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6/1/2018
1
TAINSTRUMENTS.COMTAINSTRUMENTS.COM
Waters – TA Instruments
Characterization Workshop
June 2018
Welcome
RHEOLOGY – FROM LIQUIDS TO SOLIDS
©2018 TA Instruments
TAINSTRUMENTS.COMTAINSTRUMENTS.COM
Topics in the Waters – TA Characterization Workshops
• Optimizing DSC and TGA Testing
• GPC Techniques and Applications
• Rheology from Liquids to Solids
• DMA: Rheology of Solid-Like Materials
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2
TAINSTRUMENTS.COMTAINSTRUMENTS.COM
Rheology: An Introduction
Rheology: The study of the flow and deformation of matter.Rheological behavior affects every aspect of our lives. Rheology: The study of the flow and deformation of matter.Rheological behavior affects every aspect of our lives.
TAINSTRUMENTS.COMTAINSTRUMENTS.COM
F
0 1 2 3
F
x
F
Rheology: The study of the flow and deformation of matter
Flow: Fluid Behavior; Viscous Nature
F = F(v); F ≠≠≠≠ F(x)
Deformation: Solid BehaviorElastic Nature
F = F(x); F ≠≠≠≠ F(v)
F
Viscoelastic Materials: Force depends on both Deformation and Rate of Deformation and vice versa.
Maxwell
Kelvin,
Voigt
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3
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Basic Material Behaviors
Elastic SolidsViscous Liquids
DeformationFlow Flow & Deformation
Viscoelastic
Water Oil MetalCeramic
?Soap
Egg
white
Polymer
Melt
Viscosity =Stress
StrainRate
Modulus =Stress
Strain
TAINSTRUMENTS.COMTAINSTRUMENTS.COM
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
Stress
2. Control Deformation and/or
Deformation Rate and measure
Force needed (Controlled
Displacement or Rotation,
Controlled Strain or Shear Rate)
Torque, Shear Stress
An
gu
lar
Vel
oci
ty,
Sh
ear
Rate
An
gu
lar D
ispla
cemen
t,
Stra
in
Torq
ue,
Str
ess
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TAINSTRUMENTS.COMTAINSTRUMENTS.COM
TA Instruments Rotational Rheometers
Separate Motor and Transducer
“Native Mode” = Deformation/Deformation Rate
(Strain/Shear Rate)
ARES-G2Discovery HR Rheometer
Combined Motor and Transducer
“Native Mode” = Force (Stress)
With computer feedback, the instruments can do both,
deformation/deformation rate control and force control.
TAINSTRUMENTS.COMTAINSTRUMENTS.COM
Rotational Rheometer Designs
Sample
Displacement Sensor
Measured Strain or Rotation Non-Contact
Drag Cup Motor
Applied Torque(Stress)
Static Plate
DHR
Combined motor & transducerOr Single Head
Separate motor & transducerOr Dual Head
Applied Strain or Rotation
Measured Torque(Stress)
Direct Drive Motor
Transducer
ARES
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TAINSTRUMENTS.COMTAINSTRUMENTS.COM
Steady Simple Shear Flow
Top Plate Velocity = V0; Area = A; Force = F
Bottom Plate
Velocity = 0x
y
H
vx = (y/H)*V0
γγγγ = dvx/dy = V0/H.
σσσσ = F/A
ηηηη = σσσσ/γγγγ.
Shear Rate, sec-1
Shear Stress, Pascals
Viscosity, Pa-sec
These are the fundamental flow parameters. Shear rate is always a change in velocity with respect to distance.
TAINSTRUMENTS.COMTAINSTRUMENTS.COM
Parallel Plate Shear Flow
Stress σσσσ Force or torque
Strain γγγγ Linear or angular displacement
Strain
Rate
Linear or angular velocity
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TAINSTRUMENTS.COMTAINSTRUMENTS.COM
Representative Flow Curve
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05
Shear Rate (sec-1
)
Vis
cosi
ty (
Pa-s
ec)
Newtonian
Region
Power Law
Region
Transition
Regionηηηη = ηηηη0
ηηηη = m*γγγγ (n-1)
ηηηη0 ∝∝∝∝ MW3.4
0 < n < 1 (Newtonian)
Pseudoplastic
Behavior
.
