4/2/2019
TA Instruments – Waters LLC
Materials Characterization by Rheological Methods
Gregory W Kamykowski PhD Senior Applications Scientist for Rheology TA Instruments – US West [email protected]
©2019 TA Instruments TAINSTRUMENTS.COM 1
Rheology: An Introduction
Rheology: The study of the flow and deformation of matter. Rheological behavior affects every aspect of our lives.
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Rheology: The study of the flow and deformation of matter
Flow: Fluid Behavior; Viscous Nature F F = F(v); F ≠≠≠ F(x)
Deformation: Solid Behavior F Elastic Nature
F = F(x); F ≠≠≠ F(v)
0 1 2 3 x
Viscoelastic Materials: Force F Maxwell depends on both Deformation and Rate of Deformation and vice versa.
Kelvin, F Voigt
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Basic Material Behaviors
Egg Polymer Ceramic Water Oil Soap Metal white Melt ?
Flow Flow & Deformation Deformation
Elastic Solids Viscous Liquids Visco elastic Stress Stress Modulus = Viscosity = Strain Strain Rate
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Rheological Testing - Rotational
2 Basic Rheological Methods 1. Apply Force (Torque)and measure Deformation and/or Deformation Rate (Angular Displacement, Angular Velocity) - Controlled Force, Controlled Rate Shear Angular Velocity, Velocity, Angular Stress Torque, Shear Stress
2. Control Deformation and/or Angular Displacement, Deformation Rate and measure Force needed (Controlled Strain Displacement or Rotation, Controlled Strain or Shear Rate) Torque, Stress Torque,
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Steady Simple Shear Flow
Top Plate Velocity = V 0; Area = A; Force = F
H y Bottom Plate Velocity = 0 x
vx = (y/H)*V 0
. -1 γγγ = dv x/dy = V 0/H Shear Rate, sec σσσ = F/A Shear Stress, Pascals . ηηη = σσσ/γγγ Viscosity, Pa-sec These are the fundamental flow parameters. Shear rate is always a change in velocity with respect to distance.
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Parallel Plate Shear Flow
Stress σσσ Force or torque Strain γγγ Linear or angular displacement
Strain Linear or angular velocity Rate
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SHEAR RATE CALCULATIONS IN EXTRUSION
. Extruder: γγγ = πππDN/(60*h)
D = Diameter; N = rpm; h = gap
. 3 Q = Output rate; Circular, Rod: γγγ = 32Q/( πππD ) D = orifice diameter compounding, cable . Rectangular, Slit: γγγ = 6Q/(wh 2) Q = Output rate; w = width cast film, sheet h = gap
. Annulus: γγγ = 12Q/( πππ(D1+D2)h 2) Q = Output rate; D1 = Inner diameter blown film, blow molding D2 = Outer diameter h = gap
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Representative Flow Curve
1.E+05
Newtonian Pseudoplastic Region Behavior 1.E+04 0 < n < 1 (Newtonian)
1.E+03 Transition Power Law ηηη = ηηη0 Region Region
1.E+02
Viscosity Viscosity (Pa-sec) 1.E+01 . ηηη = m* γγγ (n-1) 1.E+00 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 M 3.4 -1 ηηη0 ∝∝∝ W Shear Rate (sec )
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Idealized Flow Curve
Often we try to correlate our rheology data with actual applications. However, differences between similar materials are accentuated at the low shear 1) Sedimentation rates, where rotational rheometers excel. 2) Leveling, Sagging So, even if one does not get to high shear 3) Draining under gravity
η rates, the rheology data are still useful. 4) Chewing and swallowing 5) Dip coating
log 6) Mixing and stirring 7) Pipe flow 8) Spraying and brushing 9) Rubbing 10) Milling pigments in fluid base 11) High Speed coating
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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Simple Shear Deformation
Top Plate Displacement = X 0; Area = A; Force = F
H y Bottom Plate x Displacement = 0
x = (y/H)*X 0
γγγ = dx x/dy = X 0/H Shear Strain, unitless σσσ = F/A Shear Stress, Pascals G = σσσ/γγγ Modulus, Pa These are the fundamental deformation parameters. Shear strain is always a change in displacement with respect to distance.
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Stress Relaxation
Stress Relaxation of Soy Flour, Overlay
10 9
• Instantaneous Strain • Note the decrease in the modulus as a
) function of time.
