Polymer rheology_cap20

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Rheology is the science dealing with the deformation
and flow of materials. For polymers, understanding the
deformation and flow, both in the extruder and die, is crit-
ical to optimum operation of the extrusion process. In
coextrusion, it is critical to match resin layer viscosities
at processing temperature to eliminate interfacial insta-
bilities that would make the product useless. This chapter
covers different aspects of polymer rheology and its
importance to extrusion processes.
Polymers, unlike water, oil, organic solvents, and most
liquids encountered every day, are non-Newtonian fluids.
Fluids by definition deform when a force is applied and
continue to deform until the force is removed. In a
Newtonian fluid, the rate of deformation is directly pro-
portional to the force applied. Rheology deals with the
relationships between stress (applied force), strain (defor-
mation resulting from an applied force—elongation), and
time.[1] As a force is applied to a Newtonian fluid, elon-
gation occurs; when the force is removed, the fluid stays
in that position until another force is applied. This is
shown in Fig. 20.1, where there is no strain or elongation
until a constant stress is applied. When the constant stress
is removed, the elongation remains constant until the
stress is reapplied, at which time the fluid again moves at
a constant rate that is directly proportional to the stress
applied. Consider, as an example, a drop of water that is
pushed with your finger across a surface. The pushing is
the stress or force applied, and the elongation or strain is
the movement of the water drop from one location to
another. As the stress is applied, the drop moves; when
the stress is removed, the drop remains in its new loca-
tion. If the force is applied a second time, the drop moves
to a new location. Movement or elongation is dependent
on the force applied and the time the force is acting on
the drop. For elastic materials, when a force is applied,
deformation occurs until the force is removed, where-
upon the elastic material returns to its original configura-
tion, assuming the material has not ruptured.
Polymers in their molten state do not exhibit a direct
relationship between the rate of deformation and the
force or stress applied to the melt, producing a non-
Newtonian response. Molten polymers have both a vis-
cous and an elastic component. When the force is applied
to a polymer melt, deformation occurs; the viscous com-
ponent stays deformed when the force is removed, while
the elastic component springs back. As stress is applied
to molten polymer, three things can happen:
• Viscous flow—Material deforms as long as a stress
is applied, shown in Fig. 20.1.
• Elastic deformation—Material deforms as soon as
stress is applied, but when the stress is removed, the
material returns to its original form, shown in
Fig. 20.2.
• Rupture—Material deforms in the elastic mode to
a specific elongation where it ruptures, preventing
it from returning to its original form after the stress
is removed.
In viscous flow, the viscosity is defined as the ratio
of applied stress divided by the rate of strain. Common
viscosity units are: Pa•s, Poise, lbf s/in
2 or Newton s/m2.
In elastic deformation, the modulus is defined as applied
stress divided by recoverable deformation, measured in
Newton s/m2 or lbf /in
2. Recoverable deformation is used
because some deformation may be so extreme that rup-
ture occurs.
Molecular weight, discussed in Chapter 18, is the
single most important property in determining polymer
viscosity. The relationship in a narrow molecular weight
distribution is given by Eq. (20.1): 
(20.1)
where η = Viscosity
k = A constant
MW = Molecular weight
20 Polymer Rheology
Figure 20.1. Relationship of stress and strain in
Newtonian fluid.
Figure 20.2. Elastic behavior to stress.
Equation (20.1) teaches us that molecular weight
has strong effect on the resin viscosity. Doubling the
molecular weight gives approximately a 10-fold increase
in viscosity.
20.1 Definitions
Common terms in discussing rheology are shear,
shear rate, shear stress, shear modulus, shear flow, and
extensional flow. It is important to understand these
terms in order to grasp basic rheological concepts.
• Shear is the movement in either a solid or fluid of
parallel layers within the sample. Consider two
pieces of paper sliding past one another and gener-
ating frictional heat during the sliding operation.
This is called shear heat due to friction caused by
the sliding layers.
• Shear rate is the velocity gradient across a channel
in which the fluids are sliding past each other in
laminar flow. It is a measure of the deformation of
a polymer melt, calculated from the flow rate and
the geometry through which the melt is passing.
Shear rate is the rate of change of velocity at which
one layer passes over another. Normal shear rate
units are reciprocal seconds.
• Strain is the ratio of the change in length or volume
to the initial length or volume.
