Chemistry Reference
In-Depth Information
1.0 or j
l.m.
= 0). The finite value j
l.m.
existence possibility at tgd = 0 has the
key physical significance, that will be discussed below. In the considered
context the common dependence tgδ(j
l.m.)
absence is important, since the
data for copolymers with formal blocks content
C
form
= 0 located in left-hand
side from the common dependence and with
C
form
= 70 mol.% − in right-
hand side. This means that one more structural characteristic exists, charac-
terizing molecular mobility and, hence, the value tgd unequivocally [6, 7].
The fractal dimension of the chain part between clusters
D
ch
was pro-
posed to use as such characteristic in Refs. [6, 7] that is due to the following
reasons. Firstly, the mentioned chain part possesses self-similarity property
and has the dimension, differing from its topological dimension, that is, it
is fractal by definition [20]. Secondly, it has been shown [21], that the value
D
ch
within the range of values 1.0 <
D
ch
<
2.0 characterizes exactly molecu-
lar mobility of a chain part (free chain according to the terminology [1]) in
loosely packed matrix. The condition
D
ch
means this chain part straighten-
ing, transition from fractal behavior to Euclidean one and mobility full loss,
that is, tgd = 0. The condition
D
ch
= 2.0 means this chain part maximum
mobility, corresponding to its viscoelastic state. The value
D
ch
can be deter-
mined according to the equation [20]:
ln
n
,
(2.5)
D
=
st
(
)
(
)
ch
ln 4-
d
-
ln 3-
d
f
f
where
n
st
is statistical segments number on chain part between entangle-
ments (clusters).
FIGURE 2.1
The dependence of dielectric losses angle tangent tgd on fractal dimension of
chain part between clusters
D
ch
for copolymers SP - OPD at frequencies 1 (1) and 10 kHz [7].