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Simple Shear Deformation
Top Plate Displacement = X0; Area = A; Force = F
Bottom Plate
Displacement = 0x
y
H
x = (y/H)*X0
γγγγ = dxx/dy = X0/H
σσσσ = F/A
G = σσσσ/γγγγ
Shear Strain, unitless
Shear Stress, Pascals
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
100 101 102
103
107
108
109
time [s]
G
(t)
()
[P
a]
Stress Relaxation of Soy Flour, Overlay
G(t)
T=20°C
T=30°C
T=40°C
T=50°C
• Instantaneous Strain
• Note the decrease in
the modulus as a
function of time.
F
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Rheological Parameters
Parameter Shear Elongation Units
Rate Seconds-1
Stress Pascals
Viscosity Pascal-seconds
γγγγ.
ε.
σσσσ
ηηηη = σσσσ/γγγγ.
ττττ
E = ττττ/εεεε
ηηηηE = ττττ/εεεε.
FLUIDS TESTING
PascalsModulus
PascalsStress
UnitlessStrain
UnitsElongationShearParameter
γγγγ ε
σσσσ ττττ
SOLIDS TESTING
G(t) = σσσσ/γγγγ
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Rheological Parameters
CREEP TESTING
D = ε/τε/τε/τε/τ 1/PascalsCompliance
UnitlessεStrain
PascalsStress
UnitsElongationShearParameter
σσσσ ττττ
γγγγ
J = γγγγ /σσσσ
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Creep Testing
Stress is held constant.
Strain is the measured variable.
Compliance = Strain/Stress
Fluid
Solid
Viscoelastic
200 5 10 15
Step time (min)
3x10 -3
0x10 0
1x10 -3
2x10 -3
Co
mplia
nce
(1/P
a)
HDPE
Viscosity = 1/Stress is held constant.
Strain is Slope in steady flow regime.
Intercept = non-recoverable Compliance
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Geometry Options
Parallel
Plate
Cone and
Plate
Concentric
Cylinders
Torsion
Rectangular
Very Lowto Medium Viscosity
Very Lowto High Viscosity
Very LowViscosity
to Soft Solids
Solids
Water to Steel
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Examples for Common Configurations
Geometry Examples
Concentric CylinderCoatings BeveragesSlurries (vane rotor option)Starch pasting
Cone and Plate
Low viscosity fluidsViscosity standardsSparse materialsPolymer melts in steady shear
Parallel Plate
Widest range of materialsAdhesives Polymer meltsHydrogels AsphaltCuring of thermosetting materialsFoods Cosmetics
Torsion RectangularThermoplastic solidsThermoset solids
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Converting Machine to Rheological Parameters in Rotational Rheometry
ηγσ
γ
σ ==Ω Kx
KxM
GKx
KxM ==γσ
θ γ
σ
Machine Parameters
M: Torque
ΩΩΩΩ : Angular Velocity
θθθθ : Angular Displacement
Conversion Factors
Kσσσσ : Stress Conversion Factor
K : Strain (Rate) Conversion Factor
Rheological Parameters
: Shear Stress (Pa)
: Shear Rate (sec-1)
: Viscosity (Pa-sec)
: Shear Strain
: Shear Modulus (Pa)
γγγγ
σσσσγγγγ
γγγγηηηη
G
The conversion factors, Kσσσσ and Kγγγγ, 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
Kγγγγ Ravg/(Ro-Ri) 1111/ββββ R/h
Kσσσσ 1/(2*ππππRi2L) 3/(2ππππR3) 2/(ππππR3)
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Cone & Plate and Parallel Plate Geometric Considerations
20mm 40mm 60mm
Shear Stress
Shear StressAt given torque, Increase in diameter → Decrease in shear stress
Shear RateAt given angular velocityIncrease in cone angle → Decrease in shear rateIncrease in gap (parallel plate) → Decrease in shear rate
So, for low viscosity fluids, use the largest diameter cone or plate.For high viscosity fluids, use the smallest diameter cone or plate
Standard DHR Peltier
plate geometry diameters
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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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Rheological Methods – Unidirectional Testing
Flow
Stress/Rate Ramp
Stress/Rate Sweep
Time sweep/Peak Hold/Stress Growth
Temperature Ramp
Creep (constant stress)
Stress Relaxation (constant strain)
Time
Sweep
Ramp
Str
ess, S
hear
Rate
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Idealized Flow Curve
1
1) Sedimentation2) Leveling, Sagging3) Draining under gravity4) Chewing and swallowing5) Dip coating6) Mixing and stirring7) Pipe flow8) Spraying and brushing9) Rubbing10) Milling pigments in fluid base11) High Speed coating
2 3
6
5
8 9
1.001.00E-5 1.00E-4 1.00E-3 0.0100 0.100
shear rate (1/s)
10.00 100.00 1000.00 1.00E4 1.00E5
log
η
1.00E6
117
4
10
Often we try to correlate our rheology data
with actual applications.
