Practical Rheology LCR 7001 Capillary Rheometer Azadeh Farahanchi Rheological Scientist

38 Forge Parkway, Franklin, MA 02038 Tel: 508.541.9582 Cell: 774.287.2366

[email protected] 1 Proprietary & Confidential Outline

1. Introduction

2. Shear Sweep Test (Polymer Flow Behavior )

3. Rabinowicz and Bagley Corrections

4. Extensional Viscosity Measurements

5. Wall Slip Velocity Calculation

6. Time Sweep Test (Thermal Stability of Polymers )

7. Die Swell Measurements

8. MFR Correlation

9. Intrinsic Viscosity of PET

10. LCR Dies Information

Proprietary & Confidential 2 Introduction

3 Why Capillary Rheometer?

 The most common melt rheometer to analyze flow behavior of polymers under processing condition (shear rate, time, temperature).

 Duplication of processing parameters for design, simulation, and trouble shooting purposes in a faster way.

 Predict optimal operating condition based on correlation of rheological data from capillary rheometer to processing parameters.

www.directindustry.com/industrial-manufacturer/pp- extrusion-line www.polymersni.com/industry/extrusion-film  Analyze different materials for various www.moldex3d.com applications and design. APPLICATIONS  Polymer viscosity at wide deformation rate range  Polymer melt flow behavior  Shear thinning behavior  Polymer stability over time/temperature  Elastic properties (die swell, wall slip) http://slideplayer.com 4 Dynisco®LCR 7001

Force measurements from Load Cell  MEASURES:

 Force  Pressure  Ram rate  Time  Temperature RESULTS:  Expansion of extrudate Pressure measurement Polymer flow curve from Pressure Transducer (LabKars Software)  CALCULATES:

 Shear stress  Shear rate  Shear/extensional Viscosity  Die swell ratio

5 Proprietary & Confidential General Specification

 LCR7001 SPECIFICATION

 Temp range: 25-500 °C  Shear rate range: 1-100000 1/s  Barrel diameter: 9.55 mm  Available length: 227 mm  Working length: 125 mm  Min piston speed: 0.03 mm/min  Max piston speed: 650 mm/min  Max force measurement from load cell: 10 KN  Max pressure measurements: 1400 Bar  Accuracy of test-to-test~1.5-2%  Accuracy of rheometer-to-rheometer~8% Based on ASTM-D3835 “Standard Test Method for Determination of Properties of Polymeric Materials by Means of a Capillary Rheometer”

Proprietary & Confidential 6 Extrusion & Capillary Rheometer

Hopper Pressure Motor Transducer Screw Barrel Thermocouple Die

http://www.polymerprocessing.com

7 LCR Preparation Before Running the Test

1 2 3 4

Pour sample into funnel – Insert the die in the die Fasten die to bottom of barrel. Swing out barrel. about 10 grams. holder and die fastener. Rotate un-clockwise to close. 5 6 7

Place the piston inside Compress pellets with tamp. barrel and lock it. Lower safety shield.

Proprietary & Confidential 8 LCR Cleaning After the Test

1 2 3

Clean plunger with a brush Remove and clean die. while hot. Ensure grooves are clean. (rotate clockwise to open) 4 5

Put cotton swabs into Push cotton swabs through position to clean barrel. barrel.

Proprietary & Confidential 9 Shear Sweep Test

(Polymer Flow Behavior)

Proprietary & Confidential 10 What is Shear?

Shear ( / ) 𝟐𝟐 𝑷𝑷𝑷𝑷 𝒐𝒐𝒐𝒐𝒐𝒐 𝒎𝒎

( / ) Shear 𝟏𝟏 𝑺𝑺

11 Calculation of Rheological Data in LCR

 =  (1/s): apparent shear rate 𝟒𝟒𝟒𝟒 Apparent shear rate 𝟑𝟑  Q (mm3/sec): volumetric flow rate 𝒂𝒂 𝝅𝝅𝑹𝑹𝒄𝒄 𝒂𝒂 (based on piston speed) 𝜸𝜸휸  S𝜸𝜸휸 (mm/min): piston speed  = ( ) 𝟐𝟐  Db (mm): barrel diameter 𝝅𝝅𝑫𝑫𝒃𝒃  Rc (mm): die radios 𝑸𝑸 𝑺𝑺 𝟒𝟒

