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1
A Comprehensive Introduction
to Rheology
Practical Rheology Workshop
Rheology: An Introduction
Rheology: An Introduction
Rheology is the science of flow and deformation of matter.
Flow is a special case of deformation
The relationship between stress and deformation is a property of the material
These fundamental relations are called constitutive relations
ModulusStrain
Stress=Viscosity
rateShear
Stress=
Rheology: Study of stress-deformation relationships
Simple Steady Shear Flow
H
x
y
Top plate Area = A
Bottom Plate
Velocity = 0
Velocity = V0
Force = F
Shear Stress, PascalsViscosity, Pa-sec
0VH
yvx
=
H
V
dy
dvx 0=
=γ&
A
F=σ
Shear Rate, sec-1
Velocity at position y, m sec-1
γ
ση
&=
Viscosity is a fundamental flow parameter. Shear rate is always a change in velocity with respect
to distance. We assume the rate of momentum change is constant throughout the specimen.
2
Deformation of Solids
x(t)
V
y0
A
F=τ
A
y
xz
Modulusγ
τ=GStrain
0
)(
y
tx=γ
Viscosityγ
τη
&=
t∆
∆=
γγ&
Viscoelastic Behavior
F = F(x); F ≠ F(v)
Deformation: Solid
behavior
Flow: Fluid behavior
F = F(v); F ≠ F(x)
Purely Elastic
Purely
Viscous
Viscoelastic
Force depends on both Deformation and Rate of Deformation and vice
versa.
Deformation & Flow
Viscoelastic Behavior
t is short [< 1s] t is long [24 hours]
Behavior described by Deborah Number
PDMS (silly putty)
Understand Your Instrument First!
Rotational (Shear) Rheometers
ARES-G2 (Strain Control – SMT – Dual Head)
DHR (Stress Control – CMT – Single Head)
Solids (Tensile/Bending) Rheometers
RSA-G2 (Strain Control – SMT – Dual Head)
DMA Q800 (Stress Control – CMT – Single Head)
Two types of rotational rheometers and DMA‘s
Both techniques, depending on the configuration, have
different specification, different features and different
performance for different applications.
3
What Does a Rheometer Do?
Rheometer – an an instrument that measures both viscosity
and viscoelasticity of fluids, semi-solids and solids
It provides information about the material’s:
Viscosity – function of shear rate or stress, time &
temperature dependence
Viscoelastic properties (G’, G”, tan δ) with respect to time,
temperature, frequency & stress/strain
Transient response (relaxation modulus, creep compliance,
creep recovery)
How do Rheometers Work?
Torque
Angular Displacement
Angular Velocity
Rheology is the science of flow and deformation of matter--or--
the study of stress-strain relationships
Fundamentally a rotational rheometer will control or measure:
Rotational Rheometer Designs
Separate motor & transducerOr Dual Head
Combined motor & transducer
Or Single Head
Sample
Applied
Strain or
Rotation
Measured
Torque
(Stress)
Direct Drive
Motor
Transducer
Displacement
Sensor
Measured
Strain or Rotation Non-Contact
Drag Cup
Motor
Applied
Torque
(Stress)
Static Plate
Rotational Rheometers at TA
Controlled Strain
SMT or DH
ARES G2 DHR
Controlled Stress
CMT or SH
4
Understanding Key Rheometer Specifications
Torque range
Angular Resolution
Angular Velocity Range
Normal Force
Frequency Range
Rheology is the science of flow and deformation of matter--or--
the study of stress-strain relationships
ARES-G2 Instrument Specifications
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
Relating Instrument Specifications to Material Properties
(Pa) modulus
s) (Paosity visc
(1/s) ratestrain
) (strain
(Pa) stress )(
:parameters Calculated
γ
τ(t) G(t)
γ
τ(t)η(t)
dtdθK(t)γ
θ Kγ(t)
MKt
o
o
γ
γ
=
=
=
=
=
&
&
ττ
m) (N torque
(rad/s)locity angular ve
(rad)nt displacemeangular
:parameters Measured
M(t)
Ω(t)dt
dθ
θ(t)
=
The measured quantity (angular deformation and torque) are transferred into a material quantity (stress, strain, viscosity, etc.)
Geometry specific
constants, Kτ and Kγ, relate
the measured instrument
data with the desired
material parameter
5
Equation for Viscosity
γ
σ
γ
ση
K
KM
.
.
Ω==
&
Raw rheometer
Specifications
Geometric
Shape
Constants
Constitutive
Equation
Rheological
Parameter
In SpecDescribe
Correctly
Equation for Modulus
γ
σ
θγ
σ
K
KMG
.
.==
Raw rheometer
Specifications
Geometric
Shape
Constants
Constitutive
Equation
Rheological
Parameter
In SpecDescribe
Correctly
Ranges of Rheometers and DMA’s
Loss Modulus (E" or G")
Storage Modulus (E' or G')
log
E' (
G') a
nd
E"
(G")
Temperature
Range of DHR/ARES-G2 Rheometer
Range of DMA/RSA-G2
Some Viscoelastic
Liquid
Characterization
Possible with
Shear Sandwich
Motion
Flow(Flow, Creep,
Stress Relaxation)
Oscillation Squeeze Flow/
Pull Off
6
Geometries
Parallel
Plate
Cone and
Plate
Concentric
Cylinders
Torsion
Rectangular
Very Lowto Medium
Viscosity
Very Lowto High
Viscosity
Very LowViscosity
to Soft SolidsVery Soft to VeryRigid Solids
Water to Steel
22
Markets
Paints/Inks/Coatings
Polymers
Asphalt
Food
Organic Chemicals
Pers Care & HH Products
Adhesives & Sealants
Petroleum Products
Pharmaceuticals
Medical/Biological
Inorganics (Metals, Ceramic, Glass)
Other
Paper
Automotive
Elastomers
Aerospace
Electronics
What is DMA?
Dynamic Mechanical Analysis is a combination of:
The science of Flow and Deformation of
Matter
Measurement of any propertyas a function of time and temperature
Modes of Deformation
BendingCompressive
RectangularTorsion
Tensile
Linear
Rotational
TorsionalShear
7
Straight Line & Rotational Analogs
Straight Line Motion
Rotational Motion
Force Torque
Mass Moment of Inertia
Acceleration Angular Acceleration
Velocity Angular Velocity
Displacement Angular Displacement
TA Instruments DMA’s
Controlled StrainSMT
RSA G2 Q800
Controlled StressCMT
TA Instruments’ DMAs
Controlled StressCMT – Combined Motor &
Transducer
Controlled Strain SMT – Separate Motor &
Transducer
Motor
Applies
Force
(Stress)
Displacement
Sensor
(Measures
Strain)
Sample
Force Rebalance
Transducer (FRT)
(Measures Stress)
Actuator
Applies
deformation
(Strain)
Sample
RSA G2 Q800
DMA Q800: Schematic
8
RSA-G2: Dual Head Design
Transducer
Temperature Sensor
Drive Motor
Air Bearing
Rare Earth Magnet
Motor
Air Bearing
Air Bearing
Air Bearing
LVDT
LVDT
Upper Geometry MountLower Geometry Mount
Transducer Motor
Specifications
TA Instruments DMA Specifications
Q800 RSA G2
Max Force 18N 35N
Min Force 0.0001N 0.0005N
Force Resolution 0.00001N 0.00001N
Frequency Range 0.01 to 200 Hz 2E-5 to 100 Hz
Dynamic Sample
Deformation Range +/- 0.5 to 10,000 µm +/- 0.05 to 1,500 µm
Strain Resolution 1 nanometer 1 nanometer
Modulus Range E3 to 3E12 Pa E3 to 3E12 Pa
Modulus Precision +/- 1% +/- 1%
Tan delta Sensitivity 0.0001 0.0001
Tan delta Resolution 0.00001 0.00001
Temp range -150 to 600°C -150 to 600°C
Heating Rate 0.1 to 20°C/min 0.1 to 60°C/min
Cooling Rate 0.1 to 10°C/min 0.1 to 60°C/min
Isothermal Stability +/- 0.1°C +/- 0.1°C
Clamps (on Q800)
The array…
S/D Cantilever
3-Point Bending
Tension-Film
Tension-Fiber
Shear-Sandwich
Compression
Submersible
Compression
Submersible
Tension
Clamps (on RSA-G2)
Film/Fiber
Compression
3-Pt Bending
Cantilever
Shear Sandwich
Contact Lens
9
Measurement of Shear Modulus - Torsion and Shear Sandwich
Stress Head
(transducer)
Movable clamp
Sample
Stationary
ClampStress Head
(transducer)
Torsion (Shear Rheometer) Shear Sandwich (DMA)Limited to Soft Solids
Movable
ClampStationary
Clamp
Sample
Measurement of Young’s Modulus - Three Point Bending
Movable Fulcrum
Stress Head (transducer)
SampleStationary Fulcrum
Measurement of Young’s Modulus - Cantilever Bending
Dual Cantilever Bending
Single Cantilever Bending
Movable
clamp
Stress Head
(transducer)
Sample
Stationary
Clamp
Measurement of Young’s Modulus - Compression
Movable clamp
Stress Head (transducer)
Sample
Stationary Clamp
10
Measurement of Young’s Modulus - Tension
Movable clamp
Stress Head (transducer)
Sample(film, fiber,or thin sheet)
StationaryClamp
Four Regions of Viscoelastic Behavior for Typical
Linear and Crosslinked Amorphous Polymer
Very hard
and
Brittle
Soft rubberViscoelastic
liquid
3
7
5
9
Temperature, °C
Glassy Transition Rubbery
Plateau
(Linear)
(Lightly Crosslinked)
Resilient
leather
Flow Region
Instruments for Solids Measurements
Measurements of the shear modulus,G, can be
made on traditional stress and strain controlled shear rheometers. Measurements are conducted using torsion, and in some cases, parallel plate
geometries.
Measurements of Young’s modulus, E, can be made on traditional dynamic mechanical analyzers,
DMA . Measurements can be made in tension, compression, and bending configurations.
Measurements of the shear modulus can also be made on soft solids using a shear sandwich configuration.
Ranges of Rheometers
Loss Modulus (E" or G")
Storage Modulus (E' or G')
Temperature
Range of AR/ARES Rheometer
Range of DMA/RSA
Some Viscoelastic
Liquid
Characterization
Possible with
Shear Sandwich
11
41
Rheological Characterization
Rheology
dynamic
oscillation
G‘ und G‘‘ = f( )
linear regime
γ&
continuous
shearing
η und N1 = f( )γ&
non-linear regime,
time-dependent
elongationalflow
linear and non-
linear regime
H0 = f( )ε&
FT-Rheology
FT
non-linear regime,
time-dependent
( )( )
( )γ=ω
ωf
I
3I
1
1
DHR Dielectric Accessory
DHR Rheometer
Agilent E4980A LCR meter
Environmental test
Chamber
BNC connections to
LCR meter
Ground Geometries with
Ceramic Insulator
(standard or disposable)
Specifications
Attribute Specification
Geometry25mm Insulated SST Plate
Disposable parallel plates (8 mm, 25 mm, 40 mm)
Temperature System ETC, Environmental Test Chamber
TRIOS Software Version 2.5 or later
Temperature Range -160° to 350°C
LCR Meter Compatibility Agilent Model E4980A
DE Frequency Range 20 Hz to 2 MHz
DE LCR Meter AC Potential 0.005 to 20 Volts
Applications: Polar materials
Examples: PVC, PVDF, PMMA, PVA
12
Applications: Emulsions stability
Pond’s mechanical
response at -18C
suggests instability.
