Applications Of Rheology To Polymers
Applications of Rheologyto PolymersChris MacoskoUniversity of MinnesotaDepartment of Chemical Engineering andMaterials ScienceFor TA InstrumentsEden Prairie MNApril 12, 20191
Rheology Short Courses:Stanford University, June 11-13, hort-course/KU Leuven, September 2-6, 2019, with ity of Minnesota, June 2020, with labhttps://rheology.cems.umn.edu/2
Polymer RheologyMolecular Structure§ MW and MWD§ Chain Branching and Cross-linking§ Thermosets§ Single or Multi-Phase Structure§ Solid polymersViscoelastic Properties§ Small strain (linear viscoelastic)§ Steady shearing§ ExtensionProcessability & Product PerformanceTAINSTRUMENTS.COM
Melt Rheology: MW Effect on Zero Shear Viscosity§§log ho§Sensitive to Molecular Weight, MWFor Low MW (no Entanglements) h0 is proportional to MWFor MW Critical MWc, h0 is proportional to MW3.4h0 K Mw3.4MWclog MWh0 K Mw 3.4Ref. Graessley, Physical Properties of Polymers, ACS, c 1984.TAINSTRUMENTS.COM
Influence of MW on ViscosityThe zero shear viscosity increases with increasing molecular weight.TTS is applied to obtain the extended frequency range.710SBR Mw [g/mol]130 000230 000320 000430 00065104Zero Shear Viscosityho [Pa s]Viscosity h* [Pa s]1010310Zero ShearViscosity106Slope 3.08 /- 0.39102The high frequencybehavior(slope -1) isindependent of themolecular weight510000010Molecilar weight Mw cy w aT [rad/s]TAINSTRUMENTS.COM
Influence of MWD on ViscosityLog Viscosity (Pa.s)§A Polymer with a broad MWD exhibits non-Newtonian flowat a lower rate of shear than a polymer with the same h0,but has a narrow MWD.Narrow MWDBroad MWDLog Shear Rate (1/s)TAINSTRUMENTS.COM
Influence of MW on G‘ and G“The G‘ and G‘‘ curves are shifted to lower frequencywith increasing molecular weight.6105Modulus G', G'' [Pa]10410SBR Mw [g/mol]G' 130 000G'' 130 000G' 430 000G'' 430 000G' 230 000G'' 230 w [rad/s]Straing [%]TAINSTRUMENTS.COM
Influence of MWD on G‘ and G“6Modulus G', G'' [Pa]10510§ The maximum in G‘‘ is a goodindicator of the broadness of thedistribution410SBR polymer meltG' 310 000 broadG" 310 000 broadG' 320 000 narrowG" 320 000 quency waT [rad/s]Higher crossover frequency : lower MwHigher crossover Modulus: narrower MWD(note also the slope of G” at lowfrequencies – narrow MWD steeper slope)TAINSTRUMENTS.COM
Mixture of Linear Homogeneous ChainsRelaxation by Reptation(Brownian diffusive motion of the chain)MeReptation!reptation – PG deGennesNobel Physics 19919
Fluorescent DNAattached to a PS bead in a sea of DNA10S. Chu et al. Science, 264, 822 (1994)Nobel Physics 1997
7107G"G'(Pa)(Pa)G'(Pa)10661010(b)(a)1056510(a) 20,000to 20GN rMRT/Meo10PBD, linearN 9.12enPBD,linear1 N 19.44Nen 9.12enN 42.75Nen 19.44enN 88.59Nen 42.7551 / w λ longest relaxation(data from(datafrom eBaumgaertel3.4Baumgaerteleal.1992)N 88.59468dal. 1992)10101010441010410100010001000100!τ L !enen0.01G"(Pa)G"(Pa)1106(b)106510(b)100ω (sec-1)M 20,000 to 2M 20,000 to 2510 4104101000100010040.011001100100.011-1)4100 ω (sec 10ω (sec-1)6106103.4τd L3.4τd LBaumgaertel, Schausberger, Winter8Rheol. Acta,29, 400 (1990)1081011