10 8 G(t) ( G(t) [Pa] F
G(t) T=20°C T=30°C T=40°C T=50°C 10 7 10 0 10 1 10 2 10 3 time [s]
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Rheological Parameters
FLUIDS TESTING
Parameter Shear Elongation Units . . Rate γγγ ε Seconds -1
Stress σσσ τττ Pascals . . Viscosity ηηη = σσσ/γγγ ηηηE = τττ/εεε Pascal-seconds
SOLIDS TESTING
Parameter Shear Elongation Units
Strain γγγ ε Unitless
Stress σσσ τττ Pascals
Modulus G(t) = σσσ/γγγ E = τττ/εεε Pascals
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Rheological Parameters
CREEP TESTING
Parameter Shear Elongation Units
Stress σσσ τττ Pascals
Strain γγγ ε Unitless
Compliance J = γγγ /σσσ D = ε/τε/τε/τ 1/Pascals
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Creep Testing
Stress is held constant. Strain is the measured variable. Compliance = Strain/Stress 3x10 -3
HDPE
2x10 -3 Viscoelastic
1x10 -3 Fluid Compliance (1/Pa) Solid
0x10 0 0 5 10 15 20 Step time (min) Viscosity = 1/Stress is held constant. Strain is Slope in steady flow regime. Intercept = non-recoverable Compliance
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GEOMETRIES
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Geometry Options
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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Converting Machine to Rheological Parameters in Rotational Rheometry
Machine Parameters M x Kσ σ M: Torque = =η ΩΩΩ : Angular Velocity ΩxK γ• θθθ : Angular Displacement γ Conversion Factors
Kσσσ : Stress Conversion Factor Kγγγ : Strain (Rate) Conversion Factor MxK σ Rheological Parameters σ σσσ : Shear Stress (Pa) • = =G γγγ : Shear Rate (sec -1) ηηη : Viscosity (Pa-sec) xK γγγ : Shear Strain θ γ γ G : Shear Modulus (Pa)
The conversion factors, K σσσ and K γγγ, will depend on the following: Geometry of the system – concentric cylinder, cone and plate, parallel plate, and torsion rectangular Dimensions – gap, cone angle, diameter, thickness, etc.
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Shear Rate and Shear Stress Calculations
Geometry Couette Cone & Plate Parallel Plates Conversion Factor
Kγγγ Ravg /(R o-Ri) 111/βββ R/h
2 3 3 Kσσσ 1/(2* πππRi L) 3/(2 πππR ) 2/( πππR )
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Choosing a Geometry Size
Assess the ‘viscosity’ of your sample When a variety of cones and plates are available, select diameter appropriate for viscosity of sample Low viscosity (milk) - 60mm geometry Medium viscosity (honey) - 40mm geometry High viscosity (caramel) – 20 or 25mm geometry Examine data in terms of absolute instrument variables torque /displacemen t/speed and modify geometry choice to move into optimum working range You may need to reconsider your selection after the first run!
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Geometry Options
With the variety of cones, plates, cups and rotors available, select a geometry based on desired experimental parameters and the material properties
Cones and Plates No Solvent Trap With Solvent With Solvent Trap (NST) Trap and Heat Break (HB)
Smooth, Sandblasted, and Cross hatched
Concentric Cylinders (or Cups) and Rotors (or Bobs)
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When to use Cone and Plate
Very Low to High Viscosity Liquids High Shear Rate measurements Normal Stress Growth Unfilled Samples Isothermal Tests Small Sample Volume
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Shear Rate is Normalized across a Cone
The cone shape produces a smaller gap height closer to the inside, so the shear on the sample is constant
= h increases proportionally to dx , γ is uniform
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Cone Diameters
Shear Stress
20 mm
40 mm
60 mm
3 As diameter decreases, shear stress increases =
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Cone Angles
Shear Rate Increases
2 °
1 °
0.5 °
As cone angle decreases, shear rate increases =
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Limitations of Cone and Plate
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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Correct Sample Loading
× Under Filled sample: Lower torque contribution
× Over Filled sample: Additional stress from drag along the edges
Correct Filling
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When to use Parallel Plates
Low/Medium/High Viscosity Samples with long relaxation time Liquids Temperature Ramps/ Sweeps Soft Solids/Gels Materials that may slip Thermosetting materials Crosshatched or Sandblasted plates Samples with large particles Small sample volume
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Plate Diameters
Shear Stress
20 mm
40 mm
60 mm
2 As diameter decreases, shear stress increases =
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Plate Gaps
Shear Rate 2 mm Increases
1 mm
0.5 mm
As gap height decreases, shear rate increases =
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Effective Shear Rate varies across a Parallel Plate
For a given angle of deformation, there is a greater arc of deformation at the edge of the plate than at the center
= dx increases further from the center, h stays constant
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When to Use Concentric Cylinders
Low to Medium Viscosity Liquids Unstable Dispersions and Slurries Minimize Effects of Evaporation Weakly Structured Samples (Vane) High Shear Rates
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Peltier Concentric Cylinders
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Geometry Information – Estimated Min and Max Shear Rates
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 1 28 0.04 1.72E+04 5.73E-06 2 52 0.07 8.60E+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 1 28 0.07 Plate 2 52 0.14 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 1 28 0.29 1.72E+04 5.73E-06 2 52 0.59 8.60E+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 1 28 0.99 1.72E+04 5.73E-06 2 52 1.97 8.60E+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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Torsion Rectangular
= w = Width l = Length t = Thickness =
Advantages: Disadvantages:
High modulus samples No pure Torsion mode for Small temperature high strains gradient Simple to prepare
Torsion cylindrical also available
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Torsion and DMA Measurements
Torsion and DMA geometries allow solid samples to be characterized in a temperature controlled environment
Torsion measures G’, G”, and Tan δ DMA measures E’, E”, and Tan δ ARES G2 DMA is standard function (50 µm amplitude) 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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Examples for Common Configurations
Geometry Examples Coatings Beverages Concentric Cylinder Slurries (vane rotor option) Starch pasting Low viscosity fluids Viscosity standards Cone and Plate Sparse materials Polymer melts in steady shear Widest range of materials Adhesives Polymer melts Parallel Plate Hydrogels Asphalt Curing of thermosetting materials Foods Cosmetics Thermoplastic solids Torsion Rectangular Thermoset solids
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Geometry Overview
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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Geometry Size Selection
• DHR Most common is 40-mm parallel plate; 1000 micron gap Use 60-mm cone and plate and parallel plate for low viscosity materials, say, up to 100 mPa-sec, but 40-mm geometries can often handle these materials too. 20-mm plates are often used at higher viscosities. 25-mm parallel plates are the preferred choice for polymer melts. 40-mm 2-degree is the most common cone geometry. This is often used to verify an instrument with a viscosity standard. 8-mm plates are often used for pressure sensitive adhesives and for asphalt around room temperature. • ARES-G2 The most common geometry on the ARES-G2 is the 25-mm parallel plate. Examples would be polymer melts and thermosetting materials. Low viscosity fluids are run with 50-mm plates or cone-and-plate. Again, 8-mm plates are used for adhesives and asphalt at room temperature.