 = 𝑭𝑭  (Pa): wall shear stress ( )𝟐𝟐 Wall shear stress �𝝅𝝅𝑫𝑫𝒃𝒃  F (N): force from “load cell” on piston 𝒘𝒘 𝑳𝑳 𝝉𝝉𝒘𝒘 (based on force or driving pressure) 𝝉𝝉 𝟒𝟒 �𝑫𝑫 𝒅𝒅𝒅𝒅𝒅𝒅  Db(mm): barrel diameter  =  L/D: length to diameter ratio of the die ( ) 𝑷𝑷  Pd (Pa): driving pressure at the die 𝑳𝑳 𝝉𝝉𝒘𝒘 𝟒𝟒 �𝑫𝑫 𝒅𝒅𝒅𝒅𝒅𝒅 entrance from “pressure transducer”

Apparent shear viscosity  (Pa-s): apparent shear viscosity  =  (Pa): wall shear stress 𝒂𝒂 𝝉𝝉𝒘𝒘  𝜼𝜼 (1/s): apparent shear rate 𝜼𝜼𝒂𝒂 𝜸𝜸휸𝒂𝒂 𝝉𝝉𝒘𝒘  Assumptions: 1: Fully developed, isothermal, steady state,𝜸𝜸휸𝒂𝒂 and Laminar Flow - 2: No radial or circumferential velocity components - 3: Incompressible fluid - 4: No slip at the wall of the die 12 Proprietary & Confidential Shear Flow in Viscoelastic Polymer Melts

Random coil Stretching Oriented Highly entangled Partially aligned Highly aligned

13 Effect of Various Factors on Polymer Flow Curve

14 Flow Curve of Polymer Melts

Newtonian Narrow plateau MWD Shear thinning Transition 𝜼𝜼𝟎𝟎 (Power-law) Broad Region Region MWD

Higher Mw

Mw 𝜸𝜸휸휸𝟎𝟎 Zero-shear viscosity 𝟎𝟎 𝜼𝜼 MWD Lower Mw Characteristic shear rate 𝟎𝟎 𝜸𝜸휸 15 Molecular Weight Distribution (MWD)

Polymers with Broader MWD:  Better processablity (fluidity)  Less viscous dissipation during Narrow MWD their process  Less energy consumption during their process  Lower mechanical properties

Broad MWD

16 Analyzing Polymer Degradation from Flow Curve

Flow curve of plastic samples before process and Higher and after process at various screw speeds in an extrusion

𝟎𝟎 𝜼𝜼 𝑴𝑴𝑴𝑴 Unextruded 1000 RPM 2000 RPM Extrusion Condition 3000 RPM Heat 4000 RPM  Barrel temp Mechanical shear  Screw speed Residence time Lower and  Flow rate 𝜼𝜼𝟎𝟎 𝑴𝑴𝑴𝑴

Degradation

Farahanchi, A., Malloy, R., Sobkowicz, M.J. (2016), Polymer Engineering & Science 56: pp. 743-751

Proprietary & Confidential 17 Mw Dependence of Zero-Shear Viscosity

. ( ) molecular entanglements occur 𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 𝒘𝒘𝒘𝒘 𝑴𝑴𝑪𝑪 Fox-Flory Equation

Polymers with higher Mw:  Higher intermolecular entanglement  Higher strength  Higher chemical resistance

L.H. Sperling, Introduction to Physical Polymer Science, John Wiley & Sons, 4th Edition.

18 Quantitative Relationships for the Dependence of Viscosity upon Shear Rate

Power-law Model = 𝒏𝒏−𝟏𝟏 • k (Pa-s): Consistency • n: Power𝜼𝜼 𝜸𝜸휸-law index𝒌𝒌𝜸𝜸휸

 “Only” fits the shear-thinning (power-law) portion of the curve. Slope = 1  Shear-thinning exponents dependent on intermolecular forces.

𝒏𝒏 −  n ranges from 0.2-0.9 depending upon the type of polymer.  n equals to 1 for Newtonian materials.  n represents the processability (shear-thinning intensity).  Polymers with lower n are more sensitive to the shear rate.  n decrease with broader MWD.  k has temperature dependency and controlled by Mw. J.M. Dealy, K.F. Wissbrun, Melt Rheology and its Role in Plastics Processing: 19 Theory and Applications, Van Nostrand Reinhold, New York (1990). Quantitative Relationships for the Dependence of Viscosity upon Shear Rate

Modified Cross Model = 𝟎𝟎 𝜼𝜼 + ( 𝜼𝜼𝟎𝟎 ) ∗ 𝜼𝜼 𝜸𝜸휸 𝝉𝝉 𝜼𝜼𝟎𝟎𝜸𝜸휸 𝟏𝟏−𝒏𝒏 • (Pa-s): Zero𝟏𝟏 -shear viscosity∗ • (Pa): Critical shear𝝉𝝉 stress 𝟎𝟎 • 𝜼𝜼n∗: Power-law index 𝝉𝝉

 Combines the power-law and Newtonian regions.  Also fits the low shear Newtonian plateau.  is controlled by molecular weight.

