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Rheology Fundamentals and Instrumentation

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This document provides an outline for a course on rheology theory and applications. The course covers basics of rheology including definitions, types of rheometers, instrumentation, geometries, calibration, flow and oscillation tests, and applications. Specific topics include viscosity, linear viscoelasticity, transient testing, polymers, structured fluids, and advanced accessories. Rheology is introduced as the study of stress-deformation relationships in materials. Common geometries like parallel plates, cone and plate, and concentric cylinders are described along with considerations for choosing geometry size.

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TAINSTRUMENTS.COM TAINSTRUMENTS.COM 5KHRORJ 7KHRUDQG$SSOLFDWLRQV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM RXUVH2XWOLQH ƒ Basics in Rheology Theory ƒ TA Rheometers ƒ Instrumentation ƒ Choosing a Geometry ƒ Calibrations ƒ Flow Tests ƒ Viscosity ƒ Setting up Flow Tests ƒ Oscillation ƒ Linear Viscoelasticity ƒ Setting up Oscillation Tests ƒ Transient Testing ƒ Applications of Rheology ƒ Polymers ƒ Structured Fluids ƒ Advanced Accessories
TAINSTRUMENTS.COM TAINSTRUMENTS.COM %DVLFVLQ5KHRORJ7KHRU
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 5KHRORJ$Q,QWURGXFWLRQ Rheology: The study of stress-deformation relationships Rheology: The study of stress-deformation relationships
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 5KHRORJ$Q,QWURGXFWLRQ ƒ Rheology is the science of flow and deformation of matter ƒ The word ‘Rheology’ was coined in the 1920s by Professor E C Bingham at Lafayette College in Indiana ƒ Flow is a special case of deformation ƒ The relationship between stress and deformation is a property of the material ୗ୲୰ୣୱୱ ୗ୦ୣୟ୰୰ୟ୲ୣ ൌ ‹• ‘•‹–› ౏౪౨౛౩౩ ౏౪౨౗౟౤ ൌ ‘†—Ž—•
TAINSTRUMENTS.COM TAINSTRUMENTS.COM x y Top plate Area = A Bottom Plate Velocity = 0 Velocity = V0 Force = F Shear Stress, Pascals Viscosity, Pa⋅s t γ γ = A F = σ Shear Rate, sec-1 γ σ η = Shear Strain, % y t x ) ( = γ x(t) y 6LPSOH6WHDG6KHDU)ORZ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM r h θ Ω ߛሶ ൌ ೝ ೓ ൈΩ Ω Ω Ω ߛ ൌ ೝ ೓ ൈθ θ θ θ ߪ ൌ మ ഏೝయ ൈM Stress (σ σ σ σ) Strain (γ γ γ γ) Strain rate (ߛሶ) r = plate radius h = distance between plates M = torque (μN.m) θ = Angular motor deflection (radians) Ω= Motor angular velocity (rad/s) 7RUVLRQ)ORZLQ3DUDOOHO3ODWHV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7$,QVWUXPHQWV5KHRPHWHUV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 5RWDWLRQDO5KHRPHWHUVDW7$ Controlled Strain Dual Head SMT ARES G2 DHR Controlled Stress Single Head CMT
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 5RWDWLRQDO5KHRPHWHU'HVLJQV Applied Strain or Rotation Measured Torque (Stress) Dual head or SMT Separate motor transducer Single head or CMT Combined motor transducer Displacement Sensor Measured Strain or Rotation Applied Torque (Stress) ^ƚĂƚŝĐWůĂƚĞ Sample Direct Drive Motor Transducer Non-Contact Drag Cup Motor Static Plate Note: With computer feedback, DHR and AR can work in controlled strain/shear rate, and ARES can work in controlled stress.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM :KDWGRHVD5KHRPHWHUGR ƒ Rheometer – an instrument that measures both viscosity and viscoelasticity of fluids, semi-solids and solids ƒ It can provide information about the material’s: ƒ Viscosity - defined as a material’s resistance to deformation and is a function of shear rate or stress, with time and temperature dependence ƒ Viscoelasticity – is a property of a material that exhibits both viscous and elastic character. Measurements of G’, G”, tan δ with respect to time, temperature, frequency and stress/strain are important for characterization. ƒ A Rheometer works simply by relating a materials property from how hard it’s being pushed, to how far it moves ƒ by commanding torque (stress) and measuring angular displacement (strain) ƒ by commanding angular displacement (strain) and measuring torque (stress)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM +RZGR5KHRPHWHUVZRUN From the definition of rheology, the science of flow and deformation of matter or the study of stress (Force / Area) – deformation (Strain or Strain rate) relationships. Fundamentally a rotational rheometer will apply or measure: 1. Torque (Force) 2. Angular Displacement 3. Angular Velocity
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7RUTXHÆ Æ Æ Æ 6KHDU6WUHVV ƒ In a rheometer, the stress is calculated from the torque. ƒ The formula for stress is: σ сΜ п σ Where σ = Stress (Pa or Dyne/cm2) Μ = torque in N.m or gm.cm σ = Stress Constant ƒ The stress constant, σ, is a geometry dependent factor
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $QJXODU'LVSODFHPHQWÆ Æ Æ Æ 6KHDU6WUDLQ ƒ In a SMT Rheometer, the angular displacement is directly applied by a motor. ƒ The formula for strain is: γ сγ п θ йγ сγ п ϭϬϬ where γ = Strain γ = Strain Constant θ = Angular motor deflection (radians) ƒ The strain constant, γ, is a geometry dependent factor
TAINSTRUMENTS.COM TAINSTRUMENTS.COM γ σ θ γ σ K K M G ⋅ ⋅ = = Raw rheometer Specifications Geometric Shape Constants Constitutive Equation Rheological Parameter In Spec Describe Correctly (TXDWLRQIRU0RGXOXV The equation of motion and other relationships have been used to determine the appropriate equations to convert machine parameters (torque, angular velocity, and angular displacement) to rheological parameters.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $QJXODU9HORFLWÆ Æ Æ Æ 6KHDU5DWH ƒ In a SMT rheometer, the angular speed is directly controlled by the motor). ƒ The formula for shear rate is: where ߛሶ = Shear rate γ = Strain Constant Ω = Motor angular velocity in rad/sec ƒ The strain constant, γ, is a geometry dependent factor ߛሶ ൌ‫ܭ‬ఊ ൈ :
TAINSTRUMENTS.COM TAINSTRUMENTS.COM (TXDWLRQIRU9LVFRVLW γ σ γ σ η K K M ⋅ Ω ⋅ = = Raw rheometer Specifications Geometric Shape Constants Constitutive Equation Rheological Parameter In Spec Describe Correctly The equation of motion and other relationships have been used to determine the appropriate equations to convert machine parameters (torque, angular velocity, and angular displacement) to rheological parameters.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'LVFRYHU+EULG5KHRPHWHU6SHFLILFDWLRQV Specification HR-3 HR-2 HR-1 Bearing Type, Thrust Magnetic Magnetic Magnetic Bearing Type, Radial Porous Carbon Porous Carbon Porous Carbon Motor Design Drag Cup Drag Cup Drag Cup Minimum Torque (nN.m) Oscillation 0.5 2 10 Minimum Torque (nN.m) Steady Shear 5 10 20 Maximum Torque (mN.m) 200 200 150 Torque Resolution (nN.m) 0.05 0.1 0.1 Minimum Frequency (Hz) 1.0E-07 1.0E-07 1.0E-07 Maximum Frequency (Hz) 100 100 100 Minimum Angular Velocity (rad/s) 0 0 0 Maximum Angular Velocity (rad/s) 300 300 300 Displacement Transducer Optical encoder Optical encoder Optical encoder Optical Encoder Dual Reader Standard N/A N/A Displacement Resolution (nrad) 2 10 10 Step Time, Strain (ms) 15 15 15 Step Time, Rate (ms) 5 5 5 Normal/Axial Force Transducer FRT FRT FRT Maximum Normal Force (N) 50 50 50 Normal Force Sensitivity (N) 0.005 0.005 0.01 Normal Force Resolution (mN) 0.5 0.5 1 ,ZͲϭ ,ZͲϯ ,ZͲϮ DHR - DMA mode (optional) Motor Control FRT Minimum Force (N) Oscillation 0.1 Maximum Axial Force (N) 50 Minimum Displacement (μm) Oscillation 1.0 Maximum Displacement (μm) Oscillation 100 Displacement Resolution (nm) 10 Axial Frequency Range (Hz) 1 x 10-5 to 16
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $5(6*5KHRPHWHU 6SHFLILFDWLRQV Force/Torque Rebalance Transducer (Sample Stress) Transducer Type Force/Torque Rebalance Transducer Torque Motor Brushless DC Transducer Normal/Axial Motor Brushless DC Minimum Torque (μN.m) Oscillation 0.05 Minimum Torque (μN.m) Steady Shear 0.1 Maximum Torque (mN.m) 200 Torque Resolution (nN.m) 1 Transducer Normal/Axial Force Range (N) 0.001 to 20 Transducer Bearing Groove Compensated Air Driver Motor (Sample Deformation) Maximum Motor Torque (mN.m) 800 Motor Design Brushless DC Motor Bearing Jeweled Air, Sapphire Displacement Control/ Sensing Optical Encoder Strain Resolution (μrad) 0.04 Minimum Angular Displacement (μrad) Oscillation 1 Maximum Angular Displacement (μrad) Steady Shear Unlimited Angular Velocity Range (rad/s) 1x 10-6 to 300 Angular Frequency Range (rad/s) 1x 10-7 to 628 Step Change, Velocity (ms) 5 Step Change, Strain (ms) 10 Orthogonal Superposition (OSP) and DMA modes Motor Control FRT Minimum Transducer Force (N) Oscillation 0.001 Maximum Transducer Force (N) 20 Minimum Displacement (μm) Oscillation 0.5 Maximum Displacement (μm) Oscillation 50 Displacement Resolution (nm) 10 Axial Frequency Range (Hz) 1 x 10-5 to 16
TAINSTRUMENTS.COM TAINSTRUMENTS.COM *HRPHWU2SWLRQV Parallel Plate Cone and Plate Concentric Cylinders Torsion Rectangular Very Low to Medium Viscosity Very Low to High Viscosity Very Low Viscosity to Soft Solids Solids Water to Steel
TAINSTRUMENTS.COM TAINSTRUMENTS.COM KRRVLQJD*HRPHWU6L]H ƒ Assess the ‘viscosity’ of your sample ƒ When a variety of cones and plates are available, select diameter appropriate for viscosity of sample ƒ Low viscosity (milk) - 60mm geometry ƒ Medium viscosity (honey) - 40mm geometry ƒ High viscosity (caramel) – 20 or 25mm geometry ƒ Examine data in terms of absolute instrument variables torque/displacement/speed and modify geometry choice to move into optimum working range ƒ You may need to reconsider your selection after the first run!
