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ƒ Basics in Rheology Theory ƒ Oscillation ƒ TA Rheometers ƒ Linear Viscoelasticity ƒ Instrumentation ƒ Setting up Oscillation Tests ƒ Choosing a Geometry ƒ Transient Testing ƒ Calibrations ƒ Applications of Rheology ƒ Flow Tests ƒ Polymers ƒ Viscosity ƒ Structured Fluids ƒ Setting up Flow Tests ƒ Advanced Accessories

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Rheology: The study of stress-deformation relationships

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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

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Top plate Area = A x(t) Velocity = V0 Force = F

y y Bottom Plate Velocity = 0 x F Shear Stress, Pascals σ = A

x(t) σ γ = η = Shear Strain, % Viscosity, Pa⋅s y γ

γ -1 γ = Shear Rate, sec t

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Ω r θ

h

Stress (σ) ߪൌ మ ൈM ഏೝయ r = plate radius h = distance between plates γ ߛൌೝ ൈθ M = torque (μN.m) Strain ( ) ೓ θ = Angular motor deflection (radians) Ω= Motor angular velocity (rad/s) ೝ Ω Strain rate (ߛሶ) ߛሶ ൌ೓ ൈ

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ARES G2 DHR

Controlled Strain Controlled Stress Dual Head Single Head SMT CMT

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Dual head or SMT Single head or CMT Separate motor & transducer Combined motor & transducer

Displacement Measured Transducer Sensor Torque (Stress) Measured Strain or Rotation Non-Contact Drag Cup Motor

Applied Torque Sample (Stress)

Applied Strain or Direct Drive ^ƚĂƚŝĐWůĂƚĞStatic Plate Rotation Motor

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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)

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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

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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.mor gm.cm

<σ = Stress Constant

ƒ The stress constant, <σ, is a geometry dependent factor

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ƒ In a SMT Rheometer, the angular displacement is directly applied by a motor.

ƒ The formula for strain is: γ с<γ 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

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Describe In Spec Correctly

σ M ⋅ Kσ G = γ = θ ⋅ Kγ

Geometric Rheological Constitutive Raw rheometer Shape Parameter Equation Specifications Constants

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.

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ƒ In a SMT rheometer, the angular speed is directly controlled by the motor).

ƒ The formula for shear rate is:

ߛሶ ൌܭఊ ൈ: where ߛሶ = Shear rate <γ = Strain Constant Ω = Motor angular velocity in rad/sec

ƒ The strain constant, <γ, is a geometry dependent factor

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Describe In Spec Correctly σ ⋅ η = = M Kσ γ Ω ⋅  Kγ

Geometric Rheological Constitutive Raw rheometer Shape Parameter Equation Specifications Constants

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.

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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 ,ZͲϮ ,ZͲϯ Minimum Torque (nN.m) Steady 51020 ,ZͲϭ Shear 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 Optical Optical encoder encoder 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 DHR - DMA mode (optional) Normal/Axial Force Transducer FRT FRT FRT Maximum Normal Force (N) 50 50 50 Motor Control FRT Minimum Force (N) Oscillation 0.1 Normal Force Sensitivity (N) 0.005 0.005 0.01 Maximum Axial Force (N) 50 Minimum Displacement (μm) 1.0 Normal Force Resolution (mN) 0.5 0.5 1 Oscillation Maximum Displacement (μm) 100 Oscillation Displacement Resolution (nm) 10 Axial Frequency Range (Hz) 1 x 10-5 to 16

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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 Orthogonal Superposition (OSP) and Motor Design Brushless DC DMA modes Motor Bearing Jeweled Air, Sapphire Motor Control FRT Displacement Control/ Sensing Optical Encoder Strain Resolution (μrad) 0.04 Minimum Transducer Force (N) 0.001 Oscillation Minimum Angular Displacement (μrad) 1 Maximum Transducer Force 20 Oscillation (N) Maximum Angular Displacement (μrad) Unlimited Minimum Displacement (μm) 0.5 Steady Shear Oscillation -6 Angular Velocity Range (rad/s) 1x 10 to 300 Maximum Displacement (μm) 50 Angular Frequency Range (rad/s) 1x 10-7 to 628 Oscillation Step Change, Velocity (ms) 5 Displacement Resolution (nm) 10 Step Change, Strain (ms) 10 Axial Frequency Range (Hz) 1 x 10-5 to 16

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Concentric Cone and Parallel Torsion Cylinders Plate Plate Rectangular

Very Low Very Low Very Low Solids to Medium to High Viscosity Viscosity Viscosity to Soft Solids Water to Steel

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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!

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௥ Strain Constant: ܭఊ ൌ௛ (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)

'ĂƉ;ŚͿ Stress Constant: ܭ ൌ ଶ ఙ గ௥య (to convert torque, N⋅m, to shear stress at the ŝĂŵĞƚĞƌ;Ϯ⋅⋅⋅ƌͿ edge, Pa, for Newtonian fluids. The radius, r, is expressed in meters)

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ƒ Low/Medium/High Viscosity ƒ Samples with long relaxation time Liquids ƒ Temperature Ramps/ Sweeps ƒ Soft Solids/Gels ƒ Materials that may slip ƒ Thermosetting materials ƒ Crosshatched or Sandblasted plates ƒ Samples with large particles ƒ Small sample volume

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Shear Stress

20 mm

40 mm

60 mm

ʹ As diameter decreases, shear stress increases ߪൌܯ ߨݎଶ

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Shear Rate 2 mm Increases

1 mm

0.5 mm

ݎ As gap height decreases, shear rate increases ߛሶ ൌȳ ݄

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ƒ For a given angle of deformation, there is a greater arc of deformation at the edge of the plate than at the center

,ݔ dx increases further from the center݀ ߛൌ ݄ h stays constant

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ƒ The cone shape produces a smaller gap height closer to inside, so the shear on the sample is constant

ݔ݀ ߛൌ h increases proportionally to dx, γ is uniform ݄

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ଵ Strain Constant: ܭఊ ൌఉ (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)

ܭ ൌ ଷ Stress Constant: ఙ ଶగ௥య

(to convert torque, N⋅m, to shear stress, Pa. The radius, r, is expressed in meters)

Diameter (2⋅⋅⋅r) Truncation (gap)

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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

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Shear Stress

20 mm

40 mm

60 mm

͵ As diameter decreases, shear stress increases ߪൌܯ ʹߨݎଷ

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Shear Rate Increases

2 °

1 °

0.5 °

ͳ As cone angle decreases, shear rate increases ߛሶ ൌȳ ߚ

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Typical Truncation Heights: 1° degree ~ 20 - 30 microns 2° degrees ~ 60 microns 4° degrees ~ 120 microns

Cone & Plate Truncation Height = Gap

Gap must be > or = 10 [particle size]!!

