Rheological Properties of polymer melt

Question 1

How does the geometry of flow vary between liquids, solids and viscous materials?

Answer 1

Molecule in a fluid do not have defined positions but atoms in a solid do.
When the liquid is subjected to stress it flows(irreversible deformation) but solids deform like a spring (elastic deformation) due to the inter atomic bonds.
Viscous materials offer some resistance to flow(viscosity) from the internal friction between adjacent layers of fluid.

Question 2

What is rheology?

Answer 2

the study of deformation and flow of materials

Question 3

What are the 3 types of deformation to be considered in liquid flow?

Answer 3

Simple shear, elongational flow, bulk deformation

Question 4

What is simple shear?

Answer 4

most important type of deformation that occurs during the extrusion of materials such as processing of polymer melts
and extrusion based additive manufactures.

Question 5

What is elongational flow?

Answer 5

important in film formation, fibre
pulling, blow moulding and
vacuum forming processes.

Question 6

What is bulk deformation?

Answer 6

Important in injection moulding, where liquid flow is generated by hydrostatic pressure.

Question 7

What is a pseudoplastic?

Answer 7

where viscosity depends upon shear rate

Question 8

How is apparent viscosity defined?

Answer 8

= shear stress/strain rate. This can be combined with the Oswald equation to get a second power law for apparent viscosity. This is NOT Newtonian viscosity.

Question 9

How does the power law index determine what kind of shear the fluid is in viscosity?

Answer 9

n=1: Newtonian fluid
n<1: Shear thinning (most polymers*)
n>1: Shear thickening

Question 10

How does viscosity vary with shear rate for Newtonian and non-Newtonian fluids?

Answer 10

With bingham plastic - the shear stress linearly increases with the shear rate but this is from a higher shear stress starting point that newtonian.
Nonlinear plastic -
The newtonian - the shear stress linearly increases with the shear rate
Dilatantm pseudoplastic etc

Question 11

What is the effect of shear rate on viscosity? And how is flow behaviour described?

Answer 11

The flow of a fluid is opposed by the friction between adjacent layers in relative motion, and therefore a force is required to sustain the fluid flow.
The flow behaviour of a viscous material is described by the Ostwald-de Waelepower law, for which shear stress (τ) is given by shear rate.
If the log-log plot of shear stress vs shear strain yields a straight line it will behave like a pseudoplastic.

Question 12

what is the effect of shear rate on viscosity?

Answer 12

In pseudoplastic materials the viscosity decreases as the shear rate increases. This is caused by the disruption of interactions within the fluid or the ordering of the molecules or particles in the direction of the flow from an initial disordered state at rest. e.g creams usually display shear thinning.

Dilatant fluid exhibits the opposite behaviour, viscosity increases as shear rate increases. Some fluids do not start flowing unless the applied stress exceeds a certain critical value, known as yield stress (τy).

Non linear plastic fluids are described ny the hershel-Buckely model.
If Newtonian behaviour is exhibited then they are bingham plastics. These require a threshold shear stress before they start to flow.
Typical plastic flow behaviour= The solid-like behaviour at low shear stress can be explained by the
formation of a silica network structure arising from attractive particle-particle interactions due to hydrogen bonding between silanol groups.

Question 13

What is the difference between Newtonian, thixotropic and rheopectic materials?

Answer 13

 A Newtonian fluid, like water, has a constant viscosity that is
independent not only of the shear rate, but also of the sharing time.
 In contrast, when a constant shear stress (shaking or agitating) is
applied to a thixotropic fluid, the viscosity decreases with time, as a
result of the progressive breakage of the internal attractive interactions
by the continuous stress application.
 The opposite behaviour is found in rheopectic fluids, in which the
viscosity increases with the time of application of the shear stress. This is fairly uncommon.
Thixotropic and rheopectic effects can be reverse when applied shear stress is decreased/removed.

Question 14

How does stress and strain vary in elastic and viscous materials?

