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Rheology with Application to PolyolefinsTeresa Karjala, Ph.D. and Dr. Ir. Sylvie VervoortThe Dow Chemical Company, Packaging and Specialty PlasticsLake Jackson, Texas and Terneuzen, The NetherlandsThoi Ho and Terry Vermass Tutorial

Outline IntroductionSteady Shear FlowOscillatory Shear FlowExtensional RheologyConcluding Remarks2

Rheology Science dealing with deformation and flow of materials. Includes both molten and solid state behavior. Most commonly measured for materials such as polymers, polymer solutions,paint, food, and blood. Requires measuring the deformation resulting from a given force or measuring aforce required to produce a given deformation. Importance for polymers: Processing: extrusion, gear pumps, flow through pipes, pressure drops, etc. Relation to molecular structure such as:o Molecular weight (Mw)o Molecular weight distribution (MWD)o Long chain branching (LCB)3

Deformation Shear Measurement and analysisF Single deformation modes Straight-forward description Measure material propertiesLoLoLos Elongation Flow in applicationsFFLoLt Mixed deformation modes Complex analysis44

Viscosity (Newtonian Fluid) Viscosity relates to the resistance of a material to flow. Linear relationship between shear stress and shear rate: π h πΎ.Slope is viscosity, hShear rate (πΎ)Viscosity (h)Stress (s) For simple shear, the constant of proportionality is the viscosity, h . A material that behaves in this way is a Newtonian fluid. The viscosity does not depend on the shear rate.Shear rate (πΎ)5

Viscoelasticity and Non-Newtonian Behavior The majority of materials are neither purely elastic or viscous, but are consideredviscoelastic (exhibit viscous resistance and elasticity). In this case, the relationship between the stress and strain rate is no longer linearand cannot be described in terms of a single constant, h. Generalized equation for steady simple shear: h (πΎ) s / πΎin which the h is function of πΎ.Viscosity (h)Shear thickening/DilatantNewtonianShear rate (πΎ)Shear thinning/Pseudoplastic6

Non-Newtonian Behavior: Typical Polymer Flow Curveh or h* (Pa.s)Plateau region10000Viscosity constant Zero-shear viscosity, h0Polypropylene at 190 C1000Shear thinning regionViscosity with shear rate100steady sheardynamiccapillary100.01110010000shear rate (s-1) or frequency (rad.s-1)7

Non-Newtonian Behavior: Viscosity ModelsPower lawπ KπΎ ππ KπΎ π 1Cross:ππ0πΆππππππ’: n-1 0: shear-thinningn-1 0: shear-thickeningn 1: Newtonian fluid11 π ππΞ»πΎ1 π11 (ππΎ 2(1 π)/2h viscosity, πΎ shear rateho zero shear viscosityΞ» relaxation timen high shear rate fitting parameter[T.A. Plumley et al., SPE ANTEC Proceedings, p. 1221 (1994)]8

Temperature Dependency of Viscosity (Activation Energy)OverlayOverlayMaster curve at TRef 190 oCTemperatureTTSTemperatureNon-Newtonian polymerIsothermal frequency sweeps Viscosity with temperature Gβ and Gβ with temperatureh0 (π)Arrhenius: π π h(π)0 π ππ ππ₯ππΈπ 1π π 1ππ ππ,Ea flow activation energy9

Viscometric Flows With these flow geometries, the viscosity, as well as fluid velocities, shear rates,and pressure distributions can be determined analytically.Viscometric flowFlow exampleSteady tube flowCapillary flowSteady slit flowCast dieAnnular pressure flowBlown film dieSteady concentric flowBrookfield viscositySteady parallel disk flowDMSSteady cone and plate flowDMSSteady sliding cylinder flowWire coatingSteady helical flowSpiral dieCombined drag/P flowExtrusion10

Useful Equations for Steady Flow Through a Capillary and SlitFlow GeometryShear Rate,πΎCapillaryπΎ ππ·3 π π 3SlitπΎ ππ» 232π4πShear Stress,t or sπ 6ππΎ shear rateQ volumetric flow rateDP pressure dropV velocityR radius of capillaryL length of capillaryD diameter of capillary ππΏ4 (π·)π ππΏ2 (π ) ππΏ2 (π»)Depiction of FlowRWHQVz DQVz HW width of slitH height of slit11

