Chemistry Reference
In-Depth Information
An empirical assumptions number, taking into consideration consider-
able stronger intermolecular intercommunication in glassy polymers, usual-
ly is made for the considered concept application to such systems. Edwards
and Vilgis [31] offered the slipping links concept, which assumes division of
chain between macromolecular binary hooking's by into fragments, which
are fixed, but have considerable internal freedom. This results to polymers
limiting strain reduction in comparison with the estimated one according to
the Eq. (5.7). The authors of Ref. [52] offered more general method of the
considered above effects appreciation, based on fractal concepts application
for analysis of polymer deformation behavior.
The correctness of fractal analysis methods application to chain part be-
tween entanglements (chemical cross-linking) is proved by the indicated
parts fractality experimental confirmation [33-35]. In this case for the mac-
romolecule, simulated by freely formed chain from statistical segments, the
Eq. (2.12) was obtained, where
L
ch
=
L
e
and
R
ch
=
R
e
(
L
e
and
R
e
are chain part
length between macromolecular binary hooking's, respectively) and dimen-
sion
D
ch
characterizes the mobility (deformability) of this chain part. The
known scaling relationship [36]:
Ml
RC
m
2
=
e0
,
(7.6)
e
∞
0
where
M
e
is molecular weight of chain fragment between binary hooking's,
l
o
and
m
o
are length and molecular weight of real skeletal bond, respectively,
can be transformed with the Eq. (2.15) appreciation and by division of its
both parts by
2
st
l
to the form [32]:
2
=
LR
l
,
(7.7)
e
e
l
st
st
which is the partial case of the fractal Eq. (2.12) at
D
ch
= 2.0, that presents
itself, the limiting case of rubbers, for which, strictly speaking, the Eqs. (5.7)
and (7.6) were derived. Dividing both parts of the Eq. (2.12) by the product
R
e
l
st
and taking into account, that
L
e
/
R
e
= l [37], let us obtain the equation
fractal variant for l determination [32]:
-
=
D
1
ch
R
l
e
l
(7.8)
st