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 3DUDOOHO3ODWH Strain Constant: Stress Constant: (to convert angular velocity, rad/sec, to shear rate, 1/sec, at the edge or angular displacement, radians, to shear strain (unitless) at the edge. The radius, r, and the gap, h, are expressed in meters) (to convert torque, N⋅m, to shear stress at the edge, Pa, for Newtonian fluids. The radius, r, is expressed in meters) ŝĂŵĞƚĞƌ;Ϯ⋅ ⋅ ⋅ ⋅ƌͿ 'ĂƉ;ŚͿ ‫ܭ‬ఙ ൌ ଶ గ௥య ‫ܭ‬ఊ ൌ ௥ ௛
TAINSTRUMENTS.COM TAINSTRUMENTS.COM :KHQWRXVH3DUDOOHO3ODWHV ƒ Low/Medium/High Viscosity Liquids ƒ Soft Solids/Gels ƒ Thermosetting materials ƒ Samples with large particles ƒ Samples with long relaxation time ƒ Temperature Ramps/ Sweeps ƒ Materials that may slip ƒ Crosshatched or Sandblasted plates ƒ Small sample volume
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 3ODWH'LDPHWHUV 20 mm 40 mm 60 mm Shear Stress ߪ ൌ ‫ܯ‬ ʹ ߨ‫ݎ‬ଶ As diameter decreases, shear stress increases
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 3ODWH*DSV 2 mm 1 mm 0.5 mm ߛሶ ൌ ȳ ‫ݎ‬ ݄ As gap height decreases, shear rate increases Shear Rate Increases
TAINSTRUMENTS.COM TAINSTRUMENTS.COM (IIHFWLYH6KHDU5DWHYDULHVDFURVVD3DUDOOHO3ODWH ƒ For a given angle of deformation, there is a greater arc of deformation at the edge of the plate than at the center ߛ ൌ ݀‫ݔ‬ ݄ dx increases further from the center, h stays constant
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6KHDU5DWHLV1RUPDOL]HGDFURVVDRQH ƒ The cone shape produces a smaller gap height closer to inside, so the shear on the sample is constant h increases proportionally to dx, γ is uniform ߛ ൌ ݀‫ݔ‬ ݄
TAINSTRUMENTS.COM TAINSTRUMENTS.COM RQHDQG3ODWH Strain Constant: Stress Constant: (to convert angular velocity, rad/sec, to shear rate. 1/sec, or angular displacement, radians, to shear strain, which is unit less. The angle, β, is expressed in radians) (to convert torque, N⋅m, to shear stress, Pa. The radius, r, is expressed in meters) Truncation (gap) ‫ܭ‬ఊ ൌ ଵ ఉ ‫ܭ‬ఙ ൌ ଷ ଶగ௥య Diameter (2⋅ ⋅ ⋅ ⋅r)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM :KHQWRXVHRQHDQG3ODWH ƒ Very Low to High Viscosity Liquids ƒ High Shear Rate measurements ƒ Normal Stress Growth ƒ Unfilled Samples ƒ Isothermal Tests ƒ Small Sample Volume
TAINSTRUMENTS.COM TAINSTRUMENTS.COM RQH'LDPHWHUV 20 mm 40 mm 60 mm Shear Stress As diameter decreases, shear stress increases ߪ ൌ ‫ܯ‬ ͵ ʹߨ‫ݎ‬ଷ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM RQH$QJOHV 0.5 ° Shear Rate Increases ߛሶ ൌ ȳ ͳ ߚ As cone angle decreases, shear rate increases 1 ° 2 °
TAINSTRUMENTS.COM TAINSTRUMENTS.COM /LPLWDWLRQVRIRQHDQG3ODWH Cone Plate Truncation Height = Gap Typical Truncation Heights: 1° degree ~ 20 - 30 microns 2° degrees ~ 60 microns 4° degrees ~ 120 microns Gap must be or = 10 [particle size]!!
TAINSTRUMENTS.COM TAINSTRUMENTS.COM RUUHFW6DPSOH/RDGLQJ × Under Filled sample: Lower torque contribution × Under Filled sample: Lower torque contribution 9 Correct Filling 9 Correct Filling × Over Filled sample: Additional stress from drag along the edges × Over Filled sample: Additional stress from drag along the edges × Under Filled sample: Lower torque contribution 9 Correct Filling × Over Filled sample: Additional stress from drag along the edges
TAINSTRUMENTS.COM TAINSTRUMENTS.COM RQFHQWULFOLQGHU Strain Constant: (to convert angular velocity, rad/sec, to shear rate, 1/sec, or angular displacement, radians, to shear strain (unit less). The radii, r1 (inner) and r2 (outer), are expressed in meters) (to convert torque, N⋅m, to shear stress, Pa. The bob length, l, and the radius, r, are expressed in meters) Stress Constant: ‫ܭ‬ఙ ൌ ଵ ସగ௟ ‫ݎ‬ͳ ଶ ൅ ‫ݎ‬ʹ ଶ ‫ݎ‬ʹ ଶ‫ݎ‬ͳ ଶ ‫ܭ‬ఊ ൌ ‫ݎ‬ͳ ଶ ൅ ‫ݎ‬ʹ ଶ ‫ݎ‬ʹ ଶ‫ݎ‬ͳ ଶ *Note including end correction factor. See TRIOS Help *
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'RXEOH:DOO Strain Constant: Stress Constant: ƒ Use for very low viscosity systems (1 mPas) r1 r2 r3 r4 ARES Gap Settings: standard operating gap DW = 3.4 mm narrow operating gap DW = 2.0 mm Use equation Gap 3 × (R2 –R1) ‫ܭ‬ఊ ൌ ‫ݎ‬ͳ ଶ ൅ ‫ݎ‬ʹ ଶ ‫ݎ‬ʹ ଶ െ‫ݎ‬ͳ ଶ ‫ܭ‬ఙ ൌ ௥ଵ మା௥ଶ మ ସగ௛ή௥ଶ మ ௥ଵ మା௥ଷ మ h
TAINSTRUMENTS.COM TAINSTRUMENTS.COM :KHQWR8VHRQFHQWULFOLQGHUV ƒ Low to Medium Viscosity Liquids ƒ Unstable Dispersions and Slurries ƒ Minimize Effects of Evaporation ƒ Weakly Structured Samples (Vane) ƒ High Shear Rates
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 3HOWLHU RQFHQWULFOLQGHUV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7RUVLRQ5HFWDQJXODU w = Width l = Length t = Thickness Advantages: ƒ High modulus samples ƒ Small temperature gradient ƒ Simple to prepare Disadvantages: ƒ No pure Torsion mode for high strains ‫ܭ‬ఊ ൌ ‫ݐ‬ ݈ ͳ െ ͲǤ͵͹ͺ ௧ ௪ ଶ ‫ܭ‬ఛ ൌ ͵ ൅ ଵǤ଼ ௪ ‫ݓ‬ ή ‫ݐ‬ଶ Torsion cylindrical also available
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7RUVLRQDQG'0$0HDVXUHPHQWV ƒ Torsion and DMA geometries allow solid samples to be characterized in a temperature controlled environment ƒ Torsion measures G’, G”, and Tan δ ƒ DMA measures E’, E”, and Tan δ ƒ ARES G2 DMA is standard function (50 μm amplitude) ƒ DMA is an optional DHR function (100 μm amplitude) Rectangular and cylindrical torsion DMA 3-point bending and tension (cantilever not shown)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM *HRPHWU2YHUYLHZ Geometry Application Advantage Disadvantage Cone/plate fluids, melts viscosity 10mPas true viscosities temperature ramp difficult Parallel Plate fluids, melts viscosity 10mPas easy handling, temperature ramp shear gradient across sample Couette low viscosity samples 10 mPas high shear rate large sample volume Double Wall Couette very low viscosity samples 1mPas high shear rate cleaning difficult Torsion Rectangular solid polymers, composites glassy to rubbery state Limited by sample stiffness DMA Solid polymers, films, Composites Glassy to rubbery state Limited by sample stiffness (Oscillation and stress/strain)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 5KHRPHWHUDOLEUDWLRQVDQG 3HUIRUPDQFH9HULILFDWLRQ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM '+5² DOLEUDWLRQ2SWLRQV ƒ Instrument Calibrations ƒ Inertia (Service) ƒ Rotational Mapping ƒ Geometry Calibrations: ƒ Inertia ƒ Friction ƒ Gap Temperature Compensation ƒ Rotational Mapping ƒ Details in Appendix #4
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $5(6*² DOLEUDWLRQ2SWLRQV ƒ Instrument Calibrations ƒ Transducer ƒ Temperature Offsets ƒ Phase Angle (Service) ƒ Measure Gap Temperature Compensation ƒ Geometry Calibrations: ƒ Compliance and Inertia (from table) ƒ Gap Temperature Compensation ƒ Details in Appendix #4
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9HULI5KHRPHWHU3HUIRUPDQFH ƒ Rheometers are calibrated from the factory and again at installation. ƒ TA recommends routine validation or confidence checks using standard oils or Polydimethylsiloxane (PDMS). ƒ PDMS is verified using a 25 mm parallel plate. ƒ Oscillation - Frequency Sweep: 1 to 100 rad/s with 5% strain at 30°C ƒ Verify modulus and frequency values at crossover ƒ Standard silicone oils can be verified using cone, plate or concentric cylinder configurations. ƒ Flow – Ramp: 0 to 88 Pa at 25°C using a 60 mm 2° cone ƒ Service performs this test at installation
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 3'06)UHTXHQF6ZHHS5HVXOWV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM /RDG6WDQGDUG2LO ƒ Set Peltier temperature to 25°C and equilibrate. ƒ Zero the geometry gap ƒ Load sample ƒ Be careful not to introduce air bubbles! ƒ Set the gap to the trim gap ƒ Lock the head and trim with non-absorbent tool ƒ Important to allow time for temperature equilibration. ƒ Go to geometry gap and initiate the experiment.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )ORZ5DPS² 6WDQGDUG2LO 6HUYLFH7HVW
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6HWWLQJXS5KHRORJLFDO([SHULPHQWV )ORZ7HVWV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ Viscosity is… ƒ “lack of slipperiness” ƒ synonymous with internal friction ƒ resistance to flow 9LVFRVLW'HILQLWLRQ ƒ The Units of Viscosity are … ƒ SI unit is the Pascal.second (Pa.s) ƒ cgs unit is the Poise ƒ 10 Poise = 1 Pa.s ƒ 1 cP (centipoise) = 1 mPa.s (millipascal second)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM (TXDWLRQIRU9LVFRVLW γ σ γ σ η K K M ⋅ Ω ⋅ = = Raw rheometer Specifications Geometric Shape Constants Constitutive Equation Rheological Parameter In Spec Describe Correctly
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7SLFDO9LVFRVLW9DOXHV 3DV 6 Asphalt Binder -------------- 6 Polymer Melt ---------------- 6 Molasses --------------------- 6 Liquid Honey ---------------- 6 Glycerol ---------------------- 6 Olive Oil ---------------------- 6 Water ------------------------- 6 Air ----------------------------- 100,000 1,000 100 10 1 0.01 0.001 0.00001 Need for Log scale
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 1HZWRQLDQDQG1RQ1HZWRQLDQ)OXLGV ƒ Newtonian Fluids - constant proportionality between shear stress and shear-rate ƒ Non-Newtonian Fluids - Viscosity is time or shear rate dependent ƒ Time: ƒ At constant shear-rate, if viscosity ƒ Decreases with time – Thixotropy ƒ Increases with time - Rheopexy ƒ Shear-rate: ƒ Shear - thinning ƒ Shear - thickening
TAINSTRUMENTS.COM TAINSTRUMENTS.COM σ, Pa γ ,1/s or σ, Pa η, Pa.s γ ,1/s Ideal Yield Stress (Bingham Yield) KDUDFWHULVWLF'LDJUDPVIRU1HZWRQLDQ)OXLGV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM γ ,1/s 105 103 101 10-1 10-6 10-4 10-2 100 102 104 σ, Pa ,GHDOLHOG6WUHVV %LQJKDPSODVWLF 105 103 101 10-1 10-6 10-4 10-2 100 102 104 η, Pa.s ,1/s 105 103 101 10-1 10-1 10-0 10-1 102 103 η, Pa.s σ, Pa KDUDFWHULVWLF'LDJUDPVIRU6KHDU7KLQQLQJ)OXLGV ƒ Another name for a shear thinning fluid is a pseudo-plastic
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Log η, Pa.s Log ߛሶ, 1/s KDUDFWHULVWLF'LDJUDPVIRU6KHDU7KLFNHQLQJ)OXLGV ƒ Dilatant material resists deformation more than in proportion to the applied force (shear-thickening) ƒ Cornstarch in water or sand on the beach are actually dilatant fluids, since they do not show the time- dependent, shear-induced change required in order to be labeled rheopectic
TAINSTRUMENTS.COM TAINSTRUMENTS.COM time Viscosity Thixotropic Rheopectic Shear Rate = Constant 1RQ1HZWRQLDQ7LPH'HSHQGHQW)OXLGV ƒ Rheopectic materials become more viscous with increasing time of applied force ƒ Higher concentration latex dispersions and plastisol paste materials exhibit rheopectic behavior ƒ Thixotropic materials become more fluid with increasing time of applied force ƒ Coatings and inks can display thixotropy when sheared due to structure breakdown
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )ORZ([SHULPHQWV ƒ Flow Experiments ƒ Constant shear rate/stress (or Peak hold) ƒ Continuous stress/rate ramp and down ƒ Stepped flow (or Flow sweep) ƒ Steady state flow ƒ Flow temperature ramp
TAINSTRUMENTS.COM TAINSTRUMENTS.COM RQVWDQW6KHDU5DWH6WUHVV Stress /Rate ƒ Constant rate vs. time ƒ Constant stress vs. time USES ƒ Single point testing ƒ Scope the time for steady state under certain rate
TAINSTRUMENTS.COM TAINSTRUMENTS.COM RQVWDQW6KHDU5DWH6WUHVV 0 5.0000 10.000 15.000 20.000 25.000 30.000 time (s) 0 0.5000 1.000 1.500 2.000 2.500 3.000 3.500 shear stress (Pa) 0 0.5000 1.000 1.500 2.000 2.500 3.000 3.500 4.000 viscosity (Pa.s) Hand Wash Rate 1/s Viscosity at 1 1/s is 2.8 Pa⋅s
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ Stress is applied to material at a constant rate. Resultant strain is monitored with time. time (min) m =Stress rate (Pa/min) Deformation USES ƒ Yield stress ƒ Scouting Viscosity Run RQWLQXRXV5DPS
