Chemistry Reference
In-Depth Information
FIGURE 1.5
The dependence of clusters functionality
F
on testing temperature
T
for PC
(1) and PAr (2) [28].
Proceeding from the said above and analyzing values of polymers limit-
ing 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.
Let us note, completing this topic, that for the local order availability
substantiation in amorphous polymer matrix (irrespective to concrete struc-
tural model of medium) strict mathematical proofs of the most common
character exist. For example, according to the proved in numbers theory
Ramsey¢s theorem any large enough quantity
N
i
>
R
(
i
,
j
) of numbers, points
or objects (in the considered case - statistical segments) contains without
fail high-ordered system from
N
j
¢
R
(
i
,
j
) such segments. Therefore, absolute
disordering of large systems (structures) is impossible [37, 48].
As it is known [39], structures, which behave themselves as fractal ones
on small length scales and as homogeneous ones - on large ones, are named
homogeneous fractals. Percolation clusters near percolation threshold are
such fractals [1]. As it will be shown lower, cluster structure is a percola-
tion system and in virtue of the said above - homogeneous fractal. In other
words, local order availability in polymers condensed state testifies to there
structure fractality [21].
The percolation system fractal dimension
d
f
can be expressed as follows
[39]
