Chemistry Reference
In-Depth Information
n = 0.5 [3] contradict each other (see the Eq. (1.9)). In Refs. [7-9], the re-
lationship was obtained, coupling conditional stress s and draw ration l at
uniaxial tension (compression) of elastomaterials within the frameworks of
fractal analysis:
[
]
E
(
)
-
2
n
1
+
2
n
-
1
-
2
n
(
+
n
)
s
=
l
-
2
n
-
1
-
2
n
,
(A.2)
3
1
+
2
n
+
4
n
which differs from the classical expression (A.1) even in the limit n = 0.5,
when the Eq. (A.2) is transformed to the dependence (the Eq. (6.16)) [9].
The authors of Ref. [10] considered the elasticity and entropic high-elas-
ticity fractal concept (the Eq. (A.2)) [7-9] application for elastomaterials
deformation behavior description on the example of styrene-butadiene rub-
ber (SBR) and nanocomposite on its basis with carbon soot content of 34
mas. % (SBR-S).
The experimental curves stress-draw ratio (s − l) for SBR and nanocom-
posite SBR-2 are presented in
Fig. A.1
[11]. As one can see, the curves s − l
for these materials differ significantly even by exterior appearance: one can
visually affirmed, that nanocomposite has higher Young's modulus
E
and
much more strong strain hardening (i.e., modulus at large strains) than ma-
trix rubber SBR. For these curves theoretical description the authors of Ref.
[10] used two approaches: classical [3] and fractal [7] ones. The first from
them supposes the relation between s and l, defined by the equation [3]:
(
)
2
l
1
s
G
l
-
,
(A.3)
where
G
is shear modulus, coupled with
E
according to the equation [4.58].
The adduced in Fig. A.1 experimental data and calculated according to
the Eq. (A.3) dependences s(l) for SBR are agreed well at
E
= 1.82 MPa.
Within the frameworks of the classical high-elasticity theory the value
G
in
the Eq. (A.3) is defined as follows [3]:
G = NkT
,
(A.4)
where
N
is an active chains number per rubber volume unit,
k
is Boltzmann
constant,
T
is testing temperature.
