Chemistry Reference
In-Depth Information
Fig. 2.6
Illustration
of a plot of modulus
of elasticity against time
can reentangle. The decreased amount of entanglement results in lower viscosity of the liquid, allowing
the molecules to flow with less resistance. Actually, two factors can contribute to chain entanglement.
These are high length of the chains for very large molecules and/or bulky substituents. Stress applied
to a Newtonian liquid, outside of an initial spike, is zero. Stress, however applied to a viscoelastic fluid
starts at some initial value. This value decreases with time until it reaches an equilibrium value due
to the viscoelastic property of the material. Figure
2.6
illustrates what a plot of the modulus of elasticity
G
t
), which depends on the temperature, when plotted against time, looks like:
The equation for
shear-stress relaxation modulus
that varies with temperature can be written as
follows:
(
GðtÞ¼sðtÞ=g
0
With constant stress,
s
(
t
)
¼ Gg
0
, where creep strain
g
(
t
) is constant [
g
(
t
)
¼ s
0
/
G
] for a Hookean
solid. It would be directly proportional to time for a Newtonian liquid [(
is the
initial time at which recovery of the viscoelastic material begins. For a viscoelastic fluid, when stress
is applied, there is a period of creep that is followed by a period of recovery. For such liquids, strains
return back toward zero and finally reach an equilibrium at some smaller total strain. For the
viscoelastic liquid in the creep phase, the strain starts at some small value, but builds up rapidly at
a decreasing rate until a steady state is reached. After that the strain simply increases linearly with
time. During this linear range, the ratio of shear strain to shear stress is a function of time alone. This
is
shear creep compliance
,
g
(
t
)
¼ s
0
/
)
t
]. Here
t
J
(
t
) The equation of shear creep compliance can be written as follows:
JðtÞ¼gðtÞ=s
0
The stress relaxation modulus and the creep compliance are both manifestations of the same
dynamic process at the molecular level and are closely related. This relationship, however, is not a
simple reciprocal relations that would be expressed as
), but rather in an integral equation
that is derived from the Boltzman superposition principle. It relates recoverable compliance,
G
(
t
)
¼
1/
J
(
t
s
to
J
0
,
zero shear viscosity [
22
].
Z
1
1
0
J
s
¼
tGðtÞ
d
t
2
0
0
Z
1
0
GðtÞ
0
¼
d
t
In relaxation back to equilibrium, the polymer assumes a new conformation. At first, the response
is glassy. The modulus for such an organic glass is large,
G
g
~10
9
Pa. This modulus decreases with
