Chemistry Reference
In-Depth Information
Let us consider further
E
reduction at
h
pl
growth (Fig. 6.9) within the
frameworks of density fluctuation theory, which value y can be estimated
as follows [22]:
ρ
kT
K
n
,
(35)
y=
T
where ρ
n
is nanocomposite density,
k
is Boltzmann constant,
T
is test-
ing temperature,
K
T
is isothermal modulus of dilatation, connected with
Young's modulus
E
by the relationship [46]:
E
(36)
K
=
T
(
)
31
−
n
In Fig. 6.10, the scheme of volume of the deformed at nanoindentation
material
V
def
calculation in case of Berkovich indentor using is adduced
and in Fig. 6.11, the dependence y(
V
def
) in logarithmic coordinates was
shown. As it follows from the data of this figure, the density fluctuation
growth is observed at the deformed material volume increase. The plot
y(ln
V
def
) extrapolation to y=0 gives ln
V
def
≈
13 or
V
def
(
de
V
)=4.42
×
10
5
nm
3
.
Having determined the linear scale
l
cr
of transition to y=0 as (
cr
de
V
)
1
′
3
, let us
obtain
l
cr
=75.9 nm, that is close to nanosystems dimensional range upper
boundary (as it was noted above, conditional enough [6]), which is equal
to 100 nm. Thus, the stated above results suppose, that nanosystems are
such systems, in which density fluctuations are absent, always taking place
in microsystems.
As it follows from the data of Fig. 6.9, the transition from nano- to
microsystems occurs within the range
h
pl
=408-726 nm. Both the indicated
above values
h
pl
and the corresponding to them values (
V
def
)
1
/
3
≈814-1440
nm can be chosen as the linear length scale
l
n
, corresponding to this tran-
sition. From the comparison of these values
l
n
with the distance between
nanofiller particles aggregates
L
n
(
L
n
=219.2-788.3 nm for the considered
nanocomposites, (see Fig. 6.3) it follows, that for transition from nano- to
microsystems
l
n
should include at least two nanofiller particles aggregates
and surrounding them layers of polymer matrix, that is the lowest linear
scale of nanocomposite simulation as a homogeneous system. It is easy to
see, that nanocomposite structure homogeneity condition is harder than
the obtained above from the criterion y=0. Let us note, that such
cr