test chain!zeus.plmsc.psu.edu/ maniasSingle Reptationl1 longest relaxationb æ M ö l1 z ççkT è M o ø221.4æM ö ççè Me øG(t ) GN exp( -t / l1 )oc1g (T - Tg )logz log z g - gzeus.plmsc.psu.edu/ manias!c2 T - Tgsegment frictionGN rRT/M eoh ò G (t )dtDouble reptation, Tsenoglou mixing ruleG (t ) (Siji Gi (t ) )1/2 212C. Tsenoglou, Macromolecules, 24, 1762 (1991)
Single ReptationDouble355K71KNarrow MWDpolybutadieneF 0.88F 0.77Bimodal blendF 0.6413J. des Cloizeaux, Macromolecules 23, 3992 (1990)
400K PS (M1) 1% of 4,000K (M2)4xG’S. H. Wasserman and W. W. Graessley, 14J.Rheol. 36, 543 (1992)
Orchestrator: MWD from G’, G”(or vice versa) via double reptation400K PSGPCG”G’15
Orchestrator: MWD from G’, G” via double reptation400K PS 1% 12MGPC16
Orchestrator: MWD from G’, G” via double reptation400K PS 2% 12M17
Orchestrator: MWD from G’, G” via double reptation400K PS 4% 12MGPC18
Extrusion of HDPE tubingHDPE pipe surface defectsExtensive dieswell,oT 220 C10105104410G' rough surfaceG' smooth surfaceh* rough surfaceh* smooth surface30.1110310Complex viscosity h* [Pa s]Modulus G' [Pa]105high G’ value atlow frequencycauses surfacedefects duringextrusion ofHDPE100Frequency w [rad/s]SEC or MFI measurements did not reveal the cause of the problemTA Applications Note AAN013 Understanding Rheology of Thermoplastics19
The Cox-Merz Rule For materials that exhibit wall slip or edge fracture, one alternative way toobtain viscosity information over shear is to use the Cox-Merz rule Cox-Merz “rule” is an empirical relationship. It was observed that in manypolymeric systems, the steady shear viscosity plotted against shear rateis correlated with the complex viscosity plotted against frequencyDynamic frequency sweeph* (Pa.s) w (rad/s)Steady state flowh (Pa.s) 𝛾̇ (1/s)TAINSTRUMENTS.COM
Polymer Melt Thermal StabilityPolyester Temperature stabilityModulus G' [Pa]10Temperature stabilitygoodpoor5250225102004Temperature T [ C]275Determines if propertiesare changing over thetime of testing§ Degradation§ Molecular weightbuilding§ Crosslinking175-2024681012141618Time t [min]Important, but often overlooked!TAINSTRUMENTS.COM
Polymer RheologyMolecular Structure§ MW and MWD§ Chain Branching and Cross-linking§ Thermosets§ Single or Multi-Phase Structure§ Solid polymersViscoelastic Properties§ Small strain (linear viscoelastic)§ Steady shearing§ ExtensionProcessability & Product PerformanceTAINSTRUMENTS.COM
Extensional Flows²Where do extensional flows occur?PolymGasBubbleerGasBubbleFiber nComplex flow during process –shear extensional flowDroplet Formation(Inkjet Printing, Atomization)23
24
Extensional FlowsHow are they different than shear ?ShearExtensionMore alignment than shear&No rotation25
Dilute Rods, CoilsStiff particles orient at small strainsFlexible – high molecular weight polymers need larger strains to stretch and26 orientGupta, Ngyen, & Sridhar (1998).