Answer 14

 In purely elastic materials the stress and strain are in phase, since the
deformation is instantaneous.  In purely viscous materials, there is a 90-degree strain lag. Viscoelastic
materials exhibit a behaviour somewhere in the middle.

Question 15

What is viscoelastic behaviour and what kinds of fluids do this?

Answer 15

 Many non-Newtonian fluids are viscoelastic, exhibiting a combination of elastic (solid-like) and viscous (fluid-like) behaviour.  When a constant stress is applied, they suffer an instantaneous
deformation as a result of the stretching of the interatomic or
intermolecular bonds.
 When the stress is removed, only the elastic part of the total
deformation is recovered instantaneously, followed by a progressive recovery over time of the viscous component, until an equilibrium state, which can be a complete recovery or not.

Question 16

How is the complex modulus calculated?

Answer 16

The complex modulus G* is calculated by dividing the stress by the strain in the oscillatory test and represents the resistance of the material to deform.

Question 17

How can the complex modulus be decomposed? 2 components

Answer 17

 the storage modulus G’ that corresponds to G* cos(δ) and represents the elastic behaviour of the material.
 It is associated to the elastic stretching of the internal bonds, which results in deformation energy stored in the material.
 the loss modulus G˝ that corresponds to G* sin(δ) and represents the
viscous behaviour of the material, which arises from the internal friction between the components in a flowing fluid and is associated to the energy dissipated in the process, that cannot be recovered.

Question 18

What kinds of behaviour is exhibited when the complex modulus increases or decreases?

Answer 18

When G’ is larger than G’’ the material has a solid-like behaviour, whereas when G’’ is larger than G’ the material has a liquid-like behaviour, which means that it flows.
 The G’’/G’ ratio is the loss tangent or tan (δ) and gives information on the balance between the viscous and elastic components.

Question 19

what are the 4 steps for polymer processing?

Answer 19

1.Heating the polymer into the molten state
 Pumping the melt into the forming unit
 Forming the melt into the required shape
 Cooling and solidification

Question 20

What are pseudoplastics? In regard to molecular properties.

Answer 20

Most polymer solutions and melts exhibit shear thinning, that
is, they belong to the class of pseudoplastic materials,
 The observed shear thinning of polymer melts and solutions is
caused by disentanglement and orientation of polymer chains
during flow.
 Polymers with a sufficiently high molecular weight are always
entangled (like spaghetti) and randomly oriented when at rest.

Question 21

What happens when pseudoplastics are sheared? high & low

Answer 21

 When sheared, however, they begin to disentangle and to align which causes the viscosity to drop. The degree of disentanglement will depend on the shear rate.
 At sufficiently high shear rates the polymers will be completely
disentangled and fully aligned.
 In this regime, the viscosity of the polymer melt or solution will be
independent of the shear rate, i.e. the polymer will behave like a
Newtonian liquid again.
 The same is true for very low shear rates; the polymer chains move so slowly that entanglement does not impede the shear flow.
 The viscosity at infinite slow shear is called zero shear rate viscosity(η0).

Question 22

What is the power law equation?

Answer 22

t=K* Shear rate ^n
 K describes the overall range
of viscosities across the part
of the flow curve that is being
modelled.  If the Power Law region
includes 1s-1 shear rate then
K is the viscosity or stress at
that point.
 For a shear thinning fluid:
0<n<1. The more shear thinning the product, the closer n is to zero.

Question 23

What is viscoelasticity behaviour in polymer melts?

Answer 23

 Polymer melts exhibit both viscous and elastic behaviour.
 Melt elasticity produces a memory effect leading to phenomena such as
post extrusion swelling and orientation.
 Elasticity arises because of entanglements in the polymer chains.
 Mechanical models are derived on the basis that the deformation of the polymer is divided into an elastic and a viscous component.

Question 24

What are the main factors affect the polymer melt viscosity?

Answer 24

Temperature, molecule melt, branching, fillers, blends

Question 25

How does temperature affect the melt viscosity of a polymer?

Answer 25

described through the arrhenius equation [ref]. Dependent on activation energy but shear rate increases with temp

Question 26

How does molecular weight affect the melt viscosity of a polymer?