However, differences between similar
materials are accentuated at the low shear
rates, where rotational rheometers excel.
So, even if one does not get to high shear
rates, the rheology data are still useful.
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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
10 -1 10 0 10 1
Shear rate (1/s)
10 1
10 2
10 3
Toothpaste
Same data as those from previous slide,
but viscosity is plotted against shear rate.
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0 0.1000 0.2000 0.3000 0.4000 0.5000
shear rate (1/s)
0
25.00
50.00
75.00
100.0
125.0
150.0
175.0
200.0
225.0
250.0
sh
ear
str
ess (
Pa)
Stress Ramp with Yield
In this case, the yield point
was about 135 Pa.
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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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1.E+03
1.E+04
1.E+05
1.E+06
0.01 0.1 1 10
Shear Rate (1/sec)
Vis
cosi
ty (
Pa-s
ec)
Mw = 400,000 Mw = 250,000 Mw = 160,000
η0 = KMw3.4
Williamson Model
η = η0/(1+(σγ)c)
Rate Sweeps - Polymer Melt Flow Curves
Cone andPlate
Steady testing with cone and plate and parallel plate geometries is often limited to low shear rates.
The shear rate and shear stress are constant throughout the gap with the
cone-and-plate geometry.
Parallel plate data can be corrected with the Rabinowitsch correction.
.
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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: Paints Coatings Inks Personal Care Products Cosmetics Foods
Properties:
Yield Stress
Non-Newtonian Viscous Behavior
Thixotropy
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
1E-3 0.01 0.1 1 10 100 1000 1000010
-2
10-1
100
101
102
103
104
.
starchpeanut oil0.05% poly-acrylamide solutionsyrupCocoa butter lotionShower gelCo-polymer 240 °C
Viscosity curves of various materials
Vis
co
sity η
[Pa
s]
Shear rate γ [1/s]
Viscosity function of various structured fluids
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Viscous response of suspensions
10-4
10-3
10-2
10-1
100
101
102
103
104
105
10-3
10-2
10-1
100
101
102 Polystyrene-ethylacrylate
latex particles in water
Laun (1984,1988)
0.43%
0.47%
0.50%
0.34%0.28%0.18%0.09%water
Vis
cosity
η [
Pa s
]
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 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
σσσσxx- σσσσyy from the Stress Tensor.
• N1 = 2F/(ππππR2), where F is the measured
force.
• ΨΨΨΨ1 = N1/2 This is the primary normal
stress coefficient.
Normal Force Measurements with Cone & Plate
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Effect of HDPE Variations in Blow Molding
0 .1 1 1 01 0
1
1 02
1 03
1 04
1 05
1 06
0 .1 1 1 01 0
1
1 02
1 03
1 04
1 05
1 06
T = 1 8 0 ° C
η (γ ) M -1 C P
η (γ ) M -2 C P
η (γ ) M -1 C a p illa ry
η (γ ) M -2 C a p illa ry
B o lw M o ld in g P o lye th y le n eS
hear
vis
cosity
η(γ
) [P
a s
]
S h e a r ra te γ [1 /s ]
Ψ1(γ ) M -1
Ψ1(γ ) M -2
Norm
al str
ess c
oeff
icie
nt
Ψ1(γ
) [P
a s
2]
M-2 produces heavier bottles in blow moldingdue to increased parison swell
No differences in MFI, Viscosity, or GPC!