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TEST METHODS UNIDIRECTIONAL
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Rheological Methods – Unidirectional Testing
Flow Stress/Rate Ramp Stress/Rate Sweep Sweep Time sweep/Peak Hold/Stress Growth Temperature Ramp Ramp
Creep (constant stress) Rate Shear Stress, Stress Relaxation (constant Time strain)
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Procedure for Rate Ramp Up/Ramp Down
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Thixotropy: Up & Down Flow Curves
The area between the curves is an indication of the thixotropic nature of the material.
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Rate Ramp
Toothpaste
10 3
10 2
Same data as those from previous slide, but viscosity is plotted against shear rate.
10 1 10 -1 10 0 10 1 Shear rate (1/s)
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Stress Ramp for Yield Stress Determination
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Stress Ramp with Yield
250.0 225.0 In this case, the yield point 200.0 was about 135 Pa. 175.0 150.0 125.0 100.0 75.00 shear (Pa) stress 50.00 25.00 0 0 0.1000 0.2000 0.3000 0.4000 0.5000 shear rate (1/s)
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Ramp Selection
• Do a ramp as a preliminary scouting test, prior to the more fundamentally sound rate or stress sweep. • For rate ramps, a common acceleration rate is 1 sec -1 per second. For example, 0 to 100 sec -1 in 100 seconds. This is a starting point. The operator can select a rate or a range that is more appropriate for the sample in question. • Ramp up/Ramp down tests are common for determining thixotropy. The area between the up and down curves is often reported as a thixotropy parameter. • There have been times when the reproducibility is better with the down curve than it is with the up curve. • Ramps are good for characterizing materials that may slip or exude from the gap as the shear rate is increased. Often one can get to higher shear rates with ramps than with sweeps because one doesn’t dwell at the high rates as long. • Stress ramps are often used to get the yield point of a material. Sometimes these are not always clear-cut. Also, one has to be cautious when working with models. There have been instances where negative (!?) yield stresses are determined by software for the selected model. • For stress ramps, use the Step Termination feature to prevent over-speed.
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Steady State Flow Test
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Rate Sweeps - Polymer Melt Flow Curves
1.E+06 Williamson Model . c η = η0/(1+( σγ ) ) 1.E+05 Cone and Plate 1.E+04 Viscosity Viscosity (Pa-sec) 1.E+03 0.01 0.1 1 10 η = KM 3.4 Steady testing 0 w Shear Rate (1/sec) with cone and plate and Mw = 400,000 Mw = 250,000 Mw = 160,000 parallel plate geometries is The shear rate and shear stress are constant throughout the gap with the often limited to cone-and-plate geometry. Parallel plate data can be corrected with the Rabinowitsch correction. low shear rates.
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Structured fluids
Structured fluids are mostly colloidal dispersions and can be classified into three categories. Suspension Solid particles in a Newtonian fluid Emulsion Fluid droplets in a Newtonian fluid Foam Gas in a fluid (or solid)
Examples: Properties: Paints Yield Stress Coatings Non-Newtonian Viscous Inks Behavior Personal Care Products Cosmetics Thixotropy Foods Elasticity
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Steady State Flow at 25 C - Coatings
These are rate sweeps. Equilibration occurs at each point. Concentric Cylinder geometry
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Viscosity curve of various structured fluids
Viscosity curves of various materials 10 4 starch 10 3 peanut oil 0.05% poly- 2 acrylamide solution 10 syrup [Pa s] Cocoa butter lotion η 1 10 Shower gel Co-polymer 240 °C 10 0 Viscosity 10 -1
10 -2 1E-3 0.01 0.1 1 10 100 1000 10000 . Shear rate γ [1/s] Viscosity function of various structured fluids
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Viscous response of suspensions
10 2 0.50% Polystyrene-ethylacrylate latex particles in water 0.47% 10 1
10 0 [Pas]
η 0.43% 10 -1
Viscosity Viscosity -2 0.34% 10 0.28% 0.18%
-3 0.09% 10 water
10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 Laun (1984,1988) Shear Stress τ [Pa] Rheological parameters of interest:Yield stress, viscosity, time dependence, linear viscoelasticity
H.M. Laun Angew. Makromol. Chem. 335, 124 (1984)
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Normal Force Measurements with Cone & Plate
Normal Stress Difference: • In steady flow, polymeric materials can exert a force that tries to separate the cone and the plate. • A parameter to measure this is the Normal Stress Difference, N1, which equals
σσσxx - σσσyy from the Stress Tensor. • N1 = 2F/( πππR2), where F is the measured force. 2 • ΨΨΨ1 = N1/ This is the primary normal stress coefficient.