• Shear strain, like strain, is the ratio of deformation
to original dimensions. For shear strain it is the
deformation perpendicular to a line, rather than
parallel to it. The ratio equals tan α, where α is
the angle the sheared line makes with its original
orientation.
• Shear stress is the force per unit area required to
sustain a constant rate of movement.
• Shear modulus is the ratio of the shear stress
to the shear strain. The elastic shear modulus
(G') is a measure of the recoverable portion of the
elastic deformation; it relates to extrudate swell.
The higher G', the greater the melt elasticity,
which is associated with greater extrudate swell.
• Shear flow is molten polymer flow caused by rela-
tively parallel or concentric motion of surfaces,
such as the screw in an extruder barrel. Shear flow
can be caused by a pressure drop in the flow direc-
tion, as occurs in the die.
• Extensional flow is flow created by pulling on a
molten polymer, forcing layers to move past one
another. This occurs in the extrudate exiting the die
as it is being drawn by the puller or in a converging
flow channel.
• Viscous modulus (G") is a measure of the viscous
component of flow. A higher ratio of G" to G' is
associated with lower melt elasticity and less extru-
date swell.
• Complex viscosity, designated as η*, is equal to
the shear stress divided by the shear rate; it is a
measure of the polymer’s resistance to flow.
• Shear thinning is the decrease in the polymer vis-
cosity with increased shear rate, resulting from
alignment of polymer molecules during processing.
20.2 Measurement
Polymer viscosity is measured differently, depending
on the polymer state. The relative viscosity of one poly-
mer compared to another within the same class is nor-
mally measured by MFI or solution viscosity, also called
intrinsic viscosity. These measurements do not describe
the polymer viscosity characteristics at the shear rates
used in polymer processing. Measuring viscosity versus
shear rate is done by oscillating plate rheometry at low
shear rates (< 300 sec-1) and capillary rheometry (100 to
30,000 sec-1) at high shear rates. MFI was described in
Chapter 18. Figure 20.3 shows a shear rate versus viscos-
ity graph and the general shear rate areas where different
polymer processes occur. Low shear rate processes
include compression molding and the molding cycle in
large-part extrusion blow molding. Extruder operations
are typically between low and high shear rate processing,
with shear rates generally ranging from about 50 sec-1 to
several hundred reciprocal seconds. Injection molding is
a high shear rate process, as polymer is forced through a
nozzle, small gates, and runners at high speeds. Shear
188 POLYMERIC MATERIALS
Figure 20.3. Processing shear rates.
rates in injection molding normally range in the thou-
sands of reciprocal seconds.
An oscillating plate rheometer, or cone and plate
rheometer, has two parallel plates: one oscillates and the
other is fixed as the rheometermeasures
torque. The top plate oscillates at prede-
termined rates. Both plates are heated to
be able to measure the viscosity at a par-
ticular temperature. In addition to meas-
uring viscosity, these instruments also
determine G' (storage modulus) and G"
(loss modulus). Typical data at low shear
rates are shown in Fig. 20.4 for
polypropylene (PP) at 235˚C. The viscos-
ity decreases gradually as the shear rate
increases. G' and G" are shown to
increase with increasing shear rate; above
a shear rate of 100 sec-1, G' and G" con-
verge. To use these data, additional
graphs at other temperatures and differ-
ent melt flow polypropylene are needed
for comparison. If a lower MFI PP is
measured and the G' value is higher at a
particular shear rate based on the die land
calculations, the extrudate swell exiting
the die is anticipated to be larger.
Information on resin thermal stabili-
ty can be obtained using oscillating
plate rheometry by determining viscosity at a given
temperature and shear rate versus time. Measuring the
time when a specific resin degrades at several temperatures
provides data to use in determining the time-tempera-
ture thermal stability for a given resin system in an
extruder at specific shear rates. Thermal stability deter-
mination can be done at a shear rate that is higher than
any experienced by the resin in the extruder to provide
a safety factor in the actual process. Figure 20.5 shows
viscosity versus time at a specific shear rate and tem-
perature. The time when the resin starts
to degrade under these conditions pro-
vides a guideline for the time resin
degradation is anticipated to occur in an
extruder at a specific melt temperature
and shear rate. With several plots similar
to Fig. 20.5, one can create a time-
temperature degradation diagram similar
to Fig. 20.6. Figure 20.6 is based on a
given shear rate and shows the time it
takes for resin degradation to occur at a
particular temperature. Resins are stable
for a long time at low temperature; as the
temperature is raised, thermal degrada-
tion happens more rapidly. Each polymer
system, with its own stabilization pack-
age, has a specific time-temperature
curve for resin degradation. During pro-
cessing, knowledge of the time-tempera-
ture curve can assist in setting the
extruder temperature profile and to
understanding how many times a resin
can be reprocessed before it degrades
and loses property performance.