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× Under Filled sample: Lower torque contribution

× Over Filled sample: Additional stress from drag along the edges

9 Correct Filling

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ݎ ଶ ൅ݎ ଶ Strain Constant: ͳ ʹ ܭఊ ൌ ଶ ଶ ݎʹ ݎͳ (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)

* ݎ ଶ ൅ݎ ଶ Stress Constant: ଵ ͳ ʹ ܭఙ ൌସగ௟  ଶ ଶ ݎʹ ݎͳ

(to convert torque, N⋅m, to shear stress, Pa. The bob length, l, and the radius, r, are expressed in meters)

*Note including end correction factor. See TRIOS Help TAINSTRUMENTS.COM 'RXEOH:DOO

ƒ Use for very low viscosity systems (<1 mPas)

r1

r2 h r3

r4

ଶ ଶ ݎͳ ൅ݎʹ Strain Constant: ܭఊ ൌ ଶ ଶ ݎʹ െݎͳ మ మ ௥ଵ ା௥ଶ Stress Constant: ܭఙ ൌ మ మ మ ସగ௛ή௥ଶ ௥ଵ ା௥ଷ ARES Gap Settings: standard operating gap DW = 3.4 mm narrow operating gap DW = 2.0 mm

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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

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ݐ ܭ ൌ ఊ ௧ ଶ ݈ ͳ െ ͲǤ͵͹ͺ ௪ w = Width l = Length ͵൅ଵǤ଼ t = Thickness ܭ ൌ ௪ ఛ ݓήݐଶ

Advantages: Disadvantages:

ƒ High modulus samples ƒ No pure Torsion mode for ƒ Small temperature high strains gradient ƒ Simple to prepare

Torsion cylindrical also available

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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 DMA 3-point bending and tension cylindrical torsion (cantilever not shown)

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Geometry Application Advantage Disadvantage

Cone/plate fluids, melts true viscosities temperature ramp difficult viscosity > 10mPas

Parallel Plate fluids, melts easy handling, shear gradient across viscosity > 10mPas temperature ramp sample

Couette low viscosity samples high shear rate large sample volume < 10 mPas

Double Wall Couette very low viscosity high shear rate cleaning difficult samples < 1mPas

Torsion Rectangular solid polymers, glassy to rubbery Limited by sample stiffness composites state

Limited by sample stiffness Solid polymers, films, Glassy to rubbery DMA (Oscillation and Composites state stress/strain)

 

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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

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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

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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

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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.

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ƒ Viscosity is… ƒ “lack of slipperiness” ƒ synonymous with internal friction ƒ resistance to flow

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)

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Describe In Spec Correctly σ ⋅ η = = M Kσ γ Ω ⋅  Kγ

Geometric Rheological Constitutive Raw rheometer Shape Parameter Equation Specifications Constants

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6 Asphalt Binder ------100,000 6 Polymer Melt ------1,000 6 Molasses ------100 6 Liquid Honey ------10 Need for 6 Glycerol ------1 Log scale 6 Olive Oil ------0.01 6 Water ------0.001 6 Air ------0.00001

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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

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Ideal Yield Stress (Bingham Yield) Pa.s , Pa η, σ

γ ,1/s or σ, Pa γ ,1/s

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105 105

103 103 Pa.s 101 Pa.s 101 η, η, 10-1 10-1 10-6 10-4 10-2 100 102 104 10-1 10-0 10-1 102 103 ,1/s σ, Pa

105 ,GHDOfluid is a pseudo-plastic , Pa

σ 101

10-1 10-6 10-4 10-2 100 102 104 γ ,1/s

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ƒ Dilatant material resists deformation more than in proportion to the applied

Pa.s force (shear-thickening) η, ƒ Cornstarch in water or sand Log on the beach are actually dilatant fluids, since they do not show the time- dependent, shear-induced change required in order to Log ߛሶ,1/s be labeled rheopectic

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ƒ Rheopectic materials become more viscous Rheopectic with increasing time of applied force ƒ Higher concentration latex dispersions and Shear Rate = Constant plastisol paste materials exhibit rheopectic Viscosity behavior Thixotropic ƒ Thixotropic materials become more fluid with increasing time of applied time force ƒ Coatings and inks can display thixotropy when sheared due to structure breakdown

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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

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ƒ Constant rate vs. time

ƒ Constant stress vs. time Stress /Rate

USES ƒ Single point testing ƒ Scope the time for steady state under certain rate

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3.500 4.000 Hand Wash Rate 1/s

3.500 3.000

3.000 2.500

2.500 viscosity (Pa.s) viscosity 2.000

2.000

1.500 shear stress (Pa) Viscosity at 1 1/s is 2.8 Pa⋅s 1.500

1.000 1.000

0.5000 0.5000

0 0 0 5.0000 10.000 15.000 20.000 25.000 30.000 time (s)

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Deformation ƒ Stress is applied to material at a constant m =Stress rate rate. Resultant strain (Pa/min) is monitored with time.

time (min)

USES ƒ Yield stress ƒ Scouting Viscosity Run

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Deformation ƒ Stress is first increased, σ then decreased, at a constant rate. Resultant strain is monitored with time. time

USES ƒ “Pseudo-thixotropy” from Hysteresis loop

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Run in Stress Control TA Instruments 500.0

400.0

300.0 ZĞĚ͗&ŝƌƐƚĐLJĐůĞ ůƵĞ͗^ĞĐŽŶĚĐLJĐůĞ 200.0

shear stress (Pa) FORDB3.04F-Up step FORDB3.04F-Down step FORDB3.05F-Up step 100.0 FORDB3.05F-Down step

0 0 0.1000 0.2000 0.3000 0.4000 0.5000 shear rate (1/s)

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Deformation σ Data point saved ƒ Stress is applied to sample. Žƌ Viscosity measurement is taken ߛሶ when material has reached steady state flow. The stress is increased(logarithmically) and the time process is repeated yielding a viscosity flow curve.

Delay time σ USES Žƌ Steady State Flow ߛሶ ƒ Viscosity Flow Curves γ or σ = Constant ƒ Yield Stress Measurements

time

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ƒ A series of logarithmic stress steps allowed to reach steady state, each one giving a single viscosity data point:

Data at each Shear Rate

Shear Thinning Region

Time Viscosity

η = σ / γ/ Shear Rate, 1/s (d dt)

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Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress

Steady state algorithm

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0.8000 ^ĂŵƉůĞϭͲ&ůŽǁƐƚĞƉ ^ĂŵƉůĞϮͲ&ůŽǁƐƚĞƉ 0.7000 Which material would do a better job 0.6000 coating your throat?