Extensional Viscosity Measurements Non linear elongation flow is more sensitive for some structure elements(e.g. branching ) than shear flows Many processing flows are elongation flows. Extensional viscositymeasurements can be used to help predict processabilityTAINSTRUMENTS.COM
EVF, SER - Extensional Viscosity FixturesPolymer Melts"Elongation Viscosity hE [Pa s]106 Lupolen 1810HoT 150 C101010 5 4ARES-EVF0.01 1/s0.1 1/s10 1/s1 1/s310-210-1100101Time t [s]RMEOriginal Meissner1s-10.1 s-10.03 s-10.01 s-10.001 s-1shear viscosity----- Lodge102103SsoTECc1.5” V(1.5”
LLDPE (Low branching)106105he ([Pa-s])10410LLDPE, T 130 o C0.01 s -10.1 s -11 s -13 s -110 s -1[Steady Shear Viscosity * 3]310210110-2Warning: Overlay units don't match10-1100101102103timee [s]TAINSTRUMENTS.COM
LDPE (High branching)106105104he ([Pa-s])LDPE, T 150 o C0.003 s - 10.01 s - 10.03 s - 10.1 s - 10.3 s - 11 s- 13 s- 110 s - 130 s - 1[Steady Shear Viscosity * 3]10310210110-210-1Warning: Overlay units don't match, Frequency100101102103timee [s]TAINSTRUMENTS.COM
TAINSTRUMENTS.COM
Adhesive Tack Testing Tack testing method: ASTM D2979 Use 8mm parallel plate, axial tensile at 0.1mm/sec The maximum force required to pull the plate away is defined as thesample’s tackiness.Crosslinked PSA: Non-Crosslinked PSA:Adhesive failureCohesive failureTAINSTRUMENTS.COM
Polymer RheologyMolecular Structure§ MW and MWD§ Chain Branching and Cross-linking§ Thermosets§ Single or Multi-Phase Structure§ Solid polymersViscoelastic Properties§ Small strain (linear viscoelastic)§ Steady shearing§ ExtensionProcessability & Product PerformanceTAINSTRUMENTS.COM
Thermosetting Polymers§ Thermosetting polymers are perhaps the mostchallenging samples to analyze on rheometersas they challenge all instrument specificationsboth high and low.§ The change in modulus as a sample curescan be as large as 7-8 decades and changecan occur very rapidly.TAINSTRUMENTS.COM
Structural Development During CuringGel pointTAINSTRUMENTS.COM
At the Gel Point§Molecular weight Mw goes to infinity§§§System loses solubilityZero shear viscosity goes to infinityEquilibrium Modulus is zero and starts to riseto a finite number beyond the gel pointNote: For most applications, gel point can beconsidered as when G’ G” and tan d 1TAINSTRUMENTS.COM
Measuring the gel (pp)c!0HookeanSolidzG:(pp)ec!s, z predicted from theoryC. P. Lusignan et al. (1999)η0Ge@ GP Rheological properties intermediatebetween liquid and solidpc0“Sol”p1“Gel” Wetting properties of the liquid Cohesive strength of the solid High adhesion strength (tackiness)Insoluble gelSol fraction37
Steady State measurements -sh:(pp)c!0HookeanSolidzG:(pp)ec!s, z predicted from theoryC. P. Lusignan et al. (1999)η0Geλmax,chem !"( p - pc )- s /(1- nc ) for p pc( pc - p)- z /ncfor pc pznc z s0pcpη0 , G e time to reach steady state,need to extrapolatee.g. nanocomposites1assuming symmetry(typo in H. H. Winter (2003))η0 Network gets brokenapparent gelation delay or RGapparent gelation pointGe Detection limit38
Crosslinking Polymerization to form PolyurethaneHOOHOCN—NCO Ge lim G 'w 0OHr [NCO]/[OH] stoichiometric imbalance(assume complete conversion)h0 lim (G '' w )w 039T. Nicolai, H. Randrianantoandro, F. Prochazka, and D. Durand, Macromolecules Sci, 30 (1997), 5897.
