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
gkamykowski@tainstruments.com

©2019 TA Instruments TAINSTRUMENTS.COM

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.

F Kelvin,
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 Viscoelastic
Stress
Stress Modulus =
Viscosity = Strain
Strain Rate

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Rheological Testing - Rotational

2 Basic Rheological Methods

Angular Velocity,
1. Apply Force (Torque)and

Shear Rate
measure Deformation and/or
Deformation Rate (Angular
Displacement, Angular Velocity) -
Controlled Force, Controlled
Stress Torque, Shear Stress

2. Control Deformation and/or

Angular Displacement,
Torque, Stress
Deformation Rate and measure
Force needed (Controlled

Strain
Displacement or Rotation,
Controlled Strain or Shear Rate)

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Steady Simple Shear Flow

Top Plate Velocity = V0; Area = A; Force = F

H
Bottom Plate
y
Velocity = 0
x
vx = (y/H)*V0

.
γ = dvx/dy = V0/H Shear Rate, sec-1
σ = F/A Shear Stress, Pascals
.
η = σ/γγ 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 σ Force or torque

Strain γ Linear or angular displacement

Strain  Linear or angular velocity

Rate

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SHEAR RATE CALCULATIONS IN EXTRUSION

.
Extruder: γ = πDN/(60*h)
D = Diameter; N = rpm; h = gap

. Q = Output rate;
πD3)
Circular, Rod: γ = 32Q/(π D = orifice diameter
compounding, cable
.
Rectangular, Slit: γ = 6Q/(wh2) Q = Output rate;
w = width
cast film, sheet h = gap

.
π(D1+D2)h2)
Annulus: γ = 12Q/(π 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
Viscosity (Pa-sec)

0 < n < 1 (Newtonian)

1.E+03 Transition Power Law

η = η0 Region Region

1.E+02

1.E+01
.
η = m*γγ (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
η0 ∝ MW3.4
Shear Rate (sec-1)
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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
log η

4) Chewing and swallowing

rates, the rheology data are still useful.
5) Dip coating
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 = X0; Area = A; Force = F

y
Bottom Plate
x Displacement = 0
x = (y/H)*X0
γ = dxx/dy = X0/H Shear Strain, unitless
σ = F/A Shear Stress, Pascals
G = σ/γγ 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

109

• Instantaneous Strain
• Note the decrease in
the modulus as a
function of time.
)
[Pa]

108
G(t) (

F
G(t)
T=20°C
T=30°C
T=40°C
T=50°C
7
10
100 101 102 103

time [s]

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Rheological Parameters

FLUIDS TESTING

Parameter Shear Elongation Units

. .
Rate γ ε Seconds-1

Stress σ τ Pascals

. .
Viscosity η = σ/γγ ηE = τ/εε Pascal-seconds

SOLIDS TESTING

Parameter Shear Elongation Units

Strain γ ε Unitless

Stress σ τ Pascals

Modulus G(t) = σ/γγ E = τ/εε Pascals

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Rheological Parameters

CREEP TESTING

Parameter Shear Elongation Units

Stress σ τ Pascals

Strain γ ε Unitless

Compliance J = γ /σ
σ D = ε/τ 1/Pascals

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Creep Testing

Stress is held constant.

Strain is the measured variable.
Compliance = Strain/Stress
3x10 -3

HDPE
Compliance (1/Pa)

2x10 -3
Viscoelastic

1x10 -3 Fluid

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

to Medium Solids
to High Viscosity
Viscosity Viscosity to Soft Solids

Water to Steel
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Converting Machine to Rheological Parameters in Rotational Rheometry

M x Kσ = σ =η Machine Parameters
M: Torque
Ω : Angular Velocity

Ω x Kγ γ• θ : Angular Displacement

Conversion Factors
Kσ : Stress Conversion Factor

Mx Kσ σ
Kγ : Strain (Rate) Conversion Factor

Rheological Parameters

= =G σ : Shear Stress (Pa)

γ• : Shear Rate (sec-1)

θ xKγ γ
η : Viscosity (Pa-sec)
γ : Shear Strain
G : Shear Modulus (Pa)

The conversion factors, Kσ and Kγ, 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

Kγ Ravg/(Ro-Ri) 1/β
β R/h

Kσ πRi2L)
1/(2*π πR3)
3/(2π πR3)
2/(π

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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/displacement/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 =
2 
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Cone Angles

Shear Rate
Increases

2°

1°

0.5 °

1
As cone angle decreases, shear rate increases  = Ω
"
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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  = Ω

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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
0.5 18 1.17E-03
8 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
0.5 18 0.49 3.44E+04 1.15E-05
60 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

&
$% =
- #
' 1 ( 0.378 . w = Width
l = Length
3 0 1.2 t = Thickness
.
$/ =
3 · &#

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, Shear Rate

 Stress/Rate Ramp
 Stress/Rate Sweep Sweep

 Time sweep/Peak Hold/Stress

Growth
 Temperature Ramp Ramp
 Creep (constant stress)
Time
 Stress Relaxation (constant
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
3
10

