A Comprehensive Introduction to Rheology

Rheology: An Introduction A Comprehensive Introduction to Rheology Practical Rheology Workshop 1 Rheology: An Introduction Simple Steady Shear Flo...
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Rheology: An Introduction

A Comprehensive Introduction to Rheology Practical Rheology Workshop

1

Rheology: An Introduction

Simple Steady Shear Flow Top plate Area = A

Rheology: Study of stress-deformation relationships

Velocity = V0 Force = F

H 

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

y x

 y Velocity at position y, m sec-1 v x =  V0 H Shear Rate, sec-1

Stress = Viscosity Shear rate

Bottom Plate Velocity = 0

Stress = Modulus Strain

Shear Stress, Pascals

 dvx  V0  =  dy  H

γ& = 

F σ= A

η=

σ γ&

Viscosity, Pa-sec

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.

1

Viscoelastic Behavior

Deformation of Solids τ=

x(t)

F A

V

Deformation: Solid behavior

Purely Elastic

F = F(x); F ≠ F(v) y

z

y0 A

x

Deformation & Flow

Strain γ =

γ& =

x (t ) y0

∆γ ∆t

Modulus G =

τ γ

Viscosity η =

τ γ&

Viscoelastic Behavior PDMS (silly putty)

Viscoelastic

Force depends on both Deformation and Rate of Deformation and vice versa.

Flow: Fluid behavior

F = F(v); F ≠ F(x)

Purely Viscous

Understand Your Instrument First! Two types of rotational rheometers and DMA‘s  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)

t is short [< 1s]

t is long [24 hours]

Both techniques, depending on the configuration, have different specification, different features and different performance for different applications.

Behavior described by Deborah Number

2

What Does a Rheometer Do?  Rheometer – an an instrument that measures both viscosity and viscoelasticity of fluids, semi-solids and solids

How do Rheometers Work? Rheology is the science of flow and deformation of matter --or-the study of stress-strain relationships

 It provides information about the material’s:  Viscosity – function of shear rate or stress, time & temperature dependence

Fundamentally a rotational rheometer will control or measure:

 Viscoelastic properties (G’, G”, tan δ) with respect to time, temperature, frequency & stress/strain  Transient response (relaxation modulus, creep compliance, creep recovery)

Rotational Rheometer Designs Separate motor & transducer Or Dual Head Measured Torque (Stress)

Combined motor & transducer Or Single Head

Transducer Non-Contact Drag Cup Motor

Direct Drive Motor

Rotational Rheometers at TA ARES G2

DHR

Displacement Sensor Measured Strain or Rotation

Applied Torque (Stress)

Sample Applied Strain or Rotation

 Torque  Angular Displacement  Angular Velocity

Static Plate

Controlled Strain

Controlled Stress

SMT or DH

CMT or SH

3

Understanding Key Rheometer Specifications

ARES-G2 Instrument Specifications

Rheology is the science of flow and deformation of matter --or-the study of stress-strain relationships

 Torque range  Angular Resolution  Angular Velocity Range  Normal Force  Frequency Range

DHR Instrument Specifications Specification

HR-3

HR-2

HR-1

Bearing Type, Thrust Bearing Type, Radial Motor Design Minimum Torque (nN.m) Oscillation Minimum Torque (nN.m) Steady Shear Maximum Torque (mN.m) Torque Resolution (nN.m) Minimum Frequency (Hz) Maximum Frequency (Hz) Minimum Angular Velocity (rad/s) Maximum Angular Velocity (rad/s) Displacement Transducer Optical Encoder Dual Reader Displacement Resolution (nrad) Step Time, Strain (ms) Step Time, Rate (ms) Normal/Axial Force Transducer Maximum Normal Force (N)

Magnetic Porous Carbon Drag Cup 0.5 5 200 0.05 1.0E-07 100 0 300 Optical encoder Standard 2 15 5 FRT 50

Magnetic Porous Carbon Drag Cup 2 10 200 0.1 1.0E-07 100 0 300 Optical encoder N/A 10 15 5 FRT 50

Magnetic Porous Carbon Drag Cup 10 20 150 0.1 1.0E-07 100 0 300 Optical encoder N/A 10 15 5 FRT 50

0.005

0.005

0.01

0.5

0.5

1

Normal Force Sensitivity (N) Normal Force Resolution (mN)

HR-1

HR-2 HR-3

Relating Instrument Specifications to Material Properties The measured quantity (angular deformation and torque) are transferred into a material quantity (stress, strain, viscosity, etc.) Calculated parameters :