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Effect of HDPE Variations in Blow Molding
BolwBlow MoldingMolding Polyethylene Polyethylene
6 6 ]
1 0 1 0 2 T = 1 8 0 ° C Sample Parameter
5 5 )[Pa s γ
1 0 1 0 ( M-1 M-2 1 Ψ ) ) [Pa s]
γ MFI 0.6 0.5 ( 4 η 1 0 1 0 4 GPC-MW 131K 133K Ψ γ 3 1 ( ) M -1 3 Viscosity 8.4K 8.3K 1 0 1 0 Ψ (γ ) M -2 -1 1 at 1 sec η (γ ) M -1 C P 2 η (γ ) M -2 C P 2 Die Swell 28 42
Shear viscosity viscosity Shear 1 0 1 0 η (γ ) M -1 Capillary
η (γ ) M -2 Capillary stress Normal coefficient 1 0 1 1 0 1 0.1 1 10 Shear rate γ [1/s] No differences in MFI, Viscosity, or GPC! M-2 produces heavier bottles in blow molding due to increased parison swell
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Water at 25°C – Secondary Flow
Surface tension at low torques
Secondary flows at high shear rates
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Wall Slip
Wall slip can manifest as “apparent double yielding” Can be tested by running the same test at different gaps For samples that don’t slip, the results will be independent of the gap
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Shear Thinning or Sample Instability?
When Stress Decreases with Shear Rate, it indicates that sample is leaving the gap
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Rate and Stress Sweeps
• Sweeps are preferable to ramps because the material is given a chance to equilibrate at a particular shear rate or stress. • These are useful tests to see how materials will perform in flow, such as transporting fluid through pipes and tubing, after structure has been broken. • The most common rate range is 0.1 to 100 1/sec, 5 points per logarithmic decade. • The Steady State sensing feature is a useful tool to perform valid rate or stress sweeps in the shortest amount of time. • For materials that exhibit flow instability, the ramp may be preferable. With sweeps, the material is exposed to high shear rates for prolonged periods, whereas, with ramps, the dwell time at a particular rate is shorter.
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Stress Relaxation
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Stress Relaxation
PDMS
Stress relaxation is another unidirectional way of getting viscoelastic properties.
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Creep and Recovery
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Creep Testing on US and UK Paints
Creep and recovery can be done on both DHR and ARES rheometers
Creep is a unidirectional way of getting viscoelasticity. It is often followed by creep recovery. Creep answers the question of how much deformation to expect when a material is subjected to a constant stress, such as gravity.
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Creep Testing for Zero Shear Viscosity
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Flow Temperature Ramp – Printing Inks
1,000
Room Temperature
100
10 Viscosity (Pa-sec)
Printing Press Temperature
1 20 25 30 35 40 45 50 Temperatue (C)
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Tack Testing
The heads of the DHR and ARES-G2 can ascend or descend to measure axial properties.
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TEST METHODS DYNAMIC TESTING
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Dynamic Testing
STRAIN
ELASTIC RESPONSE 90 o VISCOUS RESPONSE Response, Strain Response, VISCOELASTIC RESPONSE δo
Polymers are viscoelastic materials. Time Both components – viscosity and elasticity – are important.
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Dynamic Rheological Parameters
Parameter Shear Elongation Units
Strain γ = γ0 sin( ωt) ε = ε0 sin( ωt) ---
Stress σσσ = σσσ0sin( ωt + δ) τττ = τττ0sin( ωt + δ) Pa
Storage Modulus G’ = ( σσσ /γ )cos δ E’ = ( τττ /ε )cos δ Pa (Elasticity) 0 0 0 0
Loss Modulus G” = ( σσσ /γ )sin δ E” = ( τττ /ε )sin δ Pa (Viscous Nature) 0 0 0 0
Tan δ G”/G’ E”/E’ ---
Complex Modulus G* = (G’ 2+G” 2)0.5 E* = (E’ 2+E” 2)0.5 Pa
Complex Viscosity ηηη* = G*/ ω ηηηE* = E*/ ω Pa-sec
.. Cox-Merz Rule for Linear Polymers: η*( ω) = η(γ) @ γ = ω
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Rheological Methods – Dynamic Oscillatory Testing
Dynamic Strain Sweep/Dynamic Stress Sweep Isothermal Dynamic Time Sweep Isothermal Dynamic Frequency Sweep Dynamic Temperature Ramp Dynamic Temperature Sweep at 1 or Multiple Frequencies.