 𝜼𝜼𝟎𝟎is stress at the beak in curve and controlled by MWD. ∗  Broader𝝉𝝉 MWD (by blending or branching) cause earlier . 20 ∗ J.M. Dealy, K.F. Wissbrun, Melt Rheology and its Role in Plastics Processing: Theory and Applications, Van Nostrand Reinhold, New York (1990). 𝝉𝝉 Viscosity-Temperature Dependence

Window into the process  Williams-Landel-Ferry (WLF) model: ( < < + )

( ) 𝒈𝒈 𝒈𝒈 log = = [ 𝑻𝑻] 𝑻𝑻 𝑻𝑻 𝟏𝟏𝟏𝟏𝟏𝟏 ( ) + η0 𝑇𝑇 −𝐶𝐶1 𝑇𝑇 − 𝑇𝑇𝑔𝑔 𝑎𝑎=𝑇𝑇 17.44 η0 𝑇𝑇𝑟𝑟𝑟𝑟𝑟𝑟 𝐶𝐶2 𝑇𝑇 − 𝑇𝑇𝑔𝑔 = 51.6 1 Increasing 𝐶𝐶 𝐶𝐶2 𝐾𝐾 temperature  Arrhenius model: ( > + )

( ) 𝑻𝑻 𝑻𝑻𝒈𝒈 1 𝟏𝟏𝟏𝟏𝟏𝟏1 = = exp[ ] (0 ) 𝑎𝑎 𝑇𝑇 η 𝑇𝑇 𝐸𝐸 𝑎𝑎 0 𝑟𝑟𝑟𝑟𝑟𝑟 − 𝑟𝑟𝑟𝑟𝑟𝑟 : η 𝑇𝑇 𝑅𝑅 𝑇𝑇 𝑇𝑇 : = 8.314 × 10 𝐸𝐸𝑎𝑎 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 . −3 𝑘𝑘𝑘𝑘� 𝑅𝑅 𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 𝑔𝑔𝑔𝑔𝑔𝑔 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑚𝑚𝑚𝑚𝑚𝑚 𝐾𝐾 21 J.M. Dealy, K.F. Wissbrun, Melt Rheology and its Role in Plastics Processing: Theory and Applications, Van Nostrand Reinhold, New York (1990). A Window into Your Process!

 At shear rate 100-1000 1/s (common at normal RPM in extrusion), the processing of which polymer cause higher Polymer 1 torque and head pressure, and viscous heating in the Polymer 2 extrusion? s) - s)  Which polymer has higher shear-thinning behavior (easier process-ability)?

 With increasing screw speed which polymer will have the highest flow rate? Log Viscosity (Pa Log Viscosity

- (Pa Viscosity Log Shear  Which polymer has the highest molecular weight?

10 100 1000  Which polymer had the Broader MWD? LogLog Shear Shear Rate (1/s) (1/s)

https://www.ptonline.com/columns/how-to-spec-a-flat-die  Which polymer might have linear might have long chain- branching and which one might have linear structure?

22 A Window into Your Process!

Polymer 1 Polymer 2

s)  Which polymer might face higher thermal degradation with - increasing temperature?

 Which polymer has wider processing temperature? Viscosity (Pa Viscosity

220 260 300 320 Temperature (°C)

23 Shear-Sweep Test Setup in LabKars

4 2 3 5 6 7 1. Add/delete Data Point Setup 1 2. Program Name 3. Start Position (mm): 89-100 mm 4. Temperature (°C): barrel temperature set point 5. Melt time (sec): 180-360 sec 6. Sensor1 ID: LC-103N 11 10 7. Die: choose entrance angle, D and L/D from list 9 8. Minimum/Maximum Speed (mm/min): 10 Min at 0.03 and Max at 650 mm/min 9. Data Acquisition mode: Steady state, Position, Time Delay, Manual 10. Speed Control range (mm/min) 8 11. Shear Rate range (1/s) 12. Send: sending test setup to rheometer 12