Answer 26

The zero-shear viscosity becomes distinctly higher with growing molar masses. The differences get the smaller the higher the shear rate. Zero shear rate viscosity decreases as shear rate increases = shear thinning. The critical molecular weight for entanglement coupling is about 2x the entanglement weight. The amount of energy required to process the polymer is directly related to the viscosity’s shear rate dependence.

Question 27

How does molecular weight distribution affect the melt viscosity of a polymer?

Answer 27

Polymers with a broad distribution tend to thin more at lower shear rates than those with a narrow distribution at the same average Mw. This can cause:  moulding and extrusion can for example be made easier by broadening a polymer’s molecular weight distribution;  finished product characteristics, such as sag and haze in blown LDPE films, or  surface smoothness in a variety of thermoplastic moulded goods can be altered by changing molecular weight distribution. The entangled polymer chains disentangled the more of their entanglements the higher the shear rates or shear stresses are, acting on the molecules.

Question 28

How does branching affect the melt viscosity of a polymer?

Answer 28

 Polymer chain branches can vary in number, length and distribution along the main chain. If the branches are few and long enough to entangle, melt viscosity will be higher at low frequency than that of a corresponding linear polymer of the same molecular weight.  The viscosity of long-branched polymers is more shear rate dependent than is the viscosity of linear polymers and long chain branching affects the elasticity of the polymer melts which shows in the normal stress difference and the storage modulus.  The extensional viscosity at high strains increases strongly with long chain branches. The pronounced viscosity increase at large elongation strains (strain hardening) is characteristic for long chain branching. Long-chain(stronger shear thinning) branches have a significant effect on viscosity functions, as they contribute to the entanglement network.

Question 29

How do fillers affect the melt viscosity of a polymer?

Answer 29

 Adding fillers to a neat polymer melt changes its rheology, influencing both the way the melt processes and the properties of the ultimate product.  Key factors are filler size and shape, filler concentration, and the extent of any interactions among the particles.  The consequences of adding fillers are an increase in melt viscosity and a decrease in die swell.  Moreover do particle interactions increase the non-Newtonian range and cause it to occur at a lower shear rate than for the unfilled polymer melt.  Filled polymers have a higher viscosity at low shear rates, and yielding may occur with increased filler concentration. At higher shear rates the effect of the filler decreases and the matrix contributions dominate.

Question 30

How do fillers affect the melt viscosity of a polymer?

Answer 30

[ref equations pg45] for incompatible and compatible polymer blends in regard to volume fraction and viscosity.

Question 31

What are the viscoelastic properties of polymer melts?

Answer 31

The elastic properties of polymer melts are of equal importance to the viscous flow properties in the practical processing of polymers.  One of the most pronounced manifestations of elastic behaviour is the extrudate swell at the exit of an extrusion die (sometimes called “die swell”).  In addition the elastic behaviour of the melt can have a strong influence on the energy required to process the polymer.

Question 32

Where do the elastic properties in polymer melts come from?

Answer 32

Elastic properties in polymer melts result from entangled polymer chains. Chains are randomly orientated in the unstressed state, but when the melt is deformed (eg. when extruded through a die) the chains become orientated in the direction of flow.  On removal of the stress (eg. when the melt exits the die) the chains return to their equilibrium random-coiled state and so there will be some elastic recovery.  Recovery is not complete because of some chain slippage during flow (viscous component).

Question 33

What is die swell caused by?

Answer 33

 Elastic recovery is largely the cause of a phenomenon known as die swell, where the thickness of the extrudate is greater than the die exit slit.  This phenomenon is important in extrusion and must be taken into account at the die design stage. faster extrusion rate = greater die swell

Question 34

What kinds of fluids tend to exhibit the volume of swell from the extrudate?

Answer 34

 The change in velocity profile at the die exit (from parabolic to plug flow) can only account for small increases in diameter of the extrudate (ie. 10-15%).  Hence Newtonian fluids (purely viscous) can exhibit a small amount of die swell.  Most die swell in polymers is due to elastic recovery.

Question 35

What is melt viscoelasticity caused by? And what forms the polymer melt swelling?

Answer 35

Melt viscoelasticity is caused by physical entanglements of the molecules.  The polymer melt as it leaves the capillary ‘remembers’ the large cross-section in the barrel and tries to return to it by swelling. Low temperatures or high relative molecular masses promote ‘long memories’ and hence large swell ratios; high temperatures or low relative molecular masses promote ‘short memories’ and hence small swell ratios

Question 36

What is a critical parameter for the effect of die dimensions on the swell ratio?

Answer 36

A critical parameter is the time that the polymer melt is constrained within the capillary. Decreasing this time either by decreasing the length of the capillary or by increasing the shear rate will cause an increase in die swell.

Question 37

How does shear stress affect the swell ratio?

Answer 37

As the shear stress increases, the swell ratio will exponentially increase with that.

Question 38

What are the main factors that affect the die swell?

Answer 38

 Decreasing processing temperature increases die swell  Increasing shear rate increases die swell  Increasing melt viscosity increases die swell  Increasing polymer molecular weight increases die swell  Decreasing the value of L/D increases die swell  Increasing the value of Dres/D increases die swell

Question 39

What is melt fracture and when does it occur?

Answer 39

 Melt fracture occurs during capillary flow at high flow rates. Its when the melt is elongated under too high stress associated with elastic behaviour of the polymer.  The extrudate becomes irregular and distorted when the applied stress exceeds the tensile strength of the melt.  The critical stress is believed to occur at the entry to the die.

Question 40

How does the die entry angle affect the shear rate?

Answer 40

As the die entrance angle increases, the shear rate where melt fracture occurs decreases.

Question 41

How does the molecular weight affect the shear rate and die entrance angle?

Answer 41

The shear rate at which melt fracture occurs increases with decreasing molecular weight of the polymer.  This is because polymer melt viscosity decreases with decreasing molecular weight and a lower applied stress is required for the polymer to exit the die.

Question 42

How to reduce the melt fracture when processing the with the die in rheometry?

Answer 42

 Modify die entrance geometry  Reduce processing rate  Use higher processing temperature (critical shear rate increases with decreasing melt viscosity)  Employ local heating of die during extrusion  Decrease molecular weight of polymer (to decrease melt viscosity) Incorporate a processing aid in the polymer (to improve melt strength)

Question 43

How does the power law describe newtonian/ non-newtonian fluids?

Answer 43

Entanglement and entropic effects mean polymers have some memory. n=1 Newtonian fluid n<1: Shear thinning (most polymers*) n>1: Shear thickening * Thinning because entanglements being broken at greater rate than new ones form

Question 44

How is the equipment used to obtain flow data divided into 2 types?

Answer 44

 Capillary Rheometer  Rotational Rheometers – including the cone and plate rheometer and the concentric cylinder rheometer.

Question 45

What are the isothermal assumptions for the equipment used to obtain flow data?

Answer 45

 There is no slip at the wall  The melt is incompressible  The flow is steady, laminar and time independent (i.e. Newtonian behaviour)  Fluid viscosity is not affected by pressure changes along the channel  End effects are negligible

Question 46

What corrections can be introduced to correct assumptions for apparent viscosity in polymer melts?

Answer 46

 The pressure drop across the die is NOT linear, being substantial at the die entrance and non-zero at the exit. This assumption can be corrected by the Bagley end correction.  The velocity profile is plug-like, not parabolic. Hence the melt flow behaviour is not Newtonian. This can be corrected by the Rabinowitsch equation.

Question 47

How is the 'true' pressure drop above the die inlet corrected?