High shear rate versus viscosity data are generated
using a capillary rheometer, shown in Fig. 20.7.
Depending on the shear rate, the viscosity data cover
flow in both extrusion and injection molding applica-
tions. A piston attached to a load cell forces molten
resin through a capillary die at different rates. The test
sequence is to place polymer in
the barrel, allow it to come to 
an equilibrium temperature, and
force it through a specific size
orifice or capillary. The force
required to push the resin through
the orifice at increasing rates is
measured. From this data a viscos-
ity versus shear rate curve is cal-
culated. A typical viscosity versus
shear rate curve at four different
temperatures for polycarbonate
(Lexan 121) is shown in Fig. 20.8.
A Newtonian fluid viscosity
curve, which is independent of
shear, is a straight line parallel to
the x-axis. Lexan 121 viscosity 
at low shear rate is relatively
Newtonian; however, at higher
shear rates the polymer becomes
POLYMER RHEOLOGY 189
Figure 20.4. Oscillating plate rheometry data for polypropylene at 235˚C.
Figure 20.5. Time vs. viscosity.
Time Onset
Cross-linking
Cross-linking
Stable
Degradation
Time Onset
Degradation
Time
V
is
co
si
ty
, P
a.
s
Figure 20.6. Time-temperature
curve.
more non-Newtonian. These data can show how sensi-
tive a resin is to temperature and shear rate. Changing
the temperature from 250˚C to 280˚C at 250 sec-1
decreases the viscosity from 1627 to 589 Pa•sec or a
factor of 3 for a 30˚C change. Changing the shear rate
from 200 to 1000 sec-1 at 280˚C changes the viscosity
from 589 to 481 Pa•sec. Linear polycarbonate viscosity
is much more temperature-dependent than shear-
dependent, meaning the viscosity changes more with
temperature changes than with shear rate changes.
Measurement errors can occur when using high rates
in capillary flow rheometers. However, unless the data
from capillary rheometry are being used for research
purposes, the data are comparative and can be used with-
out corrections. Typical corrections include the Bagley
end correction for pressure drop and the Rabinowitsch
correction for a nonparabolic flow velocity profile
through the capillary. Newtonian fluids have a parabolic
velocity profile, dilatants an extended parabolic profile,
and pseudoplastics a flattened parabolic velocity flow
profile.
The most important polymer flow in an extruder and
die is shear flow, where one molten polymer layer slides
next to another layer, applying a shearing force. The
metering section velocity profile in a single screw
extruder is due to screw drag flow and the backpressure
flow from the breaker plate and screen pack or die resist-
ance (discussed in Part 1, “Single Screw Extrusion”). The
apparent viscosity, η, is given by Eq. (20.2):
(20.2)
where shear stress, τ, is given by Eq. (20.3), and shear
rate, γ, is given by Eq. (20.4).
(20.3)
where
∆P = Pressure drop
R = Capillary radius
L = Capillary length
(20.4)
where
Q = Volumetric flow rate
R = Capillary radius
rb = Barrel radius
S = Piston or ram speed
rc = Die radius
Figure 20.9 shows shear stress versus
shear rate for pseudoplastics, Newtonian
fluids, and dilatants. With a Newtonian
fluid, the slope of the line is constant as
the shear stress and shear rate change.
With either a pseudoplastic or a dilatant
fluid, the viscosity changes as a function
of shear rate. In Fig. 20.9, η1 does not
equal η2 and η3 does not equal η4, as the
viscosity changes with shear rate and
shear stress.
190 POLYMERIC MATERIALS
Figure 20.7. Kayeness capillary rheometer.
Figure 20.8. Capillary rheometry shear rate vs. viscosity data for Lexan 121.
20.3 Viscosity in Extrusion
Polymer viscosity is important in extrusion to under-
stand the processing window, the role temperature plays
in viscosity, and the importance of shear rate during pro-
cessing. Figure 20.8 is the viscosity versus shear rate
curve for polycarbonate (Lexan 121). Typical extrusion
conditions experience 50–1000 sec-1 shear rates, and for
Lexan 121 the viscosity versus shear rate curve shows
large differences with temperature changes and only
small differences with shear rate changes. To lower
Lexan 121 viscosity during extrusion, it is more effective
to decrease the melt temperature. Going to a higher shear
screw in either single or twin screw extrusion does not
dramatically alter the resin viscosity. However, higher
shear rate does induce shear heating, which lowers the
polymer viscosity and can lead to resin degradation.