ParameterSample
M-1 M-2
MFI 0.6 0.5
GPC-MW 131K 133K
Viscosity
at 1 sec-1
8.4K 8.3K
Die Swell 28 42
Blow Molding Polyethylene
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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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Creep Testing on US and UK Paints
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.
Creep and recovery can be
done on both DHR and
ARES rheometers
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Stress Relaxation
PDMS
Stress relaxation is another unidirectional way of
getting viscoelastic properties.
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Flow Temperature Ramp – Printing Inks
1
10
100
1,000
20 25 30 35 40 45 50
Temperatue (C)
Vis
co
sit
y (
Pa
-se
c)
Room
Temperature
Printing Press
Temperature
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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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Dynamic Testing
Time
Res
ponse
, Str
ain
90o
δo
STRAIN
ELASTIC
RESPONSE
VISCOUS
RESPONSE
VISCOELASTIC
RESPONSE
Polymers are viscoelastic materials.
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 σσσσ = σσσσ0sin(ωt + δ) ττττ = ττττ0sin(ωt + δ) Pa
Storage Modulus
(Elasticity)G’ = (σσσσ0/γ0)cosδ E’ = (ττττ0/ε0)cosδ Pa
Loss Modulus
(Viscous Nature)G” = (σσσσ0/γ0)sinδ E” = (ττττ0/ε0)sinδ Pa
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 ηηηη* = G*/ω ηηηηE* = 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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Linear Viscoelasticity
Linear Region:
• Osc Stress is linear with Strain.
• G’, G” are constant.
Non-Linear Region
G’ = f(γγγγ)
End of LVR or
Critical Strain γγγγc
It is preferable to perform testing in the
linear region because you are measuring
intrinsic properties of the material, not
material that has been altered.
This is typically the first test done on unknown materials.
Stress v. Strain
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Stability is Related to Structure in Inks
100.00.1000 1.000 10.00
osc. stress (Pa)
10000
10.00
100.0
1000
G' (P
a)
Ink Samples: Oscillation Stress Sweeps @ 6.28 rad/s
This is the most reproducible way of determining a yield stress.
A 5% drop from the modulus in the Linear Region is considered being in the Non-Linear Region
DHR Testing
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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
0 .1 1 1 0 1 0 0
1 03
1 04
1 05
1 03
1 04
1 05
T = 2 2 0 oC
Co
mp
lex v
isco
sity η
* [P
a s
]
G ' ro u g h s u r fa c e
G ' s m o o th s u r fa c e
η * ro u g h s u r fa c e
η * s m o o th s u r fa c e
H D P E p ip e s u rfa c e d e fe c ts
Modulu
s G
' [P
a]
F re q u e n c y ω [ ra d /s ]
Indicated byElasticity at
low
frequency
Caused by Broader
MWD
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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
10001.000E-3 0.01000 0.1000 1.000 10.00 100.0shear rate (1/s)
10000
100.0
1000
vis
co
sit
y (
Pa.s
)
Linear Polyethylene Flow Data
Linear Polyethylene Oscillation Data [Cox Merz]
Flow instability
TAINSTRUMENTS.COMTAINSTRUMENTS.COM
Dynamic testing: Dependence on Mw and MWD
10-4
10-3
10-2
10-1
100
101
102
103
104
105
102
103
104
105
106
107
100000
105
106
Slope 3.08 +/- 0.39
Zero Shear Viscosity
Ze
ro S
he
ar
Vis
co
sit
y ηo [
Pa
s]
Molecilar weight Mw [Daltons]
Vis
co
sity
η*
[Pa
s]
Frequency ω aT [rad/s]
Molecular weight
130 000
230 000
320 000
430 000
101
102
103
104
105
106
107
108
109
1010
1011
1012
10-5
10-4
10-3
10-2
10-1
100
increasing MWD
Vis
cosity η
*/η
o
frequency ω aTη
o
SBR polymer broad,
narrow distribution
η*red
430 000
η*red
320 000
η*red
230 000
η*red
130 000
η*red
310 000
η*red
250 000
Zero shear viscosity increases
with increasing MW
When shifting along an
axis of -1, all the curves
can be superposed, unless
the width of the MWD is
not the same.
