Chemistry Reference
In-Depth Information
Using these general notions, the authors of Ref. [6, 7] offered the frac-
tal models for polymers elastic constants description. The quasiequilibrium
state of polymers structure is characterized by the criterion
D
f
= 3 [8, 9],
where
D
f
is dimension of excess energy localization domains. A loosely
packed matrix is totality of such domains. The value
D
f
can be determined
within the frameworks of free volume fractal theory according to the equa-
tion [9]:
4
ln 1
p
T
D
=
(3.5)
(
)
f
fT
gg
From the Eq. (3.5) together with the criterion (3.4) it follows, that at ar-
bitrary
T
the definite value
f
g
(
t
g
qe
) will correspond to quasiequilibrium state,
that is, this parameter is a function of temperature. Then relative deviation
of loosely packed matrix (in which the entire fluctuation free volume is con-
centrated [8, 9]) from quasiequilibrium state can be expressed as follows [6]:
qe
f
-
f
g
g
D=
(3.6)
qe
g
f
Since according to the indicated above reasons two order parameters are
required, as a minimum, for solid-phase polymers elastic constants descrip-
tion, then variable percolation threshold should be introduced in the Eq.
(3.1), that is,
p
c
should be replaced on D. Besides, it has been shown earlier,
that for polymers structure n
p
≈ 1 (see Table 1.1) [10] and therefore, h =
d
f
- 1 can be assumed in the Eq. (3.2) as the first approximation. Then the Eq.
(3.1) assumes the following form [6, 7]:
(
)
(
)
f
d
-
1
G
φ
,
D
~
φ
-D
,
(3.7)
cl
cl
since j
cl
is an order parameter of polymers structure in strict physical signifi-
cance of this term [10, 11].
(
)
f
φ
-
d
1
-D
for amorphous glassy polyarylatesulfone (PASF) is adduced,
accounting results of both quasistatic and impact tests [6]. At
(
cl
)
f
φ
-
d
1
-D
> 0.5 a good correspondence of the indicated parameters in case of impact
tests, which is worsed at smaller values
(
cl
)
f
-
-D
, corresponding to
d
1
φ
cl
