polymer rheology and processing
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Polymer Rheology and Processing
Dr. Ying-Chieh Yen
(Prof. Feng-Chih Changs group)
Ref: Polymer Rheology Lawrence E. Nielsen.
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Polymer Processing
In the use of polymers, it is generally the
mechanical properties which are important.
However, the mechanical behavior of an object is of
l ittle interestif the object first can not be fabr icated
quicklyandcheaply.
In nearly all cases, flowis involved in the
processing and fabr icationof such materials inorder to make useful objects.
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Polymer Rheology
Rheologycan be defined as the science of theflow and deformationof materials.
For many simple fluids, the study of rheologyinvolves the measurement ofviscosity. However, therheology of polymersis much more complexbecause polymeric fluids show nonideal behavior.
In addition to having complex shear viscositybehavior, polymeric fluids show elastic properties,normal stress phenomena, and prominent tensi le
viscosity.
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Polymer Rheology
All these rheological properties depend upon
the rate of shear, the molecular weight and
structureof the polymer, the concentration ofvarious additives, as well as upon the
temperature.
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Polymer Rheology
Unit: The traditional unit of viscosity is the poise,
which has the dimensions ofdyn-s/cm2.
The viscosity of water is about 0.01 poise.
Typical polymer melts have viscosities generally
of the order of103
to 104
poise.
The SI units for viscosity are Pas. Pa (N/m2)
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Measurement of Viscosity
I deal f luidsare called Newtonian. Their viscosity
is independentof the rate of shear.
The shear viscosity may be defined as follows:
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Measurement of Viscosity
Another viscosity can be measured in tension
instead of by shearing tests.
ForNewtonian liquids, the tensile viscosity isthree timesthe shear viscosity, but forpolymeric
liquidsthe tensile viscosity may be many times
the shear viscosity.
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Normal Stresses
Normal stressesare other rheological
phenomenon encountered with non-Newtonian
fluids.
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Instruments
Capil lary rheometer:
Advantage: Easy to f i l l.
Disadvantage: The rate of shearis not constantbut variesacross the capillary.
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Instruments
Coaxial cyl inder or concentr ic cyl inder
rheometer:
Advantage: Nearly constant shear rate.Calibrated easi ly.
Disadvantage:
The difficultyinfi l l ingthem.
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Instruments
Cone and plate rheometer:
Advantage: Constant shear rate. The sample sizeisvery smal l. Ease of cleaning.
Disadvantage: Lower rate of shear.
Parallel plate viscometers
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Instruments
Dynamic or oscil latory rheometers:
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Instruments
Dynamic rheometers have a great advantage
over most other types of rheometers because
instruments measure the elastic modulusof
polymer melts in addition to the viscosity.
Disadvantage: Small ampli tude of deformation
(In most fabrication processes, the polymer
undergoes very large deformation).
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Factors Affecting Viscosity
The viscosityof polymers is affected by
several factorsincludingtemperature,pressure, rate of shear, molecular weight
and structures and additives.
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Effect of Temperature
The viscosityof most polymers changes greatly
withtemperature.
ForNewtonian liquidsand for polymer fluids attemperaturesfar abovethe glass transition
temperatureorthe melting point, the viscosity
follows the Andrade or Arrhenius equationto a
good approximation:
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Effect of Temperature
The energy of activationfor flow increasesas
the size of side groups increasesand as the chain
becomes more r igid.
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Effect of Temperature
For amorphous polymers at temperatures less
than 100 C above their Tg, the Andrade equation
does not f i t the data well.
A much better equation is the Williams-Landel-
Ferryor the W-L-Fequation:
The viscosity at Tgis often about 1013poise.
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Effect of Temperature
The energy of activationfor the W-L-F equationnot onlydepends upon temperaturebut also uponthe glass transition temperature.
The energy of activationbecomes very largeasthetemperature approaches Tg, especially if Tg
is large.
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Master Curves for Temperature
Dependence
There is a great need to predict the viscosityfrom
a small amountof experimental data.
The apparent viscosity can
be calculated from suchcurves at a given shear
rate by:
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Master Curves for Temperature
Dependence
This is a very powerful technique since formany
polymersthe shif t factors areindependentof
molecular weight.