Measured parameters : θ(t) dθ

dt M(t)

angular displacement (rad) = Ω(t) angular velocity (rad/s) torque (N m)

τ (t ) = Kτ M

stress (Pa)

γ(t) = K γ θ

strain ( )

γ&(t) = K γ dθ η(t) = G(t) =

Geometry specific constants, Kτ and Kγ, relate the measured instrument data with the desired material parameter

τ(t) γ&o τ(t) γo

dt

strain rate (1/s) visc osity (Pa s) modulus (Pa)

4

Equation for Viscosity In Spec

Equation for Modulus Describe Correctly

σ M . Kσ η= = γ& Ω . K γ Rheological Parameter

Constitutive Equation

Raw rheometer Specifications

Geometric Shape Constants

In Spec

σ M . Kσ G= = γ θ . Kγ Rheological Parameter

Constitutive Equation

Raw rheometer Specifications

Geometric Shape Constants

Motion

Ranges of Rheometers and DMA’s log E' (G') and E" (G")

Describe Correctly

Some Viscoelastic Liquid Characterization Possible with Shear Sandwich

Range of DMA/RSA-G2

Range of DHR/ARES-G2 Rheometer

Flow Storage Modulus (E' or G') Loss Modulus (E" or G")

(Flow, Creep, Stress Relaxation)

Oscillation

Squeeze Flow/ Pull Off

Temperature

5

Geometries Concentric Cylinders

Cone and Plate

Parallel Plate

Markets Torsion Rectangular

Paints/Inks/Coatings Polymers Asphalt Food Organic Chemicals Pers Care & HH Products Adhesives & Sealants Petroleum Products Pharmaceuticals Medical/Biological

Very Low to Medium Viscosity

Water

Very Low to High Viscosity

Very Low Viscosity to Soft Solids

to

Inorganics (Metals, Ceramic, Glass) Other

Very Soft to Very Rigid Solids

Paper Automotive Elastomers

Steel

Aerospace Electronics 22

What is DMA?

Modes of Deformation Tensile

Dynamic Mechanical Analysis is a combination of:

Compressive

Bending

Linear

The science of Flow and Deformation of Matter

Measurement of any property as a function of time and temperature

Rotational

Torsional Shear

Rectangular Torsion

6

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’ DMAs RSA G2

TA Instruments DMA’s RSA G2

Q800

Controlled Strain SMT

Controlled Stress CMT

DMA Q800: Schematic

Q800

Controlled Strain

Controlled Stress

SMT – Separate Motor & Transducer

CMT – Combined Motor & Transducer

Force Rebalance Transducer (FRT) (Measures Stress)

Sample

Actuator Applies deformation (Strain)

Sample

Displacement Sensor (Measures Strain) Motor Applies Force (Stress)

7

RSA-G2: Dual Head Design

Specifications

Temperature Sensor Rare Earth Magnet Transducer Motor Transducer Air Bearing LVDT Air Bearing Upper Geometry Mount Lower Geometry Mount Air Bearing LVDT

Motor

Air Bearing Drive Motor

Max Force Min Force Force Resolution Frequency Range Dynamic Sample Deformation Range Strain Resolution Modulus Range Modulus Precision Tan delta Sensitivity Tan delta Resolution Temp range Heating Rate Cooling Rate Isothermal Stability

Clamps (on Q800)

TA Instruments DMA Specifications Q800 RSA G2 18N 35N 0.0001N 0.0005N 0.00001N 0.00001N 0.01 to 200 Hz 2E-5 to 100 Hz +/- 0.5 to 10,000 µm 1 nanometer E3 to 3E12 Pa +/- 1% 0.0001 0.00001 -150 to 600°C 0.1 to 20°C/min 0.1 to 10°C/min +/- 0.1°C

+/- 0.05 to 1,500 µm 1 nanometer E3 to 3E12 Pa +/- 1% 0.0001 0.00001 -150 to 600°C 0.1 to 60°C/min 0.1 to 60°C/min +/- 0.1°C

Clamps (on RSA-G2)

The array… S/D Cantilever

Tension-Film

3-Point Bending

Shear-Sandwich

Tension-Fiber

Submersible Compression

Compression

3-Pt Bending

Film/Fiber

Shear Sandwich

Submersible Tension Compression

Cantilever

Contact Lens

8

Measurement of Shear Modulus - Torsion and Shear Sandwich Torsion (Shear Rheometer)

Movable Fulcrum

Shear Sandwich (DMA) Limited to Soft Solids

Stress Head (transducer)

