependence of on crosslinking density is... 

Hence, the results stated above have shown that nanocluster structure formation for the considered epoxy systems is realised in fractal space (analogue of fractal lattice in computer simulation), which is created by a loosely packed matrix. The influence of the crosslinking density on the indicated space dimension is not unequivocal and is defined by the aggregation mechanism, which is realised at nanostructure formation. This space dimension defines unequivocally the elasticity modulus value of the considered epoxy polymers. 

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