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Master Curves for Temperature
Dependence
Most polymermelts become Newtonianat very
low rates of shearand have a zero shear viscosity,
0, which is a function of temperature.
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Effects of Pressure
The Andrade equation for the temperature
dependence of viscosity can be modified to:
The most direct inf luence onfree volumeshould
be the pressure.The viscosity of polystyrene increased by a factor
of135 timeswhen the pressure was increased
from zero to 18,000 psi at 385
F.
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Effect of Rate of Shear
An outstandingcharacteristic ofpolymer meltsis
theirnon-Newtonian behaviorwhereby the
apparent viscosity decreases as the rate of shear
increases.
ForNewtonian liquids, n = 1 and K = ; the
value of n is less than onefornon-Newtonian
polymer melts.
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Effects of Rate of Shear (Role of
Entanglement)
At very low rates of shear, the entanglements
have time to sl ip and become disengagedbefore
enough stresscan develop in them to or ient the
molecules.
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Effects of Rate of Shear on Polymer
Rheology
At higher rates of shearthe segments between
entanglements become orientedbefore the
entanglements can disappear.
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Effects of Rate of Shear on Polymer
Rheology
As a load-bearing entanglement disappears, theredevelops in the melt a steady state condition inwhich the rates of formation and destruction of
entanglements become equal.At very high rates of shearpractically noentanglements can exist. The viscosity should
reacha relatively small valuewhich becomesindependent of the shear rate. In other words,polymer meltsmay be expected to become
Newtonian in behavioratvery high ratesof
shear.
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Theories Descr ibing The Shear Rate
Dependence of Viscosity
The Cross equation (empirical) for the effect of
shear rate on the apparent viscosity is:
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Dynamic Properties
At low frequencieswhere the dynamic viscosity isindependentof, the elasticityas measured by is verysmall.
The dynamic viscosity and the steady-flow viscosity arenearly identical at low frequencies or rates of shear.
G
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Effect of Molecular Weight and
Structures
Among the structural factors determining the
rheology of a polymer, the molecular weightis the
most important.
Me is the molecular weight at which chain
entanglementsbecome important. (Me = 10,000~40,000.)
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Effect of Molecular Weight and
Structures
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Shear stress increased!!
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Effect of Molecular Weight and
Structures
y
Molecular weight increases
Molecular weight increases
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Effect of Structure on Polymer
Rheology
Branching:
Short branchesgenerally do not affectthe viscosity
of a molten polymervery much.
Branches which are long but which are sti l l shorter
than those required for entanglements decreasethe
viscositywhen compared to a linear polymer of thesame molecular weight.
y
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Effect of Structure on Polymer
Rheology
If the branches are so longthat they can participate
in entanglements, the branched polymermay havea
viscosity at low rates of sheargreaterthan that of a
linear polymer of the same molecular weight.
At high rates of shear, branched polymers in
nearly all caseshavelower viscositythan l inear
onesof the same molecular weight.
y
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Effect of Structure on Polymer
Rheology
Other structural factors:
F lexibi l i ty, specif ic interactions, and polari tywhich
affect the glass transition temperaturetend to affect
viscosity.
y
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Effect of Solvents, Plasticizers, and
Lubricants
In some cases the l iquids are addedfor a purpose
such as to plasticize the polymer, to improve its
processibilityor to stabilizethe polymer to
processing conditions.
Tg(Solvents also have Tg)
(lower than 0C or far below -100C)
Me, dilution.
y
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Effect of Solvents, Plasticizers, and
Lubricants
The Kelley-Bueche theory appears to be the best for
predicting the viscosity of concentrated polymer
solutionsusing the viscosity of the pure polymer as
the reference.
fP = 0.025 + 4.5 x 10-4 (T-Tgp)
fL = 0.025 + L (T-TgL)
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Effect of Solvents, Plasticizers, and
Lubricants
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Effect of Solvents, Plasticizers, and
Lubricants
Lubricants may be defined as materials which are
added to polymers in small amountsto improve
their processibil i ty. (soluble and insoluble)
Insoluble: waxes, mineral oil, metal stearates, and
silicon oils.
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Normal Stresses and Die Swell
Normal stressesare primarily manifestations of the
elastici ty of polymeric mater ials.