There are other resins, like PP, that are shear-sensitive
but not temperature-sensitive. Figure 20.10 shows viscosity
versus shear rate curves for PP at three different tempera-
tures. Comparing these curves with Fig. 20.8, the slope
in the shear rate range for extrusion is much steeper,
indicating that a change in shear rate affects viscosity
more than temperature. Changing the temperature from
190˚C to 230˚C at 200 sec-1 decreases the viscosity from
280 to 190 Pa•sec, while changing the shear rate from
200 to 1000 sec-1 at 210˚C changes the viscosity from
230 to 80 Pa•sec. Unlike polycarbonate, PP is a shear-
sensitive rather than temperature-sensitive polymer.
Common practice is to raise PP melt temperature during
both extrusion and injection molding to lower the vis-
cosity. Unfortunately, temperature has only a minor
effect on PP melt viscosity, so other than using more
energy and consuming more thermal stabilizer, there is
not a lot accomplished at higher processing tempera-
tures. For PP, higher shear will lower the viscosity and
provide higher flow.
Some resinsystems exhibit both strong temperature
and strong shear dependence. In these systems, while both
temperature and shear have significant effects on viscosi-
ty, changes in shear rate affect viscosity more than
changes in temperature. Screw design in both the mixing
and melting stages of either a single or twin screw extrud-
er is important in obtaining an appropriate shear rate for
the polymer being processed and getting optimum extrud-
er performance. Table 20.1 shows the temperature and/or
shear dependence for several resin systems.
The viscosity versus shear rate curve visually shows
the sensitivity to shear thinning. Numerous polymer
processors buy resin based on MFI, which is a viscosity
measurement at lower shear rates. Without having a vis-
cosity versus shear rate curve, the processor has no idea
what the resin viscosity is doing at extrusion shear rates
and temperatures used during processing. Approximate
shear rates are easy to calculate in both single and twin
screw extruders, with equations given in Parts 1 and 2.
Consider the effect of shear thinning, shown in Fig.
20.11. Polymer A has a higher viscosity at low shear rate
and a lower viscosity at high shear rate, compared to
polymer B. When viscosity versus shear rate curves
POLYMER RHEOLOGY 191
Figure 20.9. Relationship of shear stress to shear rate.
Figure 20.10. Shear rate vs. viscosity for 12 MFI PP.
Temperature Temperature and
Shear Sensitive Sensitive Shear Sensitive*
PP PC ABS
LDPE PBT PA 6
LLDPE PET PA 6,6
HDPE Rigid PVC Polystyrene
Flexible PVC
Table 20.1. Temperature/Shear Sensitivity
*Shear has stronger effect than temperature
cross, the effect of viscosity will change, depending on
the processing being done and where on the viscosity
curve the process is located.
The other area where viscosity versus shear rate data
are critical is in coextrusion.[2] To prevent interfacial
instability between adjoining polymer layers in a two-
layer coextrusion, it is essential for the resins to have the
same viscosity in the die or feed block, where the differ-
ent resin systems are brought together in melt form.
Taking Fig. 20.11 as an example, if the shear rate where
the two resins are brought together is approximately 100
sec-1, polymers A and B have the same viscosity and the
extrusion is anticipated to run very smoothly with no
interfacial instabilities. However, if the shear rate where
polymers A and B are brought together
is 50 sec-1 or 500 sec-1 instead of 100
sec-1, the resin viscosities are quite dif-
ferent and interfacial instabilities might
create a problem. To determine the prop-
er temperature to run the die and/or feed
blocks, it is important to estimate the
shear rate first and then determine the
temperature where the resins have the
same viscosities.
Once shear rate versus viscosity data
are generated at three temperatures for
each resin used in a coextrusion opera-
tion, and the proper shear rates are calcu-
lated where the resins come together, an
Arrhenius plot can be generated to pre-
dict the proper operating temperature. An
Arrhenius plot graphs log viscosity ver-
sus 1/T in Kelvin. Plotting viscosity at
three temperatures gives a straight line.