Power Law BehaviorG(t) St - nc for l0,chem t (infinite sample)chemical gelsG(t) St - nc for l0, phys t lmax, physphysical gelsPDMSnc 0.5H. H. Winter (2003)H. H. Winter and F. Chambon (1986)40
G’ G” only when nc 0.5G’ G’’empiricism of Y. M. Tung and P. J. Dynes (1982)PDMSnc 0.5Reaction time (min)F. Chambon and H. H. Winter (1985)41
Epoxy-Amine Crosslinking: Monomersdiglycidyl ether of bisphenol A(DGEBA)diamino-diphenyl sulfone(DDS)application: F-117 radar invisibilityBidstrup and Macosko, J Polym Sci, 28 (1990), 691.42
Epoxy-Amine ChemistryReaction with an epoxide group to form a secondary amineReaction with another epoxide group to form a tertiary amineReaction of the formed hydroxyl with an epoxide group43
Measure Epoxy-Amine Kineticsconversion of epoxy groupsda Ae Ea RT a ndt44
Structural Development During CuringGel pointTAINSTRUMENTS.COM
Typical Steady Shear DataData obtained from four experiments,each set measured at a different shearratetgelHow find gel time?η 104 Pa·sor1/η 0Bidstrup and Macosko, J Polym Sci, 28 (1990), 691.1/htgeltime46
Gel Time fromG’ G”tgelComparison ofDynamic η*and Steady ηoViscositiesh * (G '2 G "2 )1/2 / w47Bidstrup and Macosko, J Polym Sci, 28 (1990), 691.
Bidstrup and Macosko, J Polym Sci, 28 (1990), 691.48
Correlation of Viscosity with StructureViscosity(Pa-sec)Light ScatteringRecursive TheoryViscosity(Pa-sec)49
Viscosity(Pa-sec)Viscosity rise versusconversion of epoxidegroups at stoichiometricratios ranging from 0.6 to2.0.Bidstrup and Macosko, J Polym Sci, 28 (1990), 691.Viscosity rise vs. molecularweight of the averagelongest linear chain atstoichiometric ratios rangingfrom 0.6 to 2.0. Themolecular weight of thelongest linear chain iscalculated using therecursive theory assuming a 0.2.50
51
52Bidstrup and Macosko, J Polym Sci, 28 (1990), 691.
Curing Analysis: Isothermal CuringTA Instruments1000000G'5 minG"10000010000010000Gel Point: G' G"t 330 time (s)800.01000G'' (Pa)G' (Pa)1000010000001.0001200TAINSTRUMENTS.COM
Gel Point using Tan DeltaTAINSTRUMENTS.COM
Isothermal Curing140 C 135 C120 C125 CG’ (MPa)145 C130 CTire Compound:Effect of Curing TemperatureTime (min)TAINSTRUMENTS.COM
Temperature Ramp CuringSurface MasterÒ 905Crossover technique: Cubic / linear (Orche)Crossover modulus: 1188.26 PaCrossover x value: 132.424 CMin y: 5.474190e1 Pa.sAt x: 122.507 CTAINSTRUMENTS.COM
UV Curing Monitor UV curing: Dynamic time sweep Measure curing time with different formulations,UV intensity and temperature Measure cured adhesive modulus1.000E91.000E81.000E7 G* (Pa)1.000E61.000E5Formulation #1Formulation #2Formulation #3Formulation #4Formulation #5UV on100001000100.010.00020.00030.00040.00050.000time (s)60.00070.00080.000TAINSTRUMENTS.COM
Curing with Controlled Humidity Silicone adhesive curing under 25 C and 10%; 60% relative humidity Higher humidity, faster curingSilicone at 10% RHSilicone at 60% RHTAINSTRUMENTS.COM
Polymer RheologyMolecular Structure§ MW and MWD§ Chain Branching and Cross-linking§ Thermosets§ Single or Multi-Phase Structure§ Solid polymersViscoelastic Properties§ Small strain (linear viscoelastic)§ Steady shearing§ ExtensionProcessability & Product PerformanceTAINSTRUMENTS.COM
Immisible Blends: Useful MorphologiesDropsLaminartoughness,1 µmsurface modificationbarrierFibersCocontinuous“Morphology withoutrheology is zoology”Richard SteinU Mass.strength, thermal expansionhigh flow, adsorbentselectrical conductivity,toughness, stiffness60Macosko, Macromol. Symp. 149, 171 (2000)