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6WUHVV5DPS)ORZ0HGLD'LVSHUVLRQ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Deformation σ σ σ σ time ƒ Stress is first increased, then decreased, at a constant rate. Resultant strain is monitored with time. USES ƒ “Pseudo-thixotropy” from Hysteresis loop 7KL[RWURSLF/RRS RQWLQXRXV5DPS8SDQG'RZQ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 0.5000 0 0.1000 0.2000 0.3000 0.4000 shear rate (1/s) 500.0 0 100.0 200.0 300.0 400.0 shear stress (Pa) TA Instruments FORDB3.04F-Up step FORDB3.04F-Down step FORDB3.05F-Up step FORDB3.05F-Down step Run in Stress Control ZĞĚ͗ŝƌƐƚĐLJĐůĞ ůƵĞ͗^ĞĐŽŶĚĐLJĐůĞ 8S 'RZQ)ORZXUYHV 5HSHDWV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Deformation time Delay time Steady State Flow γ or σ = Constant time ƒ Stress is applied to sample. Viscosity measurement is taken when material has reached steady state flow. The stress is increased(logarithmically) and the process is repeated yielding a viscosity flow curve. USES ƒ Viscosity Flow Curves ƒ Yield Stress Measurements σ Žƌ ߛሶ σ Žƌ ߛሶ 6WHSSHGRU6WHDG6WDWH)ORZ Data point saved
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ A series of logarithmic stress steps allowed to reach steady state, each one giving a single viscosity data point: Shear Thinning Region Shear Rate, 1/s Viscosity Time η = σ / γ/ (d dt) 6WHSSHGRU6WHDG6WDWH)ORZ Data at each Shear Rate
TAINSTRUMENTS.COM TAINSTRUMENTS.COM '+5DQG$5(6*6WHDG6WDWH)ORZ Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress Steady state algorithm
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )ORZ6ZHHSV :DWHU%DVHG3DLQWZLWK6ROYHQW7UDS
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 1000 0.1000 1.000 10.00 100.0 shear rate (1/s) 0.8000 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 viscosity (Pa.s) ^ĂŵƉůĞϭͲůŽǁƐƚĞƉ ^ĂŵƉůĞϮͲůŽǁƐƚĞƉ Which material would do a better job coating your throat? RPSDULVRQRIRXJK6UXSV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 1000 1.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00 100.0 shear rate (1/s) 10000 0.1000 1.000 10.00 100.0 1000 viscosity (Pa.s) A.01F-Flow step B.01F-Flow step High shear rates BA Low shear rates BA Medium shear rates AB RPSDULVRQRI7ZR/DWH[3DLQWV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ Hold the rate or stress constant whilst ramping the temperature. time (min) USES ƒ Measure the viscosity change vs. temperature y y y y )ORZ7HPSHUDWXUH5DPS
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Notice a nearly 2 decade decrease in viscosity. This displays the importance of thermal equilibration of the sample prior to testing. i.e. Conditioning Step or equilibration time for 3 to 5 min 9LVFRVLW7HPSHUDWXUH'HSHQGHQFH
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )ORZ7HVWLQJRQVLGHUDWLRQV ƒ Small gaps give high shear rates ƒ Be careful with small gaps: ƒ Gap errors (gap temperature compensation) and shear heating can cause large errors in data. ƒ Recommended gap is between 0.5 to 2.0 mm. ƒ Secondary flows can cause increase in viscosity curve ƒ Be careful with data interpretation at low shear rates ƒ Surface tension can affect measured viscosity, especially with aqueous materials
TAINSTRUMENTS.COM TAINSTRUMENTS.COM :DWHUDWƒ² 6HFRQGDU)ORZ Surface tension at low torques Secondary flows at high shear rates
TAINSTRUMENTS.COM TAINSTRUMENTS.COM :DOO6OLS ƒ Wall slip can manifest as “apparent double yielding” ƒ Can be tested by running the same test at different gaps ƒ For samples that don’t slip, the results will be independent of the gap
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6KHDU7KLQQLQJRU6DPSOH,QVWDELOLW When Stress Decreases with Shear Rate, it indicates that sample is leaving the gap
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )ORZ7HVWLQJRQVLGHUDWLRQV ƒ Edge Failure – Sample leaves gap because of normal forces ƒ Look at stress vs. shear rate curve – stress should not decrease with increasing shear rate – this indicates sample is leaving gap ƒ Possible Solutions: ƒ use a smaller gap or smaller angle so that you get the same shear rate at a lower angular velocity ƒ if appropriate (i.e. Polymer melts) make use of Cox Merz Rule ( ) ( ) ω η γ η * ≡
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9LVFRHODVWLFLW
TAINSTRUMENTS.COM TAINSTRUMENTS.COM (ODVWLF%HKDYLRURIDQ,GHDO6ROLG γ1 γ2 γ3 Hooke’s Law of Elasticity: Stress = Modulus ⋅ Strain ^ƚƌĂŝŶ;࠹Ϳ ^ƚƌĞƐƐ;ʍͿ 1 2 3 3 2 1
TAINSTRUMENTS.COM TAINSTRUMENTS.COM (ODVWLF%HKDYLRURIDQ,GHDO6ROLG γ1 γ2 γ3 Hooke’s Law of Elasticity: Stress = Modulus ⋅ Strain E E E ‫ܧ‬ ൌ ߪ ߛ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9LVFRXV%HKDYLRURIDQ,GHDO/LTXLG Newton’s Law: stress = coefficient of viscosity ⋅ shear rate ^ƚƌĞƐƐ;ʍͿ ^ŚĞĂƌZĂƚĞ;࠹Ϳ Ș ߪ ൌ K ήߛሶ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9LVFRXV%HKDYLRURIDQ,GHDO/LTXLG Ș Ș Ș Ʉ ൌ ߪ ߛሶ Newton’s Law: stress= coefficient of viscosity ⋅ shear rate
sŝƐĐŽĞůĂƐƚŝĐĞŚĂǀŝŽƌ ʍ сΎɸ нɻΎĚɸͬĚƚ ĞůǀŝŶͲsŽŝŐƚDŽĚĞů;ƌĞĞƉͿ DĂdžǁĞůůDŽĚĞů;^ƚƌĞƐƐZĞůĂdžĂƚŝŽŶͿ sŝƐĐŽĞůĂƐƚŝĐDĂƚĞƌŝĂůƐ͗ŽƌĐĞ ĚĞƉĞŶĚƐŽŶďŽƚŚĞĨŽƌŵĂƚŝŽŶĂŶĚ ZĂƚĞŽĨĞĨŽƌŵĂƚŝŽŶĂŶĚǀŝĐĞǀĞƌƐĂ͘ L1 L2
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9LVFRHODVWLFLW'HILQHG Range of Material Behavior Liquid Like---------- Solid Like Ideal Fluid ----- Most Materials -----Ideal Solid Purely Viscous ----- Viscoelastic ----- Purely Elastic Viscoelasticity: Having both viscous and elastic properties ƒ Materials behave in the linear manner, as described by Hooke and Newton, only on a small scale in stress or deformation.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 3LWFK'URS([SHULPHQW ƒ Long deformation time: pitch behaves like a highly viscous liquid ƒ 9th drop fell July 2013 ƒ Short deformation time: pitch behaves like a solid ŚƚƚƉ͗ͬͬǁǁǁ͘ƚŚĞĂƚůĂŶƚŝĐ͘ĐŽŵͬƚĞĐŚŶŽůŽŐLJͬĂƌĐŚŝǀĞͬϮϬϭϯͬϬϳͬƚŚĞͲϯͲŵŽƐƚͲĞdžĐŝƚŝŶŐͲǁŽƌĚƐͲŝŶͲƐĐŝĞŶĐĞͲƌŝŐŚƚͲŶŽǁͲƚŚĞͲƉŝƚĐŚͲĚƌŽƉƉĞĚͬϮϳϳϵϭϵͬ Started in 1927 by Thomas Parnell in Queensland, Australia
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7LPH'HSHQGHQW9LVFRHODVWLF%HKDYLRU T is short [ 1s] T is long [24 hours]
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ Silly Putties have different characteristic relaxation times ƒ Dynamic (oscillatory) testing can measure time-dependent viscoelastic properties more efficiently by varying frequency (deformation time) 7LPH'HSHQGHQW9LVFRHODVWLF%HKDYLRU
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9LVFRHODVWLFLW'HERUDK1XPEHU ƒ Old Testament Prophetess who said (Judges 5:5): The Mountains ‘Flowed’ before the Lord ƒ Everything Flows if you wait long enough! ƒ Deborah Number, De - The ratio of a characteristic relaxation time of a material (τ) to a characteristic time of the relevant deformation process (T). Ğсτͬd
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'HERUDK1XPEHU ƒ Hookean elastic solid - IJ is infinite ƒ Newtonian Viscous Liquid - IJ is zero ƒ Polymer melts processing - IJ may be a few seconds High De Solid-like behavior Low De Liquid-like behavior IMPLICATION: Material can appear solid-like because 1) it has a very long characteristic relaxation time or 2) the relevant deformation process is very fast
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7LPHDQG7HPSHUDWXUH 5HODWLRQVKLS (E or G) (E' or G') (E or G) (E' or G') log Frequency Temperature log Time log Time
TAINSTRUMENTS.COM TAINSTRUMENTS.COM /LQHDU9LVFRHODVWLFLW5HJLRQ /95 'HILQHG If the deformation is small, or applied sufficiently slowly, the molecular arrangements are never far from equilibrium. The mechanical response is then just a reflection of dynamic processes at the molecular level which go on constantly, even for a system at equilibrium. This is the domain of LINEAR VISCOELASTICITY. The magnitudes of stress and strain are related linearly, and the behavior for any liquid is completely described by a single function of time. Mark, J., et. al., Physical Properties of Polymers, American Chemical Society, 1984, p. 102.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,PSRUWDQFHRI/95 ͛;Žƌ'͛Ϳ͕͟;Žƌ'͟Ϳ͕ƚĂŶδ͕ηΎ Measuring linear viscoelastic properties helps us bridge the gap between molecular structure and product performance
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6HWWLQJXS5KHRORJLFDO([SHULPHQWV 2VFLOODWRU7HVWV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 8QGHUVWDQGLQJ2VFLOODWLRQ([SHULPHQWV ƒ Define Oscillation Testing ƒ Approach to Oscillation Experimentation ƒ Stress and Strain Sweep ƒ Time Sweep ƒ Frequency Sweep ƒ Temperature Ramp ƒ Temperature Sweep (TTS)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Dynamic stress applied sinusoidally User-defined Stress or Strain amplitude and frequency Phase angle δ Strain, ε Stress, σΎ :KDWLV2VFLOODWLRQ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )UHTXHQF'HILQHG ƒ Time to complete one oscillation ƒ Frequency is the inverse of time ƒ Units ƒ Angular Frequency = radians/second ƒ Frequency = cycles/second (Hz) ƒ Rheologist must think in terms of rad/s. ƒ 1 Hz = 6.28 rad/s
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )UHTXHQF 0 0 0 0 dŝŵĞсϭƐĞĐ ω ω ω ω = 6.28 rad/s ω ω ω ω = 50 rad/s ω ω ω ω = 12.560rad/s
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $PSOLWXGH6WUDLQRU6WUHVV 0 0 0 0 ƒ Strain and stress are calculated from peak amplitude in the displacement and torque waves, respectively. dŝŵĞсϭƐĞĐ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'QDPLF0HFKDQLFDO7HVWLQJ Deformation Response Phase angle δ ƒ An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample. ƒ The material response (strain or stress) is measured. ƒ The phase angle δ, or phase shift, between the deformation and response is measured.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'QDPLF7HVWLQJ5HVSRQVHIRUODVVLFDO([WUHPHV Strain Stress δ сϬ° δ сϵϬ° Purely Elastic Response (Hookean Solid) Purely Viscous Response (Newtonian Liquid) Strain Stress
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'QDPLF7HVWLQJ9LVFRHODVWLF0DWHULDO5HVSRQVH Phase angle 0° δ 90° Stress Strain
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9LVFRHODVWLF3DUDPHWHUVRPSOH[(ODVWLF 9LVFRXV6WUHVV ƒ The stress in a dynamic experiment is referred to as the complex stress σ* Phase angle δ δ δ δ Complex Stress, σ σ σ σ* Strain, ε ε ε ε σ σ σ σ* = σ σ σ σ' + iσ σ σ σ ƒ The complex stress can be separated into two components: 1) An elastic stress in phase with the strain. σ σ σ σ' = σ σ σ σ*cosδ δ δ δ σ' is the degree to which material behaves like an elastic solid. 2) A viscous stress in phase with the strain rate. σ σ σ σ = σ σ σ σ*sinδ δ δ δ σ is the degree to which material behaves like an ideal liquid. The material functions can be described in terms of complex variables having both real and imaginary parts. Thus, using the relationship: Complex number: ‫ݔ‬ ൅ ݅‫ݕ‬ ൌ ‫ݔ‬ଶ ൅ ‫ݕ‬ଶ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9LVFRHODVWLF3DUDPHWHUV The Elastic (Storage) Modulus: Measure of elasticity of material. The ability of the material to store energy. The Viscous (loss) Modulus: The ability of the material to dissipate energy. Energy lost as heat. The Modulus: Measure of materials overall resistance to deformation. Tan Delta: Measure of material damping - such as vibration or sound damping. ᇱ ൌ ୗ୲୰ୣୱୱ‫כ‬ ୗ୲୰ୟ୧୬ ‘• Ɂ ̶ ൌ ୗ୲୰ୣୱୱ‫כ‬ ୗ୲୰ୟ୧୬ •‹ Ɂ ‫כ‬ ൌ ୗ୲୰ୣୱୱ‫כ‬ ୗ୲୰ୟ୧୬ –ƒ Ɂ ൌ ୋ̶ ୋᇱ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6WRUDJHDQG/RVVRID9LVFRHODVWLF0DWHULDO RUBBER BALL TENNIS BALL y STORAGE (G’) LOSS (G”) y Phase angle δ G* G' G Dynamic measurement represented as a vector
TAINSTRUMENTS.COM TAINSTRUMENTS.COM RPSOH[9LVFRVLW ƒ The viscosity measured in an oscillatory experiment is a Complex Viscosity much the way the modulus can be expressed as the complex modulus. The complex viscosity contains an elastic component and a term similar to the steady state viscosity. ƒ The Complex viscosity is defined as: Ș* = Ș’ + i Ș” or Ș* = G*/Ȧ Note: frequency must be in rad/sec!
