Chemistry Reference
In-Depth Information
In Fig. 6.13, two theoretical dependences of
E
n
/
E
m
on nanofiller par-
ticles size (diameter
D
p
), calculated according to the Eqs. (4)-(6) and (37),
are adduced. However, at the curve 1 calculation the value
D
p
for the initial
nanofiller particles was used and at the curve 2 calculation - nanofiller par-
ticles aggregates size
D
(see Fig. 6.3). As it was expected [5], the growth
ag
E
n
/
E
m
at
D
p
or
ag
D
reduction, in addition the calculation with
D
p
(nonaggre-
gated nanofiller) using gives higher
E
n
/
E
m
values in comparison with the
aggregated one (
D
using). At
D
p
≤
50 nm faster growth
E
n
/
E
m
at
D
p
reduc-
tion is observed than at
D
p
>50 nm, that was also expected. In Fig. 6.13,
the critical theoretical value
cr
ag
D
for this transition, calculated according
to the indicated above general principles [54], is pointed out by a vertical
shaded line. In conformity with these principles the nanoparticles size in
nanocomposite is determined according to the condition, when division
surface fraction in the entire nanomaterial volume makes up about 50%
and more. This fraction is estimated approximately by the ratio 3
l
if
/
D
p
,
where
l
if
is interfacial layer thickness. As it was noted above, the data of
(Fig. 6.1) gave the average experimental value
l
if
≈
8.7 nm. Further from the
condition 3
l
if
/
D
p
≈
0.5 let us obtain
D
p
≈
52 nm that is shown in Fig. 6.13 by
a vertical shaded line. As it was expected, the value
D
p
≈
52 nm is a bound-
ary one for regions of slow (
D
p
>52 nm) and fast (
D
p
≤52 nm)
E
n
/
E
m
growth
at
D
p
reduction. In other words, the materials with nanofiller particles size
D
p
≤52 nm (“super reinforcing” filler according to the terminology of Ref.
[5]) should be considered true nanocomposites.
Let us note in conclusion, that although the curves 1 and 2 of Fig.
6.13 are similar ones, nanofiller particles aggregation, which the curve 2
accounts for, reduces essentially enough nanocomposites reinforcement
degree. At the same time the experimental data correspond exactly to the
curve 2 that was to be expected in virtue of aggregation processes, which
always took place in real composites [4] (nanocomposites [55]). The val-
ues
d
surf
, obtained according to the Eqs. (4)-(6), correspond well to the
determined experimentally ones. So, for nanoshungite and two marks of
technical carbon the calculation by the indicated method gives the follow-
ing
d
surf
values: 2.81, 2.78 and 2.73, whereas experimental values of this
parameter are equal to: 2.81, 2.77 and 2.73, that is, practically a full cor-
respondence of theory and experiment was obtained.