Proprietary & Confidential 24 LabKars Software (Control Screen)

9 10 12 13 14 Real-time data graph during the test 255.1 1. RCAL: balance transducers! 2 8 6 4 15 11 2. Run: run the test! 16 3. Acquire: collect data! 4. Stop: stop the test! 3 5 7 1 5. Purge: purge all the material in barrel! 6. Up: move plunger upward! 7. Down: move plunger downward! 9 11 10 8. Park: go to park position (25mm)! 9. Sensor #1 (N): force on load cell 10. Sensor #2 (N): force on pressure transducer 11. Active Ram Rate (mm/min): piston speed 12. Temperature (°C): actual barrel temperature 13. Laser (mm): die swell detection 14. Plunger position (mm) 15. Run time (sec) 16. Collected point: at each shear rate

Proprietary & Confidential 25 Data Analysis

Plot of log apparent viscosity versus apparent shear rate

Click to make logarithmic scale

Right Click to change the axis

Proprietary & Confidential 26 Data Analysis

Power-law model analysis

Choose “Power Law”

Power law fitting data

Proprietary & Confidential 27 Data Analysis

Modified cross model analysis

Choose “Modified Cross”

Modified cross fitting data

Proprietary & Confidential 28 Raw Data in LabKars

Select “Single Select the type of Run/Modify” to sensor see the raw data  Sensor 1: Load cell  Sensor2: Pressure transducer

Max, min, average, mean, and standard Raw data deviation information of all parameters

Proprietary & Confidential 29 Export Raw Data in Excel

Select “Export”

Choose your data set

Select “Single File” to export the data in Excel

Raw data in Excel sheet

Proprietary & Confidential 30 Rabinowicz and Bagley Corrections

31 Corrections

 All calculations we discussed are “Apparent” values since they assume Newtonian behavior and that the entire pressure drop occurs inside through die. (Assuming no die entrance/exit effect)

 Rabinowicz correction needs to be applied in order to rectify the data for non- Newtonian character of polymer melt. (Calculation of corrected shear rate)

 Bagley correction needs to be applied to consider the extra pressure drop that may happen at the entrance/exit of the die.(Calculation of corrected shear stress)

32 Why Rabinowicz Corrections?

Flow through a die

http://www.eng.uc.edu/~beaucag/RyanBreese/Rheolog/rheology.htm

Shear rate profile Flow Velocity (Parabolic Flow) (Parabolic Newtonian fluid fluid Newtonian

𝜸𝜸휸𝑵𝑵𝑵𝑵𝑵𝑵−𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵

(Plug Flow) (Plug 𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵𝑵 Polymer melt Polymer 𝜸𝜸휸

33 Rabinowicz Corrections

3 + 1 Pseudoplastic = ( ) 4 polymer melts 𝑛𝑛 [n<1] 𝛾𝛾�𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝛾𝛾𝑎𝑎� 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑛𝑛 Correction Factor

34 How to Apply Rabinowicz Corrections in LabKars?

Click to plot viscosity versus “corrected” shear rate

Proprietary & Confidential 35 Why Bagley Corrections?

 A = : Very minor pressure drop in barrel

𝑩𝑩𝑩𝑩𝑩𝑩𝑩𝑩𝑩𝑩𝑩𝑩  B = ∆𝒑𝒑 : Excess pressure drop in die entrance

𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬  C = ∆𝒑𝒑 : Fully developed flow region in capillary die

∆𝒑𝒑𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪  Large pressure drop associated with the flow entrance region A due to viscoelasticity of polymers. B  After entrance region, The pressure gradient approaches a C constant value (fully developed flow region)

 In reality: = +

𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬 𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄  Bagley correction∆𝑷𝑷 needs∆𝑷𝑷 to be applied∆𝑷𝑷 to calculate the entrance pressure drop

36 How to Calculate the Entrance Pressure?

= L 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅4( )𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑃𝑃 −D𝑃𝑃 τ𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶where 𝑹𝑹 𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹

𝑷𝑷 = P (at = 0) 𝐿𝐿 𝑃𝑃𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 OR 𝐷𝐷 = L 𝑃𝑃𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 4(𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅+𝑅𝑅𝑅𝑅𝑅𝑅) e 𝑃𝑃 D τ𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶where 𝑳𝑳 𝑒𝑒 Three dies, same diameter 𝑫𝑫 = = but different lengths 𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬 (e.g. L/D: 10, 20, and 30) −𝑳𝑳 37 J.M. Dealy, K.F.𝒆𝒆 Wissbrun, Melt𝒆𝒆𝒆𝒆𝒆𝒆 Rheology and its𝒄𝒄 Role𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄 in Plastics Processing:𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄 Theory and Applications, Van Nostrand Reinhold, New York (1990). 𝑫𝑫 How to Apply Bagley Corrections in LabKars?