0.5000

0.4000 viscosity (Pa.s) viscosity 0.3000

0.2000

0.1000

0 0.1000 1.000 10.00 100.0 1000 shear rate (1/s)

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10000 A.01F-Flow step Low shear rates B>A B.01F-Flow step

1000

100.0

viscosity (Pa.s) 10.00 Medium shear rates A>B

1.000

High shear rates B>A

0.1000 1.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00 100.0 1000 shear rate (1/s)

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ƒ Hold the rate or stress yyyy constant whilst ramping the temperature.

time (min)

USES ƒ Measure the viscosity change vs. temperature

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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

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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

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Surface tension at low torques

Secondary flows at high shear rates

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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

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When Stress Decreases with Shear Rate, it indicates that sample is leaving the gap

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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 η γ η* () ≡ ω ( )

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Hooke’s Law of Elasticity: Stress = Modulus ⋅ Strain

γ γ γ 1 2 3

3

2 

^ƚƌĞƐƐ;ʍͿ 1

1 2 3 ^ƚƌĂŝŶ;࠹Ϳ

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Hooke’s Law of Elasticity: Stress = Modulus ⋅ Strain E > E >E

ߪ ܧൌ γ γ γ ߛ 1 2 3

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Newton’s Law: stress = coefficient of viscosity ⋅ shear rate Ș ߪൌKήߛሶ ^ƚƌĞƐƐ;ʍͿ

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TAINSTRUMENTS.COM 9LVFRXV%HKDYLRURIDQ,GHDO/LTXLG ߪ Newton’s Law: stress= coefficient of viscosity ⋅ shear rate Ʉൌ ߛሶ Ș < Ș < Ș

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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.

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ƒ Long deformation time: pitch behaves like a highly viscous liquid th ƒ 9 drop fell July 2013 ƒ Short deformation time: pitch behaves like a solid

Started in 1927 by Thomas Parnell in Queensland, Australia ŚƚƚƉ͗ͬͬǁǁǁ͘ƚŚĞĂƚůĂŶƚŝĐ͘ĐŽŵͬƚĞĐŚŶŽůŽŐLJͬĂƌĐŚŝǀĞͬϮϬϭϯͬϬϳͬƚŚĞͲϯͲŵŽƐƚͲĞdžĐŝƚŝŶŐͲǁŽƌĚƐͲŝŶͲƐĐŝĞŶĐĞͲƌŝŐŚƚͲŶŽǁͲƚŚĞͲƉŝƚĐŚͲĚƌŽƉƉĞĚͬϮϳϳϵϭϵͬ

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T is short [< 1s] T is long [24 hours]

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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)

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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

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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

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(E' or G') (E' or G') (E" or G") (E" or G")

log Frequency Temperature

log Time log Time

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"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.

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Measuring linear viscoelastic properties helps us bridge the gap between molecular structure and product performance

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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)

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Phase angle δ Strain, ε

Stress, σΎ

Dynamic stress applied sinusoidally User-defined Stress or Strain amplitude and frequency

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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

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ω = 6.28 rad/s

ω = 12.560rad/s

0 0 0 0

dŝŵĞсϭƐĞĐ ω = 50 rad/s

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ƒ Strain and stress are calculated from peak amplitude in the displacement and torque waves, respectively.

0 0 0 0

dŝŵĞсϭƐĞĐ

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Deformation ƒ An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample. Response ƒ The material response (strain or stress) is measured.

ƒ The phase angle δ, or phase shift, between the deformation Phase angle δ and response is measured.

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Purely Elastic Response Purely Viscous Response (Hookean Solid) (Newtonian Liquid) δ сϬ° δ сϵϬ°

Strain Strain

Stress Stress

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Phase angle 0°< δ < 90°

Strain

Stress

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ƒ The stress in a dynamic experiment is referred to as the complex stress σ* ƒ The complex stress can be separated into two components: 1) An elastic stress in phase with the strain. σ' = σ*cosδ σ' is the degree to which material behaves like an elastic solid. 2) A viscous stress in phase with the strain rate. σ" = σ*sinδ σ" is the degree to which material behaves like an ideal liquid.

Phase angle δ Complex Stress, σ* σ* = σ' + iσ"

Complex number: ݔ൅݅ݕ ൌ ݔଶ ൅ݕଶ The material functions can be described in Strain, ε terms of complex variables having both real and imaginary parts. Thus, using the relationship:

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כୗ୲୰ୣୱୱ כ The Modulus: Measure of materials overall resistance to ൌ ୗ୲୰ୟ୧୬ deformation. The Elastic (Storage) Modulus: כୗ୲୰ୣୱୱ Measure of elasticity of material. ᇱ ൌ ‘• Ɂ The ability of the material to store ୗ୲୰ୟ୧୬ energy. The Viscous (loss) Modulus: כ The ability of the material to ̶ ൌ ୗ୲୰ୣୱୱ •‹ Ɂ dissipate energy. Energy lost as ୗ୲୰ୟ୧୬ heat.

Tan Delta: ̶ Measure of material damping - ୋ –ƒ Ɂ ൌ ᇱ such as vibration or sound ୋ damping.

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RUBBER BALL y LOSS (G”) TENNIS BALL y

STORAGE (G’)

G* Dynamic measurement G" represented as a vector Phase angle δ G'

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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!

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Parameter Shear Elongation Units

Strain ɶсɶϬƐŝŶ;ʘƚͿ ɸ сɸϬ ƐŝŶ;ʘƚͿ ---

σ σ τ τ Stress с ϬƐŝŶ;ʘƚнɷͿ с ϬƐŝŶ;ʘƚнɷͿ Pa

Storage Modulus '͛с;σ ͬɶ ͿĐŽƐɷ ͛с;τ ͬɸ ͿĐŽƐɷ Pa (Elasticity) Ϭ Ϭ Ϭ Ϭ

Loss Modulus '͟с;σ ͬɶ ͿƐŝŶɷ ͟с;τ ͬɸ ͿƐŝŶɷ Pa (Viscous Nature) Ϭ Ϭ Ϭ Ϭ

Tan į 'ͬ͟'͛ ͬ͛͟ ---

Complex Modulus 'Ύ с;'͛Ϯн'͟ϮͿϬ͘ϱ Ύ с;͛Ϯн͟ϮͿϬ͘ϱ Pa

ηΎ η Ύ Ύ Complex Viscosity с'Ύͬʘ  с ͬʘ Pa·sec

Cox-Merz Rule for Linear Polymers: η*(Ȧ) = η(ߛሶ) @ ߛሶ = Ȧ

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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)

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ƒ The material response to increasing deformation amplitude (strain or stress) is monitored at a constant frequency and Stress or strain Time temperature.

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

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Linear Region: Modulus Non-linear Region: independent Modulus is a function of strain of strain

G'

Stress

Constant γ сCritical Strain Slope Đ

Strain (amplitude)

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ƒ In general, the LVR is shortest when the sample is in its most solid form.