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MWD and Dynamic Moduli
10-3
10-2
10-1
100
101
102
103
104
103
104
105
106
Effect of MWD on the dynamic moduliM
odulu
s G
', G
'' [P
a]
Frequency ωaT [rad/s]
SBR polymer melt
G' 310 000 broad
G" 310 000 broad
G' 320 000 narrow
G" 320 000 narrow
• The storage and loss modulus of a typical polymer melt cross over between 1 and 100 rad/s.• ωωωωc ∝∝∝∝ 1/Mw .• Gc ∝∝∝∝ 1/MWD.
Higher crossover frequency = lower Mw
Higher crossover Modulus = narrower MWD
TAINSTRUMENTS.COMTAINSTRUMENTS.COM
Experimental Frequency range
Extended Frequency range with TTSReference Temperature = 210°C
0.01000 0.1000 1.000 10.00 100.0 1000 10000 1.000E5ang. frequency (rad/s)
10.00
100.0
1000
10000
1.000E5
1.000E6
G' (
Pa
)
10.00
100.0
1000
10000
1.000E5
1.000E6
G'' (P
a)
Polystyrene Frequency Sweeps from 160°C to 220°C
ETC Application: TTS on Polymer Melt
ang. frequency (rad/s)
G” (P
a)
G’ (
Pa)
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Idealized Flow Curve - Polymers
1.001.00E-5 1.00E-4 1.00E-3 0.0100 0.100
shear rate (1/s)
10.00 100.00 1000.00 1.00E4 1.00E5
log η
Molecular Structure Compression Molding Extrusion Blow and Injection Molding
η0 = Zero Shear Viscosity
η0 = K x MWc3.4
Measure in Flow Mode
Extend Range
with Oscillation
& Cox-Merz
Extend Range
with Time-
Temperature
Superposition (TTS)
& Cox-Merz
First Newtonian Plateau
Second Newtonian
Plateau
Power Law Region
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Tack and Peel of Adhesives
0 .1 1 1 0
1 03
1 04
T a c k a n d P e e l p e r fo rm a n c e o f a P S A
p e e l
ta c k
g o o d ta c k a n d p e e l
B a d ta c k a n d p e e l
Sto
rag
e M
odu
lus G
' [P
a]
F re q u e n c y ω [ ra d /s ]Desirable PSA characteristicsTack: high G‘ at low frequencyPeel: low G‘ at high frequency
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Correlation of Rheological Parameters to Adhesive Properties
Property Rheological PropertiesPractical Adhesive
Property
Tack• Low tan δδδδ and Low G’
• Low Cross-links (G” > G’ @ ~1 Hz)High Tack
Shear Resistance• High G’ @ < 0.1 Hz
• High Viscosity @ Low Shear RatesHigh Shear Resistance
Peel Strength • High G” @ ~> 100 Hz High Peel Strength
Cohesive Strength • High G’, low tan δδδδ High Cohesive Strength
Adhesive Strength • High G”, high tan δ δ δ δHigh Adhesion Strength
with Surface
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0 5.0000 15.000 25.000 35.000time (s)
1000
10000
1.000E5
1.000E6
1.000E7
G' (P
a)
1000
10000
1.000E5
1.000E6
1.000E7
G'' (P
a)
PDMS
Dynamic Time Sweep: Material Response
The material is stable in
this time range.
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Cure of a "5 minute" Epoxy
12000 200.0 400.0 600.0 800.0 1000
time (s)
1000000
1.000
10.00
100.0
1000
10000
100000
G'
(Pa)
1000000
1.000
10.00
100.0
1000
10000
100000
G'' (P
a)TA Instruments
Gel Point - G' = G"
T = 330 s
5 mins.
G'
G"
This is an isothermal
time sweep.
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Isothermal Cure of Tire Compound Effect of Curing Temperature
145°C
140°C 135°C 130°C
125°C120°C
Time (min)
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Dynamic time sweep following shear
This shows how
rapidly the structure
is rebuilding.
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Dynamic Temperature Ramp - Torsion
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Effect of Molecular Weight
Rubbery PlateauRegion
TransitionRegion
Glassy Region
Temperature
MW has practically no effect on the modulus below Tg
Low
MW
Med.