Typical Shear Rates in Common ProcessesShear rate (s-1)ApplicationExtrusion100 - 103Polymer melts, foodMixing101 - 103Liquid manufacturingSpraying, brushing103 - 104Spray-drying, paintsRubbing104 - 105Creams & lotionsInjection molding102 - 105Polymer meltsCoating flows105 - 106PaperProcess12

Steady Shear Flow

Shear Flow: Measurement MethodsCapillary rheometerRotational rheometer Uniform simple shear flowSteady, oscillatory or creep flowRates: low (creep) to moderateVariety of tools Steady tube flow in capillary dieSteady shear flowEntry/exit effects Apparent viscosityRates: moderate to highVariety of dies14

Melt Index (ASTM D-1238, ISO 1133) Industry standard. Similar to capillary rheology except use load instead of instrumentedcrosshead and short die. Single-point measurement of flow rate:Melt index: g/10 minMelt index , viscosity For Polyethylene:T 190 oCLoad 2.16 kg (I2); 10 kg (I10); 21.16 (I21)2Rb 0.376β2R 0.0825βL/D 3.818β15

Combining Different Methods Gives Broad Flow CurvesEPDM at 190 oC16

Melt Index Correlations.Based upon modeling a melt indexer as capillary flow: 2.5I 2 Thus, the shear rate at which higher melt indexes are measured is greater. Thestress correspondingly increases with the MI load.5Viscosity (poise)10I42I1 MI30 MI101010001000.1I1102I10100 -1 1000MeltIndexWeight(kg)Shear 3 x 105430.296I554.47 x 105990.683I10108.94 x 1051981.37I2121.61.93 x 1064292.96410Shear Rate (s )17

Shear Flow: Melt Fracture at High Shear Rates, Capillary FlowSmoothSurface Melt Fracture Gross Melt Fracture18

Effect of Molecular Weight on Zero Shear ViscosityPolyethylene100,000Mw dependency h0 as Mw 3.4 Above Mw,cr: π0 πππ€10,000Viscosity (cP) 149 oCSlope 3.41,000k f(T)Mw,cr depends on polymer type100Slope 11011,000 Below Mw,cr:10,000π0 πππ€100,000Weight Average Molecular Weight, Mw (g/mol)19

Shear Flow: Effect of Polymer PropertiesMolecular Weight and h0Polymer architecture and hLLDPE w/ LCBCGC7106105h0(190 C), Pa sComplex Viscosity (poise)1. h0 increases with LCB2. Shear thinning increases with LCB510Linear10410h0 M w 2.29 10-15a 3.65 0.083102101HDS setHD set100-15-14100.013.65 0.08h0 2.29 10 (Mw)95% confidence limits10100.1110Frequency (rad/s)10024 5641023 4 563 4 56510Mw, g/mol[Karjala et al., J. Appl. Polym. Sci., 119, 636-646 (2011)]20

Shear Flow: Effect of Polymer PropertiesResinNMRGPCGPCh 0 (creep),LCBMwg/molM w/M nPa s/1000CLCB as low as 0.005 is easilydetected for resins withMw 110,000 g/mol[Karjala et al., J. .096.375.558.648.858.211.0310.02190 9,918Sensitive to identify 75.550.892.113.400.992.2521

Oscillatory Shear Flow

Shear Flow RheometersParallel platesCone and plateh(r) One part rotating at rad/s, torque M Steady or oscillatory shear flow Small amplitude oscillatory flowVh(r)23

Small Amplitude Oscillatory Shear Flow Oscillatory (dynamic, sinusoidal) deformation ( 0, ) 0: maximum amplitude, typically a small deformation : angular frequency Response: sinusoidal stress (s0, ) at a radial distance : phase angle Measure for viscoelasticity90 : viscous liquid0 : elastic solidStrain, time, tStress, s* Use: to study structured materials without disturbing the structure proxy for steady shear flow (Cox-Merz rule)24