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Dynamic Stress Sweep
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Linear Viscoelasticity
Linear Region: • Osc Stress is linear with Strain. • G’, G” are constant. This is typically the first test done on unknown materials.
Non-Linear Region G’ = f( γγγ) Stress v. Strain
End of LVR or
Critical Strain γγγc
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Stability is Related to Structure in Inks
Ink Samples: Oscillation Stress Sweeps @ 6.28 rad/s
10000 A 5% drop from the modulus in DHR Testing the Linear Region is considered being in the Non-Linear Region
1000 G'(Pa)
100.0
This is the most reproducible way of determining a yield stress. 10.00 0.1000 1.000 10.00 100.0 osc. stress (Pa) TAINSTRUMENTS.COM 73
Dynamic Time Sweep: Material Response
1.000E7 1.000E7 PDMS
1.000E6 1.000E6 The material is stable in this time range. G'' (Pa)G''
1.000E5 1.000E5 G'(Pa)
10000 10000
1000 1000 0 5.0000 15.000 25.000 35.000 time (s)
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Dynamic Time Sweep for Curing
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Cure of a "5 minute" Epoxy
TA Instruments
1000000 This is an isothermal 1000000 time sweep. G' 5 mins. 100000 100000
10000 G" 10000 G''(Pa)
1000 1000 G' G' (Pa) Gel Point - G' = G" 100.0 T = 330 s 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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Isothermal Cure of Tire Compound Effect of Curing Temperature
135°C 130°C 140°C 120°C 145°C 125°C
Time (min)
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Dynamic time sweep following shear
This shows how rapidly the structure is rebuilding.
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Frequency Sweep
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Frequency Sweep on PDMS
High frequency – elasticity predominates. Low frequency – viscosity predominates.
Most frequent test for polymer melts: ASTM D4440 – Standard Test Method for Plastics: Dynamic Mechanical Properties: Melt Rheology
100 to 0.1 rad/sec 5 pts. per decade 3 minutes of equilibration Frequency sweep takes about 6.5 min.
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Surface Defects during Pipe Extrusion
HDPE pipe surface defects
Indicated by T = 220 o C 5 5 Elasticity at 1 0 1 0 low * [Pa *s] frequency η 4 4 1 0 1 0
Caused by G ' rough surface Modulus G' [Pa] G' Modulus 3 G' sm ooth surface Broader 1 0 1 0 3
η * rough surface Complex viscosity MWD η * sm ooth surface
0.1 1 10 100 Frequency ω [rad/s]
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Coatings Frequency Sweep
Note how 2o is leveling out. 6o is descending sharply.
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Example of Cox-Merz Rule
10000
Linear Polyethylene Flow Data Linear Polyethylene Oscillation Data [Cox Merz]
1000
viscosity (Pa.s) viscosity Flow instability
100.0 1.000E-3 0.01000 0.1000 1.000 10.00 100.0 1000 shear rate (1/s)
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Dynamic testing: Dependence on M w and MWD
10 7 Molecular weight 130 000 Zero shear viscosity increases 6 230 000 10 320 000 with increasing MW 430 000
10 5 * [Pa s] η
4 10 Zero Shear [Pa s]
o Viscosity η 0 10 6 10
3
Viscosity Viscosity increasing MWD 10 Slope 3.08 +/- 0.39 Zero Shear Viscosity
5 -1 10 10 2 100000 Molecilar weight M [Daltons] 10 w o
η SBR polymer broad, -4 -3 -2 -1 0 1 2 3 4 5 -2 10 10 10 10 10 10 10 10 10 10*/ 10
η narrow distribution Frequency ω a [rad/s] T η *red 430 000 -3 η* 320 000 10 red When shifting along an η* 230 000 Viscosity Viscosity red η* 130 000 axis of -1, all the curves 10 -4 red η* 310 000 red η* 250 000 can be superposed, unless red 10 -5 the width of the MWD is 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 ω η not the same. frequency a T o
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MWD and Dynamic Moduli
Effect of MWD on the dynamic moduli • The storage and loss modulus of 10 6 a typical polymer melt cross over between 1 and 100 rad/s.
• ωωωc ∝∝∝ 1/M w .
