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1 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 Modulus Strain Stress = Viscosity rate Shear Stress = Rheology: Study of stress-deformation relationships Simple Steady Shear Flow H x y Top plate Area = A Bottom Plate Velocity = 0 Velocity = V 0 Force = F Shear Stress, Pascals Viscosity, Pa-sec 0 V H y v x = H V dy dv x 0 = = γ & A F = σ Shear Rate, sec -1 Velocity at position y, m sec -1 γ σ η & = 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.
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Page 1: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

1

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.

Page 2: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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.

Page 3: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 4: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

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

Page 5: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 6: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

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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

Page 8: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 9: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 10: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 11: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 12: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 13: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

13

Applications

• Hydraulic valves

and clutches

• Shock absorbers

• Bulletproof vests

• Polishing slurries

• Flexible electronics

(kindle…)

Introduction to Tribology

stressnormal

stressshear==

L

F

F

“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

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

Page 14: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 15: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 16: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 17: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 18: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

Page 19: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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 %

Page 20: A Comprehensive Introduction to Rheology - uab. · PDF fileA Comprehensive Introduction to Rheology Practical Rheology Workshop ... Rheology is the science of flow and deformation

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

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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)

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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‘)

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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)

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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

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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

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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

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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

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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\

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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

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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

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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

σ

γ=

=

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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

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

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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

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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

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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

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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 &&& /)()( =

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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

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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

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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)

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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

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)

tobs

= De

If the material

time is longer than

the observation

time De>1 (solid

behavior)

160

Types of Flows

Shear

Extension

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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)

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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

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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

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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

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

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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

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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

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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

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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

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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

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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)

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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

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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

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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.

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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.

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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)

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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.

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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).

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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

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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

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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

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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.

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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"

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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

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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

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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

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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 [%]

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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

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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)

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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

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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