The normal stresses differences increase with thesquare of the rate of shear:
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Normal Stresses and Die Swell
Normal stresses produce a number of phenomena
not foundwith Newtonian l iquids.
When a polymeris extrudedfrom an orifice, a
capillary, or a slit, thediameter or thicknessof the
resul ting strand isconsiderably greaterthan the
diameter ofthe holefrom which is came. (die swell)
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Normal Stresses and Die Swell
In contrast, rotating shafts in
Newtonian liquids cause a
depressing of the liquidsurface due to centrifugal
forces.
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Normal Stresses and Die Swell
Ifholes are dri l ledin the plates parallel to the
rotating axis, l iquid wil l be forced up through the
holes. (Normal stresses can be calculated by
measur ing the heightto which a liquid will ascend
up a tube for a given speed of rotation. The first
normal stress dif ference is proportional to the
height of the liquid in the tube.)
Cone and plate, two rotating plates.
Difficulty and low accuracy.
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Normal Stresses and Die Swell
The f i rst normal stress dif ference is generally positive
which means that the tension resulting from the molecular
orientation is parallel to the flow streamlines.
The second normal stress difference is generally negativeand its value is very small.
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Normal Stresses and Die Swell
For a given rate of shear, the die swell decreasesas thelength to diameter ratioof the capillary increases.
Factors which increase the shear modulus of a polymermelt tend to increase the die well. (Molecular weight, PDI,
long-chain branching)
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Extensional F low and Fracture
Phenomena
The type of viscosity calculated when tensile forces
are used is the tensile, elongation, or extensional
viscosity.
For polymers, the tensile viscosity may be hundreds
of timesgreater than the shear viscosity. (Newtonian
liquids: 3~6 times)
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Extensional F low and Fracture
Phenomena
The tensi le viscosity decreases with temperature,
but the role of such factors as molecular weight,
entanglements, and polymer structure is not clear.
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Extensional F low and Fracture
Phenomena
At low rates of shear, polymer melts flow through
capillaries, channels, and ducts to produce smooth
strands.
At higher rates of shear, several kinds of flow
instabilities can develop in which the surfaceof the
extruded strand becomes rough or nonuni formin
cross section, and the rate of f low no longer is
steady but pulsates.
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Extensional F low and Fracture
Phenomena
The surface roughness types of defects (orange peel
and sharkskin) seem to be due to a slip-stick
phenomenonat the polymer-capillary wall.
The defects which result in variations in cross
sectional areaare due to f ractur ing of the polymer
melt.
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Extensional F low and Fracture
Phenomena
Melt fracturegenerally is the result of tensi le
stresses rather than shear stresses. (Size of the flow
channel goes from a largerto a smal lercross
section.)
Experimentally, it has been observed that die swell
goes through a maximum and then decreases at rates
of shear near values of where melt fracture starts.
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Suspensions, Latices, and Plastisols
Latices may be suspensions of rigid polymer
particles in water.
Plastisols are suspensions of polymer particles in aliquid plasticizer.
The presence of a fi l lerin Newtonianliquids
produces profound effects on the rheological
behavior of the suspension.
The rheology becomes even more complexif the
liquid phase is non-Newtonian.
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Suspensions, Latices, and Plastisols
Einsteins simple equation predicting the effect of a
filler on the viscosity of a Newtonian fluid. (only for
very low concentrationof particles)
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Suspensions, Latices, and Plastisols
The equation implies that the relative viscosityis
independent ofthe size and nature of the particles.
The magnitude of the Einstein coefficient isdetermined by the degree towhich the particles
disturb the streamlines in a flowing system.
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Suspensions, Latices, and Plastisols
Mooney equation
(predicting moderate concentration):
The viscosity of a suspensionapproaches infinity as the concentrationapproaches maximum packing fraction.(large number of particle-particlecontacts restricted)
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Suspensions, Latices, and Plastisols
All three equations indicate
that particle size has no
effect on the viscosity.
However, the distr ibutionof
the size of spheres can affect
the viscosity. (large andsmall particles, packing
densely)
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Suspensions, Latices, and Plastisols
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Suspensions, Latices, and Plastisols
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Suspensions, Latices, and Plastisols