Select “Copy Table to Clipboard” under “Edit” menu to get the raw data Select “Global Preferences” under “File” menu

Short die (L 10 mm)

≤ Long die (L 15 mm)

≥

Select “Attempt Bagley Correction” Insert number “2”

38 Proprietary & Confidential Right click on each axis and select the appropriate item to plot How to Calculate True Viscosity?

= τ𝐶𝐶 where 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 η 𝐶𝐶  (Pa-s): Viscosity with Bagley γand҅ Rabinowicz Corrections  (Pa): Bagley corrected shear stress 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇  η (1/s): Rabinowicz corrected shear rate τ𝐶𝐶 γ҅𝐶𝐶

39 Viscoelasticity

40 Mechanical Models of Viscoelastic Behavior

41 Mechanical Models of Viscoelastic Behavior

42 Extensional Viscosity Measurements

43 When Extensional Viscosity is important?

Any process that has stretch!

http://www.fetuk.com/biomedical-sector/

https://www.ptonline.com/products/extrusion-new-cast-film-sheet-lines

http://www.polymersni.com/industry/extrusion-film

http://www.smg3d.co.uk/images/pc_bottle_master_blow_mol ding_resized.jpg

http://www.directindustry.com/prod/amut/product-20400-1445327.html 44 What is Extensional (Elongational) Viscosity?

 Since the diameter of the barrel versus die is very large, there is a high degree of stretching along streamlines at the entrance to the die

 Cogswell assumes that the pressure drop in entrance has two components, one due to shear and one due to extension

45 Cogswell`s Equations

 (Pa): Extensional stress  = ( + 1) Extensional Stress  : Power law index 3  𝝈𝝈𝑬𝑬𝑬𝑬𝑬𝑬 𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸 (Pa): Entrance pressure σ 8 𝑛𝑛 𝑃𝑃 𝒏𝒏 𝑷𝑷𝑬𝑬𝑬𝑬𝑬𝑬

 ϵ (1/s): Extensional rate  ϵ=҅ Extensional Rate ( 2)  (1/s): Apparent shear rate 4γ҅𝑎𝑎η𝑎𝑎 𝐸𝐸𝐸𝐸𝐸𝐸  (Pa): Entrance pressure 3 𝑛𝑛+1 𝑃𝑃 𝜸𝜸휸𝒂𝒂 𝑷𝑷𝑬𝑬𝑬𝑬𝑬𝑬 ( )  =  (Pa-s): Extensional viscosity Extensional Viscosity 2 2 9 𝑛𝑛+1 𝑃𝑃𝐸𝐸𝐸𝐸𝐸𝐸 𝑬𝑬𝑬𝑬𝑬𝑬 𝐸𝐸𝐸𝐸𝐸𝐸 2 𝜼𝜼 η 32η𝑎𝑎γ҅𝑎𝑎 J.M. Dealy, K.F. Wissbrun, Melt Rheology and its Role in Plastics Processing: Theory and Applications, Van Nostrand Reinhold, New York (1990).

46 How to Perform Extensional Viscosity Measurements in LabKars?

Select “Copy Table to Clipboard” under “Edit” menu to get the raw data Select “Global Preferences” under “File” menu

Short die (L 10 mm)

≤ Long die (L 15 mm)

≥

Select “Cogswell Extensional Viscosity Calculation” Insert number “2”

Right click on each axis and select the extensional type of47 axis Proprietary & Confidential Example!