Solid G’

Liquid

% strain

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ƒ LVR decreases with increasing frequency ƒ Modulus increases with increasing frequency

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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

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^K^ γ γ ω (t) = 0 sin( t) τ τ ω δ (t) = 0 sin( t+ )

γ γ ω >K^ (t) = 0 sin( t)

Fourier Series expansion: τ τ ω ϕ τ ω ϕ (t) = 1 sin( 1t+ 1) + 3 sin(3 1t+ 3) + τ ω ϕ 5 sin(5 1t+ 5) + ... ’ τ ω ϕ = Σ n sin(n 1+ n) n=1 odd Lissajous plot: Stress vs. Strain (shown) or stress vs. Shear rate

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ƒ The material response is monitored at a constant frequency, amplitude and

Stress or strain temperature. Time

USES ƒ Time dependent Thixotropy ƒ Cure Studies ƒ Stability against thermal degradation ƒ Solvent evaporation/drying

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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

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 Under N2 Under air

 

     

      

         

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ϭϬϬ͘Ϭ Structural Recovery after Preshear

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G' (Pa) ϰϬ͘ϬϬ

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Ϭ 0 Ϯϱ͘ϬϬ ϱϬ͘ϬϬ ϳϱ͘ϬϬ ϭϬϬ͘Ϭ ϭϮϱ͘Ϭ ϭϱϬ͘Ϭ ϭϳϱ͘Ϭ ϮϬϬ͘Ϭ ϮϮϱ͘Ϭ time (s)

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Sample “A” time sweep Delay after pre-shear = 150 sec Delay after pre-shear = 0 sec 100.0 100.0 G' (Pa) Pre-shear conditions: 100 1/s for 30 seconds

10.00 10.00 0 25.00 50.00 75.00 100.0 125.0 150.0 175.0 0.1000 1.000 10.00 100.0

time (s) osc. stress (Pa)

ƒ End of LVR is indicative of “Yield” or “Strength of Structure” ƒ Useful for Stability predictions (stability as defined by yield)

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Solvent trap cover picks up heat from Peltier Plate to insure uniform temperature

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TA Instruments 1000000 G' 1000000 5 min 100000 100000

10000 G" 10000 G'' (Pa) 1000 Gel Point: G' = G" 1000 G' (Pa) t = 330 s 100.0 100.0

10.00 10.00

1.000 1.000 0 200.0 400.0 600.0 800.0 1000 1200 time (s)

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ƒ The material response to increasing frequency (rate of deformation) is monitored at a constant amplitude (strain

ŵƉůŝƚƵĚĞ or stress) and temperature.

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)

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Transition Rubbery Region Terminal Plateau Region Region

Glassy Region

1 2 Storage Modulus (E' or G') >ŽƐƐDŽĚƵůƵƐ;ΗŽƌ'ΗͿ

log Frequency (rad/s or Hz)

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Frequency of modulus crossover correlates with Relaxation Time

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η γ η* () ≡ ω ( )

Flow instability Z

W

LDPE Freq sweep 2mm gap – Cox Merz LDPE shear rate 1mm gap LDPE Shear rate 2 mm gap

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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

3.4 G' § M · η ≈ M 3.4 and J = ≈ ¨ w ¸ 0 w e 2 ¨ ¸ (G") © M z ¹

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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.

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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

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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

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Waveforms at high frequencies

Inertial effects at high frequencies

Negligible correction at low frequencies

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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

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FRT Deflection FRT null Position Purest Measurement ! Torque to drive FRT To maintain Zero Position = Sample Torque

Motor Inertia Target NOT Part of Strain Motor Measured Measurement Displacement Or Speed

Motor torque and sample torque are Torque to separated. drive motor to desired displacement

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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. time between data points m = ramp rate (°C/min)

Temperature (°C) Temperature Denotes Oscillatory Measurement time (min)

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ƒ A step and hold temperature Soak profile is applied. The Time

material response is Step Size monitored at one, or over a

range of frequencies, at Oscillatory constant amplitude of Measurement deformation. – No thermal lag Time

Soak Time

Oscillatory Step Size Measurement

Time

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Glassy Region Transition Region Rubbery Plateau Region Terminal Region

log E' (G') and (G") E" Storage Modulus (E' or G') Loss Modulus (E" or G")

dĞŵƉĞƌĂƚƵƌĞ

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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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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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ƒ Videos available at www.tainstruments.com under the Videos tab or on the TA tech tip channel of YouTube™ (ŚƚƚƉƐ͗ͬͬǁǁǁ͘LJŽƵƚƵďĞ͘ĐŽŵͬƵƐĞƌͬddĞĐŚdŝƉƐ)

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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)

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Material fully cured At start of test have a material that starts as Maximum h or G’ reached liquid, paste, pressed power Pellet, or prepreg

η Žƌ '͛

Crosslinking reaction causes h and G’ to increase

dĞŵƉ As the temp increases Material hits minimum viscosity which depends on the viscosity of resin Max temperature, frequency, ramp rate and may depend decreases on strain or stress amplitude

Time

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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

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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

θ (t+1)1 θ (t)1

Μ (t+1)1 Μ (t)1

Point 1 or cycle

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η Žƌ '͛

Torque

Strain

Concern: How high does strain go at minimum Temp 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?

Time

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Torque Upper torque limit

Strain

η Žƌ '͛

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Time

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ARES-G2 DHR

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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

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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

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Ϭ time Response of Classical Extremes

Hookean Solid Newtonian Fluid

stress for t>0 is 0 stress for t>0 is constant Ϭ time Ϭ time

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Response of ViscoElastic Material

Stress decreases with time starting at some high value and decreasing to zero. Ϭ time

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(t)/γ

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Glassy Region Transition Region Rubbery Terminal Plateau Region Region

log time

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ϭ Ϭ͘Ϭϭ Ϭ͘ϭ ϭ ϭϬ ϭϬϬ time (s)

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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 с<γ п θ ;йγ с γ пϭϬϬͿ

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Stress Relaxation of PDMS, Overlay

105 G(t) 200% strain 50% strain 10% strain 104 )

103 [Pa] G(t) ( G(t)

102

200% strain is outside the linear region 101 0.0 5.0 10.0 15.0 20.0 25.0 30.0 time [s]

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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

t1 time t2

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t1 time t2 Response of Classical Extremes

ƒ Stain rate for t>t1 is constant ƒ Stain for t>t1 is constant ƒ Strain for t>t1 increase with time ƒ Strain for t >t2 is 0 ƒ Strain rate for t >t2 is 0

time t1 time t2 t1 t2

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Rubbery Plateau Region

Transition Region

Glassy Region Terminal Region log Creep Compliance, Jc Creep log ůŽŐƚŝŵĞ

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ƌĞĞƉσ хϬ

σ/η

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Creep σ > 0 Recovery σ = 0 (after steady state)

σ/η Less Elastic

More Elastic Creep Zone Recovery Zone

t1 t2 time

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more elastic ϭͬη : Ğ Creep Zone Je = Equilibrium recoverable compliance ;ƚͿ ƌ : :;ƚͿ

Recovery Zone time time Creep Compliance Recoverable Compliance ஓሺ୲ሻ ɀ െɀ – –ൌ –ൌ ୳ ஢ ୰ ɐ γ The material property obtained from Where u = Strain at unloading Creep experiments: γ(t) = time dependent Compliance = 1/Modulus (in a sense) recoverable strain

Mark, J., et. al., Physical Properties of Polymers, American Chemical Society, 1984, p. 102.

