Chemistry Reference
In-Depth Information
FIGURE 13.2
The relation between experimental
d
f
and theoretical
f
d
structure fractal
dimensions values for PASF film samples. The straight line shows the relation 1:1 [1]
In its turn, the value
d
f
knowledge allows to determine the value n ac-
cording to the Eq. (1.9) and proceeding from the last entanglements cluster
network n
cl
can be calculated and excess energy localization regions dimen-
sion
D
f
in polymer, which are for further calculations, can be estimated. The
value n
cl
was estimated according to the Eq. (1.10) and
D
f
- according to the
Eq. (8.7).
As it is known [2, 12], within the frameworks of cluster model the elas-
ticity modulus
E
value is defined by stiffness of amorphous polymers struc-
ture both components: local order domains (clusters) and loosely packed
tests three types: with constant strain rate, with strain discontinuous change
and on stress relaxation. As one can see, the dependences
E
(n
cl
) are approxi-
mated by three parallel straight lines, cutting on the axis
E
loosely packed
matrix elasticity modulus
E
l.m.
different values. The greatest value
E
l.m.
is
obtained in tensile tests with constant strain rate, the least one - at strain
discontinuous change and in tests on stress relaxation
E
l.m.
= 0 [1].
The different relaxation processes proceeding degree for three types of
tests, which is due to different temporal scale, is the cause of elasticity mod-
ulus such behavior. These processes, as it was to be expected, are realized
in loosely packed matrix (more in detail see chapter two). The higher the
indicated relaxation degree is (relaxation processes completion) the smaller
D
f
value is. This allows to approximate the obtained empirically linear cor-
relations
E
(
D
f
) by the common for all three tests types relationship [1]:
E = E
l.m.
+ 0.94(
D
f
− 3),
(13.3)