However, large
dielectric increase
in Nivea indicates
stronger ion
mobility due to
phase separation.
Hence change in
morphology of
Nivea as compared
to Pond’s cream.
DHR Electro-Rheology (ER) Accessory
DHR ER Accessory
• Engineering prototype as demo unit in New
Castle
• Parallel Plates geometries
• DIN Concentric Cylinder
• Compatible with Peltier Plate and Peltier
Jacket temperature systems ONLY
Specifications
Attribute Specification
Geometry25 and 40 mm ER parallel plate and 28 mm
ER conical DIN bob
Temperature System CompatibilityPeltier Plate and Peltier Concentric Cylinder
Jacket
TRIOS Software Version 2.6 or later
Temperature Range-40 to 200°C for Peltier Plate. -10 to 150°C
for Peltier Concentric Cylinder
High Voltage Power Amplifier TREK Model 609E-6
Maximum Voltage0 to 4,000 VDC; 4,000 VAC peak (8,000 peak-
peak)
Output Current Range 0 to ± 20 mA
SafetyPolycarbonate ER shield cover with interlock
switch
13
Applications
• Hydraulic valves
and clutches
• Shock absorbers
• Bulletproof vests
• Polishing slurries
• Flexible electronics
(kindle…)
Introduction to Tribology
stressnormal
stressshear==
L
F
F
Fµ
“Tribology is the study of interacting surfaces in relative motion”
Solid and liquid lubrication
Lubricating oils and greases
Friction, wear, surface damage
Surface modifications and coatings
Tribology of Lubricated Systems
Boundary
Lubrication
Mixed
Lubrication
Hydrodynamic
Lubrication
1
Co
eff
icie
nt
of
Fri
ctio
n, µ
(ηoilΩ)/FL
• In lubricated systems, the ‘Stribeck curve’ captures influence of lubricant viscosity(ηoil),
rotational velocity (Ω) and contact load (FL) on µ
• At extremely high loads, there is direct solid-solid contact between the surface asperities
leading to very high friction (Boundary Lubrication)
• At higher loads, the gap becomes smaller and causes friction to go up (Mixed Lubrication)
• At low loads, the two surfaces are separated by a thin fluid film (gap, d) with frictional effects
arising from fluid drag (Hydrodynamic Lubrication)
Tribo-rheometry Accessory (TRA)
stressnormal
stressshear==
L
F
F
Fµ
Tribological measurements require:
1) Direct contact between the two interacting surfaces (Axial force application and control)
2) Relative motion between the two surfaces (Excellent velocity control)
The tests are run at small gaps and need good alignment between the surfaces
Uniform distribution and control of normal force requires a compliant design
Disc Coupling
Stepped Disposable
Peliter Plate/ ETC
14
Tribo-rheometry Beam Coupling
Addition of beam coupling introduces axial compliance without compromising torsional stiffness
Helical spring design ensures good alignment between the two surfaces
Choice of beam couplings allow flexibility over axial compliance depending on sample stiffness
FL
Stainless Steel
Coupling
Aluminum
Coupling
Lubricant
Bottom
Surface
Top Surface
Tribo-rheometry Specifications & TRIOS Variables
Variable Definition Units
Vs (Sliding Speed) Kv*Ω m/s
ds (Sliding distance) Kv*θ m
FL (Load Force) Kl*Fz N
FF (Friction Force) Kf*M N
µµµµ (Coeff. of Friction) FF/FL Dimensionless
Gu (Gumbel Number) ηoilΩ/FL Dimensionless
• Fully integrated into TRIOS with Tribology test templates
• Complete suite of tribology relevant test variables available
Instrument Compatibility All DHRs
Temperature Systems Peltier Plate, ETC Oven
Temperature Range Peltier: -40 °C to 200 °C for All
ETC: -150 °C to 350 °C BTP and B3B
ETC: -150 °C to 180 °C RP and 3BP
Maximum Axial Force 50 N
Maximum Torque 200 mN.m
Peltier Plate Tribo-rheometry Geometries
Ball on three Plates Three Balls on Plate
Ring on Plate Ball on three Balls
Coefficient of Friction Measurement
PVC on Steel with 2.0 Pa.s oil as lubricant
Geometry: 3 Balls on Plate
Temperature: 25°C, Procedure: Flow ramp
Bo
un
da
ry L
ub
rica
tio
n
Mix
ed
Lu
bri
cati
on
Hyd
rod
yn
am
ic L
ub
rica
tio
n
15
Coefficient of Friction Measurement
PVC on Steel with 2.0 Pa.s oil as lubricant
Geometry: Ring on Plate
Temperature: 25°C, Procedure: Flow Sweep
Stepped Disposable Peltier Plate Tribo-rheometry Setup
Ideal platform for testing cosmetic products (lotions, hand cream, makeup) and lubricants
Disc
Coupling
Skin substitute ring on
disposable plate
Skin substitute on
stepped disposable plate
CoF Measurement: Personal Care application
Temperature 25°C
Speed 10 rad/s
Normal stress steps
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00
Co
eff
icie
nt
of
Fri
ctio
n
Pressure. PSI
Vaseline
Baby Oil
CoF Measurement: Personal Care application
Temperature 25°C
Velocity Ramp 1 to 50 rad/s
Normal stress 0.8 PSI
Baby Oil
Vaseline
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 20 25 30 35 40 45 50
Angular Velocity rad/s
Co
eff
icie
nt
of
Fri
cti
on
16
Wet Setup: Semiconductor Application
Polishing Pad ring on
Disposable Plate
Silicon Wafer on
Disposable Plate
Disc
Coupling
Peak hold tests at 62.25 and 177.5 rad/s (sliding speed, VS ~ 0.7 – 2 m/s)
Load force (FL) gradually increased from 0.35 to 7 N
Polishing slurry was added to the wafer/pad interface between runs
Typical Results
CoF Measurement: Semiconductor Application
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Co
eff
icie
nt
of
Fric
tio
n
Pressure, PSI
Speed 0.7 m/s
Speed 2 m/s
Degradation of Wafer Surface
Before Testing After Testing
17
ETC Oven Tribo-Rheometry Geometries
Beam
Coupling
SST Ring on
upper plate
Brake pad on
lower
disposable
plate
Ball on three Plates Three Balls on Plate
Ring on Plate Ball on three Balls
Well suited for automotive applications, high temperature greases/oils and testing lubricity of asphalt and rubber
Asphalt Lubricity Testing
Geometry: Ball on three Balls
Temperatures: 100 °C, 110 °C and 120 °C
Procedure: Flow Ramp
Optics Plate Accessory (OPA)
• Stepping stone into Rheo-Microscopy!
• Smart swap lower glass plate for easy sample viewing with user custom optics system
• Includes 3 replacement 1 mm thick glass plates and O-rings
TA Instruments Confidential Document
8 threaded holes for
custom optics installation
PN 546800.901
OPA with USB Microscope
• Smart swap OPA with Dino-lite USB microscope.
• X-Z stage for radial and axial positioning and focusing.
• Includes with 3 replacement 1 mm glass plates and O-rings
TA Instruments Confidential Document
2D Stage USB
microscope
PN 546800.902
18
OPA with USB Microscope
TA Instruments Confidential Document
Magnification 50x 240x
Working distance 11.4 mm 11.6 mm
Field of view 7.8 x 6.3 mm 1.6 x 1.3 mm
Polarization Yes
Illumination 8 White LED's
Image Capture 1280 x 1025 pixels, 30 fps
Temperature range
(UHP)-20 to 100°C
Geometries Plates and Cones up to 60 mm Diameter
Instrument
CompatibilityAll DHRs, AR-G2, and AR200ex
OPA with USB Microscope
TA Instruments Confidential Document
PDMS in PIB 240x with mirror finish geometry
At rest After shear
100 µm 100 µm
New Pressure Cell Rotors
TA Instruments Confidential Document
Standard Pressure
Cell accessory
with Conical Rotor
Optional Starch Rotor
for Pressure CellOptional Vane Rotor
for Pressure Cell
• Samples with large particles
• Better mixing to suspend particles
• Loading samples with delicate structures
PN 402815.901 PN 402828.901
Pressure Cell Vane rotor
TA Instruments Confidential Document
Pressure cell with vane rotor
Self-sealed mode
Pasta sauce with starch
Flow temperature Ramp: 2°C/min
Stress: 5 Pa
19
DHR Torsion Cylindrical
• Can accommodate samples with diameters of: 1.5, 3, and 4.5 mm
• Compatible with ETC
• Polymers, Elastomers
PN 547905.901
DHR Torsion Cylindrical
TA Instruments Confidential Document
Polycarbonate
Oscillation temperature ramp
Heating rate: 3°C/min
Frequency: 1 Hz
Strain: 0.01 %
DHR Building Materials Cell
TA Instruments Confidential Document
• Fits in Peltier Jacket
• Characterization of Cements, Mortars, Pastes
Paddle Rotor
for BM Cell• Large Cup to accommodate samples with large
particles
• Slotted Cage to minimize material slip at the wall
PN 533246.901
PN 533247.901
DHR Building Materials Cell: Cement mixing
TA Instruments Confidential Document
Sto
rag
e M
od
ulu
s G
’ (P
a)
Loss
Mo
du
lus
G”
(Pa
)
Oscilla
tion
Strain
(%)
Time (s)
Large Strain followed by low Strain Oscillation time sweeps
Temperature: 23°C
Frequency: 1 Hz
Strain: 5000 and 0.01 %
20
DHR/AR Bayonet Peltier Plate
Quick Change Plates (same as ARES-G2 APS):
Can be used as standard Peltier Plate
with Plates/Cones up to 40 mm Dia.
Solvent trap available soon
Can be used with Quick Changes Plates
(SST, Sandblasted & Crosshatched) ;
solvent trap available soon.
Also compatible with Disposable QCP.
Immersion Cup
Quoting DHR/AR Bayonet Peltier Plate (BPP)
– Bayonet Peltier Plate: 533209.901
– BPP with QCPs of various materials of construction or surface
finishes
• Quick Change Plate Holder: 402751.902
• Selection of QCP’s and corresponding diameter upper peltier
plates from price list
– BPP with Disposable plates configuration
• Quick Change Disposable Plate Holder: 402751.901
• Selection of QCDP’s from price list
• Corresponding diameter upper disposable plates from price list
• Disposable Plate upper shaft: 546320.901 (DHR &AR-G2) or
546319.901 (AR2000/1500ex)
QCP Holder QCP
QCDP Holder QCDP
New ARES-G2
Accessories
ARES-G2 Cone & Partitioned Plate
Sample fracturing occurs
when deformation for highly
viscous elastic fluids, such as
polymer melts, exceeds a
total deformation of a few
strain units. This limits LAOS
experiments on rotational
rheometers
21
ARES-G2 Cone & Partitioned Plate (CPP)
• Can only be done on Dual Head design
• Compatible with FCO
• Outer ring cylinder delays edge fracture
• Wider strain range in LAOS measurements
• Better transient Normal Force measurements
Center plate
(to transducer)
Outer ring
cylinder
Lower Cone
(to motor)
Sample
PN 402800.901
ARES-G2 CPP: LAOS example
Can reach larger strains with CPP before
sample leaves gap in standard cone an plate
ARES-G2 DWR Interfacial Accessory
TroughDWR
• Patented geometry
• Compatible with APS
temperature system
• Requires APS Plate
• Measurements of interfacial
shear rheology of thin layers
at liquid-liquid or liquid-gas
interfaces
Adapter
PN 402820.901
ARES-G2 DWR Interfacial Accessory
Sorbitan tristearate (SPAN) Surfactant at Water – Dodecane interface
Geometry: Double wall ring
Temperature: 20°C
Procedure: Oscillation time sweep followed by Oscillation Frequency Sweep
Sto
rag
e m
od
ulu
s G
’(P
a/m
)Lo
ss m
od
ulu
s G
’(P
a/m
)
Sto
rag
e m
od
ulu
s G
’(P
a/m
)
Co
mp
lex v
iscosity
η*
(Pa
.s.m)
Loss
mo
du
lus
G’
(Pa
/m)
22
Parallel Superposition
• Follow structural changes in a material under flow
• VE moduli in PSP not obvious can generate negative G‘ values !
