Chemistry Reference
In-Depth Information
(
)
tr
l.m.
2/3
ss φ
=
1
-
K
.
(15.20)
f
f
cl
s
The parameter
b
m
calculation according to the stated above technique
shows its decrease (intercomponent adhesion level enhancement) at testing
temperature raising within the range of
b
m
≈ 500 ÷ 130.
For interactions nanoclusters - loosely packed matrix estimation with-
in the range of
T
= 293÷373K the authors of Ref. [48] used the model of
Witten-Sander clusters friction, stated in Ref. [46]. This model application
is due to the circumstance, that amorphous glassy polymer structure can be
presented as an indicated clusters large number set [47]. According to this
model, Witten-Sander clusters generalized friction coefficient t can be writ-
ten as follows [46]:
f
= ln
c
+ β⋅ln
n
cl
,
(15.21)
where
c
is constant, β is coefficient,
n
cl
is statistical segments number per
one nanocluster.
The coefficient β value is determined as follows [46]:
(
)
1
-
cl
f
,
(15.22)
b
=
d
cl
f
d
is nanocluster structure fractal dimension, which is equal, as be-
fore, to 2.95 [40].
two parts. On the first of them, corresponding to the range of
T
= 293÷363 K,
the intercomponent interaction level is intensified at
f
decreasing (i.e.,
b
m
reduction is observed and on the second one, corresponding to the range of
T
= 373 ÷ 413 K,
b
m
= const independent on value
f
. These results correspond
completely to the data of
f
Fig. 15.14
,
where in the first from the indicated
temperature ranges the value
E
p
/
E
l.m.
is defined by nanoclusters friction and
in the second one by adhesion and, hence, it does not depend on friction
coefficient.
As it has been shown in Ref. [48], the interfacial (or intercomponent)
adhesion level depends on a number of accessible for the formation interfa-
cial (intercomponent) bond sites (nodes) on the filler (nanocluster) particle
surface
N
u
, which is determined as follows [49]:
where
L
N
=
,
(15.23)
u
u
