POLYMERS AS NATURAL COMPOSITES: STRUCTURE AND PROPERTIES - Fractal Mechanics of Polymers - page 291

The synergetics principles revealed structure adaptation mechanism to ex-
ternal influence and are universal ones for self-organization laws of spatial
structures in dynamical systems of different nature. The structure adaptation
is the reformation process of structure, which loses stability, with the new
more stable structure self-organization. The fractal (multifractal) structure,
which is impossible to describe within the framework of Euclidean geom-
etry, are formed in reformation process. A wide spectrum of natural and ar-
tificial topological forms, the feature of which is self-similar hierarchically
organized structure, which amorphous glassy polymers possessed [6], be-
longs to fractal structures.
The authors of Refs. [7, 8] considered the typical amorphous glassy poly-
mer (polycarbonate) structure change within the frameworks of solid body
synergetics.
The local order region, consisting of several densely packed collinear
segments of various polymer chains (for more details see chapter one) ac-
cording to a signs number should be attributed to the nanoparticles (nano-
clusters) [9]:
1) their size makes up 2÷5 nm;
2) they are formed by self-assemble method and adapted to the external
influence (e.g., temperature change results to segments number per
one nanocluster change);
3) the each statistical segment represents an atoms group and boundar-
ies between these groups are coherent owing to collinear arrange-
ment of one segment relative to another.
The main structure parameter of cluster model-nanoclusters relative frac-
tion φ cl , 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 d f value is determined according to the
Eqs. (1.9) and (2.20).
In Fig 15.1 , the dependence of φ cl on testing temperature T for PC is
shown, which can be approximated by the broken line, where points of fold-
ing (bifurcation points) correspond to energy dissipation mechanism change,
coupling with the threshold values φ cl reaching. So, in Fig, 15.1 T 1 corre-
sponds to structure “freezing” temperature T 0 [4], T 2 to loosely packed ma-
trix glass transition temperature T ′ g [11] and T 3 to polymer glass transition
temperature T g .