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
shear stress (Pa)

150.0
125.0
100.0
75.00
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
Viscosity (Pa-sec)
.
η = η0/(1+(σγ)c)
1.E+05
Cone and
Plate

1.E+04

1.E+03
0.01 0.1 1 10
η0 = KMw 3.4 Steady testing
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

4
10
starch
3
10 peanut oil
0.05% poly-
Viscosity η [Pa s]

10
2 acrylamide solution
syrup
1
Cocoa butter lotion
10 Shower gel
Co-polymer 240 °C
0
10

-1
10

-2
10
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

2
10 0.50% Polystyrene-ethylacrylate
latex particles in water
1 0.47%
10
Viscosity η [Pa s]
0
10
0.43%
-1
10

-2 0.34%
10
0.28%
0.18%
-3
0.09%
10 water
-4 -3 -2 -1 0 1 2 3 4 5
10 10 10 10 10 10 10 10 10 10
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
σxx- σyy from the Stress Tensor.
• N1 = 2F/(π πR2), where F is the measured
force.
• Ψ 1 = N1/

2 This is the primary normal
stress coefficient.

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Effect of HDPE Variations in Blow Molding

Blow
B o lw Molding
M o ld in gPolyethylene
P o ly e t h y le n e
6 6
10 10

Normal stress coefficient Ψ (γ) [Pa s ]

2
T = 180° C
Sample
Parameter
Shear viscosity η(γ) [Pa s]

5 5
10 10 M-1 M-2

1
MFI 0.6 0.5
4 4
10 10
GPC-MW 131K 133K
3
Ψ 1(γ) M -1 3 Viscosity 8.4K 8.3K
10 10
Ψ 1(γ) M -2 at 1 sec-1
η (γ) M -1 CP
2 η (γ) M -2 CP 2 Die Swell 28 42
10 10
η (γ) M -1 C a p illa r y
η (γ) M -2 C a p illa r y
1 1
10 10
0 .1 1 10
S h e a r r a te 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
Viscosity (Pa-sec)

100

10

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
Response, Strain

ELASTIC
RESPONSE
90o
VISCOUS
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 σ = σ0sin(ωt + δ) τ = τ0sin(ωt + δ) Pa

Storage Modulus
σ0/γ0)cosδ
G’ = (σ E’ = (ττ0/ε0)cosδ Pa
(Elasticity)

Loss Modulus
G” = (σ
σ0/γ0)sinδ E” = (ττ0/ε0)sinδ Pa
(Viscous Nature)

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 η* = G*/ω ηE* = 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(γγ)
Stress v. Strain

End of LVR or
Critical Strain γc

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.
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Stability is Related to Structure in Inks

Ink Samples: Oscillation Stress Sweeps @ 6.28 rad/s

A 5% drop from the modulus in
10000 the Linear Region is considered
DHR Testing
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)
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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' (Pa)

1.000E5 1.000E5

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 10000
G"
G' (Pa)

G'' (Pa)

1000 1000

Gel Point - G' = G"

100.0 100.0
T = 330 s
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

130°C
140°C 135°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

H D P E p ip e s u r f a c e d e f e c ts

Indicated by T = 220 C
o

5 5
10 10
Elasticity at

Complex viscosity η* [Pa s]

low
frequency Modulus G' [Pa] 10
4
10
4

Caused by G' ro u g h s u rfa c e

Broader 10
3 G' s m o o th s u rfa c e
10
3

η* ro u g h s u rfa c e
MWD η* s m o o th s u rfa c e

0 .1 1 10 100
F r e q u e n c y ω [r a d /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]
viscosity (Pa.s)

1000

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 Mw and MWD

7
10
Molecular weight
130 000 Zero shear viscosity increases
6 230 000
10
320 000 with increasing MW
430 000
Viscosity η* [Pa s]

5
10
Zero Shear Viscosityηo [Pa s]

4
10 Zero Shear
Viscosity

0
10
6
10
10
3
Slope 3.08 +/- 0.39
increasing MWD
-1
10
5
10

100000
2
10 Molecilar weight Mw [Daltons]
Viscosity η*/ηo

-4 -3 -2 -1 0 1 2 3 4 5 -2
SBR polymer broad,
10 10 10 10 10 10 10 10 10 1010
narrow distribution
Frequency ω aT [rad/s] η*red 430 000
10
-3 η*red 320 000
When shifting along an η*red 230 000
η*red 130 000
axis of -1, all the curves 10
-4

η*red 310 000

can be superposed, unless η*red 250 000
-5
10
the width of the MWD is 1
10 10
2 3
10
4
10 10
5 6
10
7
10
8
10
9
10 10
10 11
10
12
10

not the same. frequency ω aTηo

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MWD and Dynamic Moduli

Effect of MWD on the dynamic moduli

• The storage and loss modulus of
6
10 a typical polymer melt cross over
between 1 and 100 rad/s.
• ωc ∝ 1/Mw .
• Gc ∝ 1/MWD.
Modulus G', G'' [Pa]

