Chemistry Reference
In-Depth Information
Within the frameworks of the cluster model j
cl
estimation can be fulfilled
by the percolation relationship (the Eq. (4.66)) usage. Let us note, that in
the given case the temperature of polymers structure quasiequilibrium state
attainment, lower of which j
cl
value does not change, that is,
T
0
[32], is ac-
cepted as testing temperature
T
. The calculation j
cl
results according to the
Eq. (4.66) for the mentioned above polymers are adduced in Table 15.2,
which correspond well to other authors estimations.
Proceeding from the circumstance, that radicals-probes are concentrated
mainly in intercluster regions, the nanocluster size can be estimated, which
in amorphous PC should be approximately equal to mean distance
r
between
well to the experimental data, obtained by dark-field electron microscopy
method (≈ 30 ÷ 100 Å) [33].
Within the frameworks of the cluster model the distance between two
neighboring nanoclusters can be estimated according to the Eq. (4.63) as
2
R
cl
. The estimation 2
R
cl
by this mode gives the value 53.1 Å (at F = 41) that
corresponds excellently to the method EPR data.
Thus, the Ref. [27] results showed, that the obtained by EPR method nat-
ural nanocomposites (amorphous glassy polymers) structure characteristics
corresponded completely to both the cluster model theoretical calculations
and other authors estimations. In other words, EPR data are experimental
confirmation of the cluster model of polymers amorphous state structure.
The treatment of amorphous glassy polymers as natural nanocomposites
allows to use for their elasticity modulus
E
p
(and, hence, the reinforcement
degree
E
p
/
E
l.m.
,
where
E
l.m.
is loosely packed matrix elasticity modulus) de-
scription theories, developed for polymer composites reinforcement degree
description [9, 17]. The authors of Ref. [34] showed correctness of partic-
ulate-filled polymer nanocomposites reinforcement of two concepts on the
example of amorphous PC. For theoretical estimation of particulate-filled
polymer nanocomposites reinforcement degree
E
n
/
E
m
two equations can be
used. The first from them has the look [35]:
E
1,7
n
n
,
(15.7)
=
1 j
+
E
m
where
E
n
and
E
m
are elasticity moduli of nanocomposites and matrix poly-
mer, accordingly, φ
n
is nanofiller volume contents.
The second equation offered by the authors of Ref. [36] is:
