Practical Rheological Measurements by Vikcyb7


									  Practical Rheological Measurements
What should you measure?
     – Steady shear / oscillatory / stress relaxation / creep?
     – Shear versus elongational deformations?
     – Strain rates / temperature?

That depends…
• Measure shear viscosity if you are designing dies.
• Measure extensional (elongational) viscosity if you are using the polymer for
  fiber spinning, film blowing etc.
• Perform stress relaxation experiments if you are concerned with “frozen-in”
  stresses in your final product.
• Creep experiments will help to assess long term dimensional stability
• Measure first normal stress differences if you have problems with swelling of

Rheological Measurements               CHEE 490                             29.1
     Measurements of Shear Viscosity
• Shear viscosity is related to molecular weight and MWD, therefore its
  knowledge is very important in material selection
• Viscosity governs the flow of polymers inside processing equipment.
  Flow rates and pressure drops depend on the viscosity value
     – Knowledge of viscosity for the whole relevant shear rate range is
• You need to determine the shear viscosity if you want to design dies,
  to determine pressure drop, flow rates etc.

Rheological Measurements             CHEE 490                              29.2
                    Steady-Shear Viscosity
  Steady shear measurements cannot resolve the shear stress into a
  storage and loss component, but they remain popular for a number of
        – Steady-shear instruments are inexpensive relative to oscillatory
        – The deformation mode is often more representative of what the
          polymer will experience during processing.
        – The range of shear rates provided by steady-shear devices (i.e.
          capillary rheometers) can be outside those provided by oscillatory

Rheological Measurements              CHEE 490                                 29.3
      Measurements of Shear Viscosity
•   Melt Flow Index
•   Capillary Rheometer
•   Coaxial Cylinder Viscometer (Couette)
•   Cone and Plate Viscometer (Weissenberg rheogoniometer)
•   Disk-Plate (or parallel plate) viscometer

Rheological Measurements       CHEE 490                      29.4
                    Ranges of Shear Rates

Rheological Measurements    CHEE 490            29.5
                            1. Melt Flow Index
   MFI is determined by means of an extrusion plastometer, according to
   the ASTM D1238 test. It is often used in industry to characterize a
   polymer melt and as a simple and quick means of quality control.

                                                        MFI = grams of polymer
                     9.55 mm
                                                        extruded in 10 minutes
                 L             Die D

                               Die dimensions
                               D = 2.095 mm, L = 8 mm

Rheological Measurements                         CHEE 490                        29.6
                           Melt Flow Index
For PE the standard weight is 2.16 kg, temperature 190°C and the
corresponding shear stress is tw=1.94x104 Pa.

For PP the standard temperature is 230°C and the melt index is referred to
as Melt Flow Rate (MFR)

Low MFI means ???

MFI represents a SINGLE point on the viscosity-shear rate curve
Rheological Measurements         CHEE 490                           29.7
                            Melt Flow Index

 Sometimes the so-called High Load Melt Flow Index is calculated, with
  a load of 10 kg rather than the standard 2.16 kg. These quantities are
  designated as I10 and I2 respectively. The ratio I10/ I2 is a useful
  indication for comparison of the shear thinning behavior.

 Rheological Measurements         CHEE 490                         29.8
                    2. Capillary Rheometer
 The capillary rheometer (or
 viscometer) is the most common
 and simplest device for
 measuring melt viscosity.
 Gravity, compressed gas or a
 piston generates pressure on the
 test fluid in a reservoir.
 A capillary tube of radius R and
 length L is connected to the
 bottom of the reservoir.
 Pressure drop and flow rate
 through this tube are used to
 determine viscosity

Rheological Measurements            CHEE 490   29.9
           Capillary Rheometer Analysis
   The flow situation inside the capillary rheometer die is essentially
   identical to the problem of pressure driven flow inside a tube (Poiseuille

                                              We can record force on
                                              piston, F (or the Pressure
                                              drop DP), and volumetric
                                              flow rate, Q or piston
                                              speed, V.

Rheological Measurements           CHEE 490                           29.10
           Capillary Rheometer Analysis
The volumetric flow rate Q can be used to obtain an estimate of the shear
rate (apparent shear rate).

                     app    3

  This must be corrected to account for
  non-Newtonian behaviour (Rabinowitch

                             4Q 3n  1
                   W 
                             R 3 4n

Rheological Measurements                 CHEE 490                  29.11
           Capillary Rheometer Analysis
The pressure drop (DP) can be used to obtain an estimate of the shear

                           R  DP 
                   tW           
                           2 L 

  The viscosity is calculated:


Rheological Measurements              CHEE 490                    29.12
                   Entrance Pressure Drop
     Newtonian Fluids and some             Fluids with pronounced non-
     melts such as HDPE and PP             Newtonian behaviour

    The Bagley correction is needed to obtain the corrected pressure drop

Rheological Measurements            CHEE 490                            29.13
        Dual Bore Capillary Rheometers
 Dual-bore capillary rheometers can run two test simultaneously using
  dies of the same diameter but different lengths. They automatically
  calculate the Bagley correction to substract the error due to the
  entrance pressure drop.

Rheological Measurements        CHEE 490                         29.14
                  3. Rotational rheometers
  They are high-precision, continuously-
  variable- shear instruments in which the
  test fluid is sheared between rotating
  cylinders, cones, or plates, under
  controlled-stress or controlled-rate
  The basic rotational system consists of
  four parts: (i) a measurement tool with a
  well-defined geometry, (ii) a device to
  apply a constant torque or rotation
  speed to the tool over a wide range of
  shear stress or shear rate values, (iii) a
  device to determine the stress or shear
  rate response, and (iv) some means of
  temperature control for the test fluid and

Rheological Measurements           CHEE 490    29.15
  Measurement tools: Coaxial Cylinder (Couette)
 Best for low viscosity systems, o<100 Pa.s
 Good for relatively high shear rates
 Not suitable for polymer melts

                    M(R i )
          t( r ) 
                    2 r 2 L
M=torque, =rotational speed, =gap

Rheological Measurements           CHEE 490     29.16
   Measurement tools: Cone and Plate
 Constant shear rate throughout
 Useful for low and high viscosity materials
 Shear rate ranging from 10-2-10 s-1

                2 R 3
M=torque, =rotational speed, =angle

Rheological Measurements         CHEE 490       29.17
      Measurement tools: Parallel Plate
 Frequently used for polymer
  melts, blends and composites
 Sample preparation and loading
  very simple
 Shear rate varies in the radial

 R 
       3M  1 d lnM 
 tR       1         
         3 
      2R  3 d ln  R 
                    

Rheological Measurements       CHEE 490   29.18
                           Creep Experiments
 A constant stress is applied and the strain is monitored constantly.
 The compliance J is the ratio strain/stress
                                                   1.5                                              1.0E-02

 •   They can be done using the
     Couette, parallel plate, or
     cone and plate fixtures.
 •   Response is in the linear                     1.0

     viscoelasticity region if it is

                                       J (Pa-1))

                                                                                                              J (Pa-1)
     independent of the stress                                                                      5.0E-03

 •   Useful in differentiating                     0.5

     materials with
     branched/crosslinked                                                     uncrosslinked PP
                                                                              crosslinked PP
 •   Creep experiments can also                    0.0                                              0.0E+00
                                                         0   500    1000          1500           2000
     be done in tension, to
                                                                   Time (s)
     investigate long term stability
     of viscoelastic solids

Rheological Measurements                     CHEE 490                                              29.19
         Elongational (Extensional) Flow
Let’s consider the uniaxial stretching of a cylinder of fluid:
                       F                             F, V1
                                                A                        1
                                                                3
We define the Extensional Viscosity as:                    x1

          e 
At very low extension (stretch)

 E  3o               (Trouton ratio)

 Rheological Measurements                 CHEE 490                           29.20
   Measurements of Extensional Viscosity
• Extensional Viscosity and “Melt Strength” are related to the
  performance of polymers in processes involving stretching,
  such as film blowing, sheet extrusion, fiber spinning, blow
  molding, thermoforming.

• In these processes a high melt strength is desirable to
  ensure that the melt can be stretched without rupturing

Rheological Measurements    CHEE 490                    29.21
    Measurements of Extensional Viscosity

                                       Meissner Rheometer.
                                       Limited to very low strain rates
                                       (<1 s-1)

                                      Melt Spinning Apparatus
                                      (such as Gottfert
                                      Can achieve higher strain rates.
                                      But deformation is not uniform.
                                      The force level when the filament
                                      breaks is called the melt strength

Rheological Measurements   CHEE 490                              29.22
                       Extensional Viscosity
From capillary rheometer measurements
    It has been suggested that extensional viscosity is related to the
    entrance pressure drop inside a capillary rheometer. For a polymer
    obeying the power-law:

                                     9( n  1) 2 ( DPe ) 2
                                e 
                                          32 app
                                       4 2
       at an extension rate:    
                                   3( n  1) DPe

Rheological Measurements          CHEE 490                         29.23
                      Extensional Viscosity
SER Universal Testing Platform
• The fixture incorporates dual wind-up drums that allow for a truly
  uniform extensional deformation during measurement.
• It can be attached to most commercially available rheometers.

Rheological Measurements         CHEE 490                          29.24
                      Extensional Viscosity
• A constant strain rate deformation is achieved by applying a constant
  drum rotational speed with the SER. By collecting the time and torque
  for a given temperature and rate, the data can be easily converted to
  produce tensile stress growth curves.

                                    The strain rate is expressed in terms of the
                                   “Hencky strain rate” .

                                   For a constant drive shaft rotation rate, Ω,
                                   the Hencky strain rate applied to the sample
                                   specimen can be expressed as:

                                   dЄH/dt = 2 ΩR/L0

                                   where R is the radius of the equal dimension
                                   windup drums, and L0 is the fixed,
http://www.xpansioninstrument      unsupported length (referred to as the             "stretch zone") of the specimen sample being
Rheological Measurements         CHEE 490                             29.25
               Extensional Stress Growth
Extensional thickening effects are observed when tracking the
extensional viscosity as a function of time. .


Rheological Measurements         CHEE 490                       29.26
                    Extensional Thickening
 Although in a shear flow the viscosity of a polymeric fluid usually
 decreases with increasing deformation rate (shear thinning), in an
 extensional flow the extensional viscosity frequently increases with
 increasing extension rate.
 This phenomenon is called
 “extensional thickening”,
 or “strain hardening”.

Rheological Measurements          CHEE 490                              29.27
Usefulness of Extensional Viscosity Measurements

• Extensional Viscosity and “Melt Strength” are related to the
  performance of polymers in processes involving stretching,
  such as film blowing, sheet extrusion, fiber spinning, blow
  molding, thermoforming and foaming.
• In these processes a high melt strength is desirable to
  ensure that the melt can be stretched without rupturing

Rheological Measurements    CHEE 490                    29.28
         Shear Oscillatory Measurements

• Measured using rotational rheometers (strain or stress controlled), with
  cone-and-plate or parallel plate fixtures in the dynamic oscillatory mode.
    – Stress sweeps: To identify linear viscoelasticity region. Very sensitive to
      branching and presence of fillers.
    – Temperature sweeps: To identify temperature stability, degradation,
    – Frequency sweeps: Useful to detect structure of the material, viscous vs.
      elastic behaviour etc.
    – Stress relaxation: To detect the relaxation modulus as a function of time.
• Oscillatory measurements can also be performed on solid samples (i.e.
  rubber, polymers in the solid state) using DMA (Dynamic Mechanical
  Analyzer) instruments.
    – Temperature sweeps are commonly used to identify glass transition
      temperatures, and damping properties (tan) of the solid samples.

  Rheological Measurements              CHEE 490                              29.29
             What should you measure?
   •    Need to determine the shear viscosity if you want to design dies, to
        determine pressure drop, flow rates etc.
   •    You will need the first normal stress difference if you have problems
        with swelling of extrudates
   •    You will need stress relaxation if you worry about frozen-in stresses in
        final product, or warpage
   •    You will need extensional (elongational) viscosity if you use the
        polymers for fiber spinning, film blowing, thermoforming, foaming etc.
   •    Do creep experiments if you are worried about long term dimensional
   •    High melt elasticity has been associated to melt strength and extrudate

Rheological Measurements                CHEE 490                                29.30

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