Answer 47

 As the polymer melt flows from the reservoir into the capillary die, there is an abrupt drop in pressure at the die entry. Can be accomodated by defining 'effective die length' [ref eq pg 78]  This is due to the establishment of a converging flow at this point as the liquid is constrained to pass from the large diameter barrel into the much smaller capillary.  The true pressure drop along the capillary is therefore ‘hidden’ by an additional pressure drop at the entrance of the die, where the flowing material goes from a wide reservoir (the main cylinder or barrel) to a narrow capillary, possibly also creating turbulences.  Assuming that the same additional pressure drop takes place with different capillary lengths (but keeping constant barrel and capillary diameter, and inlet shape), it’s possible to correct the pressure reading and estimate much more accurately the true pressure drop.  This is called the Bagley correction

Question 48

How does the Bagley correction correctly plot the pressure drop in a capillary die?

Answer 48

By plotting the axial pressure variation including exit and entrance values [ref eq p75]. The reading with the bagley correction gives true shear stress and true viscosity(property of material varying with test temperature) instead of apparent viscosity(only compares different samples tested with same instrument and die for quality control) without. Can therefore be calculated( good for design, flow simulation or fundamental studies).

Question 49

What data does a Bagley correction require?

Answer 49

 the same sample,  same temperature,  same barrel and  same capillary diameter, same capillary inlet, and different capillary lengths.  The use of ‘zero-length’ dies is not recommended by international standards.  With a twin-bore capillary rheometer it is possible to get Bagley corrected viscosity right at the end of a single test run, while the same result requires two tests with a single-bore machine

Question 50

What is the need of the Rabinowitsch correction factor?

Answer 50

 A correction is often made to take into account the fact that the pseudoplastic nature of the melt means that the assumed parabolic velocity profile in the die is actually more plug-like.

Question 51

Where should data for the rabinowitsch correction be inputted?

Answer 51

 Where the data are to be used for comparative purposes, applying the correction factor will not alter the comparability of the data.  The apparent viscosity determined without the correction is at most 15% greater than the apparent viscosity determined using the Rabinowitsch method.  For practical purposes, this error (although systematic) is considered to be acceptable. This is a reasonable procedure is quality control when polymers are to be compared and no absolute quantities are required.  Where data are to be used as fundamental data, then the correction should be applied.

Question 52

How does the cone and plate rheometer vary?

Answer 52

In this apparatus the polymer to be analysed is placed between a heated cone and a heated plate.  The apex of the cone is in contact with a horizontal stationary plate and the polymer fills the gap between the cone and the plate.  The angle between the side of the cone and the plate is small (typically < 5°).  The cone is rotated relative to the plate and the torque, T, necessary to do this is measured over a range of rotational rates. [ref eq pg86/87]. The apparatus can be operated at either constant speed or constant torque; the latter method, using a dead weight and a lamp and scale to measure rotation, is probably the cheapest and simplest rheometer available for polymer melts.

Question 53

What are the advantages and disadvantages of cone and plate rheometry?

Answer 53

Advantages:-  The flow conditions are precisely defined  The shear rate is very nearly the same everywhere in the fluid, provided the gap angle is small Disadvantages:-  The shear rate range is very limited  As the shear rate is increased, the flow pattern breaks up at the free boundary, giving rise to non-steady state conditions Shear strain rates are limited in the range of 10 to 1 s-1, whereas in plastics processing equipment the strain rates are of the order of 103 to 104s-1.

Question 54

How does the concentric cylinder viscometer vary ?

Answer 54

The torque required to rotate the cylinder over a range of speeds is recorded so that viscosity and strain rates may be calculated. Apparatus is limited to low strain rates like in the cone and plate rheometer.

Question 55

Where do normal stress differences arise from?

Answer 55

The generation of unequal normal stress components arises from the anisotropic structure of a polymer fluid undergoing flow. The polymer becomes oriented in the direction of flow. The restoring forces give rise to normal forces that push the polymer upwards. These forces restrict the speed of rotational rheometers.

Question 56

What is the weissenberg effect?

Answer 56

The Weissenberg effect is a phenomenon that occurs when a spinning rod is placed into a solution of polymer.  Instead of being thrown outward, entanglements cause the polymer chains to be drawn towards the rod. It is due to a non-zero first normal stress difference.  The strain tensor of the motion of turning the rod produces a non-zero difference between the normal components of the resulting stress tensor – so there is a force up /down.