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Parameter Shear Elongation Units Strain ɶ сɶϬƐŝŶ;ʘƚͿ ɸ сɸϬ ƐŝŶ;ʘƚͿ --- Stress σ сσϬƐŝŶ;ʘƚнɷͿ τ сτϬƐŝŶ;ʘƚнɷͿ Pa Storage Modulus (Elasticity) '͛с;σϬͬɶϬͿĐŽƐɷ ͛с;τϬͬɸϬͿĐŽƐɷ Pa Loss Modulus (Viscous Nature) '͟с;σϬͬɶϬͿƐŝŶɷ ͟с;τϬͬɸϬͿƐŝŶɷ Pa Tan į 'ͬ͟'͛ ͬ͛͟ --- Complex Modulus 'Ύ с;'͛Ϯн'͟ϮͿϬ͘ϱ Ύ с;͛Ϯн͟ϮͿϬ͘ϱ Pa Complex Viscosity ηΎ с'Ύͬʘ η Ύ сΎͬʘ Pa·sec Cox-Merz Rule for Linear Polymers: η*(Ȧ) = η(ߛሶ) @ ߛሶ = Ȧ 'QDPLF5KHRORJLFDO3DUDPHWHUV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 8QGHUVWDQGLQJ2VFLOODWLRQ([SHULPHQWV ƒ Define Oscillation Testing ƒApproach to Oscillation Experimentation 1. Stress and Strain Sweep 2. Time Sweep 3. Frequency Sweep 4. Temperature Ramp 5. Temperature Sweep (TTS)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'QDPLF6WUDLQRU6WUHVV6ZHHS ƒ The material response to increasing deformation amplitude (strain or stress) is monitored at a constant frequency and temperature. Time Stress or strain ƒ Main use is to determine LVR ƒ All subsequent tests require an amplitude found in the LVR ƒ Tests assumes sample is stable ƒ If not stable use Time Sweep to determine stability
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'QDPLF6WUDLQ6ZHHS0DWHULDO5HVSRQVH Strain (amplitude) Linear Region: Modulus independent of strain G' Non-linear Region: Modulus is a function of strain Stress γĐ сCritical Strain Constant Slope
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7HPSHUDWXUH'HSHQGHQFHRI/95 ƒ In general, the LVR is shortest when the sample is in its most solid form. % strain G’ Solid Liquid
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )UHTXHQF'HSHQGHQFHRI/95 ƒ LVR decreases with increasing frequency ƒ Modulus increases with increasing frequency
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6$26YHUVXV/$26:DYHIRUPV Linear response to a sinusoidal excitation is sinusoidal and represented by the fundamental in the frequency domain Nonlinear response to a sinusoidal excitation is not sinusoidal and represented in the frequency domain by the fundamental and the harmonics
TAINSTRUMENTS.COM TAINSTRUMENTS.COM /$26$QDOVLVRI+LJKHU+DUPRQLFV K^ ^K^ γ(t) = γ0 sin(ωt) τ(t) = τ0 sin(ωt+δ) γ(t) = γ0 sin(ωt) Fourier Series expansion: τ(t) = τ1 sin(ω1t+ϕ1) + τ3 sin(3ω1t+ϕ3) + τ5 sin(5ω1t+ϕ5) + ... = τn sin(nω1+ϕn) Σ n=1 odd ’ Lissajous plot: Stress vs. Strain (shown) or stress vs. Shear rate
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'QDPLF7LPH6ZHHS ƒ The material response is monitored at a constant frequency, amplitude and temperature. USES ƒ Time dependent Thixotropy ƒ Cure Studies ƒ Stability against thermal degradation ƒ Solvent evaporation/drying Time Stress or strain
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,PSRUWDQFHRI7LPH6ZHHS ƒ Important, but often overlooked ƒVisually observe the sample ƒ Determines if properties are changing over the time of testing ƒ Complex Fluids or Dispersions ƒ Preshear or effects of loading ƒ Drying or volatilization (use solvent trap) ƒ Thixotropic or Rheopectic ƒ Polymers ƒ Degradation (inert purge) ƒ Crosslinking
TAINSTRUMENTS.COM TAINSTRUMENTS.COM WLPHPLQ@ * 3 D @ * 3 D @ *WLPHVZHHSDWr 7LPH6ZHHSRQ3((.0HOW 7KHUPDO6WDELOLW Under N2 Under air
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ϮϮϱ͘Ϭ 0 Ϯϱ͘ϬϬ ϱϬ͘ϬϬ ϳϱ͘ϬϬ ϭϬϬ͘Ϭ ϭϮϱ͘Ϭ ϭϱϬ͘Ϭ ϭϳϱ͘Ϭ ϮϬϬ͘Ϭ time (s) ϭϬϬ͘Ϭ Ϭ ϮϬ͘ϬϬ ϰϬ͘ϬϬ ϲϬ͘ϬϬ ϴϬ͘ϬϬ G' (Pa) Structural Recovery after Preshear 7LPH6ZHHSRQ/DWH[
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 175.0 0 25.00 50.00 75.00 100.0 125.0 150.0 time (s) 100.0 10.00 G' (Pa) Sample “A” time sweep 100.0 0.1000 1.000 10.00 osc. stress (Pa) 100.0 10.00 Delay after pre-shear = 0 sec Delay after pre-shear = 150 sec Pre-shear conditions: 100 1/s for 30 seconds ƒ End of LVR is indicative of “Yield” or “Strength of Structure” ƒ Useful for Stability predictions (stability as defined by yield) ,PSRUWDQFHRI:DLWLQJIRU6WUXFWXUH5HEXLOG
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6ROYHQW7UDS6VWHPIRU(IIHFWLYH(YDSRUDWLRQRQWURO Solvent trap cover picks up heat from Peltier Plate to insure uniform temperature ^ŽůǀĞŶƚdƌĂƉŽǀĞƌ ^ŽůǀĞŶƚŝŶ tĞůů WĞůƚŝĞƌ WůĂƚĞ ^ĂŵƉůĞ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM XUHRID0LQXWH(SR[ 1200 0 200.0 400.0 600.0 800.0 1000 time (s) 1000000 1.000 10.00 100.0 1000 10000 100000 G' (Pa) 1000000 1.000 10.00 100.0 1000 10000 100000 G'' (Pa) TA Instruments Gel Point: G' = G t = 330 s 5 min G' G
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )UHTXHQF6ZHHS ƒ The material response to increasing frequency (rate of deformation) is monitored at a constant amplitude (strain or stress) and temperature. ŵƉůŝƚƵĚĞ dŝŵĞ ƒ Strain should be in LVR ƒ Sample should be stable ƒ Remember – Frequency is 1/time so low frequencies will take a long time to collect data – i.e. 0.001Hz is 1000 sec (over 16 min)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )UHTXHQF6ZHHS0DWHULDO5HVSRQVH Terminal Region Rubbery Plateau Region Transition Region Glassy Region 1 2 Storage Modulus (E' or G') ŽƐƐDŽĚƵůƵƐ;ΗŽƌ'ΗͿ log Frequency (rad/s or Hz)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )UHTXHQF6ZHHS 7LPH'HSHQGHQW9LVFRHODVWLF3URSHUWLHV Frequency of modulus crossover correlates with Relaxation Time
TAINSTRUMENTS.COM TAINSTRUMENTS.COM R[0HU] ([DPSOH /'3(DWƒ LDPE Freq sweep 2mm gap – Cox Merz LDPE shear rate 1mm gap LDPE Shear rate 2 mm gap Z W ( ) ( ) ω η γ η * ≡ Flow instability
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,PSRUWDQFHRI)UHTXHQF6ZHHSV ƒ High and low rate (short and long time) properties ƒ Viscosity Information - Zero Shear Viscosity, shear thinning ƒ Elasticity (reversible deformation) in materials ƒ MW MWD differences polymer melts and solutions ƒ Finding yield in gelled dispersions ƒ Can extend time or frequency range with TTS 4 . 3 2 e 4 . 3 0 ) ( ' and ¸ ¸ ¹ · ¨ ¨ © § ≈ = ≈ z w w M M G G J M η
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )UHTXHQFLQ'+55KHRPHWHU ƒ DHR has a combined motor and transducer design. ƒ In an DHR rheometer, the applied motor torque and the measured amplitude are coupled. ƒ The moment of inertia required to move the motor and geometry (system inertia) is coupled with the angular displacement measurements. ƒ This means that BOTH the system inertia and the sample contributes to the measured signal.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,QHUWLDO(IIHFWV ƒ What is Inertia? ƒ Definition: That property of matter which manifests itself as a resistance to any change in momentum of a body ƒ Instrument has inertia ƒ Sample has inertia
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,QHUWLDO(IIHFWVLQ2VFLOODWLRQIRU'+5 ƒ Inertia consideration ƒ Viscosity limitations with frequency ƒ Minimize inertia by using low mass geometries ƒ Monitor inertia using Raw Phase in degree ƒ When Raw Phase is greater than: ƒ 150° ° ° ° degrees for AR series ƒ 175° ° ° ° degrees for DHR series ƒ This indicates that the system inertia is dominating the measurement signal. Data may not be valid Raw Phase × Inertia Correction = delta
TAINSTRUMENTS.COM TAINSTRUMENTS.COM '+5RUUHFWLRQIRU,QHUWLD Waveforms at high frequencies Access to raw phase angle only available with TA Instruments Rheometers! Access to raw phase angle only available with TA Instruments Rheometers! Negligible correction at low frequencies Inertial effects at high frequencies
TAINSTRUMENTS.COM TAINSTRUMENTS.COM )UHTXHQF6ZHHSVLQ$5(6* ƒ ARES-G2 has a separate motor and transducer design. ƒ In an ARES-G2, the motor applies the deformation independent of the torque measurement on the transducer. ƒ The moment of inertia required to move the motor is decoupled from the torque measurements. ƒ This means the motor inertia does not contribute to the test results. ƒ Benefits of ARES-G2: ƒ System inertia free ƒ Capable of running low viscosity samples up to high frequency
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $5(6*ORVHG/RRSRQWURO Motor Measured Displacement Torque to drive motor to desired displacement Torque to drive FRT To maintain Zero Position = Sample Torque Target Strain Or Speed FRT null Position Motor Inertia NOT Part of Measurement Motor torque and sample torque are separated. FRT Deflection Purest Measurement !
