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where
k
n
is proportionality coefficient, in the present work accepted em-
pirically equal to 0.9.
TABLE 6.1
The Parameters of Irreversible Aggregation Model of Nanofiller Particles
Aggregates Growth
Nanofiller
R
ag
, nm
r
n
, nm
N
R
c
, nm
T
ag
, nm
R
T
R
max
, nm
Technical carbon
34.6
10
35.4
34.7
34.7
33.9
Nanoshungite
83.6
20
51.8
45.0
90.0
71.0
Microshungite
117.1
100
4.1
15.8
158.0
255.0
The comparison of experimental
R
ag
and calculated according to the
equation (16)
a
R
values of the studied nanofillers particles aggregates ra-
dius shows their good correspondence (the average discrepancy of
R
ag
and
T
a
R
makes up 11.4 %). Therefore, the theoretical model [31] gives a good
correspondence to the experiment only in case of consideration of aggre-
gating particles real characteristics and, in the first place, their size.
Let us consider two more important aspects of nanofiller particles ag-
gregation within the frameworks of the model [31]. Some features of the
indicated process are defined by nanoparticles diffusion at nanocomposites
processing. Specifically, length scale, connected with diffusible nanopar-
ticle, is correlation length x of diffusion. By definition, the growth phe-
nomena in sites, remote more than x, are statistically independent. Such
definition allows to connect the value x with the mean distance between
nanofiller particles aggregates
L
n
. The value x can be calculated according
to the equation [31]:
ag
f
dd
ag
,
(17)
−+
2
x
2
≈
ñR
−
1
where
c
is nanoparticles concentration, which should be accepted equal to
nanofiller volume contents ϕ
n
, which is calculated according to the Eqs.
(6) and (13).
The values
r
n
and
R
ag
were obtained experimentally (see histogram of
Fig. 6.3). In Fig. 6.4 the relation between
L
n
and x is adduced, which, as
it is expected, proves to be linear and passing through coordinates origin.
This means, that the distance between nanofiller particles aggregates is