MW
High
MW
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120
160
300
1500
9000
30,000
M = MW betweencrosslinks
c
log
E' (
G')
Temperature
Effect of Crosslinking
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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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TA Instruments Rotational Rheometers
Separate Motor and Transducer
“Native Mode” = Deformation/Deformation Rate
(Strain/Shear Rate)
ARES-G2Discovery HR Rheometer
Combined Motor and Transducer
“Native Mode” = Force (Stress)
With computer feedback, the instruments can do both,
deformation/deformation rate control and force control.
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DHR Instrument Specifications
HR-1HR-3HR-2
Specification HR-3 HR-2 HR-1Bearing Type, Thrust Magnetic Magnetic Magnetic
Bearing Type, Radial Porous Carbon Porous Carbon Porous Carbon
Motor Design Drag Cup Drag Cup Drag Cup
Minimum Torque (nN.m) Oscillation 0.5 2 10
Minimum Torque (nN.m) Steady Shear 5 10 20
Maximum Torque (mN.m) 200 200 150
Torque Resolution (nN.m) 0.05 0.1 0.1
Minimum Frequency (Hz) 1.0E-07 1.0E-07 1.0E-07
Maximum Frequency (Hz) 100 100 100
Minimum Angular Velocity (rad/s) 0 0 0
Maximum Angular Velocity (rad/s) 300 300 300
Displacement Transducer Optical encoder Optical encoder Optical encoder
Optical Encoder Dual Reader Standard N/A N/A
Displacement Resolution (nrad) 2 10 10
Step Time, Strain (ms) 15 15 15
Step Time, Rate (ms) 5 5 5
Normal/Axial Force Transducer FRT FRT FRT
Maximum Normal Force (N) 50 50 50
Normal Force Sensitivity (N) 0.005 0.005 0.01
Normal Force Resolution (mN) 0.5 0.5 1
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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-1 HR-2HR-3
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ARES-G2 Specifications
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Minimum Torque Specs
Oscillation Steady
ARES-G2 50 100
DHR-1 10 20
DHR-2 2 10
DHR-3 0.5 5
0.1
1
10
100
1000
Min
imu
m T
orq
ue (
nN
-m)
ARES-G2
DHR-1
DHR-2
DHR-3
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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
(1.6e-6 to 100 Hz)
6.28e-3 to 1250 rad/s
(0.001 to 200 Hz)
6.3e-5 to 100 rad/s
(1.0e-5 to 16 Hz)
6.3e-5 to 100 rad/s
(1.0e-5 to 16 Hz)
Dynamic
Deformation Range
+/- 0.05 to 1,500µm +/- 0.005 to 1e4 µm +/- 1 to 50 µm +/- 1 to 100 µm
Control
Stress/Strain
Control Strain (SMT) Control Stress (CMT) Control Strain
(CMT)
Control Stress
(CMT)
Heating Rate 0.1oC to 60oC/min 0.1oC to 20oC/min 0.1oC to 60oC/min 0.1oC to 60oC/min
Cooling Rate 0.1oC to 60oC/min 0.1oC to 20oC/min 0.1oC to 60oC/min 0.1oC to 60oC/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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SER2 DHR Data
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Fix drum connected to transducer
Rotating drum connected to the motor:
rotates around its axis
rotates around axis of fixed drum
Extensional Viscosity Measurements
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10-2 10-1 100 101 102 103101102103104105106
timee [s] η e () [Pa-s] LDPE, T 150 LDPE, T 150 LDPE, T 150 LDPE, T 150 ooooCCCC 0 0 0 0....003003003003 s s s s-1-1-1-1 0 0 0 0....01010101 s s s s-1-1-1-1 0 0 0 0....03030303 s s s s-1-1-1-1 0 0 0 0....1111 s s s s-1-1-1-1 0 0 0 0....3333 s s s s-1-1-1-1 1 1 1 1 s s s s-1-1-1-1 3 3 3 3 s s s s-1-1-1-1 10 10 10 10 s s s s-1-1-1-1 30 30 30 30 s s s s-1-1-1-1 [[[[Steady Steady Steady Steady Shear Viscosity * 3]Shear Viscosity * 3]Shear Viscosity * 3]Shear Viscosity * 3]Warning: Overlay units don't match, Frequency
LDPE (High branching)
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Large Angle Oscillatory Shear: Higher Harmonics
1 E -4 1 E -3 0 .0 1 0 .1 1 1 0 1 0 0
1 0
1 0 0
0 .0 0
0 .0 5
0 .1 0
0 .1 5P IB 2 4 9 0T = 2 8 .1 o Cω = 1 ra d /s
Mo
du
lus G
', G
", [
Pa
]
S tra in γ [ ]
Ha
rmo
nic
s I
3/I
1,
I 5/I
1,
I 7/I
1
70 75 80
-80
-60
-40
-20
0
20
40
60
80
P IB 2490
T = 28.1 oC
ω =1 rad/s
γ=100%
σ( t )S
tra
in
Tim e
linear Non-linear
70 75 80
-600
-400
-200
0
200
400
600
PIB 2490
T= 28.1 oC
ω=1 rad/s
γ=3000%
σ( t )S
tra
in
Tim e
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.