LDPE LLDPE LLDPE (Linear structure) is stiffer than LDPE (branched structure) in shear but softer in extension

48 http://www.eng.uc.edu/~beaucag/RyanBreese/Rheolog/rheology.htm Wall Slip Velocity & Melt Farcture

Proprietary & Confidential 49 Wall Slip in Capillary Flow

=

𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘 𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘 𝑽𝑽 𝟎𝟎 𝑽𝑽 ≠ 𝟎𝟎  Wall slip velocity increases dramatically above critical shear stress (~0.1 MPa).  Slippage reduces apparent viscosity. Also, the surface of the extrudate begins to be rough (melt fracture).  Wall slip happens due to elastic properties of polymer materials. Smooth surface Melt fracture  Critical shear stress is lower for polymers with higher molecular weight  Trouble shooting by using larger die diameter, Laminar flow (no wall slip) Wall slip longer die, tapering the die, higher temperature, or lower shear rate. http://www.rapidcolour.co.uk

50 Effect of Wall Slip on Capillary Rheometer Results

c

R.D. Chien, W.R. Jong, S.C. Chen, Study on Rheological Behavior of Polymer Melt Flowing Through S. G. Hatzikiriakos, Wall Slip of Molten Polymers, Progress in Polymer Science, 37 (2012), 624-643 Micro-Channels Considering the Wall-Slip Effect, J. Micromech. Microeng. 15, (2005), 1389

Wall slip causes formation of plug flow and a discontinuity in flow curve.

51 How to Calculate Wall Slip Velocity?

1 = 4 + where  (mm/sec): Wallγ҅𝑎𝑎 slip velocity𝑉𝑉𝑤𝑤 𝑋𝑋  (1/s): apparent shear rate at a𝐶𝐶 given value of shear stress 𝒘𝒘 𝑅𝑅  𝑽𝑽 (mm): Capillary die radios 𝒂𝒂  𝜸𝜸휸: Dimensionless parameter (a function of the shear stress) 𝑪𝑪 𝑹𝑹 Critical shear stress 𝑿𝑿

Steps: 1. Produce a series of flow curves using a set of dies of varying radius ( ).

2. At a given value of shear stress, make a plot of apparent shear rate ( 𝐶𝐶) versus inverse radius ( ). 𝑅𝑅 1 3. Slip velocity at a given shear stress will be one quarter of the slope ofγ 𝑎𝑎҅ -vs- plot. 𝑅𝑅𝐶𝐶 1 4. Repeat the test at other shear stresses and calculate the slip velocity at each specific shear stress. γ҅𝑎𝑎 𝑅𝑅𝐶𝐶 5. Make the plot of slip velocity versus shear stresse.

Reference: J.M. Lupton, H.W. Regester, Melt Flow of Polyethylene at High Rates, Polym. Eng. Sci. 5, 235-245 (1965) 52 How to Notice Wall Slippage from Flow Curve in LCR?

Slippage affect Power- Law model parameters D: 0.04 inches

NOT overlapping of results from two dies means slippage D: 0.03 inches happened at the smaller die

Perform shear rate sweep on two dies with same L/D but different diameters Viscosity is lower when slippage

Proprietary & Confidential happens in smaller die diameter.53 Melt Fracture Trouble Shooting in Extrusion Process

http://file.scirp.org/Html/2-1740143_70424.htm

This phenomena happens due to elasticity of polymer melts. Any procedure that reduces the melt elasticity will help to troubleshoot. e.g.:  Increasing temperature  Reducing screw speed (shear rate)  Increasing the die length or die diameter  Tapering the die

54 Time Sweep Test

(Thermal Stability of Polymers)

55 Thermal Stability of Polymer Melt

Polymerization

Polymerization

 The stability test can determine the resistance of a material to a change in viscosity at the test temperature.  The stability of polymer melts varies depending on temperature, time at temperature, formulation, and contaminants.  This test can be used to show the presence of moisture or reactive chemicals in a polymer.  This test can be used to measure the degradation rate or reactivity of a sample

56 How to Set up Thermal Stability Test (Time Sweep) in LabKars?

= × 13 6.5 2 mm∆𝑳𝑳mm/sec𝑺𝑺 ∆sec𝒕𝒕 Where Select  : Piston travel distance “Position” between points Test Type ∆𝑳𝑳  : Piston speed (130 mm) = 𝑺𝑺 𝑴𝑴𝑴𝑴𝑴𝑴 𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑 𝒕𝒕𝒕𝒕𝒕𝒕(e.g.20𝒕𝒕𝒕𝒕𝒕𝒕 min) 𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕  : Piston time travel between points ∆𝒕𝒕 (e.g.20 min) = # (e.g.10) Appling the same speed and 𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 𝒐𝒐𝒐𝒐 𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑 Proprietary & Confidential shear rate multiple times 57 How to Set up Thermal Stability Test (Time Sweep) in LabKars?