Time
Str
ain
, γ γ
γ
γ (
An
gu
lar)
Motor
X-d
uce
rTorque Transducer outputs
combination of torque from
steady shear and oscillation
torque from dynamic
measurement
Shear Rate, γγγγ.
Orthogonal Superposition (OSP) on ARES-G2
• Alternative to parallel superposition to follow structural changes in a material under flow
• Implementation of orthogonal superposition on the RMS800 by modifying the normal force FRT
transducer (Vermant; Ellis -1997)
• Development of a flow cell for simultaneous angular and axial shear
• Using 2D SAOS measurements to quantify anisotropy in materials (Mobuchon-2009)
Time
Shear Rate, γγγγ.
Str
ain
, γ γ
γ
γ (
An
gu
lar)
Str
ain
, γ γ
γ
γ (
Ax
ial)
Motor
X-d
uce
r
Torque Transducer outputs
torque from steady shear
Normal Force Transducer
applies Axial deformation
and measures Axial
Oscillation Force
Parallel vs. Orthogonal
Parallel
Orthogonal
12
3
γ.
||γ
⊥γ
Steady Shear
Force rebalance transducer in OSP mode
• The FRT transducer measures the axial force by balancing the sample
force and controlling the transducer position to a null position
• When an oscillatory position signal is fed into this control loop, the
transducer performs an axial displacement, while measuring the
normal force (principle of the ‚controlled stress rheometer‘)
23
OSP Features on ARES-G2
• OSP on steady shear to monitor structural
changes in materials (alternative to LAOS
measurements)
• 2D-SAOS measurments to quantify anisotropy
in materials
• DMA tension/compression on solid films &
fibres and bending of standard solid specimen
• Simultaneous multiaxial testing of soft solids
such as gels, foams, rubbers,...
OSP
2D - SAOS
Outer cylinder
Center cylinder
Inner cylinder
Inner Double Gap
Cup with Slots
OSP Geometry
Outer Double Gap
Cup
Bob with Slots
(Patent
pending)
Flow field
between Bob and
Cup in Orthogonal
direction
Orthogonal
oscillation
Slots in Cup
minimize axial
pumping effects
Slots in Bob
minimize
surface
tension effects
OSP Slotted Cup PN: 402782.901
OSP Slotted DG Bob PN: 402796.901
OSP Slotted Narrow DG Bob PN: 402796.902
Structure breakdown monitored by OSP
Steady shear breaks
downs gel structure
and moves flow
region to shorter
times scales (high
frequencies)
Anisotropy detection by 2D-SAOS
• Dental adhesive paste pre-sheared
• Same oscillation strain applied in both angular and axial directions
• Directional stress response stronger in orthogonal stress response (measure of anisotropy)
24
ARES-G2 DMA mode
In DMA mode:
1. Motor is locked in a position
aligning the test fixtures such
as tension and bending
geometries
2. The normal force transducer
applies a deformation (up to 50
micron) in axial direction and
records the force like a DMA.
ARES-G2 DMA mode
Small Amplitude
Oscillation
3 Pt. Bend
532069.901
Cantilever
532070.901
Tension
708.01458
ARES-G2 RSA-G2 DMA Q800
Maximum Force (N) 20 35 18
Minimum Force (N) 0.001 0.0005 0.0001
Maximum Oscillation Displacement (µm) 50 1500 10000
Minimum Oscillation Displacement (µm) 1 0.05 0.5
Displacement resolution (nm) 10 1 1
Frequency range (Hz) 1E-5 to 16 2E-5 to 100 1E-2 to 200
Temperature range (°C) -150 to 600 -150 to 600 -150 to 600
Motor Locked to
alignment position
ABS bar in 3 Point Bending
T W L (mm): 3 x 12 x 40
Ramp rate: 3 C/min
Strain: 0.05 %
ABS bar in 3 Point Bending, TTS
T W L (mm): 3 x 12.8 x 40
Temp step: 10 and 5 °C
Strain: 0.04 %
Reference Temp: 20°C
25
Packaging Foam in Compression
D T (mm): 6.5 x 2.6
Ramp rate: 3 C/min
Strain: 0.1 % with AutoStrain
PET Temperature ramp in Tension
PET Temperature ramp in Tension, TTS Dual Cantilever: Epoxy cure on glass braid
Application of
epoxy mixture
on glass braid
26
Single Cantilever: Elastomer temperature ramp
W T (mm): 5.4 x 1.6
Ramp rate: 3 C/min
Strain: 0.06 %
ARES-G2 FCO & APS Tribology Accessory
TA Instruments Confidential Document
Ring on Plate Ball on 3 Plates Ball on 3 Balls 3 Balls on Plate
• High temperature with FCO
• Applications:
• Automotive
• High temp. greases/oils
• Asphalt
• Rubber
• Close to RT requires APS & Plate
• Applications:
• Personal care products
• Lubricants
• Foods
Extensional Rheology
Sample sizes less than 150mg can be used to
characterize LVE & NVE properties at steady
Hencky strain rates up to 30s-1
Provides analytical insight with regard to
molecular architecture, size, and structure
processing behavior
Applications: polymer melts, uncured elastomers,
TPE melts, highly viscous/semi-solid foodstuffs
LVE LVE & NVE
Step Extension Tensile Stress Growth Cessation of Extension
Butyl in Stress Growth
As the polarized ambient light passes through the sample, the refractive index of the stretching specimen changes as a function of molecular orientation and the onset of FIC
Uniaxial Extension
Hencky strain rate = 1.0 s-1
27
Butyl in Stress Growth
As the polarized white light source passes through the sample, the refractive index of the stretching specimen changes as a function of molecular orientation and the onset of FIC
Uniaxial Extension
Hencky strain rate = 1.0 s-1
Small Angle Light Scattering
• Simultaneous rheology and
structure information
• Laser Light creates interference
pattern
• Pattern reflects size, shape,
orientation and arrangements of
objects that scatter
• Objects scatter due to differences in
refractive index
Shear Induced Phase Separation
T = 25°C
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
28
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
UV Cure Profile Changes with Intensity
UV Cure Profile Changes with Temperature DHR Starch Pasting Cell
• Smart Swap temperature system
• Heating/Cooling rates up 30°C/min
• Higher accuracy for greater
reproducibility
• Robust Cup and Impeller
• Impeller keeps unstable particles
suspended in liquid phase during
measurements
• Impeller design minimizes loss of water
or other solvents
• Sample temperature measured directly
• All rheometer test modes available for
advanced measurements on gelled
starches and other materials
• Optional conical rotor for traditional
rheological measurements\
29
SPC Application: Gelatinization of Starch Products
0 250.0 500.0 750.0 1000 1250 1500 1750 2000 2250global time (s)
0
0.2500
0.5000
0.7500
1.000
1.250
1.500
1.750
vis
cosity (
Pa.s
)
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
tem
pera
ture
(°C)
Red symbols: Dent Corn Starch
Blue symbols: Waxy Maize Starch
Two Scans Each of Dent Corn and Waxy Maize Starch
Tem
pera
ture
(°C)
Time (s)
Vis
cosity
(Pa.s
)
DHR Interfacial Accessories
Qualitative Viscoelastic
measurements at
air/liquid and
liquid/liquid interface.
Steady Shear Viscosity at
air/liquid and
liquid/liquid interface.
•Interfacial shear rheology of thin layers at liquid-liquid or liquid-
gas interfaces.
•Effect of particles, surfactants or proteins at the interface
•Applications: food, biomedical, enhanced oil recovery
Quantitative Viscoelastic
measurements at
air/liquid and
liquid/liquid interface.
Bicone DuNouy Ring Double Wall Ring
0 1 2 3 4 5 6 7 8
Inte
rfacia
l Com
ple
x v
iscosity
(Pasm
)
10 -7
10 -6
10 -5
10 -4
10 -3
10 -2
10 -1
100
101
Needle 2
Needle 3
Needle 4
Needle 5
Bicone
Double Wall Ring
Needle 1
Inte
rfacia
l C
om
ple
x V
iscosity
(Pasm
)
Oscillation Experiments at 0.1 Hz
Patented DWR Interfacial System Surface Concentration Effects on Interfacial Viscosity
30
117
Non linear behavior
Structure properties:
γ>γc
10-1 100
101
10 %2103
10-1
100
101
0.0
1.0
γγγγc=
Tan δ
G‘
G“
If a structure is strained to its limits it will eventually break. Before breaking the structure will behave very
non-linear. During this phase, higher harmonics become important
118
Non-linear System Response
-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5-6
-4
-2
0
2
4
6
8
10
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
20
Strain:
1%
5%
20%Torque
Anglular
displacement
To
rqu
e M
[g
cm
]
Time t [s]
An
gu
lar
dis
pla
ce
me
nt
φ [
mra
d]
The raw signal response (torque) becomes a distorted, non symmetric periodic signal in the non linear regime
The non even harmonics in addition to the fundamental responseare needed to describe the complete material behavior
119
Fourier Rheology
0 10 20 30 40 50 60 70-3
-2
-1
0
1
2
shear
str
ess [
τ]
time [s]
0,1 0,5 0,9 1,3 1,7 2,1
0,0
0,2
0,4
0,6
0,8
1,0
x 100
- 2400 % strain
x I(ω) ~ 1/ω
response [
norm
aliz
ed]
frequency [Hz]
Polyisobutylene (Mv = 4.6· 106
g/mol), 2400 % strain 0.1 Hz:
Non-linear behaviour generates higher harmonic contributions
120
3rd harmonic Contribution
0.01 0.1 1 10 10010
0
101
102
103
0.0
0.1
0.2
0.3
0.4
0.5
G'
G''
Body Lotion Strain sweep
Mod
ulu
s G
'; G
'' [P
a];
Vis
co
sity
η* [P
as]
Strain γ [%]
I(3ω)/I(ω) Intensitity ratio I(3ω)/I(ω) At the onset of the non linear behavior, the 3rd harmonic contribution becomes important and increases with the strain
The third harmonic contribution is normalized with the intensity of the fundamental response
31
Soft Hand Cream
0.01 0.1 1 10 100 1000100
1000
10000
10
100
1000
10000
1E5Soft Cream
T = 25 oC
preshear 10s at 10 1/s
γ=1%
#2 Nivea soft Freq Swp
Sto
rag
e,
Lo
ss M
odu
lus [
Pa
]
G'
G"
Angular Frequency ω [rad/s]
Co
mp
lex V
isco
sity
[Pa.s
]
η*
Linear viscoelastic reponse for a soft cream
Soft Hand Cream
-500 0 500
-600
0
600Stress σ [Pa]
Strain Rate g [1/s]
-8000 0 8000
-600
0
600
γ=6320 %
Stress σ [Pa]
Strain γ [%]
-50 0 50
-300
0
300Stress σ [Pa]
Strain Rate g [1/s]
-800 0 800
-300
0
300
γ=632.0
Stress σ [Pa]
Strain γ [%]
-5 0 5
-200
0
200 Stress σ [Pa]
Strain Rate g [1/s]
-80 0 80
-200
0
200
γ=63.2
Stress σ [Pa]
Strain γ [%]
-0.5 0.0 0.5
-100
-50
0
50
100 Stress σ [Pa]
Strain Rate g [1/s]
-8 0 8
-120
0
120
γ=6.32
Stress σ [Pa]
Strain γ [%]
Soft cream , Temperature T=25o C Frequency f =1Hz
Sample changes from elastic to viscous fluid
Note: measured stress
doesn’t go through origin
– yield stress
Soft Hand Cream
0.01 0.1 1 10 100 1000 10000 1E50.1
1
10
100
1000
1E-6
1E-5
1E-4
1E-3
0.01
0.1
I2/1
I3/1
I5/1
I7/1
I9/1
.