Most polymer pairs are immiscibleBut two-phase systems can have desirable properties Surface modificationDynamar (Dyneon)MB (Dow Corning)PE/PTFE, 1%PP/PDMS ToughnessHIPSABS“super tough nylon” (Dupont)styrene polymerized with PBSAN/PB latexPA6,6/EPR Gas barrierSelar (Dupont)PE/PA6,6 ProcessibilityNoryl GTX (Sabic)TPO (ExxonMobil, others)PA6/PPO/SBPP/EP Thermal expansionVectraPET/LCP61Macosko, Macromol. Symp. 149, 171 (2000)
Deformable Sphereshsg!aaGal é1 3fH ùG Gs êúë1 - 2fH ûH hs aG4(G a )(5Gd 2Gs ) (Gd - Gs )(19Gd 16Gs )40(G a )(Gd Gs ) (2Gd 3Gs )(19Gd 16Gs ) H (G a , Gd , Gs )62Palierne, Rheol. Acta, 29, 204 (1990)
10% PMMA2% PMMAin PS20% PMMA5% PMMAin PSl hs aG63Ch. Friedrich et al, J. Rheol. 39,1411 (1995)
Cocontinuous Blends non-equilibrium melt processing phase size: 1-10 μm phase extraction yieldsporous matrixLopez-Barron, Macosko Langmuir 2009, 201064
cocontinuousPDMS0PIBVinckier et al., Colloid and Surfaces. A: 150, 217 (1999)65
Application: Lubricating StripsCocontinuousstructure, containingpolyethylene oxideas lubricating agent.100 μmRazor image from Proctor and Gamble“Lubricious polymer blends comprising polyethylene oxide, polyethylene and a polylactone.” US Patent #558954566A
COCONTINUOUS BLENDS DURING COARSENINGDroplet-matrix vs. cocontinuous67Lopez-Barron; Macosko, J.Rheol. 56,1315 (2012)
Polymer RheologyMolecular Structure§ MW and MWD§ Chain Branching and Cross-linking§ Thermosets§ Single or Multi-Phase Structure§ Solid polymersViscoelastic Properties§ Small strain (linear viscoelastic)§ Steady shearing§ ExtensionProcessability & Product PerformanceTAINSTRUMENTS.COM
Testing Solids: Torsion and DMA§Torsion and DMA geometries allow solid samples to be characterizedin a temperature controlled environment§§Torsion measures G’, G”, and Tan dDMA measures E’, E”, and Tan d§§DMA mode on ARES G2 (max 50 µm amplitude)DMA mode on DHR ( max 100 µm amplitude)Torsion rectangularand cylindrical clampsE 2G(1 ν)ν : Poisson’s ratioDMA cantilever, 3-point bending and tension clampsTAINSTRUMENTS.COM
Modulus (E or G)Amorphous, Crystalline and Crosslinked sslinkingTemperatureTAINSTRUMENTS.COM
Dynamic Temp Ramp Test Measure moduli, tan δ and transitions115.2 C105.5 C105.9 CTAINSTRUMENTS.COM
How to Measure Glass TransitionG' Onset: Occurs at lowest temperature - Relates tomechanical failureG" Peak: Occurs at middle temperature - more closelyrelated to the physical property changes attributed to theglass transition in plastics. It reflects molecular processes agrees with the idea of Tg as the temperature at the onsetof segmental motion.tan d Peak: Occurs at highest temperature - usedhistorically in literature - a good measure of the "leatherlike"midpoint between the glassy and rubbery states - heightand shape change systematically with amorphous content.Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 980.TAINSTRUMENTS.COM
The Glass & Secondary TransitionsGlass Transition - Cooperative motion among a large number ofchain segments, including those from neighboring polymer chainsSecondary Transitions§ Local main-chain motion - intramolecular rotational motion ofmain chain segments four to six atoms in length§ Side group motion with some cooperative motion from the mainchain§ Internal motion within a side group without interference fromside group§ Motion of or within a small molecule or diluent dissolved in thepolymer (e.g. plasticizer)Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I.,Academic Press, Brooklyn, New York, P. 487.TAINSTRUMENTS.COM