Add delay time to increase the stability test time while keeping shear rate constant

Proprietary & Confidential 58 Thermal Stability Test Results (Time Sweep) in LabKars

Plot of apparent viscosity versus residence time

Proprietary & Confidential 59 Die Swell

60 Die swell Ratio

= × 𝑫𝑫𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬 − 𝑫𝑫𝒅𝒅𝒅𝒅𝒅𝒅 𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝒅𝒅𝒅𝒅𝒅𝒅 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝟏𝟏𝟏𝟏𝟏𝟏 𝑫𝑫𝒅𝒅𝒅𝒅𝒅𝒅  Expansion (re-coiling) of extrudate after exiting die. 𝑫𝑫𝒅𝒅𝒅𝒅𝒅𝒅  Qualitative measure of melt elasticity. 

𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬 Relaxed die swell is used to predict part dimension

𝑬𝑬𝑬𝑬  Running die swell is used to predict productivity of 𝑫𝑫 extrusion process.  Analysis of extrudate smoothness.  Trouble shooting by using larger die diameter, longer die, tapering the die, lower shear rate, or higher temperature. https://www.azom.com

61 Die Swell Measurement in LCR

 Detection: CCD element

 Light source: 800 nm laser 𝑫𝑫𝒅𝒅𝒅𝒅𝒅𝒅  Resolution: 2.75 µm

 Measuring range: 0.13-23 mm

 Response time: 1.4 ms

 ± 𝑫𝑫𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬 Accuracy: 0.003 mm

Proprietary & Confidential 62 Die Swell Measurement in LCR

Melt Fracture Melt fracture produce a noisy die swell measurements.

Ram rate

Percent die swell

https://www.azom.com/article.aspx?ArticleID=13578

63 Die Swell Trouble Shooting in Extrusion Process

http://www.rheoheat.se/ve_rheo.html

This phenomena happens due to elasticity of polymer melts. Any procedure that reduces the melt elasticity will help to troubleshoot. e.g.:  Increasing temperature  Reducing screw speed (shear rate)  Increasing the die length or die diameter  Tapering the die

64 MFR Correlation

Proprietary & Confidential 65 How to Calculate MFR from Capillary Rheometer?

Weight in MFR test Shear stress (kg) (Pa) 2.16 19350 1. Calculate the shear stress in the melt flow rate tester 5.00 44792 (using a standard die) 10.00 89584 21.60 193502

2. Determine the shear rate achieved at this shear stress from material flow curve

Proprietary & Confidential 66 How to Calculate MFR from Capillary Rheometer?

3. Calculation of melt volume rate (MVR) as follow: = 𝟑𝟑 where 𝝅𝝅𝑹𝑹 𝑴𝑴𝑴𝑴𝑴𝑴 𝟔𝟔𝟔𝟔𝟔𝟔𝜸𝜸휸  ( /10min): Melt volume𝟒𝟒 rate  ( ): Shear3 rate determined at “step 2” 𝑀𝑀𝑀𝑀𝑀𝑀 𝑐𝑐𝑐𝑐  (1 ): Standard melt flow rate tester die radius γ҅҅ 𝑠𝑠 𝑅𝑅 𝑐𝑐𝑐𝑐

4. MFR calculation knowing polymer melt density as follow: = × where 𝒎𝒎  ( ): Polymer𝑴𝑴 melt𝑴𝑴𝑴𝑴 density𝑴𝑴𝑴𝑴𝑴𝑴 𝝆𝝆 𝑔𝑔 𝑚𝑚 3 ρ 𝑐𝑐𝑐𝑐 Proprietary & Confidential 67 How to Measure MFR in LabKars?

Select “Interpolate” Set “Coefficient in Polynomial” as 3

Insert “Load” in g and polymer “Melt Density” in / in “Melt Flow” section 𝟑𝟑 𝒈𝒈 𝒄𝒄𝒄𝒄

Proprietary & Confidential 68 How to Measure Melt Density in LCR?

