Polymer rheology and processing

7/27/2019 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.

Polymer Research Center


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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).


l h


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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.


P l R h C


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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:


P l R h C


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The energy of activationfor flow increasesas

the size of side groups increasesand as the chain

becomes more r igid.


P l R h C t


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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.


P l R h C t


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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.


P l R h C t


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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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Dependence

This is a very powerful technique since formany

polymersthe shif t factors areindependentof

molecular weight.




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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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Structures


Shear stress increased!!



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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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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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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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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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Lubricants



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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 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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In contrast, rotating shafts in

Newtonian liquids cause a

depressing of the liquidsurface due to centrifugal

forces.



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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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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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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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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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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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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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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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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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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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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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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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Polymer rheology and processing

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