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'QDPLF7HPSHUDWXUH5DPS ƒ A linear heating rate is applied. The material response is monitored at a constant frequency and constant amplitude of deformation. Data is taken at user defined time intervals. Temperature (° C) time (min) Denotes Oscillatory Measurement time between data points m = ramp rate (° C/min)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7HPSHUDWXUH6ZHHS RU6WHS 6LQJOH0XOWL)UHTXHQF ƒ A step and hold temperature profile is applied. The material response is monitored at one, or over a range of frequencies, at constant amplitude of deformation. – No thermal lag Time Soak Time Step Size Oscillatory Measurement Time Step Size Oscillatory Measurement Soak Time
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'QDPLF7HPSHUDWXUH5DPSRU6ZHHS0DWHULDO5HVSRQVH dĞŵƉĞƌĂƚƵƌĞ Terminal Region Rubbery Plateau Region Transition Region Glassy Region Loss Modulus (E or G) Storage Modulus (E' or G') log E' (G') and E (G)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM :KORRNDWWHPSHUDWXUHGHSHQGHQFH ƒ Solid in torsion rectangular ƒ Look at Tg, secondary transitions and study structure- property relationships of finished product. ƒ Themosetting polymers ƒ Follow curing reactions ƒ Polymer melts and other liquids ƒ Measure temperature dependence of viscoelastic properties
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM '+5$[LDO)RUFHRQWURO ƒ It is important to setup normal force control during any temperature change testing or curing testing ƒ Some general suggestions for normal force control ƒ For torsion testing, set normal force in tension: 1-2N ± 0.5-1.0N ƒ For curing or any parallel plate testing, set normal force in compression: 0 ± 0.5N
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7$7HFK7LS² $[LDO)RUFHRQWURO ƒ Videos available at www.tainstruments.com under the Videos tab or on the TA tech tip channel of YouTube™ (ŚƚƚƉƐ͗ͬͬǁǁǁ͘LJŽƵƚƵďĞ͘ĐŽŵͬƵƐĞƌͬddĞĐŚdŝƉƐ)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ Cures are perhaps the most challenging experiments to conduct on rheometers as they challenge all instrument specifications both high and low. ƒ The change in modulus as a sample cures can be as large as 7-8 decades and change can occur very rapidly. ƒ AR, DHR, and ARES instruments have ways of trying to cope with such large swings in modulus ƒ AR: Non-iterative sampling (w/ Axial force control) ƒ DHR: Non-iterative sampling (w/ Axial force control) and Auto-strain (w/ Axial force active) in TRIOS v3.2 or higher ƒ ARES: Auto-strain (w/ Axial force or auto-tension active) XUHRU7KHUPRVHW0DWHULDOV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7KHUPRVHWWLQJ3ROPHUV η Žƌ '͛ Time dĞŵƉ At start of test have a material that starts as liquid, paste, pressed power Pellet, or prepreg As the temp increases the viscosity of resin decreases Crosslinking reaction causes h and G’ to increase Material hits minimum viscosity which depends on Max temperature, frequency, ramp rate and may depend on strain or stress amplitude Material fully cured Maximum h or G’ reached
TAINSTRUMENTS.COM TAINSTRUMENTS.COM '+5DQG$5'DWDROOHFWLRQ2SWLRQV ƒNon-Iterative Sampling – motor torque is adjusted based on previous stress value and predicts new value required to obtain the target strain (good for rapid measurements) ƒPrecision Sampling – motor torque is adjusted at the end of an oscillation cycle in order to reach commanded strain ƒContinuous Oscillation (direct strain)* – motor torque is adjusted during the oscillation cycle to apply the commanded strain *Continuous oscillation only available with DHR-2 and DHR-3
TAINSTRUMENTS.COM TAINSTRUMENTS.COM RQWLQXRXV2VFLOODWLRQRQ6LQJOH+HDG5KHRPHWHU Point 1 or cycle Μ(t)1 θ(t)1 Μ(t+1)1 θ(t+1)1 Continuous oscillation (or direct strain control): incremental approach controls the strain and hits the target during a single cycle Non-iterative: uses the settings entered for the first data point and then uses previous cycle Precision: iterates using the initial settings entered for each data point
TAINSTRUMENTS.COM TAINSTRUMENTS.COM '+5DQG$51RQLWHUDWLYH6DPSOLQJ Time Temp η Žƌ '͛ Torque Strain Concern: How high does strain go at minimum viscosity. Does higher strain inhibit the cure (break structure that begins to form as material crosslinks). Does this affect time to minimum viscosity or gel time?
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $5(6$5(6*DQG'+5$XWR6WUDLQ η Žƌ '͛ Time Temp Torque Strain Upper torque limit Lower torque limit
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7KHUPRVHW7HVWLQJRQVLGHUDWLRQV ƒ Strain ƒ Depends on sample ƒ Verify the LVR in the cured state ( e.g. 0.05%) ƒ Normal force control or auto-tension ƒ Requires active to adjust for sample shrinkage and/or thermal expansion in parallel plates ƒ Temperature ƒ Isothermal ƒ Fast ramp + isotherm: the fastest ramp rate ƒ Continuous ramp rate: 3 – 5 ° C/min. ƒ Frequency ƒ Typically 1Hz (6.28 rad/s), 10 rad/s or higher
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6HWWLQJXS5KHRORJLFDO([SHULPHQWV 7UDQVLHQW7HVWV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6WUHVV5HOD[DWLRQ([SHULPHQW ƒ Strain is applied to sample instantaneously (in principle) and held constant with time. ƒ Stress is monitored as a function of time σ(t). ƒ DHR and AR ƒ Response time dependent on feedback loop Strain Ϭ time
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6WUHVV5HOD[DWLRQ([SHULPHQW Response of Classical Extremes time Ϭ time Ϭ stress for t0 is constant time Ϭ stress for t0 is 0 Hookean Solid Newtonian Fluid
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6WUHVV5HOD[DWLRQ([SHULPHQW Response of ViscoElastic Material ƒ For small deformations (strains within the linear region) the ratio of stress to strain is a function of time only. ƒ This function is a material property known as the STRESS RELAXATION MODULUS, G(t) G(t) = σ σ σ σ(t)/γ γ γ γ Stress decreases with time starting at some high value and decreasing to zero. time Ϭ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6WUHVV5HOD[DWLRQ0DWHULDO5HVSRQVH Terminal Region Rubbery Plateau Region Transition Region Glassy Region log time
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6WUHVV5HOD[DWLRQRQ3'06 ϭϬϬ Ϭ͘Ϭϭ Ϭ͘ϭ ϭ ϭϬ time (s) ϭ͘ϬϬϱ ϭ ϭϬ ϭϬϬ ϭϬϬϬ ϭϬϬϬϬ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 'HWHUPLQLQJ6WUDLQ)RU6WUHVV5HOD[DWLRQ ƒ Research Approach, such as generation of a family of curves for TTS, then the strain should be in the linear viscoelastic region. The stress relaxation modulus will be independent of applied strain (or will superimpose) in the linear region. ƒ Application Approach, mimic real application. Then the question is what is the range of strain that I can apply on the sample? This is found by knowing the Strain range the geometry can apply. ƒ The software will calculated this for you. γ сγ п θ ;йγ с γ п ϭϬϬͿ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6WUHVV5HOD[DWLRQDQG/LQHDU5HJLRQ 0.0 5.0 10.0 15.0 20.0 25.0 30.0 10 1 10 2 103 104 105 time [s] G(t) ( ) [Pa] Stress Relaxation of PDMS, Overlay G(t) 200% strain 50% strain 10% strain 200% strain is outside the linear region
TAINSTRUMENTS.COM TAINSTRUMENTS.COM UHHS5HFRYHU([SHULPHQW ƒ Stress is applied to sample instantaneously, t1, and held constant for a specific period of time. The strain is monitored as a function of time (γ(t) or ε(t)) ƒ The stress is reduced to zero, t2, and the strain is monitored as a function of time (γ(t) or ε(t)) ƒ Native mode on AR (1 msec) Stress time t1 t2
TAINSTRUMENTS.COM TAINSTRUMENTS.COM UHHS5HFRYHU([SHULPHQW Response of Classical Extremes ƒ Stain for tt1 is constant ƒ Strain for t t2 is 0 time time time ƒ Stain rate for tt1 is constant ƒ Strain for tt1 increase with time ƒ Strain rate for t t2 is 0 t2 t1 t1 t2 t2 t1
TAINSTRUMENTS.COM TAINSTRUMENTS.COM UHHS0DWHULDO5HVSRQVH Terminal Region Rubbery Plateau Region Transition Region Glassy Region ůŽŐƚŝŵĞ log Creep Compliance, Jc
TAINSTRUMENTS.COM TAINSTRUMENTS.COM UHHS5HFRYHU5HVSRQVHRI9LVFRHODVWLF 0DWHULDO ƌĞĞƉσ хϬ ƚŝŵĞ ƚ 1 ƚ2 σ/η ^ƚƌĂŝŶƌĂƚĞĚĞĐƌĞĂƐĞƐ ǁŝƚŚƚŝŵĞŝŶƚŚĞĐƌĞĞƉ njŽŶĞ͕ƵŶƚŝůĨŝŶĂůůLJ ƌĞĂĐŚŝŶŐĂƐƚĞĂĚLJƐƚĂƚĞ͘ DĂƌŬ͕:͕͘Ğƚ͘Ăů͕͘WŚLJƐŝĐĂůWƌŽƉĞƌƚŝĞƐŽĨWŽůLJŵĞƌƐ͕ŵĞƌŝĐĂŶŚĞŵŝĐĂů^ŽĐŝĞƚLJ͕ϭϵϴϰ͕Ɖ͘ϭϬϮ͘
TAINSTRUMENTS.COM TAINSTRUMENTS.COM UHHS5HFRYHU5HVSRQVHRI9LVFRHODVWLF 0DWHULDO ƌĞĞƉσ хϬ ƚŝŵĞ ƚ 1 ƚ2 ZĞĐŽǀĞƌĂďůĞ ^ƚƌĂŝŶ ZĞĐŽǀĞƌLJσ сϬ;ĂĨƚĞƌƐƚĞĂĚLJƐƚĂƚĞͿ σ/η ^ƚƌĂŝŶƌĂƚĞĚĞĐƌĞĂƐĞƐ ǁŝƚŚƚŝŵĞŝŶƚŚĞĐƌĞĞƉ njŽŶĞ͕ƵŶƚŝůĨŝŶĂůůLJ ƌĞĂĐŚŝŶŐĂƐƚĞĂĚLJƐƚĂƚĞ͘ /ŶƚŚĞƌĞĐŽǀĞƌLJnjŽŶĞ͕ƚŚĞǀŝƐĐŽĞůĂƐƚŝĐ ĨůƵŝĚƌĞĐŽŝůƐ͕ĞǀĞŶƚƵĂůůLJƌĞĂĐŚŝŶŐĂ ĞƋƵŝůŝďƌŝƵŵĂƚƐŽŵĞƐŵĂůůƚŽƚĂůƐƚƌĂŝŶ ƌĞůĂƚŝǀĞƚŽƚŚĞƐƚƌĂŝŶĂƚƵŶůŽĂĚŝŶŐ͘ DĂƌŬ͕:͕͘Ğƚ͘Ăů͕͘WŚLJƐŝĐĂůWƌŽƉĞƌƚŝĞƐŽĨWŽůLJŵĞƌƐ͕ŵĞƌŝĐĂŶŚĞŵŝĐĂů^ŽĐŝĞƚLJ͕ϭϵϴϰ͕Ɖ͘ϭϬϮ͘ hŶƌĞĐŽǀĞƌĂďůĞ ^ƚƌĂŝŶ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM UHHS5HFRYHU([SHULPHQW time Recovery Zone Creep Zone Less Elastic More Elastic Creep σ 0 Recovery σ = 0 (after steady state) σ/η t1 t2
TAINSTRUMENTS.COM TAINSTRUMENTS.COM UHHS5HFRYHUUHHSDQG5HFRYHUDEOHRPSOLDQFH Mark, J., et. al., Physical Properties of Polymers, American Chemical Society, 1984, p. 102. :;ƚͿ ϭͬη time Creep Zone : ƌ ;ƚͿ time Recovery Zone Creep Compliance Recoverable Compliance ୰ – ൌ ɀ୳ െ ɀ – ɐ Where γu = Strain at unloading γ(t) = time dependent recoverable strain – ൌ ஓሺ୲ሻ ஢ Je = Equilibrium recoverable compliance more elastic :Ğ The material property obtained from Creep experiments: Compliance = 1/Modulus (in a sense)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9LVFRHODVWLF5LQJLQJ² '+5RU$5 • The ringing oscillations can be rather short-lived and may not be apparent unless using log time scale. • The sudden acceleration, together with the measurement system’s inertia, causes a strain overshoot. For viscoelastic materials, this can result in viscoelastic ringing, where the material undergoes a damped oscillation just like a bowl of Jell-o when bumped. Creep ringing in rheometry or how to deal with oft-discarded data in step stress tests! RH Ewoldt, GH McKinley - Rheol. Bull, 2007
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $5(6*6WUHVVRQWURO/RRS ƒ Stress is controlled by closing the loop around the sample Æ requires optimization of control PID parameters ƒ Pretest to determine material’s response and PID Constants DĂƚĞƌŝĂůƌĞƐƉŽŶƐĞ W/ ŵŽƚŽƌ Zd ƐĂŵƉůĞ σĐŵĚ;ƚͿ ŝŶƚĞŐƌĂƚŽƌ /ŶŶĞƌ DŽƚŽƌWŽƐŝƚŝŽŶŽŽƉ θ;ƚͿ ŝŶĞĂƌƌĞƐƉŽŶƐĞ σ;ƚͿ Δσ;ƚͿ θ;ƚͿ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 3URJUDPPLQJUHHSRQDQ$5(6* ƒ Set up a pre-test and get the sample information into the loop ƒ Stress Control Pre-test: frequency sweep within LVR
