Chemistry Reference
In-Depth Information
FIGURE 12.3
The dependence of microhardness
H
v
on loosely packed matrix structure
fractal dimension
l.m.
f
d
for epoxy polymers EP-2 (1) and EP-2-200 (2) [9].
The Eq. (12.7) shows, that the condition
H
v
= 0 can be realized for linear
object with dimension
d
f
=
d
= 1 only (in fact for separate stretched lin-
ear macromolecule [15]), that is, for real solids, having dimension within
the range of 2.0 ÷ 2.95, zero value
H
v
is unattainable. At minimum value
l.m.
f
d
= 2.0 the magnitude
H
v
= 150 MPa, for loosely packed matrix structure
with the greatest density, that is, in the case, when nanoclusters and loosely
packed matrix structures are undistinguishable, the value
H
v
= 293 MPa.
The loosely packed matrix microhardness
l.m.
v
H
can also be calculated
according to the mixtures rule [1, 8]:
cl
l.m.
( )
HH
=+-
,
f
H
1
f
(12.8)
v
v
cl
v
cl
cl
H
is nanoclusters microhardness, by the indicated above reasons
accepted equal to 293 MPa.
where
l.m.
v
H
on
K
st
are adduced. As one
can see, at
K
st
= 0.50 and 1.50 (the least values n
c
= (4 ÷ 9) × 10
26
m
-3
) the
values
H
v
and
l.m.
v
H
are close and at higher values in
c
= (10 ÷14) × 10
26
m
-3
in
the case of
K
st
= 0.75 ÷ 1.25 the distinction between
H
v
and
l.m.
v
H
can reach
80 MPa, that indicates high degree of loosely packed matrix loosening.