I25/1
Soft Cream
T = 25 oC
preshear 10s at 10 1/s
delay 100 cycles
f=1 Hz
Nivea soft Strain Swp
Sto
rag
e,
Lo
ss M
odu
lus [
Pa
]
G'
G"
Strain γ [%]
Ha
rmon
ic In
tensity
In/1
Harmonic ratio reaches steady state at high strain
Minimum & Large Strain Modulus
0.01 0.1 1 10 100-100
0
100
200
300
-100
-50
0
50
100
150
200
250
300Xanthan Gum 4%
50.04 cone plate
f=1Hz; T=RT
MITLAOS
ARES-G2 StrnSwp
DFT
Min
imu
m S
tra
in M
od
ulu
s G
M'
[P
a]
Strain γ [ ]
La
rge
Stra
in M
od
ulu
s G
L '
[Pa
]
-30 -20 -10 0 10 20 30-600
-400
-200
0
200
400
600
str
ess σ
(t)
strain γ(t) []
stress
-σ'
'
o
LG
γ γ
σ
γ=
=
'
0
M
dG
dγ
σ
γ=
=
32
Minimum & Large Strain Rate Viscosity
0.01 0.1 1 10 100
0
5
10
15
20
-2
0
2
4
6
8
10
12
14
16
18
20
Xanthan Gum 4%
50.04 cone platef=1Hz; T=RT
MITLAOS
ARES-G2 StrnSwp
DFT
Min
imu
m S
he
ar
Vis
co
sity η
M'
[P
a.s
]
Strain γ [ ]
Large Strain Shear Viscosity ηL ' [Pa.s]-30 -20 -10 0 10 20 30-600
-400
-200
0
200
400
600
str
ess
σ(t
)
strainrate/frequency g(t)/ω
stress σ"
'
0
M
d
dγ
ση
γ=
=&
&
'
o
L
γ γ
ση
γ=
=& &
&
Stiffening/Softening & Thickening/Thinning Ratio
0.01 0.1 1 10 100-3
-2
-1
0
1
2
-3
-2
-1
0
1
2
Xanthan Gum 4%
50.04 cone plate
f=1Hz; T=RT
MITLAOS
ARES-G2 StrnSwp
DFT
Stiffe
nin
g/S
often
ing
Ratio S
[ ]
Strain g [ ]
only 4 har-
monics are
taken into
account in
a Strn Swp
Th
ickenin
g/T
hin
nin
g R
atio
T
[ ]
'' '
3
' ' '
1 3
"' '
3
' " "
1 3
4 ..
..
4 ..
..
L M
L
L M
L
GG GS
G G G
GT
G G
η η
η
− +−≡ =
− +
+−≡ =
+ +
Soft Hand Cream
0.01 0.1 1 10 100 1000 10000 1E5
0
500
1000
1500
2000
0
1
Soft Cream
T = 25 oC
preshear 10s
at 10 1/s
delay 100 cycles
f=1 Hz
Nivea soft Strain Swp
La
rge
Str
ain
, M
inim
um
Str
ain
, S
tora
ge
M
od
ulu
s [
Pa
]
GL
GM
G'
Strain γ [%]
Stiffe
nin
g ra
tio S
0.01 0.1 1 10 100 1000 10000 1E5
0
20
40
60
-3
-2
-1
0
Soft Cream
T = 25 oC
preshear 10s at 10 1/s
delay 100 cycles
f=1 Hz
Nivea soft Strain Swp
Larg
e R
ate
, M
inim
um
Ra
te,
Dyn
am
ic V
isco
sity
[Pa
]
ηL
ηM
η'
Strain γ [%]
Th
icken
ing ra
tio
T
Stiffening/softening ratio
Thickening/Thinning ratio
- increases with strain and reaches maximum
- increses initially-- decreases at high strain
128
Introduction to Rheology
Basics...
...and More
Types of test modes
Types of flows
Solids deform
Fluids flow
Concept of time
Non linear behaviour
Thermo-mechanical
33
129
Flow phenomenon 1
• Pseudo-plastic130
Flow phenomenon 2
Short contact [< 1s] Long contact[>1 hour]
• Elasticity
• Viscosity
• Time dependent
131
Flow phenomenon 3
• Linear flow regime • Non linear behavior
• Structure breaking
slow fast
132
Flow phenomenon 4
Honey
Mayonnaise
• Yield
• Non linear flow
34
133
Flow phenomenon 5
• Flow induced structure• Low viscosity at rest
134
Fluids Flow
Common Characterization tool for fluids 50 years ago:
Viscometry
Applied rate
Measured stress
DIN standard ASTM standard
135
Flow - Viscometry
Single point measurement of the viscosity
Time
str
ess
rate
<σ>
γση &/=
Viscosity=shear stress/shear rate
136
Typical Viscosity Values (Pa s)
• Asphalt Binder ------------------
• Polymer Melt --------------------
• Molasses --------------------------
• Liquid Honey --------------------
• Glycerol --------------------------
• Olive Oil -------------------------
• Water -----------------------------
• Air ---------------------------------
100,000
1,000
100
10
1
0.01
0.001
0.00001
Need for
Log scale
35
137
Viscosity curve of various fluids
Viscosity function of various structured fluids
1E-3 0.01 0.1 1 10 100 1000 1000010
-2
10-1
100
101
102
103
104
.
starch
peanutoil
0.05% poly-
acrylamide solution
PIB at 20°C
sirup
Cocoa butter lotion
Shower gel
Co-polymer 240 °C
Vis
co
sity η
[P
a s
]
Shear rate γ [1/s]
138
Types of Flow Curves
Sh
ear
Str
ess,
σ
Newtonian
•
Shear Rate, γ
Bingham Plastic(shear-thinning w/yield stress)
Shear Thickening (Dilatent)σσσσ
y
Shear Thinning (Pseudoplastic)
Bingham (Newtonian w/yield stress)
139
Shear Rate Ranges for Many Applications
Situation Shear Rate Range Examples
Sedimentation of fine powders in liquids 10-6 to 10-3 Medicines, Paints, Salad dressing
Leveling due to surface tension 10-2 to 10-1 Paints, Printing inks
Draining off surfaces under gravity 10-1 to 101 Toilet bleaches, paints, coatings
Extruders 100 to 102 Polymers, foods
Chewing and Swallowing 101 to 102 Foods
Dip coating 101 to 102 Confectionery, paints
Mixing and stirring 101 to 103 Liquids manufacturing
Pipe Flow 100 to 103 Pumping liquids, blood flow
Brushing 103 to 104 Painting
Rubbing 104 to 105 Skin creams, lotions
High-speed coating 104 to 106 Paper manufacture
Spraying 105 to 106 Atomization, spray drying
Lubrication 103 to 107 Bearings, engines
γω &11 ==t
The Idealized Flow Curve
1
1) Sedimentation2) Leveling, Sagging
3) Draining under gravity4) Chewing and swallowing
5) Dip coating6) Mixing and stirring7) Pipe flow
8) Spraying and brushing9) Rubbing
10) 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
36
141
Steady Rate Sweep
In a steady rate experiment the equilibrium stress upon a step in the
strain rate is measured. The equilibrium stress or viscosity is recorded
as a function of the strain rate.
In a steady experiment, only the equilibrium value is measured over a manual selected time period
rate
time
Vis
co
sity
rate
Delay time
Steady State Flowγ = Constant
σ
142
Structured Fluid: Steady State Flow
The viscosity decreases with a slope of -1 versus strain rate and the stress becomes rate independent => material with yield stress
Stepped rate test on
ARES
Shear rates are stepped at equal intervals
=> smooth curve
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
100
101
102
103
104
105
106
107
108
109
1010
103
104
105
106
107
4 Pa
slope 1
Viscosity [mPas]
Vis
cosity η
[m
Pas]
Rate g [1/s]
T= 25 °C
Rate ramp: high to low
Printing paste
Stress [mPa]
Str
ess σ
[m
Pa]
143
Polymers: Steady State Flow
• With stress controlled AR, the viscosity can easily be measured down and below 10-6 1/s
• ARES with LS motor can control rates down to 10-6
1/s1E-6 1E-5 1E-4 1E-3 0,01 0,1 1
105
106
Oscillation
Creep
.
viscosity in Pa s
HDPE viscosity curve
T= 210 °C
Vis
co
sity
η;
η* [
Pa
s]
Shear rate γ [1/s] or Frequency ω [rad/s]
144
Thixotropic Loop
Shear ramp up and down or thixotropic loop
str
ess
rate
Time
σ(γ).
up down
If the material is time dependent, the up and down curves are
different
The stress represents the instantaneous response to the applied rate.
γγσγη &&& /)()( =
37
145
Thixotropy
0 100 200 300 400 500
0
20
40
60
80
100
Thixotropic loop for 3 Mayonnaise emulsions
.
sample A up
sample A down
sample B up
sample B down
sample C up
sample C down
Str
ess σ
[P
a]
Rate γ [1/s]
Up and down ramps do not superpose
Area under the curve is a measure of thixotropy
Thixotropic materials
146
Thixotropic Loop
0 2 4 6 8 10
100
0
2
4
6
first ramp up
viscosity [Pas]
Children Advil suspension
Vis
cosity
η(t
) [P
as]
rate γ(t) [1/s]
peak at stress 1.3 Pa
.
stress [Pa]
Str
ess τ
[P
a]
Non-thixotropic
material
Up and down ramps superpose –except the first one
=> Start up from zero
147
Ramp in stress controlled mode
The stress is increased from zero to a finite value and the deformation is measured as a function of time.
An instantaneous viscosity can be calculated from the applied stress and the time derivative of the deformation
str
ess
de
form
atio
n
Time
γ(t)
Stress ramp
)(/)( σγσση &=148
Yield stress in a stress ramp
1 10 100
1
10
100
1000
1E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
η [Pa s]
Yield stress of a cosmetic lotion
Yield stess
at maximum = 5.4 Pa
at intercept ) 11 Pa
Vis
co
sity
η [
Pa
s]
Stress [Pa]
Strain
Str
ain
(x1
0-6
)
The maximum viscosity method allows a more representative and unique determination of the yield stress
38
149
Solids Testing
Modulus & Glass transition
-150 -100 -50 0 50 100 150
106
107
108
109
Injection molded ABS part
G' ABS unannealed
G' ABS annealed
Modulu
s G
' [P
a]
Temperature T [°C]
Tg
Modulus
At the transition from solid to fluid, the modulus changes over several decades
150
Hookean Body
forced oscillation
For a Hookean body, the response to a sinusoidal excitation is also sinusoidal and in phase with the excitation
0 20 40 60 80 100
-0 .2
-0 .1
0 .0
0 .1
0 .2 σ o= G γo
Str
ess
T ime
0 20 40 60 80 100
-1
0
1 γo
Str
ain
Time
o
oGγ
σˆ
ˆ=
151
Newtonian Fluid
forced oscillation
For a Newtonian fluid, the response to a sinusoidal excitation is also sinusoidal and out off phase with the strain rate
0 20 40 60 80 100
-0 .2
-0 .1
0 .0
0 .1
0 .2 σ o= G γo
Str
ess
T ime
o
o
γση ˆˆ
&=
0 20 40 60 80 100
-1
0
1 go
Str
ain
ra
te Time
152
General Solids Behavior
For most solids, response and excitation are not in phase.