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $5(6*6WUHVVRQWURO3UHWHVW Pretest Æ Frequency Sweep from 2 to 200 rad/s Æ data analyzed in software to optimize Motor loop control PID constants LDPE melt Freq. Sweep T = 190° C
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 0 2000.000 4000.000 6000.000 8000.000 10000.000 time global (s) 0 0.50000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 % strain HDPE Creep Recovery at 200° C UHHSRQ+'3(0HOW
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ Application Approach - If you are doing creep on a solid, you want to know the dimension change with time under a specified stress and temperature, then the questions is what is the max/min stress that I can apply to the sample?. This is found by knowing the Stress range the geometry can apply. ƒ The software will calculated this for you. ƒ Research Approach - If you are doing creep on a polymer melt, and are interested in viscoelastic information (creep and recoverable compliance), then you need to conduct the test at a stress within the linear viscoelastic region of the material. σ = Kσ x Μ 'HWHUPLQLQJ6WUHVV)RUUHHS([SHULPHQW
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM Three main reasons for rheological testing: ƒ Characterization MW, MWD, formulation, state of flocculation, etc. ƒ Process performance Extrusion, blow molding, pumping, leveling, etc. ƒ Product performance Strength, use temperature, dimensional stability, settling stability, etc. 3XUSRVHRID5KHRORJLFDO0HDVXUHPHQW
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 3ROPHU7HVWLQJDQG5KHRORJ Molecular Structure ƒ MW and MWD ƒ Chain Branching and Cross-linking ƒ Interaction of Fillers with Matrix Polymer ƒ Single or Multi-Phase Structure Viscoelastic Properties As a function of: ƒ Strain Rate(frequency) ƒ Strain Amplitude ƒ Temperature Processability Product Performance
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 5KHRORJ$SSOLFDWLRQVLQ3ROPHUV Material Property Composites, Thermosets Viscosity, Gelation, Rate of Cure, Effect of Fillers and Additives Cured Laminates Glass Transition, Modulus Damping, impact resistance, Creep, Stress Relaxation, Fiber orientation, Thermal Stability Thermoplastics Blends, Processing effects, stability of molded parts, chemical effects Elastomers Curing Characteristics, effect of fillers, recovery after deformation Coating, Adhesives Damping, correlations, rate of degree of cure, glass transition temperature, modulus
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 0RVWRPPRQ([SHULPHQWVRQ3ROPHUV ƒ Oscillation/Dynamic ƒ Time Sweep ƒ Degradation studies, stability for subsequent testing ƒ Strain Sweep – Find LVER ƒ Frequency Sweep – G’, G”, η* ƒ Sensitive to MW/MWD differences melt flow can not see ƒ Temperature Ramp/Temperature Step ƒ Transitions, viscosity changes ƒ TTS Studies ƒ Flow/Steady Shear ƒ Viscosity vs. Shear Rate Plots ƒ Find Zero Shear Viscosity ƒ Low shear information is sensitive to MW/MWD differences melt flow can not see ƒ Creep and Recovery ƒ Creep Compliance/Recoverable Compliance ƒ Very sensitive to long chain tails
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Determines if properties are changing over the time of testing ƒ Degradation ƒ Molecular weight building ƒ Crosslinking -2 0 2 4 6 8 10 12 14 16 18 10 4 10 5 -2 0 2 4 6 8 10 12 14 16 18 175 200 225 250 275 Temperature stability good poor Modulus G' [Pa] Time t [min] Polyester Temperature stability Temperature T [° C] Important, but often overlooked! 3ROPHU0HOW7KHUPDO6WDELOLW
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,GHDOL]HG)ORZXUYH² 3ROPHU0HOWV 1.00 1.00E-5 1.00E-4 1.00E-3 0.0100 0.100 shear rate (1/s) 10.00 100.00 1000.00 1.00E4 1.00E5 log η Molecular Structure Compression Molding Extrusion Blow and Injection Molding η0 = Zero Shear Viscosity η0 = K x MW 3.4 Measure in Flow Mode Extend Range with Oscillation Cox-Merz Extend Range with Time- Temperature Superposition (TTS) Cox-Merz First Newtonian Plateau Second Newtonian Plateau Power Law Region 1.00 1.00E-5 1.00E-4 1.00E-3 0.0100 0.100 shear rate (1/s) 10.00 100.00 1000.00 1.00E4 1.00E5 log η Molecular Structure Compression Molding Extrusion Blow and Injection Molding η0 = Zero Shear Viscosity η0 = K x MW 3.4 Measure in Flow Mode Extend Range with Oscillation Cox-Merz Extend Range with Time- Temperature Superposition (TTS) Cox-Merz First Newtonian Plateau Second Newtonian Plateau Power Law Region
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 0HOW5KHRORJ0:(IIHFWRQ=HUR6KHDU9LVFRVLW MWc log MW log η o 3.4 Ref. Graessley, Physical Properties of Polymers, ACS, c 1984. η η η η0 с⋅ ⋅ ⋅ ⋅Dǁ ϯ͘ϰ ƒ Sensitive to Molecular Weight, MW ƒ For Low MW (no Entanglements) η0 is proportional to MW ƒ For MW Critical MWc, η0 is proportional to MW3.4 η η η η0 с⋅ ⋅ ⋅ ⋅Dǁ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,QIOXHQFHRI0:RQ9LVFRVLW The zero shear viscosity increases with increasing molecular weight. TTS is applied to obtain the extended frequency range. The high frequency behavior (slope -1) is independent of the molecular weight 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 2 10 3 10 4 10 5 10 6 10 7 100000 10 5 10 6 Slope 3.08 +/- 0.39 Zero Shear Viscosity Zero Shear Viscosity η o [Pa s] Molecilar weight Mw [Daltons] Viscosity η * [Pa s] Frequency ω aT [rad/s] SBR Mw [g/mol] 130 000 230 000 320 000 430 000
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,QIOXHQFHRI0:'RQ9LVFRVLW ƒ A Polymer with a broad MWD exhibits non-Newtonian flow at a lower rate of shear than a polymer with the same η0, but has a narrow MWD. Log Shear Rate (1/s) Narrow MWD Broad MWD
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,QIOXHQFHRI0:RQ*¶DQG*´ The G‘ and G‘‘ curves are shifted to lower frequency with increasing molecular weight. 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 1 10 2 10 3 10 4 10 5 10 6 Modulus G', G'' [Pa] SBR Mw [g/mol] G' 130 000 G'' 130 000 G' 430 000 G'' 430 000 G' 230 000 G'' 230 000 Freq ω [rad/s]
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,QIOXHQFHRI0:'RQ*¶DQG*´ ƒ The maximum in G‘‘ is a good indicator of the broadness of the distribution 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 3 10 4 10 5 10 6 Modulus G', G'' [Pa] Frequency ωaT [rad/s] SBR polymer melt G' 310 000 broad G 310 000 broad G' 320 000 narrow G 320 000 narrow Higher crossover frequency : lower Mw Higher crossover Modulus: narrower MWD (note also the slope of G” at low frequencies – narrow MWD steeper slope) EĂƌƌŽǁ ƌŽĂĚ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM +LJK0:RQWULEXWLRQV 400,000 g/mol PS 400,000 g/mol PS + 1% 12,000,000 g/mol 400,000 g/mol PS + 4% 12,000,000 g/mol Macosko, TA Instruments Users’ Meeting, 2015
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,PSRUWDQFHRI9HULILQJ7KHUPDO6WDELOLW ƒ Good thermal stability ƒ one crossover point, ƒ Ș* plateaus at low Ȧ ƒ Poor thermal stability ƒ multiple crossover points ƒ Ș* continues to increase over time ƒ Time Sweep can verify if the sample is unstable
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6XUIDFH'HIHFWVGXULQJ3LSH([WUXVLRQ Blue-labled sample shows a rough surface after extrusion ƒ Surface roughness correlates with G‘ or elasticity → broader MWD or tiny amounts of a high MW component 0.1 1 10 100 10 3 10 4 10 5 10 3 10 4 10 5 T = 220 o C Complex viscosity η * [Pa s] G' rough surface G' smooth surface η* rough surface η* smooth surface HDPE pipe surface defects Modulus G' [Pa] Frequency ω [rad/s]
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7DFNDQG3HHORI$GKHVLYHV 0.1 1 10 10 3 10 4 Tack and Peel performance of a PSA peel tack good tack and peel Bad tack and peel Storage Modulus G' [Pa] Frequency ω [rad/s] ƒ Bond strength is obained from peel (fast) and tack (slow) tests ƒ It can be related to the viscoelastic properties at different frequencies Tack and peel have to be balanced for an ideal adhesive
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ Non linear effects can be detected in recovery before they are seen in the creep (viscosity dominates) 0.1 1 10 100 1000 10 -5 10 -4 10 -3 10 -2 10 -1 10 -5 10 -4 10 -3 10 -2 10 -1 slope 1 increasing stress LDPE Melt T=140 o C Recoverable Compliance Jr(t) [1/Pa] 10 Pa 50 Pa 100 Pa 500 Pa 1000 Pa 5000 Pa LDPE Melt creep recovery Compliance J(t) [1/Pa] Time t [s] UHHS DQG5HFRYHUZLWK,QFUHDVLQJ6WUHVV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM (IIHFWRI)LOOHURQ0HOW9LVFRVLW 1E-5 1E-4 1E-3 0.01 0.1 1 10 100 1000 10000 10 2 10 3 10 4 10 5 10 6 10 7 . . Temperature 180 o C LDPE filled LDPE neat Neat and Filled LDPE Viscosity η ( γ ) [Pa s] Shear rate γ [1/s] ƒ ŝůůĞƌƐŝŶĐƌĞĂƐĞƚŚĞ ŵĞůƚǀŝƐĐŽƐŝƚLJ ƒ ƵĞƚŽŝŶƚĞƌͲƉĂƌƚŝĐůĞ ŝŶƚĞƌĂĐƚŝŽŶƐ͕ƚŚĞ ŶŽŶͲEĞǁƚŽŶŝĂŶ ƌĂŶŐĞŝƐĞdžƚĞŶĚĞĚƚŽ ůŽǁƐŚĞĂƌƌĂƚĞƐĂŶĚ ƚŚĞnjĞƌŽƐŚĞĂƌ ǀŝƐĐŽƐŝƚLJŝŶĐƌĞĂƐĞƐ ĚƌĂŵĂƚŝĐĂůůLJ The material has a yield, when rate and viscosity are inverse proportional at low rate.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Fix drum connected to transducer Rotating drum connected to the motor: ƒ rotates around its axis ƒ rotates around axis of fixed drum ([WHQVLRQDO9LVFRVLW0HDVXUHPHQWV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM :KLV(ORQJDWLRQ9LVFRVLW,PSRUWDQW ƒ Application to processing: many processing flows are elongation flows - testing as close as possible to processing conditions (spinning, coating, spraying) ƒ Relation to material structure: non linear elongation flow is more sensitive for some structure elements than shear flows (branching, polymer architecture) ƒ Testing of constitutive equations: elongation results in addition to shear data provide a more general picture for developing material equations
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7KHUPRVHWWLQJ3ROPHUV ƒ Thermosetting polymers are perhaps the most challenging samples to analyze on rheometers as they challenge all instrument specifications both high and low. ƒ The change in modulus as a sample cures can be as large as 7-8 decades and change can occur very rapidly.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7KHUPRVHWV$QDOVLV ƒ Monitor the curing process ƒViscosity change as function of time or temperature ƒ Gel time or temperature ƒ Test methods for monitoring curing ƒTemperature ramp ƒIsothermal time sweep ƒCombination profile to mimic process ƒ Analyze cured material’s mechanical properties (G’, G”, tan δ , Tg etc.)
