Chemistry Reference
In-Depth Information
state at physical aging [67].
Let us estimate further the value j
cl
at quasiequilibrium state reaching.
This can be conducted according to the Eq. (10.31), determining the value
b
T
= b
p
as follows [32]:
1
b==
.
(10.32)
T
p
d
f
c
φ
= 0.619. Further the
cr
Calculation according to the Eq. (10.31) gives
value
f
d
= 2.45,
which corresponds well to the adduced above estimations. Thus, the thermal
cluster model is adequate at polymers structure description, particularly, at
quasiequilibrium state realization condition description. The estimations of
cr
d
cr
f
can be estimated according to the Eq. (1.12), that gives
cr
D
value according to the Eqs. (3.5), (8.7) and (8.9) gave accordingly 2.68,
2.85 and 2.82, that also demonstrates the indicated techniques good corre-
spondence.
Let us estimate physical aging duration
a
t
, necessary for the quasiequi-
librium state reaching. This can be conducted, using the equation, obtained
in Ref. [64]:
cr
)
(
)
(
cr
φ φt
-
d
2
dd
-
cr
cl
,
(10.33)
=
f
f
f
1
cl
ag
where
C
1
is the constant, which is equal to 0.14 [64], j
cl
is clusters relative
fraction for initial polymer, and the value t
ag
is given in seconds.
The estimation of including in the Eq. (10.33) parameters can be con-
ducted as follows. The value
c
φ
was calculated at the aging temperature
T
ag
= 403 K according to the Eq. (10.31) and the value j
cl
- at
T
ag
as well
according to the Eq. (1.9). Then the values
d
f
and
cr
cr
f
d
at
T
ag
were calculated
according to the Eq. (1.12) at corresponding, values j
cl
and
cr
c
φ
. The value
a
t
, calculated at the mentioned conditions according to the Eq. (10.33) and
equal approximately to 435 h, is shown in
Fig. 10.19(a
,
b)
b
y the vertical
shaded line. As one can see,
cr
a
t
corresponds well to value t
ag
, conforming
to the transition of the dependences
A
p
(t
ag
) and
d
f
(t
ag
) to asymptotic branch.
This allows to determine transitional (nonstationary) period duration
cr
cr
a
t