5
10

4
10
SBR polymer melt
G' 310 000 broad
3
G" 310 000 broad
10
G' 320 000 narrow
G" 320 000 narrow
-3 -2 -1 0 1 2 3 4
10 10 10 10 10 10 10 10

Frequency ωaT [rad/s]

Higher crossover frequency = lower Mw

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”G''(Pa)
G’G'(Pa)
(Pa)

(Pa)

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. frequency (rad/s)
ang. frequency (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
η0 = K x MW c 3.4
Extend Range
log η

with Time-
Temperature
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

(Pa.s)

η0 = A*exp(Eact/(R*T))
.
η = η0/(1+(η0*γ/σcrit)c)
Viscosity

Parameter LDPE LLDPE

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

T a c k a n d P e e l p e rfo rm a n c e o f a P S A

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
Storage Modulus G' [Pa]

4
10

peel

3
10

ta c k

0 .1 1 10
F r e q u e n c y ω [r a d /s ]
Desirable PSA characteristics
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 δ 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 δ 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
Low Med.
MW
MW MW

Temperature

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Effect of Crosslinking

Mc = MW between
crosslinks

120

160
log E' (G')

300

1500
9000

30,000

Temperature

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Rubber Compound: Similar cure curve, different processing

Good Bad
High Strain tan δ
Viscosity, η* Similar
tan δ (low γ) 1.0 0.8
S' [dNm ]

tan δ (high γ) 5.7 3.0

15.0

14.0

13.0

12.0

11.0

10.0

9.0

8.0

Storage Modulus, G’ (kPa)

7.0

Shear Modulus G' [kPa]

6.0 Tan Delta
Tan Delta
5.0

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
Tim e [m in]
11.0 12.0
5 5
13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0

SCARABAEUS GMBH - inf o@sc arabaeus-gmbh.de - Tel.:+49 (0) 6441/56777-0

4 4

1010 3 3

2 2

1 1

1 0 0
0.1 1 10 100 1000

0.1 1 10Strain [%] 100 1000

% Strain
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Level 2: Examination of Higher Harmonics

SAOS γ(t) = γ0 sin(ωt)

σ(t) = σ0 sin(ωt+δ)

LAOS
γ(t) = γ0 sin(ωt)

Fourier Series expansion:

σ(t) = σ1 sin(ω1t+ϕ1) + σ3 sin(3ω1t+ϕ3) + σ5 sin(5ω1t+ϕ5) + ...

∞

= Σ σ sin(nω +ϕ )
n=1
n 1 n LAOS is often called Fourier Transform Rheology, or FT Rheology.
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
P IB 2 4 9 0 Ability to “fingerprint”
T = 2 8 .1 o C a material.

7 1
Harmonics I /I , I /I , I /I
100 ω = 1 ra d /s
Modulus G', G", [Pa]

5 1
80

60
σ (t )
600

400
σ (t )
0 .1 0
40
200
20
T im e Tim e

Strain
Strain
0 0
70 75 80 70 75 80

3 1
-20
P IB 2 4 9 0 -200
PIB 2490
-40 o o
T = 2 8 .1 C T= 28.1 C
ω =1 ra d /s -400 ω =1 rad/s
-60
γ =1 0 0 % γ=3000%
-80 -600

linear Non-linear 0 .0 5
10

0 .0 0

1 E -4 1 E -3 0 .0 1 0 .1 1 10 100
S tra in 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)

5
10 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

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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
Sensor Transducer
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
Minimum Torque (nN.m) Oscillation
Drag Cup
0.5
Drag Cup
2
Drag Cup
10 HR-2 HR-3
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
Motor Control FRT
Maximum Normal Force (N) 50 50 50
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-1 HR-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
Angular Velocity Range (rad/s) 1x 10-6 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

Minimum Torque (nN-m)

100

10
ARES-G2
DHR-1
1 DHR-2
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-5to 100 rad/s 6.3e-5to 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 1,500µm +/- 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 0.1oC 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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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/cm2
• 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/cm2
• 455 nm wavelength with peak intensity
of 350 mW/cm2
• 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

Coefficient of
Friction, µ
1

(ηoilΩ)/FL

• In lubricated systems, the ‘Stribeck curve’ captures influence of lubricant viscosity(ηoil),

rotational velocity (Ω) and contact load (FL) 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=20o C
ω=1rad/s 2
G's Span 65 [molecul/nm ]
G"s 0.1 4.3 0.36
Storage & Loss Modulus [N/m]

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

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

Temperature Isohume, Isothermal Isothermal, RH Ramp Isohume, Temp Ramp

Temperature

Temperature
RH

RH

RH
time time time
Isothermal, RH Step Isohume, Temp Step RH Step, Temp Step
Temperature

Temperature

Temperature
RH

RH

RH
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

DiffusionDiffusion

• 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
 rsupport@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

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Rheology, and Microcalorimetry

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