Chemistry Reference
In-Depth Information
The usage of l
mol
values at s calculation according to the Eq. (A.3) does
It is known through Ref. [14] that filler introduction in polymer matrix
changes Poisson's ratio and for composites the value n can be estimated ac-
cording to the equation:
n
= n
p
(1−j
n
) + n
n
j
n
,
(A.6)
where n
p
and n
n
are the Poisson's ratio values for polymer matrix and nano-
filler accepted equal to 0.50 and 0.25 accordingly [13]. Then n = 0.433 for
nanocomposite SBR-S.
One can see a good conformity of theory and experiment one can see
(Fig. A.1) at the comparison of calculation according to the Eq. (A.2) results
at
E
= 2.76 MPa u n = 0.433 and the experimental curve s(l). The similar
comparison, but at other initial conditions (
E
= 2.01 MPa, n = 0.50), has
shown, that at l = 5 faster growth of theoretical curve s(l) in comparison
with experiment begins. In other words, the incompressibility condition ac-
ceptance for nanocomposite (n makes up 0.50) worsens the theory and ex-
periment conformity. And at last, the calculation according to the Eq. (A.2)
was carried out at nominal value l,
E
= 2.56 MPa and n = 0.433. In this case
the lower calculated values s at l > 3 in comparison with the experiment are
obtained (Fig. A.1).
The parameter
E
increases from 1.82 MPa for SBR up to 2.76 MPa for
SBR-S means according to the Eq. (A.4) n
c
enhancement from 1.52 ¢ 10
26
m
-3
up to 2.52 ¢ 10
26
m
-3
or
M
c
reduction from 4400 g/mole for SBR up to
3400 g/mole for SBR-S. It can be assumed, that this n
c
enhancement is the
consequence of interfacial regions formation on the polymer - filler inter-
facial boundary, in which segments molecular mobility is frozen owing to
filler particles fractal surface influence. This corresponds to the generalized
definition of physical entanglements cluster network in amorphous state of
polymers [15, 16], where each contact of two segments with freezing mobil-
ity is considered as the indicated network node. In this case relative volume
fraction of such nodes (clusters) of entanglements network j
cl
is estimated
according to the Eq. (1.11). For the constituent SBR polybutadiene (PB) and
polystyrene (PS) the values
C
¢
,
l
o
and
S
are equal to 5.5 and 10 Å [17], 1.47
and 1.54 Å, 19.3 and 69.8 Å
2
[18], accordingly. In SBR case as
C
¢
,
l
o
and
S
the average values of these parameters for PB and PS were used. Then the
value j
cl
will be equal to 0.121 and the possibility of independent calculation