Movable Clamp

Measurement of Young’s Modulus - Three Point Bending

Sample

Stationary Fulcrum

Sample Stationary Clamp

Movable clamp

Sample Stationary Clamp

Stress Head (transducer)

Measurement of Young’s Modulus - Cantilever Bending

Sample

Dual Cantilever Bending

Stress Head (transducer)

Measurement of Young’s Modulus - Compression Stationary Clamp

Sample

Single Cantilever Bending Movable clamp Movable clamp

Stationary Clamp

Stress Head (transducer) Stress Head (transducer)

9

Measurement of Young’s Modulus - Tension

Stationary Clamp

Four Regions of Viscoelastic Behavior for Typical Linear and Crosslinked Amorphous Polymer Glassy

Transition

Rubbery Plateau

Flow Region

9

Very hard and Brittle

Sample (film, fiber,or thin sheet) 7

(Lightly Crosslinked)

Movable clamp

5

Resilient leather

(Linear)

Soft rubber

Stress Head (transducer)

Viscoelastic liquid

3

Temperature, °C

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 Some Viscoelastic Liquid Characterization Possible with Shear Sandwich

Range of DMA/RSA Range of AR/ARES Rheometer Storage Modulus (E' or G') Loss Modulus (E" or G")

Temperature

10

Rheological Characterization

DHR Dielectric Accessory

Rheology DHR Rheometer dynamic oscillation

continuous shearing

FT-Rheology

elongational flow Environmental test Chamber

 FT

linear regime

I(3ω1 ) = f (γ ) I(ω1 )

η und N1 = f( γ& )

G‘ und G‘‘ = f( γ& )

non-linear regime, time-dependent

non-linear regime, time-dependent

H0 = f( ε& ) linear and nonlinear regime

Agilent E4980A LCR meter BNC connections to LCR meter

Ground Geometries with Ceramic Insulator (standard or disposable)

41

Specifications

Applications: Polar materials Examples: PVC, PVDF, PMMA, PVA

Attribute

Specification

Geometry

25mm 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

11

Applications: Emulsions stability

DHR Electro-Rheology (ER) Accessory

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 ER Accessory

Specifications Attribute

• Engineering prototype as demo unit in New Castle • Parallel Plates geometries • DIN Concentric Cylinder • Compatible with Peltier Plate and Peltier Jacket temperature systems ONLY

Specification 25 and 40 mm ER parallel plate and 28 mm ER conical DIN bob Peltier Plate and Peltier Concentric Cylinder Temperature System Compatibility Jacket TRIOS Software Version 2.6 or later -40 to 200°C for Peltier Plate. -10 to 150°C Temperature Range for Peltier Concentric Cylinder High Voltage Power Amplifier TREK Model 609E-6 0 to 4,000 VDC; 4,000 VAC peak (8,000 peakMaximum Voltage peak) Output Current Range 0 to ± 20 mA Polycarbonate ER shield cover with interlock Safety switch Geometry

12

Applications

Introduction to Tribology

• Hydraulic valves and clutches • Shock absorbers • Bulletproof vests • Polishing slurries • Flexible electronics (kindle…)

“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

Coefficient of Friction, µ

Boundary Lubrication

Mixed Lubrication

Tribo-rheometry Accessory (TRA)

Disc Coupling

1 FF shear stress = FL normal stress Stepped Disposable Peliter Plate/ ETC

(ηoilΩ)/FL

• • •

FF shear stress = FL normal stress

Hydrodynamic Lubrication

µ=



µ=

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)

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

13

Tribo-rheometry Beam Coupling

Tribo-rheometry Specifications & TRIOS Variables Instrument Compatibility

All DHRs

Temperature Systems

FL Lubricant

Temperature Range

Peltier Plate, ETC Oven 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

Top Surface Maximum Axial Force

Bottom Surface

Stainless Steel Coupling

Aluminum Coupling

50 N

Maximum Torque

200 mN.m

Variable

 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

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

µ (Coeff. of Friction)

FF/FL

Dimensionless

ηoilΩ/FL

Dimensionless

Gu (Gumbel Number)

• •

Fully integrated into TRIOS with Tribology test templates Complete suite of tribology relevant test variables available

Peltier Plate Tribo-rheometry Geometries

Coefficient of Friction Measurement

Ring on Plate

Hydrodynamic Lubrication

Three Balls on Plate

Mixed Lubrication

Ball on three Plates

Boundary Lubrication

PVC on Steel with 2.0 Pa.s oil as lubricant Geometry: 3 Balls on Plate Temperature: 25°C, Procedure: Flow ramp