LDPE 621 (2.3 MI) 190 C Ares-2 5% strainOscillatory Shear Flow10)Eta* ([Pa-s]55.050.045.0LDPE 621 (2.3 MI) 190 C Ares-2 5% strain10210540.0-110010110 2)Freq [rad/s]104)G" ([Pa]60.010 3)1010 3G' ([Pa] Polymer melts Viscoelastic materials Structured materials65.0PhaseAngle ([ ]h*: complex viscosityGβ: Storage modulus (elastic)Gβ: Loss modulus (viscous) tan Gβ/G: damping factor Typical use:75.070.0 Properties measured: 410 210 -110 010 110 2Freq [rad/s]25

Oscillatory Shear g Typical liquid- Frequency dependent- Gβ Gβlog Typical solid- Frequency independent- Gβ Gβ26

Oscillatory Shear FlowG GβTypically measured rangeModulus ar frequency (log)Polymer behaviorSmall scale motions27

van Gurp - Palmen (vGP) Plot ( G* ) Impression of sample topology/ morphology Verify TTS Reduced vGP plot ( G* /GN0) Polymer topology Across chemistries28

Extensional Rheology

Uniaxial Elongational Flow Devices Rotating drums on rotational rheometers Different vendors, different names EVF, SER, UXF, Homogeneous deformation Only for high viscosity materials sample should not sag Limited to relatively low elongation rates Max. H 4 Sources of error: slip, necking, sagging30

Extensional Flow: Strain Hardening1 MI LDPE150 oC Strain-hardening if hE LVE envelopeπ Strain-hardening factor ππ»πΉ πΈ3ππ Strain-hardening required to withstandflow in stretching processes LCB contributes heavily31

Extensional Flow: Melt Strength by Rheotens Fiber is drawn from a die at increasing pulloff velocity (increasing force) until filamentbreaksCan reach high stretch rates, processingTransient, non-uniform stretching Melt strengthDrawabilityDraw resonance32

Extensional Flow: Melt Strength3025190 oC28190 oC26LDPE-0.18MI202422 cN20LDPE-0.65MIMelt Strength (cN)Melt Strength (cN)22LDPE-1.85MI181614 cN14121088 00350400Velocity (mm/s)4500102030405060708090100% LDPE (in LLDPE-1 or DOWLEXTM 2045G)[Karjala et al., SPE ANTEC Proceedings (2016)] Effect of Mw (MI) Effect of polymer structure33 Trademark of The Dow Chemical Company (βDowβ) or an affiliated company of Dow

Concluding Remarks

Summary35

References General rheology references T.G. Mezger, Applied Rheology, Anton Paar GmbH (2015).F. A. Morrison, Understanding Rheology, Oxford (2001).R.G. Larson, The Structure and Rheology of Complex Fluids, Oxford (1998).C. W. Macosko, Rheology: Principles, Measurements, and Applications, VCH (1994).A.A. Collyer et al., Rheological Measurement, Springer (1993).J. E. Mark et al., Physical Properties of Polymers, 2nd Ed., ACS (1993).J. M. Dealy et al., Melt Rheology and Its Role in Plastics Processing, Wiley (1990).H. A Barnes et al., An Introduction to Rheology, Elsevier (1989).J. M. Dealy, Rheometers for Molten Plastics, SPE (1982).36

References Continued Detailed (classic references) R.B. Bird, R.C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Wiley (1987).J. D. Ferry, Viscoelastic Properties of Polymers, 3rd Ed., Wiley (1980). Fluid mechanics M. M. Denn, Process Fluid Mechanics, Prentice-Hall (1980).R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, Wiley (1960). Polymer Processing Z. Tadmor and C. G. Gogos, Principles of Polymer Processing, Wiley (1979).S. Middleman, Fundamentals of Polymer Processing, McGraw-Hill (1977). Journals/Proceedings J. Applied Polymer Science, J. Polymer Science, J. Rheology, Rheologica Acta,Macromolecules, Polymer Engineering and Science, Applied Rheology Society of Plastics Engineers ANTEC Proceedings37

Acknowledgements: Teresita Kashyap of The Dow Chemical CompanyQuestions, feel free to contact either presenter at:Teresa Karjala (tpkarjala@dow.com)Sylvie Vervoort (svervoort@dow.com)

Rheology with Application to Polyolefins Teresa Karjala, Ph.D. and Dr. Ir. Sylvie Vervoort . to study structured materials without disturbing the structure . F. A. Morrison, Understanding Rheology, Oxford (2001). R.G. Larson, The Structure and Rheology of Complex Fluids, Oxford (1998).

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