Chemistry Reference
In-Depth Information
Fig. 2.5
Illustration
of a physical crosslink
in molten polymers
This is accomplished with some degree of coordination, but results in the whole chain shifting.
Based on experimental evidence, the viscosity can be defined as,
ln
¼
3
:
4ln
M
w
þ C þ E=RT
C
M
w
is weight average molecular weight (see Sect.
2.7
) Chain length,
Z
where
, or the
molecular weight of polymers is an important variable that influences flow properties of polymers.
The relationship of a Newtonian viscosity of an amorphous polymer to the chain length when shear
stress is low can be expressed as [
19
,
22
,
25
],
is a constant.
log
¼
3
:
4 log
Z
w
þ k
where the constant
is temperature-dependent. By the same token, based on experimental evidence,
the relationship of viscosity to temperature and to chain length at low shear rates, for many polymers
can be expressed as follows:
k
þ T T
g
Þþk
0
log
¼
3
:
4 log
Z
w
17
:
44
ðT T
g
Þ=ð
51
:
6
k
0
is specific for each polymer and
where constant
T
g
is
discussed in Sect.
2.2.3
). Although linear molten polymers exhibit well-defined viscosities, they
also exhibit elastic effects. These effects are present even in the absence of any crosslinks or a rubber
network. It is referred to as
creep
. This creep is attributed to entanglement of polymeric chain to form
temporary physical crosslinks: This is illustrated in Fig.
2.5
.
Deviations from Newtonian flow can occur when shear stress does not increase in direct proportion
to shear rate. Such deviation may be in the direction of thickening (called
dilatent flow
) and in the
direction of thinning (called
pseudo plastic
). Related to non-Newtonian flow is the behavior of
thixotropic liquids when subjected to shear, as explained above. Flow behavior can be represented by
the following equation:
T
g
is the glass transition temperature (
t ¼ Ag
B
A
B
A ¼
B ¼
where
1. All
polymers tend to exhibit shear thinning at high shear rates. This is commonly explained by molecular
entanglement, as mentioned above. Certainly, in the amorphous state there is considerable entangle-
ment of the polymeric chains. Low shear rates may disrupt this to a certain degree, but the chains will
still remain entangled. As the shear rates increases, disruption can occur at a faster rate than the chain
is a constant and
is the index of flow. For Newtonian liquids
and