Ball on three Balls

14

Coefficient of Friction Measurement

Stepped Disposable Peltier Plate Tribo-rheometry Setup

PVC on Steel with 2.0 Pa.s oil as lubricant Geometry: Ring on Plate Temperature: 25°C, Procedure: Flow Sweep Disc Coupling

Skin substitute ring on disposable plate

Skin substitute on stepped disposable plate

Ideal platform for testing cosmetic products (lotions, hand cream, makeup) and lubricants

CoF Measurement: Personal Care application

CoF Measurement: Personal Care application

0.4

0.6

 Temperature 25°C  Velocity Ramp 1 to 50 rad/s  Normal stress 0.8 PSI

0.35

Vaseline Baby Oil

Coefficient of Friction

0.3

Coefficient of Friction

0.5

0.25

0.2

0.15

0.1

 Temperature 25°C  Speed 10 rad/s  Normal stress steps

0.05

0 0.00

2.00

4.00

6.00

8.00

Pressure. PSI

10.00

12.00

0.4

Baby Oil Vaseline 0.3

0.2

0.1

14.00

0 0

5

10

15

20

25

30

35

40

45

50

Angular Velocity rad/s

15

Wet Setup: Semiconductor Application

Typical Results

Disc Coupling

Silicon Wafer on Disposable Plate

Polishing Pad ring on Disposable Plate

 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

CoF Measurement: Semiconductor Application

Degradation of Wafer Surface

0.6

Speed 0.7 m/s

0.5

Coefficient of Friction

Speed 2 m/s 0.4

0.3

0.2

0.1

Before Testing

After Testing

0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Pressure, PSI

16

ETC Oven Tribo-Rheometry Geometries

Asphalt Lubricity Testing Geometry: Ball on three Balls Temperatures: 100 °C, 110 °C and 120 °C Procedure: Flow Ramp

Beam Coupling SST Ring on upper plate

Ring on Plate

Ball on three Balls

Brake pad on lower disposable plate

Well suited for automotive applications, high temperature greases/oils and testing lubricity of asphalt and rubber Ball on three Plates

Three Balls on Plate

Optics Plate Accessory (OPA)

OPA with USB Microscope

PN 546800.901

• Stepping stone into RheoMicroscopy! • 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

8 threaded holes for custom optics installation

TA Instruments Confidential Document

• 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

PN 546800.902

2D Stage

USB microscope

TA Instruments Confidential Document

17

OPA with USB Microscope

Magnification Working distance Field of view Polarization Illumination Image Capture Temperature range (UHP) Geometries Instrument Compatibility

50x 11.4 mm 7.8 x 6.3 mm

OPA with USB Microscope

240x 11.6 mm 1.6 x 1.3 mm

After shear

At rest

Yes 8 White LED's 1280 x 1025 pixels, 30 fps -20 to 100°C Plates and Cones up to 60 mm Diameter 100 µm

All DHRs, AR-G2, and AR200ex

100 µm

PDMS in PIB 240x with mirror finish geometry TA Instruments Confidential Document

TA Instruments Confidential Document

New Pressure Cell Rotors

Pressure Cell Vane rotor

PN 402815.901

Optional Vane Rotor for Pressure Cell Standard Pressure Cell accessory with Conical Rotor

PN 402828.901

Pressure cell with vane rotor Self-sealed mode Pasta sauce with starch Flow temperature Ramp: 2°C/min Stress: 5 Pa

Optional Starch Rotor for Pressure Cell

• Samples with large particles • Better mixing to suspend particles • Loading samples with delicate structures TA Instruments Confidential Document

TA Instruments Confidential Document

18

DHR Torsion Cylindrical

DHR Torsion Cylindrical

PN 547905.901 Polycarbonate Oscillation temperature ramp Heating rate: 3°C/min Frequency: 1 Hz Strain: 0.01 %

• Can accommodate samples with diameters of: 1.5, 3, and 4.5 mm • Compatible with ETC • Polymers, Elastomers

DHR Building Materials Cell

TA Instruments Confidential Document

DHR Building Materials Cell: Cement mixing

• Fits in Peltier Jacket • Characterization of Cements, Mortars, Pastes

Paddle Rotor for BM Cell PN 533247.901

Oscillation Strain (%)

PN 533246.901 • Large Cup to accommodate samples with large particles • Slotted Cage to minimize material slip at the wall

Storage Modulus G’ (Pa) Loss Modulus G” (Pa)

Large Strain followed by low Strain Oscillation time sweeps Temperature: 23°C Frequency: 1 Hz Strain: 5000 and 0.01 %

Time (s) TA Instruments Confidential Document

TA Instruments Confidential Document

19

DHR/AR Bayonet Peltier Plate

Quoting DHR/AR Bayonet Peltier Plate (BPP) – Bayonet Peltier Plate: 533209.901

– BPP with QCPs of various materials of construction or surface finishes 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.

