Chemistry Reference
In-Depth Information
Calculation according to the Eq. (31) has given the following values g
L
:
13.6 for the first part and 1.50 for the second one. Let us note the first from
g
L
adduced values is typical for intermolecular bonds, whereas the second
value g
L
is much closer to the corresponding value of Grüneisen parameter
G
for intrachain modes [46].
Poisson's ratio n can be estimated by g
L
(or
G
) known values according
to the formula [46]:
1
+
n
.
(32)
g
=
0.7
L
12
−
n
The estimations according to the Eq. (32) gave: for the dependence
E
(
h
pl
)
first part n=0.462, for the second one - n=0.216. If for the first part the
value n is close to Poisson's ratio magnitude for nonfilled rubber [36], then
in the second part case the additional estimation is required. As it is known
[48], a polymer composites (nanocomposites) Poisson's ratio value n
n
can
be estimated according to the equation:
φ
φ
nnn
−
=+
,
1
1
n
n
(33)
n
TC
m
where ϕ
n
is nanofiller volume fraction, n
TC
and n
m
are nanofiller (technical
carbon) and polymer matrix Poisson's ratio, respectively.
The value n
m
is accepted equal to 0.475 [36] and the magnitude n
TC
is
estimated as follows [49]. As it is known [50], the nanoparticles TC ag-
gregates fractal dimension
ag
f
d
value is equal to 2.40 and then the value
n
TC
can be determined according to the equation [50]:
)
(
)
(
ag
f
=−+
.
(34)
d
d
11
n
TC
According to the Eq. (34) n
TC
=0.20 and calculation n
n
according to the
Eq. (33) gives the value 0.283, that is close enough to the value n=0.216
according to the Eq. (32) estimation. The obtained by the indicated meth-
ods values n and n
n
comparison demonstrates, that in the dependence
E
(
h
pl
)
(
h
pl
<0.5 mcm) the first part in nanoindentation tests only rubber-like poly-
mer matrix (n=n
m
≈
0.475) is included and in this dependence the second
part-the entire nanocomposite as homogeneous system [51] - n=n
n
≈
0.22.