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• 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

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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

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ƒ Set up a pre-test and get the sample information into the loop ƒ Stress Control Pre-test: frequency sweep within LVR

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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

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3.5000 HDPE Creep Recovery at 200°C

3.0000

2.5000

2.0000

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1.0000

0.50000

0 0 2000.000 4000.000 6000.000 8000.000 10000.000 time global (s)

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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. 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.

σ = Kσ x Μ

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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.

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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

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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

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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

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Polyester Temperature stability 275 Determines if properties Temperature stability are changing over the good poor time of testing 5 250 10 ƒ Degradation ƒ Molecular weight 225 building ƒ Crosslinking

Modulus G'[Pa] 200 104 Temperature T [°C]

175 -2024681012141618 Time t [min]

Important, but often overlooked!

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Power Law Region

First Newtonian Plateau η 0 = Zero Shear Viscosity η 3.4 0 = K x MW Extend Range ηη with Time- Temperature log log Superposition (TTS) Measure in Flow Mode & Cox-Merz

Extend Range Second Newtonian with Oscillation Plateau & Cox-Merz

Molecular Structure Compression Molding Extrusion Blow and Injection Molding

1.00E-5 1.00E-4 1.00E-3 0.0100 0.100 1.00 10.00 100.00 1000.00 1.00E4 1.00E5 shear rate (1/s)

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ƒ Sensitive to Molecular Weight, MW η ƒ For Low MW (no Entanglements) 0 is proportional to MW η 3.4 ƒ For MW > Critical MWc, 0 is proportional to MW

o 3.4 η MWc log

η ⋅⋅⋅ ϯ͘ϰ η с<⋅⋅⋅Dǁ 0 с< Dǁ 0 log MW

Ref. Graessley, Physical Properties of Polymers, ACS, c 1984.

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The zero shear viscosity increases with increasing molecular weight. TTS is applied to obtain the extended frequency range.

107 SBR M [g/mol] The high frequency w 130 000 behavior 106 230 000 (slope -1) is 320 000 independent of the 430 000 molecular weight 105 * [Pa s]* [Pa η

4 Zero Shear [Pas]

10 o Viscosity η

106 3 Viscosity Viscosity 10 Slope 3.08 +/- 0.39 Zero Shear Viscosity

105 2 100000 Molecilar weight M [Daltons] 10 w

10-4 10-3 10-2 10-1 100 101 102 103 104 105 Frequency ω a [rad/s] T

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ƒ A Polymer with a broad MWD exhibits non-Newtonian flow η at a lower rate of shear than a polymer with the same 0, but has a narrow MWD.

Narrow MWD

Broad MWD

Log Shear Rate (1/s)

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The G‘ and G‘‘ curves are shifted to lower frequency with increasing molecular weight.

106

105

104 SBR M [g/mol] w 3 G' 130 000 10 G'' 130 000 G' 430 000

Modulus G', G'' [Pa] Modulus 2 G'' 430 000 10 G' 230 000 G'' 230 000 101 10-4 10-3 10-2 10-1 100 101 102 103 104 105 Freq ω [rad/s]

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106

105 ƒ The maximum in G‘‘ is a good indicator of the broadness of the 104 distribution SBR polymer melt G' 310 000 broad Modulus G',Modulus G'' [Pa] 3 G" 310 000 broad 10 G' 320 000 narrow G" 320 000 narrow EĂƌƌŽǁ -3 -2 -1 0 1 2 3 4 10 10 10 10 10 10 10 10 ƌŽĂĚ Frequency ωa [rad/s] T

Higher crossover frequency : lower Mw Higher crossover Modulus: narrower MWD (note also the slope of G” at low frequencies – narrow MWD steeper slope)

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400,000 g/mol PS 400,000 g/mol PS 400,000 g/mol PS + 1% 12,000,000 g/mol + 4% 12,000,000 g/mol

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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

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HDPE pipe surface defects

o ƒ Surface roughness T = 220 C 5 5 correlates with G‘ or 10 10 elasticity → broader MWD or tiny amounts of a high * [Pa s] * [Pa η MW component 4 10 104

G' rough surface Modulus G' [Pa] G' Modulus 3 G' smooth surface 10 103

η* rough surface viscosity Complex η* smooth surface

0.1 1 10 100 Frequency ω [rad/s]

Blue-labled sample shows a rough surface after extrusion

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Tack and Peel performance of a PSA

ƒ Bond strength is obained from peel good tack and peel (fast) and tack Bad tack and peel (slow) tests 104 ƒ It can be related to the viscoelastic properties at peel different frequencies 103

Storage Modulus G' [Pa] Modulus Storage tack

0.1 1 10 Frequency ω [rad/s] Tack and peel have to be balanced for an ideal adhesive

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LDPE Melt creep recovery

-1 10 10-1 LDPE Melt ƒ Non linear effects 10 Pa T=140 oC 50 Pa can be detected in -2 slope 1 recovery before 10 100 Pa 10-2 500 Pa they are seen in the 1000 Pa increasing creep (viscosity stress -3 5000 Pa dominates) 10 10-3

-4 10 10-4 Compliance J(t)[1/Pa]

-5 Compliance Recoverable Jr(t)[1/Pa] 10 10-5 0.1 1 10 100 1000 Time t [s]

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Neat and Filled LDPE

7 ƒ &ŝůůĞƌƐŝŶĐƌĞĂƐĞƚŚĞ 10 o Temperature 180 C ŵĞůƚǀŝƐĐŽƐŝƚLJ LDPE filled 106 LDPE neat ƒ ƵĞƚŽŝŶƚĞƌͲƉĂƌƚŝĐůĞ ŝŶƚĞƌĂĐƚŝŽŶƐ͕ƚŚĞ 105 . s] ) [Pa γ ŶŽŶͲEĞǁƚŽŶŝĂŶ ( η ƌĂŶŐĞŝƐĞdžƚĞŶĚĞĚƚŽ 4 10 ůŽǁƐŚĞĂƌƌĂƚĞƐĂŶĚ ƚŚĞnjĞƌŽƐŚĞĂƌ Viscosity Viscosity 103 ǀŝƐĐŽƐŝƚLJŝŶĐƌĞĂƐĞƐ ĚƌĂŵĂƚŝĐĂůůLJ 102 1E-5 1E-4 1E-3 0.01 0.1 1 10 100 1000 10000 . Shear rate γ [1/s]

The material has a yield, when rate and viscosity are inverse proportional at low rate.

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Fix drum connected to transducer

Rotating drum connected to the motor: ƒ rotates around its axis ƒ rotates around axis of fixed drum

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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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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.

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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’, δ G”, tan , Tg etc.)