• Quick Change Plate Holder: 402751.902 • Selection of QCP’s and corresponding diameter upper peltier plates from price list

QCP Holder

QCP

QCDP Holder

QCDP

– BPP with Disposable plates configuration Quick Change Plates (same as ARES-G2 APS):

Immersion Cup

• • • •

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)

ARES-G2 Cone & Partitioned Plate

New ARES-G2 Accessories

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

20

ARES-G2 Cone & Partitioned Plate (CPP)

ARES-G2 CPP: LAOS example Can reach larger strains with CPP before sample leaves gap in standard cone an plate

PN 402800.901

Center plate (to transducer) • • • • •

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

Outer ring cylinder Sample Lower Cone (to motor)

ARES-G2 DWR Interfacial Accessory

ARES-G2 DWR Interfacial Accessory

Trough

Loss modulus G’ (Pa/m)

Complex viscosity η* (Pa.s.m)

• 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

Loss modulus G’ (Pa/m)

Sorbitan tristearate (SPAN) Surfactant at Water – Dodecane interface Geometry: Double wall ring Temperature: 20°C Procedure: Oscillation time sweep followed by Oscillation Frequency Sweep

PN 402820.901

Storage modulus G’ (Pa/m)

Adapter

Storage modulus G’ (Pa/m)

DWR

21

Parallel Superposition •

Shear Rate, γ

Motor

.

Shear Rate, γ

X-ducer

Torque Transducer outputs torque from steady shear

Strain, γ (Axial)

.

Torque Transducer outputs combination of torque from steady shear and oscillation torque from dynamic measurement

Alternative to parallel superposition to follow structural changes in a material under flow

Strain, γ (Angular)

X-ducer

Follow structural changes in a material under flow

Strain, γ (Angular)



Orthogonal Superposition (OSP) on ARES-G2

Normal Force Transducer applies Axial deformation and measures Axial Oscillation Force

Motor

Time Time





VE moduli in PSP not obvious  can generate negative G‘ values ! • •

Parallel vs. Orthogonal

3 1 2

. γ

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)

Force rebalance transducer in OSP mode

Steady Shear

Parallel

γ ||

γ⊥

Orthogonal

• 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‘)

22

OSP Features on ARES-G2

OSP Geometry Slots in Bob minimize surface tension effects

• OSP on steady shear to monitor structural changes in materials (alternative to LAOS measurements)

OSP

Outer cylinder

• 2D-SAOS measurments to quantify anisotropy in materials

Center cylinder

• DMA tension/compression on solid films & fibres and bending of standard solid specimen • Simultaneous multiaxial testing of soft solids such as gels, foams, rubbers,...

Orthogonal oscillation

Outer Double Gap Cup

2D - SAOS

Inner Double Gap Cup with Slots

Bob with Slots (Patent pending)

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

Flow field between Bob and Cup in Orthogonal direction

Inner cylinder

Slots in Cup minimize axial pumping effects

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)

Steady shear breaks downs gel structure and moves flow region to shorter times scales (high frequencies)

23

ARES-G2 DMA mode

ARES-G2 DMA mode Tension 708.01458

3 Pt. Bend 532069.901

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.

ABS bar in 3 Point Bending

T W L (mm): 3 x 12 x 40 Ramp rate: 3 C/min Strain: 0.05 %

Cantilever 532070.901

Small Amplitude Oscillation

Motor Locked to alignment position

ARES-G2

RSA-G2

Maximum Force (N)

20

35

DMA Q800 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

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

24

Packaging Foam in Compression

PET Temperature ramp in Tension

D T (mm): 6.5 x 2.6 Ramp rate: 3 C/min Strain: 0.1 % with AutoStrain

PET Temperature ramp in Tension, TTS

Dual Cantilever: Epoxy cure on glass braid

Application of epoxy mixture on glass braid

25

Single Cantilever: Elastomer temperature ramp

ARES-G2 FCO & APS Tribology Accessory Ring on Plate

W T (mm): 5.4 x 1.6 Ramp rate: 3 C/min Strain: 0.06 %

Ball on 3 Plates

• High temperature with FCO • Applications: • Automotive • High temp. greases/oils • Asphalt • Rubber

3 Balls on Plate

Ball on 3 Balls

• Close to RT requires APS & Plate • Applications: • Personal care products • Lubricants • Foods

