Chemistry Reference
In-Depth Information
FIGURE 6.6
The dependences of covering quadrates number
N
i
on their area
S
i
,
corresponding to the Eq. (25), in double logarithmic coordinates for nanocomposites on
the basis of BSR. The designations are the same, that in Fig. 6.5.
As it has been shown in Ref. [44], the usage for self-similar fractal
objects at the Eq. (25) the condition should be fulfilled:
S
−
D
.
(26)
NN
−
~
i
i
−
1
i
In Fig. 6.7, the dependence, corresponding to the Eq. (26), for the three
studied elastomeric nanocomposites is adduced. As one can see, this de-
pendence is linear, passes through coordinates origin that according to
the Eq. (26) is confirmed by nanofiller particles (aggregates of particles)
“chains” self-similarity within the selected α
i
range. It is obvious, that this
self-similarity will be a statistical one [44]. Let us note, that the points,
corresponding to α
i
=16 mm for nanocomposites butadiene-styrene rub-
ber/technical carbon (BSR/TC) and butadiene-styrene rubber/microshun-
gite (BSR/microshungite), do not correspond to a common straight line.
Accounting for electron microphotographs of Fig. 6.2 enlargement this
gives the self-similarity range for nanofiller “chains” of 464-1472 nm. For
nanocomposite butadiene-styrene rubber/nanoshungite (BSR/nanoshung-
ite), which has no points deviating from a straight line of Fig. 6.7, α
i
range