Stimulus (stress or strain)
Response (strain or stress)
-1.5
0
1.5
0 6.3
Angle
phase angle, δ
Viscoelasticity
In the linear regime, linear viscoelasticity, the ratio of strain and stress amplitude and the phase fully characterize the system
39
153
Solids and Melts testing
Glass
Transition
Plateau
Flow
(atomic groups)
(main chain)
(chain segments)
(polymer chain)
TimeTemperature
Melts testing
Solids testing
154
Transition from Solid to Liquid
stiff
0 20 40 60 80 100
-1
0
1
phase δ
Solid
Strain
Stress
Viscoelastic Solid
Str
ain
; S
tre
ss
Time
0 20 40 60 80 100
-1
0
1
phase δ
Liquid
Strain
Stress
Viscoelastic Fluid
Str
ain
; S
tress
Time
soft
What does change?
G
tan δ
155
Viscoelastic Response of an Adhesive
-50 0 50 10010
2
103
104
105
106
107
108
109
1010
0
2
4
Typical PSA Temperature scan
Mod
ulu
s G
' [P
a]
Temperature T [oC]
G'
Shear
ResistanceTack
Lowest use temperature
Modulus
at use
temperature
tan δ
Lo
ss t
an
δ
Using parallel plates with small radius and large gap permits measurements from the solid into the liquid phase
8mm
>2mm
156
Relaxation or Material Time
TENNIS
BALL
STORAGE
(G’)
LOSS
(G”)
SUPER
BALL
STORAGE
(G’)
LOSS
(G”)
/Gτ = η τ(Tennisball) < τ(Superball)
40
157
Material & Process Time
The material (re-arrangement)
time of a material τ depends on
temperature
tτ = τ ≅ exp(EA/kT)
The observation time is the
process time or the end use
time
tapp
tτ
tobs
= De
If the material time is
shorter De<1 (fluid
behaviour)
If the material time is
longer De>1 (solid
behaviour)
158
Photography
Observation time long
Blurred image
Observation time short
Clear image
De>1
Solid behavior
De<1
Liquid behavior
159
Dynamic Mechanical Behavior
10-3 10-2 10-1 100 101
102
10 -1
100
101
102
103
104
105
106
10 3
104
105
G‘‘ = ωηωηωηωη
|ηηηη*| = ηηηη
De = 0Liquid
10-3 10
-210
-110
010
1
10 2
10 -1
100
101
102
103
104
105
106
103
104
105
G‘ = G
|ηηηη*| = G/ωωωω
De = ∞∞∞∞Solid
10-3 10 -2 10 -1 100 101
10 2
10-1
100
101
102
103
104
105
106
103
104
105
G“
G‘
|ηηηη*|
De <<1 De=1 De>>1
If the material
time is shorter than
the observation
time De<1 (fluid
behavior)
tτ
tobs
= De
If the material
time is longer than
the observation
time De>1 (solid
behavior)
160
Types of Flows
Shear
Extension
41
161
Shear Deformation
x1
x2
x3
y
σ21
n2
dt
d
dy
du
γγ
αγ
=
==
&
tan1α
du1
162
Extensional Deformation
x1
x2
x3
dx=Lo
σ11
n2
du1=∆L
y
dt
d
L
L
dx
du
o
εε
ε
=
∆==
&
1
163
Poison ratio µ
Young‘s Modulus E
Extension Viscosity ηE
Shear Modulus G
Shear viscosity η
Young‘s Modulus
Extension Viscosity ηE
E ; ηE 2G(1+µ) ; 2η(1+µ)
Shear modulus
Shear viscosity ηE/(2(1+µ));ηE/(2(1+µ)) G ; η
The Poison ratio for an incompressible material µ=0.5
=> E=3G and η=3ηE
164
Principle
Material
under
test
deformation
γγγγ(t)
σσσσ(t)
γγγγ(t)
Material Function
stress
σσσσ(t)
42
165
Material Functions
Input Output Materialfunction Description
σo γ(t) γ(t)/ σo=J(t) Compliance
γo σ(t) σ(t)/γo=G(t) Modulus
go σ(t) σ(t)/go=η(t) Viscosity
dg/dt σ(t) ------ Rate Ramp
ds/dt γ(t) ------- Stress Ramp
• Material parameters are defined by the test mode
• For an elongation deformation, the stress is σE,, the deformation (rate) e(f), the compliance D(t), the modulus E(t), the viscosity ηE(t)
166
Oscillation Time Sweep
AutoStrain and AutoTension are available in this mode
In a time sweep, no test parameters are varied. Strain, stress
amplitude and phase shift are recorded as a function of time to
follow the evolution of the material.
Str
ain
Time 0 200 400 600 800 1000 1200 1400
G'
G"
Time
G' G"
167
Structured Fluid: Pre-Testing
-2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 01 0
1
1 02
1 03
-2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0
0
1 0
2 0
G ' [ P a ]
G ' ' [P a ]
A R E S a m p l i tu d e te s t o f a la te x p a in t
Modu
lus G
'; G
'' [P
as]
t im e t [ m in ]
s tra in
0 .1 % 1 % 1 2 % 1 % 0 .1 %
str
ain
γ [%
]
1. 2. 3.
• Select low strain high enough to generate a good signal, typical > 0.1%. The high strain should be 10 to 100 times higher than the low strain
• Switch strain manually (ARES) or go to next step (AR2000) when equilibrium has been reached.
168
Oscillation Strain Sweep
In a strain sweep, the strain is varied linear or logarithmic over the
selected range. Strain, stress amplitude and phase shift are recorded.
The non-linear monitor (NLM) senses the end of the linear viscoelastic range
Str
ain
Time 0.01 0.1 1 10 100
G' &
G"
Strain %
G'
G"
NLM
NLM
43
169
Testing in the Linear Region - Strain Sweep
0.1 1 10 100 1000
0.1
1
10
ττττy=G'γγγγ
c
critical
strain γc
Strain sweep of a cosmetic cream
Mod
ulu
s G
', G
'' [P
a]
Strain γ [%]
G'
G''
Estimate the yield stress from the on-set of linear behavior
If the material has shown significant thixotropy, the next test should be a “dynamic time sweep” after pre-shearing at the typical application shear rate
Structured sample
170
Oscillation Frequency Sweep
Str
ain
Time
In a frequency sweep, the frequency is varied linear or logarithmic
over the selected range. Strain, stress and phase are recorded.
Control oscillation tests on strain
100
101
102
102
103
104
G',
G'',
η*
Frequency
G" G'
η*
171
Polymers: Frequency Dependence
• Represents the viscoelastic nature of a material in time
• Provides information about the material at different processing or application rates (ω~γ)
The upper frequency is limited by the instrument, the lower frequency is typically 10-5 rad/s, a practical limit is 0.1 or 0.01 rad/s
.
100
101
102
102
103
104
G' [
Pa], G
'' [P
a];
η*
[Pa
s]
Frequency ω [rad/s]
C
A
η* [Pas]
G’
G”
172
Structured fluids: Frequency Dependence
• G’ and G” are
virtually
independent of
frequency, as well
as tan δ.
• Also the material
behaves
predominately
elastic (G’>G”) =>
which stands for
structure in the
material, capable
of storing energy0.1 1 10
101
102
0.1
1
10
tan δ = G''/G' > 0.5 to 1
gel like behaviour
G' [Pa]
G'' [Pa]
Mod
ulu
s G
', G
'' [P
a]
frequency ω [rad/s]
Cosmetic lotion
tan δ
ta
n δ
44
173
Thermo-Mechanical Characterization
Temperature
Rate γ
Heat
Torque
.
Viscoelastic &
Thermo-mechanical
characterization
τ(γ)
γγγγ, T.
t
.
174
Oscillation Temperature Ramp
In all temperature dependent test, the AutoTension function is available
In a temperature ramp, the temperature is varied continuously, in a
temperature sweep discretely over the selected range. Strain, stress
amplitude and phase shift are recorded.
Str
ain
Time
Temperature ramp
Te
mpe
ratu
re
G',
G"
Temperature
G'
G"
175
Advanced solids testing - DMA
-150 -100 -50 0 50 100 150
106
107
108
109
0.01
0.1
1
Injection molded ABS part
G' ABS unannealed
G' ABS annealed
Mod
ulu
s G
' [P
a]
Temperature T [°C]
tan δ ABS unannealed
tan δ ABS annealed
Loss t
an
δ
Modulus, Glass transition, ß-transition
Tg
Tß
Modulus
At Tg the relaxation of the polymer backbone is in phase with the
input strain
Increased energy dissipation is reponsible for the maximum of tan δ
176
Temperature Ramp in Torsion
-150.0 -100.0 -50.0 0.0 50.0 100.0 150.0 200.01061071081091010101110-310-210-1100101
0.00.51.01.52.02.53.03.5Temp [°C] G' () [dyn/cm2] G" () [dyn/cm2] tan_delta () [ ] DeltaL () [mm]PMMA Temperature Ramp 1Hz 3°min
Peak(104.1,0.966)Peak(117.98,1.6543)Peak(17.92,0.07413)tan_delta = 0.01405 [ ]Temp = -92.002 [°C](-CH2-C-(CH3)-(COOCH 3)-)n
• AutoTension is
used to control the
expansion of the
sample during the
test.
• A significant
change in the
expansion
coefficient occurs
at the glass
transition
temperature
45
177
Thermoset Polymer - Temperature Ramp
80 100 120 140 160
103
104
105
106
107
103
104
105
106
Mo
du
li G
', G
'' [P
a]
Temperature T [C]
G'
G''
Minimum viscosity
approx. gel point
η*
Co
mp
lex v
isco
sity
η*
[Pa
s]
Temperature ramp 5 C/min
Cure cycle of an epoxy compund Gel point and minimum viscosity AutoStrain
increases the
strain to keep
the torque within
the instrument
range in order to
accurately
measure the
viscosity
minimum
178
TTS to Extend the Frequency Range
100
101
102
102
103
104
105
Temperature range: 180 to 230 deg C
G' [
Pa
]
Frequency ω [rad./s]
G' Frequency Sweeps over a range of Temperatures
10-1
100
101
102
103
102
103
104
105
G';
G''
[Pa]
F requency ω /aT [rad /s]
G '
G ''
Extended freq. range
TTS is an empirical relationship and works only when the material is “thermo-rheologically simple”
TTS, BrieflyOscillation Example
G’
frequency
200
TTS, BrieflyOscillation Example
G’
frequency
200
Higher frequencies
experimentally
inaccessible
46
TTS, BrieflyOscillation Example
G’
frequency
200
180
160
140
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
47
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
48
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
TTS, BrieflyOscillation Example
200
180
160
140
G’
frequency
49
TTS, BrieflyOscillation Example
G’
frequency
Master-curve at 200
TTS, BrieflyOscillation Example
G’
frequency
200
180
160
140
aT=180
TTS, BrieflyOscillation Example
G’
frequency
200
180
160
140
aT=160
TTS, BrieflyOscillation Example
G’
frequency
200
180
160
140aT=140
50
TTS, BrieflyOscillation Example
a T
Temperature
200180160140
0.0
TTS, BrieflyOscillation Example
a T
Temperature
200180160140
0.0
Arrhenius or WLF
TTS, BrieflyOscillation Example
a T
Temperature
200180160140
0.0
Arrhenius or WLF(temperature dependence of
VE properties)
200
Transient Relaxation
The measured torque and deformation are used to calculate the Relaxation modulus
In a relaxation test, a step strain is applied to the material and the
stress is recorded over time.