5 • Gc ∝∝∝ 1/MWD. 10
10 4 SBR polymer melt G' 310 000 broad Modulus G', G'' G', [Pa] Modulus 3 G" 310 000 broad 10 G' 320 000 narrow G" 320 000 narrow
10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 Frequency ωa [rad/s] T
Higher crossover frequency = lower M w Higher crossover Modulus = narrower MWD
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ETC Application: TTS on Polymer Melt
Polystyrene Frequency Sweeps from 160 °C to 220 °C
1.000E6 1.000E6 Extended Frequency range with TTS Reference Temperature = 210 °C
1.000E5 1.000E5
10000 10000 G” (Pa)G” G'' (Pa) G' (Pa) G' G’ (Pa) G’ 1000 1000
100.0 Experimental 100.0 Frequency range
10.00 10.00 0.01000 0.1000 1.000 10.00 100.0 1000 10000 1.000E5 ang.ang. frequency frequency (rad/s) (rad/s)
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Shift Factors from TTS for LDPE
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Idealized Flow Curve - Polymers
Power Law Region
First Newtonian Plateau
η0 = Zero Shear Viscosity 3.4 η0 = K x MW c Extend Range η 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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Example: Dynamic Frequency Sweeps
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Dynamic Frequency Sweeps
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Fitting Data to Williamson/Arrhenius Models
η0 = A*exp(Eact /(R*T)) (Pa.s) . c η = η0/(1+( η0*γ/σcrit ) ) Parameter LDPE LLDPE Viscosity A 2.09E-3 1.01E0
Eact (kJ/mol-deg) 54.2 32.5
σcrit (Pa) 8.84E3 8.48E4 c 0.60 0.56
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Tack and Peel of Adhesives
Tack and Peel perform ance of a PSA
good tack and peel Bad tack and peel
1 0 4
peel
1 0 3
Storage Modulus G' Modulus [Pa] Storage ta c k
0.1 1 10
Desirable PSA characteristics Frequency ω [rad/s] Tack: high G‘ at low frequency Peel: low G‘ at high frequency
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Correlation of Rheological Parameters to Adhesive Properties
Practical Adhesive Property Rheological Properties Property
• Low tan δδδ and Low G’ Tack High Tack • Low Cross-links (G” > G’ @ ~1 Hz)
• High G’ @ < 0.1 Hz Shear Resistance High Shear Resistance • High Viscosity @ Low Shear Rates
Peel Strength • High G” @ ~> 100 Hz High Peel Strength
Cohesive Strength • High G’, low tan δδδ High Cohesive Strength
High Adhesion Strength Adhesive Strength • High G”, high tan δ with Surface
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Dynamic Temperature Ramp - Torsion
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Effect of Molecular Weight
Glassy Region Rubbery Transition Plateau Region Region MW has practically no effect on the modulus below Tg
High Med. Low MW MW MW
Temperature
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Effect of Crosslinking
Mc = MW between crosslinks
120
160
300
1500 log E' (G') logE' 9000
30,000
Temperature
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Rubber Compound: Similar cure curve, different processing
High Strain tan δ Good Bad Viscosity, η* Similar tan δ (low γ) 1.0 0.8
S' [dNm] 15.0
14.0tan δ (high γ) 5.7 3.0
13.0
12.0
11.0
10.0
9.0
8.0
7.0 Storage Modulus, G’ (kPa) 6.0 Tan Delta Shear Modulus G' [kPa] 5.0 Tan Delta
4.0 6 6
3.0
2.0
1.0
0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0 Time [min] 5 5
SCARABAEUS GMBH - inf [email protected] - Tel.:+49 (0) 6441/56777-0
4 4
10 10 3 3
2 2
1 1
1 0 0 0.1 1 10 100 1000 0.1 1 10 Strain [%] 100 1000 % Strain TAINSTRUMENTS.COM 97
Level 2: Examination of Higher Harmonics
SAOS t t γ( ) = γ0 sin( ω ) t t+ σ( ) = σ0 sin( ω δ)
LAOS t t γ( ) = γ0 sin( ω )
Fourier Series expansion: t t+ t+ t+ σ( ) = σ1 sin( ω1 ϕ1) + σ3 sin(3 ω1 ϕ3) + σ5 sin(5 ω1 ϕ5) + ... ∞ n = Σ σn sin( ω1+ϕn) LAOS is often called Fourier Transform Rheology, or FT Rheology. n=1 A useful way of quantifying non-linear behavior is to compare odd intensity ratios like σ3/σ1, σ5/σ1.
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Large Angle Oscillatory Shear: Higher Harmonics
0 .1 5 PIB 2490 Ability to “fingerprint” T=28.1 oC
a material. 1 /I 1 0 0 ω =1 rad/s 7 , , I 1
80 600
0 .1 0 /I ( t ) 60 σ σ ( t ) 400 5 40 200 20 Tim e Tim e 0 0 70 75 80 70 75 80 , I Strain Strain -20 -200 PIB 2490 PIB 2490 1 o -40 T= 28.1 C T= 28.1 oC ω =1 rad/s -400 -60 ω=1 rad/s γ=100% γ=3000% /I -80 -600 3
linear Non-linear 0 .0 5 1 0 ModulusG",G', [Pa] Harmonics I
0 .0 0
1E-4 1E-3 0.01 0.1 1 10 100 Strain γ []
The transition from linear to nonlinear regime for viscoelastic materials shows in a decrease of G’ & G” and an increase of the magnitude of the harmonics.
