Chemistry Reference
In-Depth Information
From the Eq. (4.38) n increase follows and from the Eq. (1.9) - the
d
f
increase at drawing ratio l growth. In its turn, the value l is connected with
the strain e by a simple relationship (in the case of affine deformation) [80]:
l
= 1 + e.
(4.39)
FIGURE 4.18
The dependence of measurement scale
L
on structure fractal dimension
d
f
for
PC at
T
= 293 K. Horizontal shaded lines indicate nondeformed PC structure self-similarity
boundaries (
l
st
and
R
cl
) and the shaded region - deformation fractal behavior range [73].
In Fig. 4.18, the dependence of
L
on
d
f
is adduced, which is calculated
according to the Eqs. (2.5), (2.12), (2.15), (4.38) and (4.39) combination and
at the condition, that the parameters
C
∞
d
f
are connected with each other as
follows [18]:
2
d
4
.
(4.40)
f
C
∞
=
+
--
)
(
)
(
dd
1
d d
3
f
As it follows from the data of Fig. 4.18,
L
growth at
d
f
increase is ob-
served and within the range of
d
f
≈ 2.80 ÷ 2.89 polymer deformation pro-
ceeds in fractal space. At
d
f
> 2.90 the deformation space transition from
fractal to Euclidean one is observed (PC yielding is achieved at
d
f
= 2.85
[23]) and structure PC approaching to true rubber state (
d
f
=
d
= 3) induces