Str
ain
Time
strain
0.01 0.1 1 10 10010
1
102
103
104
105
Str
ain
Time
strain G(t
)
G(t)
51
201
Stress Relaxation
• Fast visco-elastic characterization of a polymer
• Results less accurate for short and for long times
0 10 20 30 40 500.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
increasing strain
T=140 oC
strain 10%
strain 20%
strain 50%
strain 100%
strain 200%
strain 400%
LDPE Melt Relaxation
Mo
du
lus G
(t)
[KP
a]
Time t [s]
0.01 0.1 1 10 100
0.01
0.1
1
10 increasing strain
T=140 oC
strain 10%
strain 20%
strain 50%
strain 100%
strain 200%
strain 400%
LDPE Melt Relaxation M
odu
lus G
(t)
[KP
a]
Time t [s]
202
Transient Creep
The recoil test is the most sensitive test to determine aq material’s elasticity
In a creep test, a step stress is applied to the material and the
deformation is recorded over time. If the stress is removed after a time
t1 the recoverable deformation (recoil) is obtained.
Str
ess
Time
Str
ain
m
Time
strain Recoverable strain
Re
co
ve
rab
le s
tra
in
203
Creep on PDMS
• The best test approach to measure long relaxation (retardation) times
• Recovery is the most sensitive parameter to measure elasticity
0 20 40 60 80 100 120-5
0
5
10
15
20
25
30
35
50 60 70 80 90 100 110 1200.0
0.5
1.0
1.5
2.0
Re
co
ve
rab
le S
tra
in
Time [s]
Recoverable Strain
Str
ain
γ [ ]
Time t [s]
PDMS at RT
Recoverable strain
Non-recoverable
strain
σo/η
Time and Temperature
(E" or G")
(E' or G')
(E" or G")
(E' or G')
log Frequency Temperature
log Time log Time
52
205
Transient Stress growth
Select the step rate test to measure the transient viscosity or normal stress difference
In a step rate test (stress growth), a step strain rate is applied to the
material and the stress and normal force is recorded over time.
Vis
co
sity
Time
rate 200 1/s
str
ain
rate
time
step-rate
Str
ain
strain in step-rate
206
Stress Growth of the NIST Ref 2490
0.01 0.1 1 10 100
0.1
1
10
100
Ref 2490 Transient T=25°C 50mm cone 0.04 ARES
Vis
co
sity η
(t)
[Pa
s]
Time t [s]
Rate:
LV start up
0.001s-1 0.3 s-1
0.003 s-1 1 s-1
0.01 s-1 10 s-1
3 s-1 30 s-1
0.03 s-1 300 s-1
0.1 s-1 100 s-1
• The step rate experiments determines the transient non linear response of a material.
• Good for materials with a long relaxation time
• Normal force provides elastic information
Applications of Dynamic Mechanical Analysis of Solids
DMA / Rheology Applications
Material Property
Composites, Thermosets Viscosity, Gelation, Rate of Cure, Effect of Fillers and Additives
Cured Laminates Glass Transition, Modulus Damping, impact resistance, Creep, Stress Relaxation, Fiber
orientation, Thermal Stability
Thermoplastics Blends, Processing effects, stability of molded parts, chemical effects
Elastomers Curing Characteristics, effect of fillers, recovery after deformation
Coating, Adhesives Damping, correlations, rate of degree of cure, glass transition temperature, modulus
53
Polymer Structure
• The mechanical properties of a polymer are a consequence of
• Chemical Composition of the Polymer • Dictates where changes in mechanical properties occur
• Physical Molecular Structure of the Polymer• Dictates how changes in mechanical properties will occur
• A DMA/rheometer can be used to measure the mechanical properties of a polymer material and relate them to differences in composition and molecular structure (chemical and physical differences).
Chemical
Composition
Physical
Molecular
Structure
Mechanical
Strength
(DMA)
Where
Changes
Occur
How
Changes
Occur
Use DMA to measure the mechanical properties of a polymer material and relate them to differences in composition and molecular structure (chemical and physical differences).
Polymer Structure
Physical Structure: Effects of Crystallinity,
Molecular Weight, and Crosslinking
Increasing MW
Cross-linked
Amorphous Crystalline
Increasing
Crystallinity
Tm
Temperature
log M
odulu
s
3 decade drop
in modulus at Tg
How
Changes
Occur
Molecular Motions/Transitions/Relaxations
Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 486.
In general, transitions are associated with different localized or medium-to long-range cooperative motions of molecular segments.
THESE MOLECULAR MOTIONS ARE REFERRED TO AS RELAXATIONS.
54
–Glass Transition - Cooperative motion among a large number of
chain segments, including those from neighboring polymer chains
–Secondary Transitions
–Local Main-Chain Motion - intramolecular rotational motion of
main chain segments four to six atoms in length
Side group motion with some cooperative motion from the main
chainInternal motion within a side group without interference from side
group.
Motion of or within a small molecule or diluent dissolved in the
polymer (eg. plasticizer.)
The Glass & Secondary Transitions
Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 487.
LDPE: Primary and Secondary Transitions
96.33°C
-118.12°C
-10.55°C0.05
0.10
0.15
0.20
0.25
[ ] T
an D
elta
10
100
1000
10000
[ ] L
oss M
odulu
s (
MP
a)
10
100
1000
10000
[ ] S
tora
ge M
odulu
s (
MP
a)
-150 -100 -50 0 50 100 150
Temperature (°C)
Sample: Polyethylene in TensionSize: 8.4740 x 5.7500 x 1.0000 mm
Comment: 15 microns, 120% Autostrain, -150°C to 100°C
DMAFile: F:...\DMADATA\Peten.tr1Operator: RRURun Date: 18-Jan-99 16:10
Universal V2.5D TA Instruments
α -Relaxation, TgCooperative Motion of Amorphous Phase
γ -RelaxationAn amorphous phase relaxationA local-mode, simple, non-cooperative relaxation process
β -RelaxationOriginates in amorphous phase Related to glass transition
Primary and Secondary Transition in PET Film
119.44°C
-55.49°C0.05
0.10
0.15
[
] T
an D
elta
10
100
1000
10000
[ ]
Lo
ss M
odulu
s (
MP
a)
10
100
1000
10000
[
] S
tora
ge
Mo
dulu
s (
MP
a)
-150 -100 -50 0 50 100 150 200 250
Temperature (°C)
Sample: PET Film in Machine DirectionSize: 8.1880 x 5.5000 x 0.0200 mmMethod: 3°C/min rampComment: 1Hz; 3°C/min from -140° to 150°C, 15 microns,
DMAFile: A:\Petmd.001Operator: RRURun Date: 27-Jan-99 13:56
Universal V2.5D TA Instruments
The Importance of the Glass Transition Measurement
• Below the glass transition temperature, many amorphous polymers are hard, rigid glasses
• modulus is > 109 Pa
• In the glassy region, thermal energy is insufficient to surmount the potential barriers for translational and rotational motions of segments of the polymer molecules. The chain segments are frozen in fixed positions.
• Above Tg, the amorphous polymer is soft and flexible.
• modulus in this rubbery region is about 105 or 106 Pa.
• Because of the four orders of magnitude change in modulus between the glassy and rubbery state, the Tg can be considered the most important material characteristic of a polymer.
Nielsen, Lawrence E., Mechanical Properties of Polymers and Composites, Marcel Dekker, Inc., New York, 1974, p. 19.
55
E' Onset: Occurs at lowest temperature - Relates to mechanical Failure
E' Onset, E" Peak, and tan δδδδ Peak
Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 980.
tan δδδδ Peak: Occurs at highest temperature - used historically in literature - a good measure of the "leatherlike" midpoint between the glassy and rubbery states - height and shape change systematically with amorphous content.
E" Peak:Occurs at middle temperature - more closely related to the physical property changes attributed to the glass transition in plastics. It reflects molecular processes - agrees with the idea of Tg as the temperature at the onset of segmental motion.
PSA: Glass Transition Measurement
Fiber Reinforced Vinyl Ester Composite
Secondary Transition Measurements
Effect of Orientation on Tensile Modulus and
Damping
Temperature (°C)
Transverse
Direction
Machine
Direction
DMA Multi-Frequency - Tension Film
Sto
rage M
odulu
s
(GP
a)
56
General Case for Semicrystalline Polymers - Increasing Crystallinity will increase the
glass transition temperature, decrease the intensity of the glass transition, and broaden
the transition temperature range.
Effect of % Crystallinity on Glass Transition
xx x x x x x x x x xx
x
xx
xx
xx
x xx x x x x x
x
20 40 60 80 100 120 140 1600.01
0.1
1.0
Temperature (°C)
Ta
n δδ δδ
0.1
0.5
1.0
5
10
x x x x x xx
xxx
x
x
x
x
x
xxxxxx
20 40 60 80 100 120 140 1600.01
0.1
1.0
Temperature (°C)
Ta
n δδ δδ
0.1
0.5
1.0
5
10
AMORPHOUS PET CRYSTALLINE PET
Redrawn with permission from Thompson and Woods, Trans. Faraday Soc., 52, 1383 (1956)
“The major effect of the crystallite in a sample is to act as a crosslink in the polymer matrix. This makes the polymer behave as though it was a crosslinked
network, but as the crystallite anchoring points are thermally labile, they disintegrate as the temperature approaches the melting temperature, and the
material undergoes a progressive change in structure until beyond Tm, when it is molten”
Effect of % Crystallinity on Modulus
0% Crystallinity (100% Amorphous)
25%
40%
65%
M.P.
Temperature
Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, Blackie academic & Professional, and imprint of
Chapman & HallBishopbriggs, Glasgow, 1991p. 330-332. ISBN 0 7514 0134 X
The Main Points1. “Crystallinity only affects the mechanical
response in the temperature range Tg to Tm, and below Tg the effect on the modulus is
small.”2. “The Modulus of a semi-crystalline
polymer is directly proportional to the degree of crystallinity, and remains
independent of temperature if the amount of crystalline order remains unchanged.”
Molecular Structure - Effect of Molecular Weight
Rubbery PlateauRegion
TransitionRegion
Glassy Region
Temperature
MW has practically no effect on the modulus below Tg
Increasing MW
Below Mc
With the exception of low molecular
weight (below Mc where there are no
entanglements), the rubbery plateau
region above Tg is strongly dependent on
MW. In the absence of true crosslinks,
the behavior is determined by
entanglements. The length of the
rubbery plateau is a function of the
number of entanglements per molecule.
Blending of Amorphous Polymers
Blending may produce a polymer whose modulus-temperature curve shows two transition regions
If the polymers blended are completely compatible, then the blend behaves like an ordinary amorphous polymer with a single transition region and an intermediate glass transition temperature.
Tobolsky, A.V., Properties and Structure of Polymers, John Wiley & Sons, Inc., New York, 1967, p.81.