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LAOS on PDMS
PDMS for LAOS Corr (1)
10 5 0.3
0.2
10 4 0.1
0.0
10 3 -0.1 10 1 10 2 10 3 Oscillation strain (%)
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LAOS with Transient Data Acquisition
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LAOS with Transient Data Acquisition
PDMS_LAOS_2015_Transient -h
1.0 1.5
0.8 1.0
0.6 0.5
0.4
0.0 0.2
-0.5 0.0
-0.2 -1.0 10 1 10 2 10 3 Oscillation strain (%)
Transient data acquisition with ARES-G2 or DHR-2, DHR-3 TAINSTRUMENTS.COM 102
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Dynamic Testing
• Of all the tests performed on a rheometer, dynamic oscillatory testing is the most common. Typically, this is the most convenient way of getting a material’s viscous and elastic nature. • Dynamic Stress or Strain sweeps are useful for determining a dynamic yield point of a material and can suggest strains or stresses to use in subsequent tests, such as frequency sweeps or temperature ramps. • Dynamic Frequency sweeps are the most useful tests for characterizing polymer melts and adhesives. They provide information on the molecular weight and molecular weight distribution of a material. • Time temperature superposition can often be used to provide knowledge beyond the usual limits of 0.1 to 100 rad/sec. • The rheometer can be used as a DMA to provide glass transition temperatures and thermal mechanical integrity.
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THE RHEOMETERS
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Five Important Rheometer Specifications
Torque range Angular Resolution Angular Velocity Range Frequency Range Normal Force
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TA Instruments Rotational Rheometers
Discovery HR Rheometer ARES-G2
Combined Motor and Transducer Separate Motor and Transducer “Native Mode” = Force (Stress) “Native Mode” = Deformation/Deformation Rate (Strain/Shear Rate)
With computer feedback, the instruments can do both, deformation/deformation rate control and force control.
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Rotational Rheometer Designs
DHR ARES Separate motor & transducer Combined motor & transducer Or Dual Head Or Single Head Displacement Measured Transducer Sensor Torque Measured (Stress) Strain or Non-Contact Rotation Drag Cup Motor Applied Torque (Stress)
Sample Applied Direct Drive Static Plate Strain or Motor Rotation
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Discovery Hybrid Rheometer Specifications
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 HR-3 Minimum Torque (nN.m) Oscillation 0.5 2 10 HR-2 Minimum Torque (nN.m) Steady 5 10 20 HR-1 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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DHR Instrument Model Features
All Discovery Hybrid Rheometers Feature: Moving from HR-1 to HR-2 Adds: Moving from HR-2 to HR-3 Adds: - Patented Ultra-low Inertia Drag-Cup Motor - 5X better low torque in Oscillation - 4X better low torque in Oscillation - Single-Thrust & Dual-Radial Bearing Design - 2X better low torque in steady Shear - 2X better low torque in steady Shear - Patented Second Generation Magnetic Bearing - 25% Higher torque - Optical Encoder Dual Reader (pat. Pend.) - Nano-Torque Motor Control - 2X better NF Sensitivity - 5X better angular resolution - High-Resolution Optical Encoder - Direct Strain Oscillation - 3X better phase angle resolution - Superior Stress and Strain Control - Fast data sampling - No encoder drift - Force Rebalance Normal Force (FRT) - Transient Data Acquisition/LAOS - Patented Smart Swap Geometries - Stress Growth (Transient NF) - True Position Sensor (Patent Pending) - Access to UV Curing Options - Ultra-low Compliance Single-Piece Frame - Access to SALS Option - Heat and vibration Isolated Electronics Design - Access to Interfacial Options - Smart Swap™ Temperature Systems - Superior Peltier Technology - Patented Heat Spreader Technology - Patented Active Temperature Control - Color Display - Capacitive Touch Keypad - TRIOS Software - Navigator Software - Electronic Bearing Lock - NIST Traceable Torque Calibration
HR-1HR-3 HR-2
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ARES-G2 Rheometer Specifications
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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Minimum Torque Specs
1000
100
10 ARES-G2 DHR-1 1 DHR-2
Minimum Torque (nN-m) Minimum Torque DHR-3 0.1 Oscillation Steady ARES-G2 50 100 DHR-1 10 20 DHR-2 2 10 DHR-3 0.5 5
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SELECTED ACCESSORIES
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DHR Accessories – Visual Display
You can see the updated list of accessories on our website, www.tainstrument.com .
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DHR Accessories – Visual Display
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ARES-G2 Accessories
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DMA Capabilities
The DMA capabilities of the DHR and ARES-G2 are unique for commercial rheometers.