TA Instruments Confidential Document

Extensional Rheology LVE

Butyl in Stress Growth

LVE & NVE

Uniaxial Extension

Step Extension 



 



Tensile Stress Growth

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

Cessation of Extension

Hencky strain rate = 1.0 s-1

 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

26

Butyl in Stress Growth

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

 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

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

27

UV LED Curing Accessory

UV Cure Profile Changes with Intensity

• 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 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\

28

SPC Application: Gelatinization of Starch Products Two Scans Each of Dent Corn and Waxy Maize Starch 100.0

1.500

90.0

1.250

80.0

1.000

70.0

0.7500

60.0

0.5000

50.0

Red symbols: Dent Corn Starch Blue symbols: W axy Maize Starch

0.2500

0

0

250.0

500.0

750.0

1000 1250 global time (s)

1500

1750

2000

40.0

30.0 2250

•Interfacial shear rheology of thin layers at liquid-liquid or liquidgas interfaces. •Effect of particles, surfactants or proteins at the interface •Applications: food, biomedical, enhanced oil recovery Bicone

DuNouy Ring

Double Wall Ring

temperature (°C) (°C) Temperature

viscosity (Pa.s) Viscosity (Pa.s)

1.750

DHR Interfacial Accessories

Steady Shear Viscosity at air/liquid and liquid/liquid interface.

Qualitative Viscoelastic measurements at air/liquid and liquid/liquid interface.

Quantitative Viscoelastic measurements at air/liquid and liquid/liquid interface.

Time (s)

Patented DWR Interfacial System

Surface Concentration Effects on Interfacial Viscosity

Oscillation Experiments at 0.1 Hz

Interfacial Complex Viscosity (Pasm)

10 1

Bicone

10 0

Needle 5 10 -1 10 -2

Needle 3 Needle 1

10 -3 10 -4

Needle 4 10 -5

Double Wall Ring

Interfacial Complex viscosity (Pasm)

10 -6

Needle 2

10 -7 0

1

2

3

4

5

6

7

8

29

Non linear behavior

Non-linear System Response 10

γ>γc

G“ 0

10

Tan δ

10-1 10-1

0

10

1

10

γ c=10 2 %

0.0 103

Structure properties: 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

20

Anglular displacement

8

The raw signal response (torque) becomes a distorted, non symmetric periodic signal in the non linear regime

15 10 5

6

0

4

-5

Strain: 1% 5% 20%

2 0

-10 -15

Torque

-20 -25 -30

-2

-35 -40

-4

Angular displacement φ [mrad]

1.0

G‘

Torque M [g cm]

101

-45

-6 -0.5

-50

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Time t [s]

The non even harmonics in addition to the fundamental response are needed to describe the complete material behavior

117 118

3rd harmonic Contribution

Fourier Rheology

Body Lotion Strain sweep 0.5

0 -1 -2

- 2400 % strain x I( ω) ~ 1/ω

0,8 0,6 0,4

x 100

0,2

10

20

30 40 time [s]

50

60

70

0,1

0,5

0,9

1,3

1,7

2,1

frequency [Hz]

0.4

0.3

2

10

0.2 1

10

0.1

0

10

0.01

0.0

0.1

1

10

100

o ti a r y ti ti s n te n I

)

ω

1,0

0,0

-3 0

10

( /I )

ω

1

G' G'' I(3ω)/I(ω)

3

*

response [normalized]

shear stress [τ]

2

Modulus G'; G'' [Pa]; Viscosity η [Pas]

6

Polyisobutylene (Mv = 4.6· 10 g/mol), 2400 % strain 0.1 Hz:

3 ( I

At the onset of the non linear behavior, the 3rd harmonic contribution becomes important and increases with the strain

Strain γ [%]

Non-linear behaviour generates higher harmonic contributions

119

The third harmonic contribution is normalized with the intensity of the fundamental response 120

30

Soft Hand Cream

Soft Hand Cream Soft cream , Temperature T=25o C Frequency f =1Hz

#2 Nivea soft Freq Swp Soft Cream o T = 25 C preshear 10s at 10 1/s γ=1%

1E5

120

Complex Viscosity [Pa.s] η*

Storage, Loss Modulus [Pa] G' G"

10000

10000

1000

1000

100

10

200

Stress σ [Pa]

0 -8

0

Strain γ [%] 8

0

-80

100

-800

Strain γ [%]

-8000

800

300

Stress σ [Pa]

0

Strain γ [%]

8000

-600

-300

200

Stress σ [Pa]