57
Mixture of Two Styrene-butadiene Copolymers
-60 -40 -20 0 20
01
1
10
100
TEMPERATURE (°C)
MO
DU
LU
S P
RO
PO
RT
ION
AL
ITY
FA
CT
OR 100
60
50
40
30
20
0
Higher Styrene
Low Styrene
Nielsen, Lawrence E., Mechanical Properties of Polymers and Composites, Marcel Dekker, Inc., New York, 1974, p. 212.
Mixture of two copolymers very different in styrene content (16% and 50%). Numbers on curve show % of polymer with the higher styrene content.
Two steps in modulus are
characteristic of immicible
two-phase system
Impact Resistance
Blending may produce a polymer whose modulus-temperature curve shows
two transition regions
Immicible Blend - PS/SB
-50 0 50 100 1500.01
0.10
1.0
10
Temperature (°C)
Logarith
mic
decre
ment
Shear
modulu
s,
G,
(Nm
)
109
108
107
106
105
(Tobolsky, A.V., Properties and Structure of Polymers, John Wiley & Sons, Inc., New York, 1967, p.81).
Polymer Blend - Aerospace Coating
100 % Polymer A
100%
Polymer B
Polymer Blend
A + B
1
10
100
1000
10000
Sto
rag
e M
od
ulu
s (
MP
a)
-25 0 25 50 75 100 125
Temperature (°C)
–––––– Polymer A – – – Polymer Blend: A + B–––– · Polymer B
Universal V2.5D TA Instruments
•If the polymers blended are completely compatible, then the blend behaves like an
ordinary amorphous polymer with a single transition region and an intermediate glass
transition temperature. (Tobolsky, A.V., Properties and Structure of Polymers, John Wiley & Sons, Inc., New York, 1967, p.81).
58
Polymer Blend - Aerospace Coating
89.77°C
76.19°C
46.46°C
-0.5
0.0
0.5
1.0
1.5
Tan D
elta
-25 0 25 50 75 100 125
Temperature (°C)
–––––– Polymer A – – – Polymer Blend: A + B–––– · Polymer B
Universal V2.5D TA Instruments
100 % Polymer B
100%
Polymer A
Polymer Blend
A + B
Importance of MWD
Property/Process
Parameter
Effect of high Mw Effect of low Mw
Impact strength High Low
Melt viscosity High Low
Processing temperature High Low
Flex life Low High
Brittleness High Low
Drawability Low High
Softening temp High Low
Stress crack resistance Low High
Melt flow Low High
Why use Rheology data for MWD?
• Size Exclusion Chromatography [SEC] is the traditional technique, but has some disadvantages
• Insensitive to high molecular weight species
• Insensitive to long chain branching
• Many polymers are difficult to dissolve and require ‘nasty’ solvents [e.g. HDPE, PTFE]
• Rheological measurements are generally straightforward
• Measurements can be made directly on the melt
• Sensitive to high molecular weight species
• Sensitive to long chain branching
Why use Rheology data for MWD?
• Contained within the rheological data is information on the sample modulus and relaxation times, which are significantly affected by molecular entanglements and the molecular weights of the polymer species in the sample
• Rheology will not replace SEC for MWD. It should be seen as a complementary technique
59
100.01.000E-3 0.01000 0.1000 1.000 10.00
ang. frequency (rad/sec)
1.000E6
10.00
100.0
1000
10000
1.000E5
G' (P
a)
1.000E6
10.00
100.0
1000
10000
1.000E5
G'' (P
a)
115k
‘Low’ Mw mono dispersed sample
64 5Log [Molar mass (g/Mol)]
1.200
0
0.2000
0.4000
0.6000
0.8000
1.000
w(M
)
Resulting MWD: ‘Low’ Mw
1.0001.000E-5 1.000E-4 1.000E-3 0.01000 0.1000
ang. frequency (rad/sec)
1.000E6
100.0
1000
10000
1.000E5
G' (P
a)
1.000E6
100.0
1000
10000
1.000E5
G'' (P
a)
1150k
‘High’ Mw mono dispersed sample
74 5 6
Log [Molar mass (g/Mol)]
0.6000
0
0.1000
0.2000
0.3000
0.4000
0.5000
w(M
)
Resulting MWD: ‘High’ Mw
60
10001.000E-5 1.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00 100.0
ang. frequency (rad/sec)
1.000E6
10.00
100.0
1000
10000
1.000E5
G' (P
a)
1.000E6
10.00
100.0
1000
10000
1.000E5
G'' (P
a)
115k 1150k Blend
Blend of ‘Low’ and ‘High’ Mw
74 5 6Log [Molar mass (g/Mol)]
0.3000
0
0.05000
0.1000
0.1500
0.2000
0.2500
w(M
)
Resultant MWD: ‘Low’ and ‘High’ Mw
10001.000E-5 1.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00 100.0
ang. frequency (rad/sec)
1.000E6
10.00
100.0
1000
10000
1.000E5
G' (P
a)
115k
1150k
115k 1150k Blend
G’ Comparison
10001.000E-5 1.000E-4 1.000E-3 0.01000 0.1000 1.000 10.00 100.0
ang. frequency (rad/sec)
1.000E9
1000
10000
1.000E5
1.000E6
1.000E7
1.000E8
|n*|
(P
a.s
)
115k
1150k
115k 1150k Blend
Molecular weight (WLF)
n0: 1.691E5 Pa.s
Mw: 1.606E5 g/mol
Molecular weight (WLF)
n0: 2.020E7 Pa.s
Mw: 6.613E5 g/mol
Molecular weight (WLF)
n0: 1.365E8 Pa.s
Mw: 1.164E6 g/mol
ηηηη* Comparison
61
74 5 6
Log [Molar mass (g/Mol)]
1.200
0
0.2000
0.4000
0.6000
0.8000
1.000
w(M
)
115k
1150k
115k 1150k
Molecular weight
Mn: 5.705E5 g/Mol
Mw: 9.938E5 g/mol
Mz: 1.623E6 g/Mol
Mz+1: 2.567E6 g/Mol
Polydispersity: 1.742
Molecular weight
Mn: 2.385E5 g/Mol
Mw: 6.505E5 g/mol
Mz: 1.537E6 g/Mol
Mz: 2.756E6 g/Mol
Polydispersity: 2.728
Molecular weight
Mn: 1.392E5 g/Mol
Mw: 1.552E5 g/mol
Mz: 1.688E5 g/Mol
Mz+1: 1.814E5 g/Mol
Polydispersity: 1.115
MWD Comparison Effect of Plasticizer
Plasticizers are generally low molecular weight organic additives which are used to soften rigid polymers
Plasticizers are typically added to a polymer for two reasons:
• 1. To lower the Tg to make a rigid polymer become soft and rubbery.
• 2. To make the polymer easier to process.
Plasticizers make it easier for a polymer to change molecular conformation.
Therefore plasticizers will have the effect of:
• 1. Lowering the glass transition temperature and
• 2. Broadening the tan δ peak
Plasticization
Molecular Mobility Molecular Structure - Crosslinking
• Linear polymers can be chemically or physically joined at points to other chains along their length to create a crosslinked structure. Chemically crosslinked systems are typically known as thermosetting polymers because the crosslinking agent is heat activated.
Ward, I.M., Hadley, D.W., An Introduction to the Mechanical Properties of Solid Polymers, John Wiley & Sons Ltd., New York, 1993, p.2.
62
Effect of Crosslinking
120
160
300
1500
9000
30,000
M = MW between
crosslinksc
Temperature
•Introducing crosslinks into a polymer will proportionally increase the density. As the
density of the sample increases, molecular motion in the sample is restricted causing an
rise in the glass transition temperature. Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition,
Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991 p.262
ISBN 0 7514 0134 X
Thermosets
Temperature Ramp at constant frequency
Viscosity dependence on temperature (i.e.
minimum viscosity)
Gel temperature
Gel time
Time sweep at constant temperature and frequency
Viscosity change with time
Gel time
Or combination profile to mimic process
19.51MPa
40
60
80
100
120
140
[ –
––
––
· ]
Te
mp
era
ture
(°C
)
0.001
0.01
0.1
1
10
100
[ –
– –
– ]
Lo
ss M
od
ulu
s (
MP
a)
0.001
0.01
0.1
1
10
100
Sto
rag
e M
od
ulu
s (
MP
a)
0 10 20 30 40 50 60 70
Time (min)
Comment: 1 Hz, 20 microns
Universal V2.6D TA Instruments
Frequency = 1HzAmplitude = 20 microns
Sheet Molding Compound Cure in Shear SandwichCure 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"
63
50000 1000 2000 3000 4000
global time (s)
10000
10.00
100.0
1000
n*
(P
a.s
)
175.0
25.0
50.0
75.0
100.0
125.0
150.0
tem
pera
ture (
Deg
C)
TA Instruments
COOKIE.04O-temp sweep
COOKIE.05O-temp sweep
COOKIE.06O-temp sweep
COOKIE.07O-temp sweep
"Baking" Cookie Dough
Temp
n*
120000 2000 4000 6000 8000 10000
global time (s)
1.000E7
1000
10000
1.000E5
1.000E6
G' (P
a)
1.000E7
1000
10000
1.000E5
1.000E6
G'' (P
a)
Cross-over points: 1
global time: 10970 sG': 1.474E6 Pa
Time = >3hrs
Automotive Industry
Structural Adhesive Isothermal Cure at 25°C
1750-250.0 0 250.0 500.0 750.0 1000 1250 1500
global time (s)
1.000E8
10000
1.000E5
1.000E6
1.000E7
G' (P
a)
1.000E8
10000
1.000E5
1.000E6
1.000E7
G'' (P
a)
200.0
25.0
50.0
75.0
100.0
125.0
150.0
175.0
tem
pe
ratu
re (
De
g C
)
Gel Pointglobal time: 787.3 sG': 1.963E5 Pa
Isothermal step run in controlled strain mode to ensure data taken
within displacement resolution -0.01% Strain used in test shown.
NOTES:Temperature Ramped from 25°C to
175°C at 10°C/min and held Isothermally at
175°C for 15 min.
1.5 grams of powder pressed into pellet
20 mm parallel plate geometry used
Frequency 10 rad/s
G’
G”
Temp
Electronics Industry: Powder Resin Ramp and Hold Cure
17500 250.0 500.0 750.0 1000 1250 1500
global time (s)
1.000E7
10000
1.000E5
1.000E6
|n*|
(P
a.s
)
200.0
25.0
50.0
75.0
100.0
125.0
150.0
175.0
tem
pera
ture
(Deg C
)
Minimum Viscosity
global time: 702.0 s
|n*|: 15420 Pa.s
•NOTES:Temperature Ramped from 25°C to 175°C at 10°C/min and held Isothermally at 175°C for 15 min.