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ARES-G2 DMA Mode
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ARES-G2 DMA Testing
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DMA Specifications
RSA G2 DMA 850 ARES G2 DMA DHR DMA (optional) Max Force 35N 18N 20N 50N
Min Force 0.0005N 0.0001N 0.001N 0.1N
Frequency Range 1e-5 to 628 rad/s 6.28e-3 to 1250 rad/s 6.3e -5 to 100 rad/s 6.3e -5 to 100 rad/s (1.6e-6 to 100 Hz) (0.001 to 200 Hz) (1.0e -5 to 16 Hz) (1.0e -5 to 16 Hz) Dynamic +/- 0.05 to 1,500 µm +/- 0.005 to 1e4 µm +/- 1 to 50 µm +/- 1 to 100 µm Deformation Range Control Control Strain (SMT) Control Stress (CMT) Control Strain Control Stress Stress/Strain (CMT) (CMT) Heating Rate 0.1 oC to 60 oC/min 0.1 oC to 20 oC/min 0.1 oC to 60 oC/min 0.1 oC to 60 oC/min
Cooling Rate 0.1 oC to 60 oC/min 0.1 oC to 20 oC/min 0.1 oC to 60 oC/min 0.1 oC to 60 oC/min
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SER2 for DHR Rheometers
This is an interesting application of using the rotational rheometer to determine elongational viscosity
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Extensional Viscosity Measurements
Fix drum connected to transducer
Rotating drum connected to the motor: rotates around its axis rotates around axis of fixed drum
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Extensional Viscosity
• Extensional rheology is very sensitive to polymer chain entanglement. Therefore it is sensitive to LCB • The measured extensional viscosity is 3 times of steady shear viscosity
ηΕ = 3 x η0 • LCB polymer shows strain hardening effect
Linear Branched
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UV Light Guide Curing Accessory
• Collimated light and mirror assembly insure uniform irradiance across plate diameter • Maximum intensity at plate 300 mW/cm 2 • Broad range spectrum with main peak at 365 nm with wavelength filtering options • Cover with nitrogen purge ports • Optional disposable acrylic plates
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UV LED Curing Accessory
• Mercury bulb alternative technology • 365 nm wavelength with peak intensity of 150 mW/cm 2 • 455 nm wavelength with peak intensity of 350 mW/cm 2 • No intensity degradation over time • Even intensity across plate diameter • Compact and fully integrated design including power, intensity settings and trigger • Cover with nitrogen purge ports • Optional disposable Acrylic plates
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UV Curing Procedure
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UV Curing Procedure
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UV Cure Profile Changes with Intensity
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Tribology
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COF – Single Speed Tests
Skin substitute ring on skin substitute plate
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Tribology of Lubricated Systems
Boundary Mixed Hydrodynamic Lubrication Lubrication Lubrication µ 1 Friction, Coefficient of Coefficient
(ηoil Ω)/FL
• In lubricated systems, the ‘Stribeck curve’ captures influence of lubricant viscosity( ηoil ), rotational velocity ( Ω) and contact load (F L) on µ • At low loads, the two surfaces are separated by a thin fluid film (gap, d) with frictional effects arising from fluid drag ( Hydrodynamic Lubrication ) • At higher loads, the gap becomes smaller and causes friction to go up ( Mixed Lubrication ) • At extremely high loads, there is direct solid-solid contact between the surface asperities leading to very high friction ( Boundary Lubrication )
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DHR Immobilization Cell
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DETA on DHR and ARES-G2
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Dielectric Example in Trios
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Interfacial Rheology
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Surface Concentration Effects on Interfacial Viscosity
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SPAN65 ® Layer Spread on Water
Interfacial properties Span65 layer on water T=20 o C ω=1rad/s Span 65 [molecul/nm 2] s s 0.1 4.3 0.36 G" G' 1.8 0.0 1.08 0.01 Both dynamic and
steady flow tests can be performed 1E-3 with the interfacial
geometry. This is an example of a
1E-4 dynamic strain sweep. subphase base line
1E-5 Storage Loss & Modulus [N/m]
1E-4 1E-3 0.01 0.1 1 Strain γ [ ]
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DHR-RH Accessory Temperature- Technology Controlled Transfer Line
Geometry Heat Breaks
Chamber Heat Spreaders Humidity Generator Sample Chamber
Peltier-controlled Sample Chamber
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DMA-RH Experimental Options
Isohume, Isothermal Isothermal, RH Ramp Isohume, Temp Ramp RH RH RH Temperature Temperature Temperature
time time time
Isothermal, RH Step Isohume, Temp Step RH Step, Temp Step RH RH RH Temperature Temperature Temperature
time time time
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Test Geometries
•Wide variety of test geometries: Standard parallel plate Disposable parallel plate Annular Ring Surface Diffusion Rectangular Torsion •Innovative geometries for RH: true humidity-dependent rheology, not dominated by diffusion •True Axial DMA: Film Tension Three-point Bending
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Annular Ring Geometry
Diffusion Diffusion
• Parallel plate: long diffusion length • Remove center section • Annular ring: short diffusion length • Provides quantitative bulk rheology with less delay and gradients associated with diffusion
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Surface Diffusion Geometry
Ring Vessel
Fluid Shear field surface
• Surface rheological properties and process kinetics • Very simple sample loading • Ideal for: Fast evolving systems Samples with shallow interaction depth Drying, curing…
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Rheo-Raman Accessory
Rheo-Raman on a hand lotion
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Need Some Assistance?
• Instrument Manuals • Help Feature in Trios • TA Instruments website • TA Instruments Rheology Helpline [email protected]
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Website: www.tainstruments.com
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Website: www.tainstruments.com
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TA Tech Tips
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On Line Training
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DHR Quick Start Guide
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Sampling of Available Webinars
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Thank You
The World Leader in Thermal Analysis, Rheology, and Microcalorimetry
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