Ability to “fingerprint” a material.
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Trios Software
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Trios Software
• Trios is non-restricted. Anyone can download Trios from our website at no
cost and install it on any computer.
• Trios is versatile and friendly. It combines the best of Rheology Advantage
(AR Rheometers) and Orchestrator (ARES) and has additional features too.
• Trios has all the necessary procedures for conventional as well as
specialized testing.
• In Trios, with the DHR rheometer, you can add steps and modify steps that
haven’t started while the test is in progress.
• There is the Auto-tension feature, which is used in torsion rectangular
testing and linear DMA testing.
• There is the Auto-strain feature, which allows the strain to change during an
experiment based on the torque. This is useful for temperature ramps and
curing tests.
• The graphics quality is excellent. Formatting graphs is easy with the
Automatic options and very versatile with the Customized graphing.
• Data can be read in spreadsheet form. If you copy and paste into Excel,
you will get the data and the headings.
• There are numerous variables to select from, but you can also construct
user-defined variables.
• Trios can read data from Rheology Advantage and Orchestrator data files.
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Trios Screen
The Control Panel is shown
on the next slide.
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You can control many things from the
Control Panel section:
1. Gap
2. Temperature
3. Spindle speed
4. The laser for SALS
5. Axial force.
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Geometry Information
This information will be stored with the geometry
file. It will be accessed when the magnetic reader
scans the magnetic strip at the top of the
geometry.
There is a friendly Geometry wizard that
guides you through preparing a new
geometry.
Double-pressing the Bearing Lock icon on
the touch-pad and loading the geometry in
the same location. enables you to retain at
least most of the mapping
√√√√
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Trios Software Procedures
These are the choices in Trios for the DHR.
There are minor differences with the
choices for the ARES-G2.
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Oscillation Procedure
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Display of Frequency Sweep Data
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Flow Procedure
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Display of Flow Data
10 -2 10 -1 10 0 10 1 10 2 10 3
Shear rate (1/s)
10 -2
10 -1
10 0
S60 Viscosity Standard
Viscosity(Pa.s)Mean = 0.103204SD = 9.17835e-3Rel. SD = 0.0889342Var. = 8.42421e-5
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TA InstrumentsRubber Testing Products
• Rheometer
• Viscometer
• Density Meter
• Hardness Tester
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RPA Elite
RPA elite
Rubber & Polymer Analyzer
We obtained the RPA and others for rubber testing
when we acquired Scarabaeus recently.
DensitometerShore A
Hardness
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ASTM D5289: MDR/RPA Isothermal Curing
• ML is minimum torque during test
• MH is highest torque obtained during a specified period of time
• Tsx are scorch points at time X• TCxx are points to reach XX% of
torque difference MH - ML
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Need Some Assistance?
• Instrument Manuals
• Help Feature in Trios
• TA Instruments website
• TA Instruments Rheology Helpline
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Website: www.tainstruments.com
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Website: www.tainstruments.com
Thank you for attending
Don’t forget http://www.tainstruments.com/
If you have questions or need help
Contact the TA Instruments Technical Helpline
http://www.tainstruments.com/support/applications
/applications-hotline/