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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

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TA Instruments 1000000 G' 1000000 5 min 100000 100000

10000 G" 10000 G'' (Pa)

1000 1000

G' (Pa) Gel Point: G' = G" t = 330 s 100.0 100.0

10.00 10.00

1.000 1.000 0 200.0 400.0 600.0 800.0 1000 1200 time (s)

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• 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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135°C 130°C 140°C 120°C 125°C 145°C G’ (MPa) G’

Tire Compound: Effect of Curing Temperature

Time (min)

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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

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ƵƉƚŽϱϬƉŽŝŶƚƐ ƉĞƌƐĞĐŽŶĚ

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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.

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G' Onset: Occurs at lowest temperature - Relates to mechanical failure

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. tan 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.

Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 980.

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ƒ Allows samples to be Addition of Water characterized while fully 1.000E10 100.0 immersed in a temperature controlled fluid using Peltier Isotherm with 90.0 Concentric Cylinder Jacket water at 22 °C Isotherm 1.000E9 ƒ Track changes in mechanical with water 80.0 properties such as swelling or at 95 °C plasticizing

70.0 1.000E8 temperature (°C)

Temperature 60.0 G' (Pa) ramp to 95 °C G’ (Pa) G’ 1.000E7 50.0

40.0

1.000E6

30.0

1.000E5 20.0 0 10.0 20.0 30.0 40.0 50.0 60.0 timetime global (min) (min)

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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

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Modulus: G’, G”, G* Modulus: E’, E”, E*

Rectangular and DMA 3-point bending and tension cylindrical torsion (Cantilever not shown)

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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)

Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 487.

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Increasing Crystallinity

Amorphous Crystalline log Modulus 3 decade drop Cross-linked

in modulus at Tg

Increasing MW Tm Temperature

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ƒ Multiphase systems consisting of a dispersed phase (solid, fluid, gas) in surrounding fluid phase

ƒExamples are: ƒ Properties: ƒ Paints ƒ Yield Stress ƒ Coatings ƒ Non-Newtonian ƒ Inks Viscous Behavior ƒ Personal Care Products ƒ Thixotropy ƒ Cosmetics ƒ Elasticity ƒ Foods

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What shear rate?

4) Chewing, swallowing 8) Spraying and brushing 1) Sedimentation 5) Dip coating 9) Rubbing 2) Leveling, Sagging 6) Mixing, stirring 10) Milling pigments 3) Draining under gravity

η 7) Pipe flow 11) High Speed coating log

4 5 6 8 9 1 2 3 7 10 11

1.00E-5 1.00E-4 1.00E-3 0.0100 0.100 1.00 10.00 100.00 1000.00 1.00E4 1.00E5 1.00E6

shear rate (1/s)

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This viscosity is often called η the Zero Shear Viscosity, 0, or the Newtonian Viscosity

First Newtonian η Plateau Possible log Increase in Second Viscosity Power-Law Newtonian Shear Thinning Plateau

σ∝ߛሶ m or, equivalently, η∝ߛሶ m-1 m is usually 0.15 to 0.6 log ߛሶ

Reference:Barnes, H.A., Hutton, J.F., and Walters, K., An Introduction to Rheology, Elsevier Science B.V., 1989. ISBN 0-444-87469-0

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Brownian diffusion randomizes

Shear field aligns particles along η streamlines Turbulent flow pushes ůŽŐ particles out of alignment, destroying order and causing increase in viscosity (shear thickening)

Shear thinning Shear thickening

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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’

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ϮϱϬ Exponential Close ϮϬϬ

ϭϱϬ Fast Linear Close G' (Pa) ϭϬϬ

ϱϬ

Ϭ Ϭ ϮϬϬ ϰϬϬ ϲϬϬ ϴϬϬ ϭϬϬϬ Time (s) Lowering the gap can introduce shear, breaking down weakly structured samples Reducing the gap closure speed can minimize this effect

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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

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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.)

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1. 2. 3.

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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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.

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

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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

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Yield Stress

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When the Yield Stress is small, a flow rate sweep from high to low shear rate is preferred

ƒ Eliminates start-up effects for more accurate measurements

slope: -0.995 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

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1000 ƒ Perform strain or stress Sun Block Lotion sweep in oscillation

ƒ Yield stress is the on set of G’ curve. It is the critical

G' (Pa) stress at which irreversible Onset point osc. stress: 1.477 Pa plastic deformation occurs. G': 346.6 Pa End condition: Finished normally

100.0 0.01000 0.1000 1.000 10.00 osc. stress (Pa)

Yield stress of a sun block lotion

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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

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104 At Rest Processing Performance

103 LSV MSV HSV 102 Roling

1 Brushing [Pas] 10 Spraying h 100 Mixing -1 Leveling 10 Pumping Viscosity Viscosity Sagging Consistency 10-2 Sedimentation Appearence

10-3 0.1 1 10 100 1000 10000 100000 shear rate g [1/s]

The two coatings show the same consistency after formulation, but they exhibit very different application performance

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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

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Stress is ramped up linearly, and then back down, over the same duration

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

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after preshear η* Structure build up G'

* [Pas] G'' Pre-shear the sample η 102 G' to break down oo structure. Then monitor the increase of the modulus or complex viscosity as Frequency 1Hz G' strain 2% function of time. o preshear 10s at 60 s-1 Modulus G', G'' [Pa]; Viscosity Viscosity G'' [Pa]; Modulus G',

0 20406080100120 time t min]

ᇱ ௧Ȁఛ τ Ԣ௢ሻሺͳ െ ݁ ) = characteristic recovery timeܩԢஶ െܩԢ௢ ൅ሺܩݐൌ ܩ

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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

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100.0

Paint A

10.00 Paint B

Paint C viscosity (Pa.s)

1.000 Paint D

0.1000 0.01000 0.1000 1.000 10.00 100.0 shear rate (1/s)

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120.0 Thixotropy (Pa/s): Paint A = 657.0 Paint B = 436.5 100.0 Paint C = 254.0 Paint D = 120.3

80.00

Paint A

60.00 shear stress (Pa)

Paint B 40.00

Paint C

20.00

Paint D

0 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)

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15.00

Paint A

12.50

10.00

7.500 G' (Pa)

5.000 Paint B

2.500 Paint C

Paint D

0 0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 time (s)

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Paint A Paint B

Paint C Paint D

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Roll-ons: Rheology and end-use performance The viscosity has to be balanced to provide the correct viscosity at a given shear rate

storage viscosity application

shear rate

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Sticks: Rheology and process performance

ƒ use small particles to reduce sedimentation speed

ƒ add rheological modifier like clay to stabilize the suspension and keep the particles in suspension

ϭнϬϴ x x x x x x x ϭнϬϳ x The temperature x ϭнϬϲ x dependence of the modulus governs the ϭнϬϱ x behavior during the ϭнϬϰ x application to the skin DŽĚƵůƵƐ'Ζ΀WĂ΁ ϭнϬϯ Ϭ ϭϬϮϬϯϬϰϬϱϬϲϬϳϬ dĞŵƉĞƌĂƚƵƌĞ΀΁

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Cosmetic lotion ƒ Many dispersion exhibit 2.0 solid like behavior at rest 103 1.5 * [Pa s] * [Pa η ƒ The frequency 1.0 dependence and the δ 102 0.5 δ absolute value of tan correlate with long time tan tan 0.0 stability complex viscosity

G' -0.5 101 G'' tan δ -1.0 Modulus G', G'' [Pa]; Modulus Viscosity 0.1 1 10 100 frequency ω [rad/s]

ƒ Note: strain amplitude has to be in the linear region

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DIN Vane

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ƒ Browse the contents list or search using the search tab.