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM $WWKH*HO3RLQW ƒ Molecular weight Mw goes to infinity ƒ System loses solubility ƒ Zero shear viscosity goes to infinity ƒ Equilibrium Modulus is zero and starts to rise to a finite number beyond the gel point Note: For most applications, gel point can be considered as when G’ = G” and tan δ = 1
TAINSTRUMENTS.COM TAINSTRUMENTS.COM XULQJ$QDOVLV,VRWKHUPDOXULQJ 1200 0 200.0 400.0 600.0 800.0 1000 time (s) 1000000 1.000 10.00 100.0 1000 10000 100000 G' (Pa) 1000000 1.000 10.00 100.0 1000 10000 100000 G'' (Pa) TA Instruments Gel Point: G' = G t = 330 s 5 min G' G
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM $WWKH*HO3RLQWRQWLQXHG« • The process of viscosity increasing takes place in two stages: the gelation process (frequency independent) and vitrification (related to the network Tg relative to cure temperature and is frequency dependent). • When you look at an isothermal cure at a constant frequency the modulus crossover point has both the information of gelation and vitrification. ƒ To avoid this, run multiple isothermal runs at different frequencies and plot the cross over in tan delta. This is the frequency independent gel point. ‹ Alternatively, use a single mutliwave test
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM 145° C 140° C 135° C 130° C 125° C 120° C G’ (MPa) Time (min) Tire Compound: Effect of Curing Temperature ,VRWKHUPDOXULQJ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 89/LJKW*XLGHXULQJ$FFHVVRU ƒ Collimated light and mirror assembly insure uniform irradiance ƒ Maximum intensity at plate 300 mW/cm2 ƒ Broad range spectrum with main peak at 365 nm ƒ Cover with nitrogen purge ports ƒ Optional disposable acrylic plates
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 89XUH3URILOHKDQJHVZLWK7HPSHUDWXUH ƵƉƚŽϱϬƉŽŝŶƚƐ ƉĞƌƐĞĐŽŶĚ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ Glass transition ƒ Secondary transitions ƒ Crystallinity ƒ Molecular weight/cross-linking ƒ Phase separation (polymer blends, copolymers,...) ƒ Composites ƒ Aging (physical and chemical) ƒ Curing of networks ƒ Orientation ƒ Effect of additives Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 489. 3ROPHU6WUXFWXUH3URSHUWKDUDFWHUL]DWLRQ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM G' Onset: Occurs at lowest temperature - Relates to mechanical failure +RZWR0HDVXUH*ODVV7UDQVLWLRQ Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 980. tan δ δ δ δ Peak: Occurs at highest temperature - used historically in literature - a good measure of the leatherlike midpoint between the glassy and rubbery states - height and shape change systematically with amorphous content. G Peak: Occurs at middle temperature - more closely related to the physical property changes attributed to the glass transition in plastics. It reflects molecular processes - agrees with the idea of Tg as the temperature at the onset of segmental motion.
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7HVWLQJ6ROLGVRQD5KHRPHWHU ƒ Torsion and DMA geometries allow solid samples to be characterized in a temperature controlled environment – DMA functionality is standard with ARES G2 and optional DHR Rectangular and cylindrical torsion DMA 3-point bending and tension (Cantilever not shown) Modulus: G’, G”, G* Modulus: E’, E”, E* сϮ';ϭнʆͿ ʆ ͗WŽŝƐƐŽŶ͛ƐƌĂƚŝŽ
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM Glass Transition - Cooperative motion among a large number of chain segments, including those from neighboring polymer chains Secondary Transitions ƒ Local main-chain motion - intramolecular rotational motion of main chain segments four to six atoms in length ƒ Side group motion with some cooperative motion from the main chain ƒ Internal motion within a side group without interference from side group ƒ Motion of or within a small molecule or diluent dissolved in the polymer (e.g. plasticizer) 7KH*ODVV 6HFRQGDU7UDQVLWLRQV Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 487.
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM UVWDOOLQLW0ROHFXODU:HLJKWDQGURVVOLQNLQJ Increasing MW Cross-linked Amorphous Crystalline Increasing Crystallinity Tm Temperature log Modulus 3 decade drop in modulus at Tg
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ Multiphase systems consisting of a dispersed phase (solid, fluid, gas) in surrounding fluid phase ƒExamples are: ƒ Paints ƒ Coatings ƒ Inks ƒ Personal Care Products ƒ Cosmetics ƒ Foods 6WUXFWXUHG)OXLGV ƒ Properties: ƒ Yield Stress ƒ Non-Newtonian Viscous Behavior ƒ Thixotropy ƒ Elasticity
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,GHDOL]HG)ORZXUYH 1 1) Sedimentation 2) Leveling, Sagging 3) Draining under gravity 2 3 6 5 8 9 1.00 1.00E-5 1.00E-4 1.00E-3 0.0100 0.100 shear rate (1/s) 10.00 100.00 1000.00 1.00E4 1.00E5 log η 1.00E6 11 7 4 10 What shear rate? 8) Spraying and brushing 9) Rubbing 10) Milling pigments 11) High Speed coating 4) Chewing, swallowing 5) Dip coating 6) Mixing, stirring 7) Pipe flow
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Reference:Barnes, H.A., Hutton, J.F., and Walters, K., An Introduction to Rheology, Elsevier Science B.V., 1989. ISBN 0-444-87469-0 log η log ߛሶ First Newtonian Plateau Power-Law Shear Thinning Second Newtonian Plateau Possible Increase in Viscosity *HQHUDO9LVFRVLWXUYHIRU6XVSHQVLRQV σ ∝ ߛሶm or, equivalently, η ∝ ߛሶm-1 m is usually 0.15 to 0.6 This viscosity is often called the Zero Shear Viscosity, η0, or the Newtonian Viscosity
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 5HDVRQIRU6KDSHRI*HQHUDO)ORZXUYH Brownian diffusion randomizes Shear thinning Shear thickening ůŽŐ η Turbulent flow pushes particles out of alignment, destroying order and causing increase in viscosity (shear thickening) Shear field aligns particles along streamlines
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ORVLQJ WKH*DS ƒLinear or Exponential speed profile after reaching ‘Closure Distance’ ƒNormal Force set not to exceed a certain value after reaching the user defined ‘Closure Distance’
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Ϭ ϮϬϬ ϰϬϬ ϲϬϬ ϴϬϬ ϭϬϬϬ Ϭ ϱϬ ϭϬϬ ϭϱϬ ϮϬϬ ϮϱϬ Time (s) G' (Pa) Fast Linear Close Exponential Close RPSDULVRQRI/LQHDUDQG([SRQHQWLDOORVLQJ Lowering the gap can introduce shear, breaking down weakly structured samples Reducing the gap closure speed can minimize this effect
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 8VLQJ3UH6KHDULQJ ƒ Monitor the viscosity signal during the pre-shear to determine if the rate and duration are appropriate ƒ If the viscosity is increasing during the pre-shear, the sample is rebuilding. The pre-shear should be higher than the shear introduced during loading to erase sample loading history ƒ The viscosity should decrease and then level off ƒ Typical Pre-Shear: 1- 100 sec-1, 30-60 seconds ƒ Use an amplitude sweep to determine what strain to use for time sweep ƒ A high strain will break down the sample, and not allow rebuilding ƒ A low strain will give a weak signal ƒ Based on the Time Sweep, determine an appropriate equilibration time for that sample
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 3UHVKHDURQGLWLRQV ƒ The goal for pre-shear is to remove the sample history at loading ƒ For high viscosity sample, use low rate (10 1/s) and long time (2 min.) ƒ For low viscosity sample, use high rate (100 1/s) and short time (1 min.)