0

0

-200

Stress σ [Pa]

600

Stress σ [Pa]

0

Strain γ [%] 80

0

-120

300

Stress σ [Pa]

600

Stress σ [Pa]

Stress σ [Pa]

50 Strain Rate g [1/s]

0 -0.5

0.0

Strain Rate g [1/s]

0 -5

0.5

0

Strain Rate g [1/s]

0

5

-50

0

Strain Rate g [1/s]

0 -500

50

0

500

-50 -100

-200

γ=6.32

-600

-300

γ=6320 %

γ=632.0

γ=63.2

100 0.01

0.1

1

10

100

1000

Note: measured stress doesn’t go through origin – yield stress

Angular Frequency ω [rad/s]

Linear viscoelastic reponse for a soft cream

Sample changes from elastic to viscous fluid

Minimum & Large Strain Modulus

Soft Hand Cream

10

0.1 0.01

Soft Cream o T = 25 C preshear 10s at 10 1/s delay 100 cycles f=1 Hz

1E-3 1E-4 1E-5

GL' =

400

stress -σ'

200

1

10

-200

-400

-600 -30

-20

-10

0

10

20

strain γ(t) []

100

1000 10000

1E5

Strain γ [%]

Harmonic ratio reaches steady state at high strain

γ =γ o

0

1E-6 0.1

σ γ

dσ G = dγ ' M

γ =0

30

300

300

Xanthan Gum 4% 50.04 cone plate f=1Hz; T=RT

200

250 200 150

100

100 50

0

0 MITLAOS ARES-G2 StrnSwp DFT

-100 0.01

0.1

1

Large Strain Modulus GL' [Pa]

1

I2/1

0.01

Minimum Strain Modulus GM' [Pa]

100

600

0.1

stress σ(t)

I3/1 I5/1 I7/1 I9/1 . I25/1

Harmonic Intensity In/1

Storage, Loss Modulus [Pa] G' G"

Nivea soft Strain Swp 1000

-50 -100 10

100

Strain γ [ ]

31

Stiffening/Softening & Thickening/Thinning Ratio

600

' L

stress σ(t)

200

0

γ& =γ&o

-200

20

20

-600 -30

-20

-10

0

10

20

strainrate/frequency g(t)/ω

dσ d γ&

γ& = 0

Xanthan Gum 4% 50.04 cone plate f=1Hz; T=RT

15

18

L a rg e S tr a in S h e a r V is [P co s a .s ity ] L'

16 14 12

10

10 8 6

5

4 MITLAOS ARES-G2 StrnSwp DFT

0

2

1

2

Xanthan Gum 4% 50.04 cone plate f=1Hz; T=RT

1

0

0 MITLAOS ARES-G2 StrnSwp DFT only 4 harmonics are taken into account in a Strn Swp

-1

-2

-3 0.01

η

η M' =

30

Minimum Shear Viscosity ηM' [Pa.s]

-400

2

0.1

1

Strain g [ ]

0 -2

0.01

0.1

1

10

-1

S≡ 10

100

0

0 0.1

1

10

100

1000 10000

1E5

Thickening/Thinning ratio - increses initially -- decreases at high strain

Fluids flow Solids deform Concept of time

Nivea soft Strain Swp 60 0 40 -1

20

0

Soft Cream o T = 25 C preshear 10s at 10 1/s delay 100 cycles f=1 Hz

0.01

0.1

1

10

-2

100

1000 10000

...and More

Thickening ratio T

Strain γ [%]

Large Rate, Minimum Rate, Dynamic Viscosity [Pa] ηL ηM η'

Soft Cream o T = 25 C preshear 10s at 10 1/s delay 100 cycles f=1 Hz

Stiffening ratio S

Large Strain, Minimum Strain, Storage Modulus [Pa] GL GM G'

Basics...

- increases with strain and reaches maximum

1500

0.01

Introduction to Rheology

1

500

η L' − η M' 4G " + .. = " 3 " ' G1 + G3 + .. ηL

Stiffening/softening ratio

Nivea soft Strain Swp 2000

1000

−4G ' + .. GL' -2− GM' = ' 3' ' G G1 − G3 + .. -3 L

100

T≡

Strain γ [ ]

Soft Hand Cream

Thickening/Thinning Ratio T []

σ η = γ&

stress σ"

400

Stiffening/Softening Ratio S []

Minimum & Large Strain Rate Viscosity

Types of flows Types of test modes Thermo-mechanical Non linear behaviour

-3 1E5

Strain γ [%]