ƒ Access to Getting Started Guides also found through the help menu.

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ƒFrom www.tainstruments.com click on Videos, Support or Training

ƒSelect Videos for TA Tech Tips, Webinars and Quick Start Courses

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Quickstart e-Training Courses Strategies for Better Data - Rheology

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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: [email protected] or [email protected] or [email protected] 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

TAINSTRUMENTS.COM Thank You

The World Leader in Thermal Analysis, Rheology, and Microcalorimetry

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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

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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

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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

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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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aT=140

aT=150

aT=160

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ƒ Master Curves can be generated using shift factors derived from the Williams, Landel, Ferry (WLF) equation

log aT= -c1(T-T0)/c2+(T-T0)

ƒ aT = temperature shift factor

ƒ T0 = reference temperature

ƒ c1 and c2 = constants from curve fitting

ƒ Generally, c1=17.44 & c2=51.6 when T0 = Tg

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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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Polystryene

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Polystryene

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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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Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress

ƒ Thixotropic loop be done by adding another ramp step

TAINSTRUMENTS.COM Thixotropic loop

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Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress

Steady state algorithm

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To minimize thermal lag, the ramp rate should be slow. 1-5°C/min.

Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress

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Control variables: ƒ Osc torque ƒ Osc stress ƒ Displacement ƒ % strain ƒ Strain

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Pre-shear can be setup by adding a “conditioning” step before the time sweep.

ƒ The strain needs to be in the LVR

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Pre-shear step

Structure Recovery

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ƒ Strain control mode ƒ Stress control mode

ƒ Fast data acquisition is used for monitoring fast changing reactions such as UV initiated curing ƒ The sampling rate for this mode is twice the functional oscillation frequency up to 25Hz. ƒ The fastest sampling rate is 50 points /sec.

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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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Control variables: ƒ Osc torque ƒ Osc stress ƒ Displacement ƒ % strain ƒ Strain

ƒ The strain needs to be in the LVR

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To minimize thermal lag, recommend using slow ramp rate e.g. 1-5°C/min.

ƒ The strain needs Control variables: to be in the LVR ƒ Osc torque ƒ Osc stress ƒ Displacement ƒ % strain ƒ Strain

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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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Creep Recovery

ƒ Rule of thumb: recovery time is 2-3 times longer than creep time

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Requires measured modulus to start feed back loop

ƒ Motor and transducer work in a feedback loop

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ƒ Set up a pre-test and get the sample information into the loop ƒ Stress Control Pre-test: frequency sweep within LVR

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Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress

ƒ Multiple rate can be done by adding more peak hold steps

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Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress

ƒ Thixotropic loop be done by adding another ramp step ƒ Or go through the template

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Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress

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Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress

Steady state algorithm

ƒ During the test, the dependent variable (speed in controlled stress mode or torque in controlled shear rate mode) is monitored with time to determine when stability has been reached. ƒ An average value for the dependent variable is recorded over the Sample period. ƒ When consecutive average values (Consecutive within tolerance) are within the Percentage tolerance specified here, the data is accepted. ƒ The software will also accept the point at the end of the Maximum point time, should the data still not be at a steady state value.

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To minimize thermal lag, the ramp rate should be slow. 1-5°C/min.

Control variables: ƒ Shear rate ƒ Velocity ƒ Torque ƒ Shear stress

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Variables: Stress Torque

ƒ For running an unknown sample, it is recommended to sweep torque instead of stress. Because stress is geometry dependent ƒ The starting torque can be from the lowest of the instrument specification ƒ The maximum torque is sample dependent. You can setup a high number and manually stop the test when it gets outside the LVR.

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Control variables: ƒ Osc torque ƒ Osc stress ƒ Displacement ƒ % strain ƒ Strain

ƒ The strain needs to be in the LVR

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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.)

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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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Control variables: ƒ Osc torque ƒ Osc stress ƒ Displacement ƒ % strain ƒ Strain

ƒ The strain needs to be in the LVR

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To minimize thermal lag, recommend using slow ramp rate e.g. 1-5°C/min.

Control variables: ƒ Osc torque ƒ Osc stress ƒ Displacement ƒ % strain The strain needs to be in the LVR ƒ ƒ Strain

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During a test

Before starting a test

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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ƒ Motor and transducer work in a feedback loop

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ƒ Rule of thumb: recovery time is 2-3 times longer than creep time

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Default values shown

ƒ During the test, the angular velocity is monitored with time to determine when stability has been reached. ƒ An average value for the angular velocity is recorded over the Sample period. ƒ When consecutive average values (Consecutive within tolerance) are within the tolerance specified here, the data is accepted.

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ƒ Instrument Calibrations

ƒ Inertia (Service)

ƒ Rotational Mapping

ƒ Oscillation Mapping (recommended for interfacial measurements)

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ƒ Go to the Calibration tab and select Instrument

ƒ Make sure there is no geometry installed and then click calibrate

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ƒ Geometry Calibrations:

ƒ Inertia

ƒ Friction

ƒ Gap Temperature Compensation

ƒ Rotational Mapping

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ƒ Videos available at www.tainstruments.com under the Videos tab or on the TA tech tip channel of YouTube™ (http://www.youtube.com/user/TATechTips)

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ƒ Instrument Calibrations ƒ Temperature Offsets ƒ Phase Angle (Service) ƒ Measure Gap Temperature Compensation ƒ Transducer

ƒ Geometry Calibrations: ƒ Compliance and Inertia (from table) ƒ Gap Temperature Compensation

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ƒ Gap Temperature Compensation ƒ Enter manually or run calibration

ƒ Compliance and Inertia ƒ (from table in Help menu)

ƒ Geometry Constants ƒ Calculated based on dimensions

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What if the online table does not list a compliance value for my specific geometry? Use the compliance value for a geometry of the same/similar dimension, type, and material.

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ƒ Air Supply ƒ Dry particulate-free air (dew point -40 °C) ƒ Check filters/regulators on a periodic basis to ensure proper pressure, free of moisture/oil/dirt buildup. ƒ If air must be turned off, then make sure that the bearing lock is fastened

ƒ NOTE: Do not rotate drive-shaft if air supply is OFF!

