Chemistry Reference
In-Depth Information
ln
ln
N
,
(23)
D
=
n
ρ
where
N
is a number of particles with size ρ.
Particles sizes were established on the basis of atomic-power micros-
copy data (see Fig. 6.2). For each from the three studied nanocomposites
no less than 200 particles were measured, the sizes of which were united
into 10 groups and mean values
N
and ρ were obtained. The dependences
N
(ρ) in double logarithmic coordinates were plotted, which proved to be
linear and the values
D
n
were calculated according to their slope (see Fig.
6.5). It is obvious, that at such approach fractal dimension
D
n
is deter-
mined in two-dimensional Euclidean space, whereas real nanocomposite
should be considered in three-dimensional Euclidean space. The following
relationship can be used for
D
n
recalculation for the case of three-dimen-
sional space [42]:
1/ 2
(
)
2
dD
+±− −
�
2
dD
22
�
,
(24)
D
3
=
2
where
D
3 and
D
2 are corresponding fractal dimensions in three- and two-
dimensional Euclidean spaces,
d
=3.
FIGURE 6.5
The dependences of nanofiller particles number
N
on their size ρ for
nanocomposite BSR/TC (1), BSR/nanoshungite (2) and BSR/microshungite (3).