The lines for the different coextrusion
resins can then be extrapolated to a temperature where the
resins have the same viscosity. If the temperature is an
appropriate melt processing temperature for each resin
system, the two polymers can be expected to coextrude
without any interfacial instability. However, if the select-
ed temperature is not a suitable processing temperature
for either resin, another polymer has to be substituted for
one of the resins using either a higher or lower viscosity,
depending on the intercept obtained in the first set of
experiments.
For example, assume polycarbonate is going to be
coextruded with polypropylene. What melt flow
polypropylene is required and what melt temperature is
optimum to run the coextrusion? Assume the resins are
coming together in the die or feed block at very low shear
rates, 10 sec-1. Table 20.2 contains some rheology data
collected at 10 sec-1 on polycarbonate (Lexan 121) and
polypropylene with 0.5, 5, 12, and 35 MFI. Figure 20.12
shows the Arrhenius plot for the viscosity versus inverse
temperature. If the melt temperature of PP and Lexan 121
is 236˚C, the correct PP to use in coextrusion is 0.5 MFI.
However, 236˚C is too low a processing temperature
for Lexan 121, so 0.5 MFI is an inappropriate choice for
192 POLYMERIC MATERIALS
Tem- 0.5 5 12 35 Lexan
perature MFI PP MFI PP MFI PP MFI PP 121
235° C 2976 1326 705 323 3444
250° C 2576 1219 547 180 1683
265° C 2386 911 409 140 907
Table 20.2. Viscosity Data at 10 sec–1
for Different MFI PP and Lexan 121
Figure 20.11. Two polymers at the same temperature
with different shear rate vs. viscosity curves.
 
Polymer A
Higher Viscosity
Polymer B
Higher Viscosity
Both materials have
the same viscosity
V
is
co
si
ty
, P
a.
s
Shear Rate, sec
–1
B
101 102 10
3
Figure 20.12. Viscosity vs temperature data.
PP resin. Five MFI PP resin at 261˚C has the same vis-
cosity as Lexan 121 at a shear rate of 10 sec-1, and 261˚C
is an appropriate processing temperature for both PP and
Lexan 121. Twelve MFI matches the viscosity of Lexan
121 at 300˚C melt temperature at a shear rate of 10 sec-1;
this is on the high end of the processing range for PP.
Consequently, the resins of choice in this coextrusion
application are
• 5 MFI PP with Lexan 121 at 261˚C melt tem-
perature
• 12 MFI PP with Lexan 121 at 300˚C melt tem-
perature
• An 8 or 10 MFI PP with Lexan 121 at an inter-
mediate melt temperature
For multiple-layer coextrusion, more detailed analysis
of the relative layer viscosities is required and is beyond the
scope of this book. In general, the layer viscosities should
decrease, moving from the inner polymer layer toward the
outermost layers to avoid interfacial instabilities.
REFERENCES
1. Cheremisinoff, Nicholas P., An Introduction to Poly-
mer Rheology and Processing, CRC Press, Ann
Arbor, 1993.
2. Butler, Thomas I., Veazey, Earl W., Co-Ed, Film
Extrusion Manual: Process, Materials, Properties,
TAPPI Press, Chapter 4, 1992.
POLYMER RHEOLOGY 193
Review Questions
1. What is meant by a viscoelastic material?
2. What is the difference between a Newtonian and non-Newtonian fluid as stress is applied to the
fluid over a specific time period?
3. What is the definition of viscosity?
4. Explain how changes in molecular weight alter the polymer viscosity.
5. What are two methods of measuring polymer viscosity and how do they differ?
6. Explain how viscosity can be used to measure resin thermal stability and generate a time-
temperature curve.
7. What is the purpose of a time-temperature curve?
8. At what range of shear rates do the following chemical processes occur: injection molding,
compression molding, extrusion, and coextrusion?
9. Name three polymers whose viscosities are both shear- and temperature-sensitive, three that are
temperature-sensitive, and three that are shear-sensitive.
10. Why is viscosity important to understand in extrusion?
11. What is meant by a shear-sensitive polymer?
12. Can two polymers have the exact same melt flow index but have different resin viscosities in the
extruder? Explain your answer.
13. What effect does raising the melt temperature 30˚C have on HDPE viscosity?
14. What effect does raising the melt temperature 30˚C have on PBT viscosity?
15. What effect in extrusion is expected by changing the mixing head on a single screw extruder
that is extruding PP? Assume the change is from pin mixing to a Maddock mixer.