ƒ Location ƒ Isolate the instrument from vibrations with a marble table or Sorbathane pads. ƒ Drafts from fume hoods or HVAC systems and vibrations from adjacent equipment can contribute noise to measurements, particularly in the low torque regime. Use a Draft Shield to isolate instrument from drafts.

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ƒ Circulator Maintenance ƒ Proper operation of a fluid circulator is vital for correct and efficient operation of Peltier-based temperature control devices.

ƒ Check fluid levels and add anti-fungal additive regularly. ƒ Note: if operating circulator below 5°C then it is recommended to fill the circulator with a mixture or material with a lower freezing point than water to prevent permanent circulator damage. ƒ Example: add ~20% v/v ethanol to water ƒ Keep it clean!

ƒ Flush and clean circulator, Peltier system, and tubing at first sight of contamination.

ƒ When not in use, it is strongly recommended to deactivate the Peltier device and turn off the circulator.

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Sample Max Shear Rate Min Shear Rate Geometry Diameter (mm) Degree Gap (micron) Volume (mL) (approx) 1/s (approx) 1/s 0 1000 0.05 1.20E+03 4.00E-07 0 500 0.03 8 0.5 18 1.17E-03 1 28 2.34E-03 2 52 4.68E-03 4 104 9.37E-03 0 1000 0.31 3.00E+03 1.00E-06 0.5 18 0.02 3.44E+04 1.15E-05 20 1280.041.72E+04 5.73E-06 2520.078.60E+03 2.87E-06 4 104 0.15 4.30E+03 1.43E-06 0 1000 0.49 3.75E+03 1.25E-06 Parallel Plate 0.5 18 0.04 and Cone and 25 1280.07 Plate 2520.14 4 104 0.29 0 1000 1.26 6.00E+03 2.00E-06 0.5 18 0.15 3.44E+04 1.15E-05 40 1280.291.72E+04 5.73E-06 2520.598.60E+03 2.87E-06 4 104 1.17 4.30E+03 1.43E-06 0 1000 2.83 9.00E+03 3.00E-06 0 500 1.41 60 0.5 18 0.49 3.44E+04 1.15E-05 1280.991.72E+04 5.73E-06 2521.978.60E+03 2.87E-06 4 104 3.95 4.30E+03 1.43E-06 Conical Din Rotor 19.6 4.36E+03 1.45E-06 Recessed End 6.65 4.36E+03 1.45E-06 Concentric Double Wall 11.65 1.59E+04 5.31E-06 Cylinder Pressure Cell 9.5 Standard Vane 28.72

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ƒ Polymer samples come in different forms (e.g. powder, flakes, pellets) and can be sensitive to environmental conditions ƒ Careful sample preparation techniques are required to prepare good test specimens for reproducible testing

ƒ Molding a sample

ƒ Handling powders, flakes

ƒ Controling the environment

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ƒ The best approach is to mold a sample plate (50x50 mm2 or 100x100 mm2) ƒ Molding temperature: 10 - 20°C > than test temperature ƒ Apply pressure: 8 – 12,000 lbs ƒ Keep at elevated temperature long enough to let the sample relax ƒ Cool down slowly under pressure to avoid orientations ƒ Punch out a sample disk (8 or 25 mm)

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ƒ Before molding at high temperature, the sample has to be compacted cold to reduce the volume ƒ The compacted samples are transferred to the mold ƒ Follow steps from the molding pellets procedure ƒ Note: Sample may need to be stabilized or dried to avoid degradation

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ƒ Cut rectangular sheets of prepreg or adhesive (30x30mm) ƒ Alternate direction of layer approx. 5 layer on top of each other (remove release paper from PSA) ƒ Compress the stack of sample layers in a press (4 – 5000 lbs) ƒ Punch out 25 mm disks

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ƒ Polypropylene and Polyolefines in general tend to degrade fast – need to be stabilized by adding antioxidents ƒ Moisture sensitive materials such as polyamides and polyester require drying in vacuum or at temperatures around 80°C. ƒ Materials such as Polystyrene or Polymethyl- methacrylate (PMMA) also absorb moisture. In the melt phase, the gas separates into bubbles and the sample foams ƒ Pre-drying in vacuum is essential prior to testing Vacuum oven

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Geometry gap and Trim gap icons

Set Environmental System to test temperature

Load molded disk onto lower plate

Close the oven and Monitor Axial or After sample Close the oven and bring the upper Normal force relaxes, open the adjust gap to plate to the trim during this oven and trim geometry/test gap gap position period excess sample

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Set Environmental System to test temperature

Mount melt ring onto the lower plate and load pellets

Bring the upper After few minutes, After sample Close the oven and plate close to top of open the oven, relaxes, open the adjust gap to melt ring and close remove melt ring oven and trim geometry/test gap the oven and go to trim gap excess sample

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ƒ Structured fluids can range in consistency from low viscosity (e.g. milk) to high viscosity, pasty materials (e.g. tooth paste) ƒ Structured materials are very sensitive to mechnical and environmental conditions ƒ Be aware of largest particle size in sample and choose the geometry appropriately (cone vs parallel plate vs vane geometry) ƒ Samples can also be time dependent – how you treat the sample (handling, loading, pre-conditioning) may affect test results!

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ƒ Fluid samples which pour freely are relatively easy to handle prior to loading ƒ Keep the container closed to avoid evaporation of solvent or continuous phase ƒ Shake or stir sample to remove concentration gradients in suspensions ƒ Adequate shelf temperature may be necessary to avoid phase separation in emulsions ƒ Never return used sample into original flask to avoid contamination

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ƒ Deposit fluid in the middle of the plate ƒ Set a motor velocity of ~ 1 rad/s and move to geometry gap ƒ Add additional material along the sides of the geometry – capillary forces will draw the sample between the gap ƒ When finished, click on the “Stop Motor” button ƒ NOTE: If the sample is a structured fluid, setting a motor velocity will introduce shear history onto the sample and can destroy the sample structure!

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ƒ The structure of high viscosity pastes and slurries may change with time ƒ Food samples, like dough, can change continuously ƒ The test samples need to be prepared carefully and consistently for each experiment to obtain reproducibility ƒ Slurries that may settle can gradually build a cake – these samples have to be tested before sedimentation

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ƒ Scoop up the paste with a spatula and deposit it at the center of the lower plate ƒ For less viscous materials, a syringe with a cut-off tip can be used ƒ Load ~ 10-20 excess material to ensure complete sample filling ƒ Set the gap to the trim gap and use exponential gap closure profile to minimize shear in the sample ƒ Lock the bearing, trim excess material and set final gap

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ƒ Gels, especially chemical gels, may change irreversibly when large deformations are applied (for example, while loading) ƒ Prepare (formulate) the sample in the final shape required for the measurement so it can be loaded without deforming (cut, punch, …) ƒ Alternatively, prepare the sample in situ – on the rheometer Æ systemic rheology ƒ Take care to avoid introducing air bubbles!

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