1.5 grams of powder pressed into pellet
20 mm parallel plate geometry used
Frequency 10 rad/s
Electronics Industry: Powder Resin Ramp and Hold Cure
64
Temperature Sweep - Rheometer - ABS
-50.0 0 50.0 100.0 150.0 200.0 250.0
temperature (°C)
1.000E5
1.000E6
1.000E7
1.000E8
1.000E9
1.000E10
G' (
Pa)
1.000E5
1.000E6
1.000E7
1.000E8
1.000E9
1.000E10
G'' (P
a)
0
0.2500
0.5000
0.7500
1.000
1.250
1.500
1.750
2.000
2.250
2.500
tan(d
elta)
ABS -150degC 1Hz AR2000-0001o
117.6 °C
ABS 0.025 % strain, 1Hz
Temperature Sweep-DMA-Polycarbonate
145.98°C
0.5
1.0
1.5
Ta
n D
elta
0
100
200
300
400
500
Lo
ss M
odu
lus (
MP
a)
0
500
1000
1500
2000
2500
Sto
rage
Mod
ulu
s (
MP
a)
20 40 60 80 100 120 1 40 160 180
Temperature (°C)
Sam ple: PolycarbonateSize: 17.5000 x 11.85 00 x 1.62 00 m mMethod: ram p 3°C /m inCom m ent: A m plitude 30µ m
DMAFile : C :\TA\Data\DMA \Dm a-pc.001Ope rator: Apps . LabRu n Date: 0 2-Jan-1997 17:03Instrum ent: 2980 DM A V1.0 F
Universal V4.1D TA Instrum ents
Primary / Secondary Transitions in PET Film
119.44°C
-55.49°C0.05
0.10
0.15
[ ] T
an D
elta
10
100
1000
10000
[ ] L
oss M
odulu
s (
MP
a)
10
100
1000
10000
[ ] S
tora
ge M
odulu
s (
MP
a)
-150 -100 -50 0 50 100 150 200 250
Temperature (°C)
Sample: PET Film in Machine DirectionSize: 8.1880 x 5.5000 x 0.0200 mmMethod: 3°C/min rampComment: 1Hz; 3°C/min from -140° to 150°C, 15 microns,
DMAFile: A:\Petmd.001Operator: RRURun Date: 27-Jan-99 13:56
Universal V2.5D TA Instruments
–Tg
–β–Transition
Temperature Ramp on Thermoforming
Packaging Films
0.1
1
10
100
1000
10000
Sto
rage
Mod
ulu
s (
MP
a)
25 35 45 55 65 75 85 95
Temperature (°C)
–––––– Poor Performance–––––– Good Performance–––––– Excellent Performance
Universal V3.4C TA Instruments
–DMA 2980
–Film Clamp
–Temp Ramp@ 1 Hz
–85°C: Thermoforming Temperature
–Poor
–Good
–Excellent
65
Testing: Scope
• Rheology is used in
• Product performance
• Product processing
• Formulation (structure)
• …because Rheology
• is very sensitive to small changes in formulation
• provides a direct measurement of process parameters
• correlates with final product performance
Testing: Scope (cont’d…)
• Rheology measures
• Physical quantities like viscosity, modulus, …
• Stored and dissipated mechanical energy
• Changes in material’s which are related to its physical or chemical structure
• Objective => How to design a testing strategy?
• which provides the desired information for product development/formulation or
• Makes use of Rheology as a problem solver in Process control or QC
How to develop a testing strategy
• Rheology measures viscosity, time dependent changes, mechanical losses, etc..
• The application largely determines which tests need to be performed.
• Often it is already known from experience which testing strategy to use
Considerations:
Testing strategy: Development steps
• Step 1
• Analyze the requirements and postulate which are the best rheological parameters to measure
• Step 2
• Select samples, which evidently show significant differences (good, bad) in performance
• Step 3
• Run a series of standard tests (see examples) i.e. set up an empirical test plan
66
Testing strategy: Development steps (cont’d)
• Step 4
• Evaluate the results and compare with the postulated assumptions
• Step 5
• Do the results show the desired response (ranking)?
• If yes go to step 6
• If no, change assumption and start over with 1
• Step 6
• Set up final test procedure
How to develop a testing strategy
• When working with new materials or applications -the approach is empirical or semi-empirical. The goal is to understand the Structure –Rheology relation (Rheology is not a direct measurement of material’s structure)
• Rheology can not replace the final performance test, but it will eliminate all the samples which do not fulfill the requirements. As such Rheology reduces the quantity of performance testing – thus reducing costs and test time
Limitations
Typical example: Polymers
• Sample preparation:
• Shape: - discs or pellets
• Conditioning: - stabilization to prevent degradation, drying to prevent foaming or post-reactions
• Set T>Tgor Tm and run a log “strain sweep”; low to high
• Why dynamic testing?
• Dynamic testing is fast
• No end effects since the applied strain is small
• Determines the on-set of the linear viscoelastic range
• Minimum instruments effects
Polymers: Strain sweep
10-1
100
101
102
103
104
105
Linear viscoelastic range
G' [
Pa
]; η
* [P
as]
STRAIN %
G'
Eta
• Determine the critical strain γc
• Note: sometimes not possible, because no strain independent plateau can be found (filled materials, blends)
0.1 1
101
Temperature:40o C
Test frequency: 1Hz
Bad dispersion
Medium dispersion
Godd dispersion
Rubber compund with different types of Carbon Black
Sto
rag
e M
od
ulu
s G
'x1
0-5 [
Pa
]
Strain γ [%]
67
Polymers: Strain sweep cont’d…
1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 10
103
104
105
106
10710
-210
-110
010
110
210
310
410
5
101
102
103
104
105
increasing
frequency
G' [
Pa
]
Strain γ
G' vs. strain
0.1 Hz
0.3 Hz
1 Hz
3 Hz
10 Hz
Stress t [Pa]
G' vs. stress
0.1 Hz
0.3 Hz
1 Hz
3 Hz
10 Hz
G' [
Pa
]
0.1 1 10 100
1000
10000
100000
Frequency sweep at 0.15 strain units
G',
G''
[Pa]
Frequency ω [rad/s]
G'
G''
• The linear viscoelastic region or the critical strain is a function of frequency
• The critical strain decreases with frequency
• The critical stress increases with frequency
Polymers: Frequency sweep
• ...the optimum strain selected, run a “frequency sweep”; high to low
• Why from high to low?
• Eliminates degradation effects
• Minimizes relaxation effects
• Provides data faster
266
Polymers: Frequency sweep cont’d…
100
101
102
102
103
104
G' [
Pa
], G
'' [P
a];
η*
[Pa
s]
Frequency ω [rad/s]
C
A
η* [Pas]
• Represents the viscoelastic nature of the material
• Provides information about the material at different processing or application rates
• The viscoelastic response is characteristic of the material’s structure
Upper frequency is limited by the instrument, the low
frequency is typically 0.1 rad/s, a practical limit is 0.01 rad/s
Polymers: What next…?
0.1 1 10 100
102
103
104
105
104
105
106
No
rma
l str
ess
coe
ffic
ien
t [P
as2
]
Shear rate γ [1/s]
10 1/s
5 1/s 1 1/s
0.5 1/s
0.1 1/s 0.01 1/s
Vis
cosi
ty [
Pas]
.
• …is it necessary to extend the frequency range to lower or higher frequencies? Is flow curve information required?
• either do a steady or transient test at low shear rates (<0.01)
• or use the t-TS to extend the range to lower or higher rates/ frequencies
Note:•t-TS cannot be used with complex
materials
•Normal force provides an
elasticity measurement
•Creep recovery tests may be
considered to measure small
changes in material’s elasticity
68
Polymers: Temperature sweep
100
101
102
100
1000
10000
100000
Temperature range: 180 to 230 deg C
G' [P
a]
frequency w [rad./s]
G'
0.1 1 10 100 1000
100
1000
10000
100000
G'; G
'' [P
a]
Frequency w/aT [rad/s]
G'
G''
• t-TS only possible if material “thermo-rheological simple” => master curve
• If t-TS not possible, make a 3D plot to extract significant information
• Below Tg => solids testing torsion measurements, DMA
150160
170
180
190
200
103
104
105
0.1
1
10
Mod
ulu
s G
' [P
a]
Frequency [rad/s]
Temperature T
[°C]
Example: Complex fluids
• Sample loading:
• Load with spatula or pipette onto the plate
• Use automated sample loading feature for reproducibility
• Use concentric cylinders if sample evaporation is an issue, or special geometries if sedimentation or slip is an issue
• Set temperature and run a “dynamic time sweep” with manual strain switching (pre-test)
• Why a time sweep?
• to apply a low-high-low strain profile
• pretest material to understand basic material behavior
Complex fluids: Pre-testing
50 100 150 200 250 300 350 400
100
200
300
400
500
600
700
Ketchup pre-test with manual strain switching
G',
G''
[Pa
]
time t [s]
G' [Pa]
G'' [Pa]
• Select low strain high enough to generate a good signal, typical 0.1%. The high strain should be 10 to 100 times higher than the low strain
• Switch strain manually when equilibrium has been reached.
Complex fluids: results of the pre-testing
• The pre-test provides the following information:
• Does the material exhibit a yield? (significant differences between moduli in the low and high strain section)
• Is my material thixotropic? (time require to obtain equilibrium in section 3)
• What is the effect of the chosen sample loading technique? (difference between equilibrium in section 1 and 3)
69
Complex fluids: strain sweep
0.1 1 10 100 1000
0.1
1
10
ττττy=G'*γγγγ
c
criticalstrain γ
c
Strain sweep of a cosmetic cream
G',
G''
[Pa]
Strain γ [%]
G' G'
G''G''
• Run a log “ strain sweep” from low to high at 1Hz or 1rad/s
• Note: conduct the test on the same sample without disturbing the sample after equilibrium has been reached during the pre testing
Estimate the yield stress
from the on-set of linear
behaviour
If the material has shown
significant thixotropy, the
next test should be a
“dynamic time sweep” after
pre-shearing at the typical
application shear rate
Complex fluid: time sweep after pre-shear
• Load new sample , pre-shear for a time longer than needed for breaking structure (section 2 during the pre-test) and follow structure building at low amplitude at 1 Hz i.e. 1rad/s
0 100 200 300 400 500
10τ
Go
Goo
Structure recovery after preshear
G',
G''
[Pa]
Time t [s]
G' G'
G'' G'')exp1)(()( '
0
''
−−= ∞
τ
tGGtG
τ is a characteristic
restructuring time
Complex fluids: What next?
• How to continue testing, depends on the testing objective
• Product stability => frequency sweep
• Classical yield stress measurement => stress ramp
• Flow curve required => rate or stress sweep
• Temperature stability => steady or dynamic Temperature ramp
Complex fluids: Stability- Shelf live
0.1 1 10 100
1
10
100
Frequency sweep of a cosmetic cream
Mo
dulu
s G
', G
'' [P
a]
Frequency ω [rad/s]
G' G'
G'' G''
η* ETA
• tan δ must be between 1 - 1.5 for best stability
• tan δ <1: elasticity too high, interparticle forces cause aggregation
• tan δ >1.5: purely viscous behaviour, no interparticle forces prevent coagulation
70
Complex fluids: Yield
0 50 100 150 200
1
10
100
1000
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0 h [Pas]
Yield stress of a cosmetic lotion
Yield stess (at maximum) = 5.4 Pa
Vis
cosity η
[P
as]
Stress [Pa]
Strain
Str
ain
(x10-6
)
The maximum in viscosity is more representative and reproducible then the extrapolation of the strain
Complex fluids: Flow curve
100
101
102
103
104
105
106
107
108
109
1010
10-2
10-1
100
101
Flow cuve of an ink paste
Viscosity
Vis
cosity η
[m
Pas]
Rate [1/s]
0.009 Pa
slope -1
Stress
Str
ess
τ [m
Pa
]
For a material with a yield stress, the viscosity decreases with a slope of -1 with the strain rate and the stress becomes rate independent.
Conclusion
• Rheology is sensitive to material’s structure
• Rheology is not a unique measurement of structure
• Rheology correlates also with performance and processing properties
• This correlation is empirical or semi-empirical
• General rules for developing test methods for different types of materials can be established (viscoelastic fluids, complex fluids, reactive materials. ..)
• Understanding the relationship structure-rheology is the key to predict or interpret material’s performance during processing or as a final product
Any Questions ????
280
Thanks for
Attending
Recommended