Densely packed regions

Figure 8.8 Nucleation and growth in a polymer chain (numerical simulation with Brownian dynamics Sakaue et al., unpublished). After staying for a long time in an elongated state, a nucleation centre appears spontaneously on a chain. Then, the densely packed region grows quickly to form a toroid. Essentially the same process has been observed in an experiment with single DNA observations (Yoshikawa and Matsuzawa, 1995,1996).

The interrelation of elasticity modulus and amorphous chain s tightness characterized by fractal dimension of chain part between its fixation points for nanocomposites based on the polypropylene is shown. This assumes the polymeric matrix stmcture change in comparison with initial polymer the role of densely-packed regions for it is played by interphase areas. An offered fractal model allows estimation of elasticity modulus limiting values. 

Let us fulfill several estimations, confirming self-congmence of the obtained results. For nanocomposites the relative Auction of densely-packed regions that is, ((p +(pjj ), can be determined with the aid of the equation [3] ... 

As it is known [4], fractal clusters in their stmcture center form densely-packed region of size a, the value of which can be determined with the aid of the following equation [4] ... 

These qualitative effects can be described quantitatively within the framework of percolation model of reinforcement and multifractal model of gas transport processes for nanocomposites polymer/organoclay [3, 4]. It has been supposed that two structural components are created for a barrier effect to fire spreading actually organoclay and densely packed regions on its surface with relative volume fractions (p and (p respectively. In other words, it has been supposed, that the value should be a diminishing function of the sum ((p -l-(pp. For this supposition verification let us estimate the values (p and (p The value (p is determined according to the well-known equation [5] ... 

As it has been shown above using position spectroscopy methods [22], the yielding in polymers is realized in densely packed regions of their structure. Theoretical analysis within the frameworks of the plasticity fractal concept [35] demonstrates that the Poisson s ratio value in the yielding point, can be estimated as follows ... 

The value is determined as linear defects length per polymer volume unit (see the Eq. (4.1)). Since in the cluster model a segment included in densely packed regions (crystallites or clusters) is assumed as linear defect (dislocation analog) then value p is determined as follows [3] ... 

This result corresponds well to the experimental data of Yech [30] and Perepechko [31], who obtained the values 0.60 and 0.63 for densely packed regions relative fraction in amorphous polymers. 

Independent checking of the accuracy of quantitative estimations of values of 5 and can be carried out as follows. Within the frameworks of the plasticity fractal concept [38, 39] and the cluster model of the amorphous state structure of polymers [5, 6] it has been shown that the yield process is realised in densely packed regions of the structure (clusters). In addition, the relative fraction of the clusters is equal to the yield process realisation probability (1 -%) [39]. The probability (1 x) calculation method is given in paper [39] and the value

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