Chemistry Reference
In-Depth Information
The experimental data about rubbers deformation are usually interpreted
within the frameworks of the high-elasticity entropic theory [1-3], elabo-
rated on the basis of assumptions about high-elastic polymers incompress-
ibility (Poisson's ratio n = 0.5) and polymer chains Gaussian statistics. As it
is known [4], the Gaussian statistic is characteristic only for the networks,
prepared by chains concentrated solution curing, in the case of their com-
pression or weak (draw ratio l < 1.2) tension. For such structures the fractal
dimension
d
f
= 2 and in case of n = 0.5 the following classical expression
was obtained [3]:
E
(
)
l
2
s
=
l
-
,
(A.1)
3
where
E
is Young's modulus, proportional to temperature, the expressions
of which through polymer structure parameters are made more exact repeat-
edly [1-3]. Calculations according to the Eq. (A.1) with fitted
E
value cor-
respond quite well to the experiment in the relatively small strains only (l <
1.2). At 1.2
<
l
<
2 the dependence (A.1) plot is disposed, as a rule, higher
and at l > 2 - essentially lower than an experimental curve s(l), which at l
> 4 usually reaches asymptote s ~l
2
[5].
The dependence (A.1) precision improvement was carried out tradition-
ally by the usage of entropic theory phenomenological modifications, the
main achievements of which are united in monography [3]. Moreover, the
required exactness of calculation and experiment agreement is reached ow-
ing to the usage of agreement additional parameters, which are in reality
fitted ones. Hence, the high-elasticity entropic theory loses the main advan-
tage in comparison with the approach [6], based on the empirical depen-
dences of elastic potential on strain and temperature invariants using, which
at the agreement fitted parameters enough number ensures any beforehand
given precision of an experimental data approximation. The main deficien-
cy of both the entropic theory empirical modifications and elastic potential
empirical model apart from a large number and not always clear physical
significance of agreement parameters is the necessity of the same elastic-
ity parameter, for example,
E
, different values using for both experimental
data description, obtained at different loading conditions, and for the same
data description, but within the frameworks of the entropic theory of various
modifications or elastic potential [3, 5]. This gives vagueness of both elastic-
ity parameters absolute value and relations between them [7].
Balankin [7-9] has shown that two main assumptions of elastomateri-
als entropic elasticity classical theory, mentioned above: (1)
d
f
= 2 and (2)