Manage the positions to Select have 14 mm of piston “Position” travel distance between Test Type points

Five measurements of melt density Whenever the plunger is in its delay time, cut the extrudate and weigh it

Proprietary & Confidential 69 Intrinsic Viscosity of PET

70 What is Intrinsic/Solution Viscosity (IV)?

 Creating a dilute solution of the polymer and comparing the flow rate of the solution to the flow rate of the pure solvent

 Advantages  Performing at room temperature  No need to melt the polymer  No need to dry hygroscopic polymers (e.g. PET, PA)  Common flowability specification (rather than MFR) among the manufactures of hygroscopic and filled polymers

 Disadvantages  Delicate apparatus  Using of noxious chemicals as solvent  Not environmental friendly http://alokrj.weebly.com/dpt-3rd-sem.html

71 Relationship between Melt Viscosity and Intrinsic Viscosity

= ( ) . Melt viscosity Fox-Flory 3 4 Equation η0 𝐾𝐾1 𝑀𝑀𝑊𝑊 η𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝛼𝛼 𝑀𝑀𝑤𝑤 [ ] = + 3. [ ] 𝑙𝑙𝑙𝑙 η0 𝑙𝑙𝑙𝑙𝐾𝐾1 4𝑙𝑙𝑙𝑙 𝑀𝑀𝑊𝑊

= ( ) Mark-Houwink 𝑎𝑎 Intrinsic viscosity 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 2 𝑊𝑊 Equation η 𝐾𝐾 𝑀𝑀 η𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝛼𝛼 𝑀𝑀𝑤𝑤 [ ] = + [ ] L.H. Sperling, Introduction to Physical Polymer Science, John Wiley & Sons, 4th Edition. 𝑙𝑙𝑙𝑙 η𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝑙𝑙𝑙𝑙𝐾𝐾2 𝑎𝑎𝑎𝑎𝑎𝑎 𝑀𝑀𝑊𝑊

[ ] = + . 𝒂𝒂 𝒍𝒍𝒍𝒍 𝜼𝜼𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰 Proprietary & Confidential𝐥𝐥 𝐧𝐧 𝜼𝜼𝟎𝟎 𝑲𝑲푲 72 𝟑𝟑 𝟒𝟒 PET Melt Viscosity Versus Intrinsic Viscosity

[ ] = + . 𝒂𝒂 𝒍𝒍𝒍𝒍 𝜼𝜼𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰 𝐥𝐥 𝐧𝐧 𝜼𝜼𝟎𝟎 𝑲𝑲푲 Slope: . For𝟑𝟑 𝟒𝟒 PET: a=0.75 Intercept:𝑎𝑎 3 4 𝐾𝐾�

Proprietary & Confidential 73 How to Determine IV of PET in LCR Capillary Rheometer?

Use Modified Cross to Get IV Button for PET at 285 C

74 Proprietary & Confidential LCR Dies Information

Proprietary & Confidential 75 LCR Die Part Number Code

Formula for die part number:

ADDD-LL

where  A: entry angle (W=60°, Y=90°, X=120°, Z=180°)

 DDD: diameter in inches×10000

 LL: length to diameter ratio

Proprietary & Confidential 76 Die Diameter

 Smaller diameter produces higher shear rates. D: 1 mm D: 0.38 mm  Larger diameter causes less elastic deformation applied at the entrance of the die.

 larger diameter cause less entrance pressure drop, less die swell, less extensional deformation, and less slippage.

 For calculation of wall slip velocity at least 2 dies with Die Diameter (mm) Max shear rate (1/s) different diameters (same L/D) are required. 0.38 142000 0.75 18700 1.00 7900 1.50 2300 2.00 980

Proprietary & Confidential 77 Die Length

 The portion of fully developed flow in compare with entrance region increases with increasing the die length

 The percent error produced by entrance region is less with longer die.

L: 1 mm L: 10 mm L: 20 mm  Short die for measuring elastic deformation (e.g. die swell, slippage) and long die for measuring shear viscosity.

 Noisy reading from short die at very low shear rates

 For calculation of entrance pressure (Bagley correction) and extensional viscosity, at least 2 dies with different L/D ratio (same diameter) are required. 78 Proprietary & Confidential Die Entrance Angle

 Entrance angle has effect on flow patterns at the entrance to the capillary die. 180°/flat 120° 90°

 Lower angle causes smoother flow, less vortex flow, and less energy consumption at the die entrance.

 Lower angle reduces the elastic deformations (e.g. less Z X Y

entrance pressure drop, extensional deformation, die http://www.4spepro.org/view.php?source=004100-2012-05-14 swell, melt fracture and wall slippage).

 Lower angle favors shear flow.

Stationary vortex flows in the corner region http://slideplayer.com/slide/3432579/ Flow pattern at the entrance to a die with a flat entrance (180°) 79

Proprietary & Confidential “Everything Flows”-Heraclitus

QUESTIONS ?

80