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 1. 2. 3. 6WUXFWXUHG)OXLG3UHWHVWLQJ Three consecutive time sweeps: ƒ Time sweep within LVR (check if loading destroyed structure) ƒ Time sweep at large strain ƒ Time sweep back to LVR (check structure rebuild)
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM Why modify the yield behavior? ƒ to avoid sedimentation and increase the shelf live ƒ to reduce flow under gravity ƒ to stabilize a fluid against vibration LHOG6WUHVV ƒStructured fluids exhibit yield-like behavior, changing from ‘solid-like’ to readily flowing fluid when a critical stress is exceeded. Rheological modifiers are often used to control the yield behavior of fluids. ƒThere are multiple methods to measure Yield stress. The apparent yield stress measured is not a single value, as it will vary depending on experimental conditions.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM LHOG6WUHVVLQD)ORZ6WUHVV5DPS ƒ Stress is ramped linearly from 0 to a value above Yield Stress and the stress at viscosity maximum can be recorded as Yield Stress ƒ The measured yield value will depend on the rate at which the stress is increased. The faster the rate of stress increase, the higher the measured yield value
TAINSTRUMENTS.COM TAINSTRUMENTS.COM LHOG6WUHVVLQD)ORZ6WUHVV5DPS Yield Stress
TAINSTRUMENTS.COM TAINSTRUMENTS.COM LHOG6WUHVV)ORZ6ZHHS'RZQ 5DWHRQWURO ƒ Eliminates start-up effects for more accurate measurements ƒ Initial high shear rate acts as a pre-shear, erasing loading effects ƒ Steady State sensing allows the sample time to rebuild ƒ The plateau in shear stress is a measure of the yield stress. ƒ At the plateau, Viscosity vs. Shear Rate will have a slope of -1 slope: -0.995 When the Yield Stress is small, a flow rate sweep from high to low shear rate is preferred
TAINSTRUMENTS.COM TAINSTRUMENTS.COM LHOG6WUHVV6WUDLQ6ZHHS0HWKRG 0.01000 0.1000 1.000 10.00 osc. stress (Pa) 100.0 1000 G' (Pa) Onset point osc. stress: 1.477 Pa G': 346.6 Pa End condition: Finished normally Sun Block Lotion Yield stress of a sun block lotion ƒ Perform strain or stress sweep in oscillation ƒ Yield stress is the on set of G’ curve. It is the critical stress at which irreversible plastic deformation occurs.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒ Low shear viscosity 10-3 to 1 s-1 ƒ leveling, sagging, sedimentation ƒ Medium shear viscosity10-103 s-1 ƒ mixing, pumping and pouring ƒ High shear viscosity 103 - 106 s-1 ƒ brushing, rolling spraying 9LVFRVLW5DQJHVRI3DLQWVRDWLQJV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9LVFRVLW5DQJHVRI3DLQWVRDWLQJV The two coatings show the same consistency after formulation, but they exhibit very different application performance 0.1 1 10 100 1000 10000 100000 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 HSV MSV LSV Roling Brushing Spraying Mixing Pumping Consistency Appearence Leveling Sagging Sedimentation At Rest Processing Performance Viscosity h [Pas] shear rate g [1/s]
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7KL[RWURS The thixotropy characterizes the time dependence of reversible structure changes in complex fluids. The control of thixotropy is important to control: ƒ process conditions for example to avoid structure build up in pipes at low pumping rates i.e. rest periods, etc.... ƒ sagging and leveling and the related gloss of paints and coatings, etc.. Sag Leveling
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7KL[RWURSLF/RRS7HVW In a thixotropic material, there will be a hysterisis between the two curves The further the up ramp and down ramp curves differ, the larger the area between the curves, the higher the thixotropy of the material. See also AAN 016 – Structured Fluids Stress is ramped up linearly, and then back down, over the same duration
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 0 20 40 60 80 100 120 10 2 G'o G'oo after preshear Frequency 1Hz strain 2% preshear 10s at 60 s -1 η* G' G'' Modulus G', G'' [Pa]; Viscosity η * [Pas] time t min] Structure build up Pre-shear the sample to break down structure. Then monitor the increase of the modulus or complex viscosity as function of time. ‫ܩ‬ᇱ ‫ݐ‬ ൌ ‫ܩ‬Ԣ௢ ൅ ሺ‫ܩ‬Ԣஶ െ ‫ܩ‬Ԣ௢ሻሺͳ െ ݁௧Ȁఛ) τ = characteristic recovery time 6WUXFWXUH5HFRYHU
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7KL[RWURSLF,QGH[ 5HFRYHU7LPH ƒThe non-sagging formula (with additive) has both a shorter recovery time and a higher final recovered viscosity (or storage modulus), and the recovery parameter takes both of these into account to predict significantly better sag resistance. ƒThe ratio η(∞) /t, is the recovery parameter (a true thixotropic index), and has been found to correlate well to thixotropy-related properties such as sag resistance and air entrainment. Rheology in coatings, principles and methods RR Eley - Encyclopedia of Analytical Chemistry, 2000 - Wiley Online Library
TAINSTRUMENTS.COM TAINSTRUMENTS.COM DVH6WXGRI3DLQWV 0.01000 0.1000 1.000 10.00 100.0 shear rate (1/s) 0.1000 1.000 10.00 100.0 viscosity (Pa.s) Paint A Paint C Paint D Paint B
TAINSTRUMENTS.COM TAINSTRUMENTS.COM DVH6WXGRI3DLQWV 0 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.0 shear rate (1/s) 0 20.00 40.00 60.00 80.00 100.0 120.0 shear stress (Pa) Paint C Paint A Paint D Paint B Thixotropy (Pa/s): Paint A = 657.0 Paint B = 436.5 Paint C = 254.0 Paint D = 120.3
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 time (s) 0 2.500 5.000 7.500 10.00 12.50 15.00 G' (Pa) Paint A Paint C Paint D Paint B DVH6WXGRI3DLQWV
TAINSTRUMENTS.COM TAINSTRUMENTS.COM DVH6WXGRI3DLQWV Paint A Paint D Paint C Paint B
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $QWLSHUVSLUDQW'HRGRUDQW The viscosity has to be balanced to provide the correct viscosity at a given shear rate shear rate viscosity application storage Roll-ons: Rheology and end-use performance
TAINSTRUMENTS.COM TAINSTRUMENTS.COM $QWLSHUVSLUDQW'HRGRUDQW x x x x x x x x x x x x Ϭ ϭϬ ϮϬ ϯϬ ϰϬ ϱϬ ϲϬ ϳϬ dĞŵƉĞƌĂƚƵƌĞ΀΁ ϭнϬϯ ϭнϬϰ ϭнϬϱ ϭнϬϲ ϭнϬϳ ϭнϬϴ DŽĚƵůƵƐ'Ζ΀WĂ΁ ƒ use small particles to reduce sedimentation speed ƒ add rheological modifier like clay to stabilize the suspension and keep the particles in suspension The temperature dependence of the modulus governs the behavior during the application to the skin Sticks: Rheology and process performance
TAINSTRUMENTS.COM TAINSTRUMENTS.COM (ODVWLFLW2VFLOODWLRQ)UHTXHQF6ZHHS 0.1 1 10 100 10 1 10 2 10 3 0.1 1 10 100 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 complex viscosity G' G'' Modulus G', G'' [Pa]; Viscosity η * [Pa s] frequency ω [rad/s] tan δ tan δ ƒ Many dispersion exhibit solid like behavior at rest ƒ The frequency dependence and the absolute value of tan δ correlate with long time stability Cosmetic lotion ƒ Note: strain amplitude has to be in the linear region
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM 75,26+HOS0HQX ƒ Browse the contents list or search using the search tab. ƒ Access to Getting Started Guides also found through the help menu.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ƒFrom www.tainstruments.com click on Videos, Support or Training ƒSelect Videos for TA Tech Tips, Webinars and Quick Start Courses ,QVWUXFWLRQDO9LGHRV ^ĞĞĂůƐŽ͗ŚƚƚƉƐ͗ͬͬǁǁǁ͘LJŽƵƚƵďĞ͘ĐŽŵͬƵƐĞƌͬddĞĐŚdŝƉƐ
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ,QVWUXFWLRQDO9LGHR5HVRXUFHV Strategies for Better Data - Rheology Quickstart e-Training Courses
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 1HHG$VVLVWDQFH ƒ Check the online manuals and error help. ƒ Contact the TA Instruments Hotline ƒ Phone: 302-427-4070 M-F 8-4:30 EST ƒ Select Thermal , Rheology or Microcalorimetry Support ƒ Email: thermalsupport@tainstruments.com or rheologysupport@tainstruments.com or microcalorimetersupport@tainstruments.com ƒ Call your local Technical or Service Representative ƒ Call TA Instruments ƒ Phone: 302-427-4000 M-F 8-4:30 EST ƒ Check out our Website: www.tainstruments.com ƒ For instructional videos go to: www.youtube.com/user/TATechTips
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7LPHDQG7HPSHUDWXUH 5HODWLRQVKLS (E or G) (E' or G') (E or G) (E' or G') log Frequency Temperature ƒ Linear viscoelastic properties are both time-dependent and temperature-dependent ƒ Some materials show a time dependence that is proportional to the temperature dependence ƒ Decreasing temperature has the same effect on viscoelastic properties as increasing the frequency ƒ For such materials, changes in temperature can be used to “re-scale” time, and predict behavior over time scales not easily measured
TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7LPH7HPSHUDWXUH6XSHUSRVLWLRQLQJ%HQHILWV ƒ TTS can be used to extend the frequency beyond the instrument’s range ƒ Creep TTS or Stress Relaxation TTS can predict behavior over longer times than can be practically measured ƒ Can be applied to amorphous, non modified polymers ƒ Material must be thermo-rheological simple ƒ One in which all relaxations times shift with the same shift factor aT
TAINSTRUMENTS.COM TAINSTRUMENTS.COM :KHQ1RWWR8VH776 ƒ If crystallinity is present, especially if any melting occurs in the temperature range of interest ƒ The structure changes with temperature ƒ Cross linking, decomposition, etc. ƒ Material is a block copolymer (TTS may work within a limited temperature range) ƒ Material is a composite of different polymers ƒ Viscoelastic mechanisms other than configuration changes of the polymer backbone ƒ e.g. side-group motions, especially near the Tg ƒ Dilute polymer solutions ƒ Dispersions (wide frequency range) ƒ Sol-gel transition
TAINSTRUMENTS.COM TAINSTRUMENTS.COM *XLGHOLQHVIRU776 ƒ Decide first on the Reference Temperature: T0. What is the use temperature? ƒ If you want to obtain information at higher frequencies or shorter times, you will need to conduct frequency (stress relaxation or creep) scans at temperatures lower than T0. ƒ If you want to obtain information at lower frequencies or longer times, you will need to test at temperatures higher than T0. ƒ Good idea to scan material over temperature range at single frequency to get an idea of modulus-temperature and transition behavior.
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM :KHQQRWWRXVHWKH:/)(TXDWLRQ ƒ Sometimes you shouldn’t use the WLF equation (even if it appears to work) ƒ If T Tg+100° C ƒ If T Tg and polymer is not elastomeric ƒ If temperature range is small, then c1 c2 cannot be calculated precisely ƒ In these cases, the Arrhenius form is usually better ln aT = (Ea/R)(1/T-1/T0) ƒ aT = temperature shift factor ƒ Ea = Apparent activation energy ƒ T0 = reference temperature ƒ T = absolute temperature ƒ R = gas constant ƒ Ea = activation energy
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM 5HIHUHQFHVIRU776 1) Ward, I.M. and Hadley, D.W., Mechanical Properties of Solid Polymers, Wiley, 1993, Chapter 6. 2) Ferry, J.D., Viscoelastic Properties of Polymers, Wiley, 1970, Chapter 11. 3) Plazek, D.J., Oh, Thermorheological Simplicity, wherefore art thou? Journal of Rheology, vol 40, 1996, p987. 4) Lesueur, D., Gerard, J-F., Claudy, P., Letoffe, J-M. and Planche, D., A structure related model to describe asphalt linear viscoelasticity, Journal of Rheology, vol 40, 1996, p813.
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM RQWLQXRXV5DPS Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress ƒ Thixotropic loop be done by adding another ramp step
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM '+5DQG$5(6*6WHDG6WDWH)ORZ Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress Steady state algorithm
TAINSTRUMENTS.COM TAINSTRUMENTS.COM '+5DQG$5(6*)ORZ7HPS5DPS Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress To minimize thermal lag, the ramp rate should be slow. 1-5° C/min.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM '+56WUDLQ6WUHVV6ZHHSV Control variables: ƒ Osc torque ƒ Osc stress ƒ Displacement ƒ % strain ƒ Strain
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM )UHTXHQF6ZHHS Control variables: ƒ Osc torque ƒ Osc stress ƒ Displacement ƒ % strain ƒ Strain ƒ Common frequency range: 0.1 – 100 rad/s. ƒ Low frequency takes long time ƒ As long as in the LVR, the test frequency can be set either from high to low, or low to high ƒ The benefit doing the test from high to low ƒ Being able to see the initial data points earlier
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TAINSTRUMENTS.COM TAINSTRUMENTS.COM '+57HPSHUDWXUH5DPS Control variables: ƒ Osc torque ƒ Osc stress ƒ Displacement ƒ % strain ƒ Strain To minimize thermal lag, recommend using slow ramp rate e.g. 1-5° C/min. ƒ The strain needs to be in the LVR
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Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
Rheology Fundamentals and Instrumentation
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