Polycarbonate in TorsionTAINSTRUMENTS.COM
Tack and Peel of AdhesivesTack and Peel performance of a PSA§ It can be related tothe viscoelasticproperties atdifferentfrequenciesgood tack and peelBad tack and peelStorage Modulus G' [Pa]§ Bond strength isobained from peel(fast) and tack(slow) tests104peel103tack0.1110Frequency w [rad/s]Tack and peel have to be balanced for an ideal adhesiveTAINSTRUMENTS.COM
Rheology Short Courses:Stanford University, June 11-13, hort-course/KU Leuven, September 2-6, 2019, with rsity of Minnesota, June 2020, with labhttps://rheology.cems.umn.edu/TAINSTRUMENTS.COM
Thermosetting Polymers § Thermosetting polymers are perhaps the most challenging samples to analyze on rheometers as they challenge all instrument specifications both high and low. § The change in modulus as a sample cures can be as large as 7-8 decades and change can occur very rapidly.
applications. In 1997 Annika was honoured with ‘The Rheology Award of the Year’ by The Nordic Rheology Society for her skills in teaching understandable rheology, combining theoretic rheology with practical examples and demonstrations to address different learning styles. By now Annika has more than 1000 satisfied clients.
Polymers can be classified based on the source, backbone of the polymer chain, structure of polymers, composition of polymers, mode . Rheology or flow-properties of polymer nanocomposites are lie between those of the pure polymer (melt) rheology and the rheology of . supramolecular structure. It is well known that the formation of filler
Polymers Nitinol Memory Wire Amazon 14.95 Polymers Silly Putty Amazon 9.95 Polymers Plastic cups Kroger 6.54 Polymers Plastic spoons Kroger 3.69 Polymers Measuring spoons Kroger 5.45 Polymers Isopropyl alcohol Kroger 8.70 Polymers Dry Ice 21.63lbs Kroger 29.55 .
of linear telechelic polymers [4, 5], or polymers with stickers along the backbone [6-8], or linear entangled polymers with stickers along the backbone [9-11]. Our goal in this paper is to produce a "toy" (i.e. "single mode") constitutive model that captures elements of the non-linear rheology of entangled telechelic polymers, and .
polymers and the effect of branching topology on the melt rheology. The effect of linear spacers on the rheology of dendritic polymers in solution has been studied experimen-tally for branched aromatic etherimide copolymers11 and theoretically for bead-spring-dumbbell model perfectly branched polymers using Brownian dynamics techniques12
A Basic Introduction to Rheology RHEOLOGY AND VISCOSITY Introduction Rheometry refers to the experimental technique used to determine the rheological properties of materials; rheology being defined as the study of the flow and deformation of matter which describes the interrelation between force, deformation and time.
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).
PRINCIPLES OF RHEOLOGY AND ITS MEASUREMENT TECHNIQUES Viscosity – Elasticity – Viscoelasticity October 17–18, 2016 Malmö – Sweden This course is held for the 23rd time and it has been updated continuously. Course outline An introduction to rheology A general presentation of the science of rheology and its application in different .