128

32

Flow phenomenon 2

Flow phenomenon 1

• Elasticity • Viscosity • Time dependent

Short contact [< 1s] Long contact[>1 hour] • Pseudo-plastic 129

130

Flow phenomenon 3

slow

Flow phenomenon 4

fast Honey

Mayonnaise • Linear flow regime

131

• Non linear behavior • Structure breaking

• Yield • Non linear flow 132

33

Flow phenomenon 5

Fluids Flow Common Characterization tool for fluids 50 years ago:

Viscometry Applied rate • Flow induced structure • Low viscosity at rest

Measured stress

DIN standard 133

ASTM standard

134

Flow - Viscometry

Typical Viscosity Values (Pa s)

Single point measurement of the viscosity

• •

stress





• • •

η = σ / γ&

rate

• •

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

Time

Viscosity=shear stress/shear rate 135

136

34

10

4

10

3

10

2

10

1

10

0

10

-1

10

-2

Types of Flow Curves

starch peanutoil 0.05% polyacrylamide solution PIB at 20°C sirup Cocoa butter lotion Shower gel Co-polymer 240 °C

1E-3

0.01

0.1

1

10

100

.

1000

Bingham (Newtonian w/yield stress)

Shear Stress, σ

Viscosity η [Pa s]

Viscosity curve of various fluids

Bingham Plastic (shear-thinning w/yield stress) Shear Thinning (Pseudoplastic) Newtonian

σy

Shear Thickening (Dilatent)



10000

Shear Rate, γ

Shear rate γ [1/s]

Viscosity function of various structured fluids 137

138

The Idealized Flow Curve

Shear Rate Ranges for Many Applications

t=

1

ω

=

1

γ& 1) Sedimentation 2) Leveling, Sagging 3) Draining under gravity 4) Chewing and swallowing 5) Dip coating 6) Mixing and stirring 7) Pipe flow 8) Spraying and brushing 9) Rubbing 10) Milling pigments in fluid base 11) High Speed coating

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

5

Rubbing

104 to 105

Skin creams, lotions

6

High-speed coating

104 to 106

Paper manufacture

Spraying

105 to 106

Atomization, spray drying

Lubrication

103 to 107

Bearings, engines

log η

Situation

4

1 1.00E-5

2 1.00E-4

1.00E-3

0.0100

3

7

0.100

1.00

8

9

10 10.00

100.00

1000.00

11 1.00E4

1.00E5

1.00E6

shear rate (1/s)

139

35

Structured Fluid: Steady State Flow

Steady Rate Sweep

Printing paste 10

10

Viscosity η [mPas]

7

10

6

10

5

10

4

Stress [mPa]

8

10

Viscosity

rate

10

T= 25 °C

9

10

Viscosity [mPas]

7

10

6

10

slope 1

5

10

4

10

3

Stress σ [mPa]

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.

10

2

10

Delay time

σ

4 Pa

1

10

Steady State Flow γ = Constant

time

Rate ramp: high to low

0

rate

10

10 -6

10

-5

10

-4

10

10

-3

-2

10

10

-1

10

0

1

10

10

2

3

10

10

4

5

10

10

3

6

Stepped rate test on ARES Shear rates are stepped at equal intervals => smooth curve

Rate g [1/s]

In a steady experiment, only the equilibrium value is measured over a manual selected time period 142

Polymers: Steady State Flow

*

Viscosity η; η [Pa s]

6

10

viscosity in Pa s 5

10

Creep

Oscillation 1E-6

1E-5

1E-4

.

1E-3

0,01

0,1

Shear rate γ [1/s] or Frequency ω [rad/s] 143

1

Shear ramp up and down or thixotropic loop

• 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/s

The stress represents the instantaneous response to the applied rate.

up

down

stress

HDPE viscosity curve T= 210 °C

Thixotropic Loop

.

σ(γ)

rate

141

The viscosity decreases with a slope of -1 versus strain rate and the stress becomes rate independent => material with yield stress

Time If the material is time dependent, the up and down curves are different

η (γ& ) = σ (γ& ) / γ&

144

36

Thixotropy

Thixotropic Loop Thixotropic materials

Children Advil suspension

Stress σ [Pa]

60

sample A up sample A down sample B up sample B down sample C up sample C down

40 20 0 0

100

200

300

400

Area under the curve is a measure of thixotropy

Viscosity η(t) [Pas]

Up and down ramps do not superpose

80

4

10

first ramp up

0

2

peak at stress 1.3 Pa 0

0

500

2

4

.

6

8

10

146

Ramp in stress controlled mode

Yield stress in a stress ramp Yield stress of a cosmetic lotion

Stress ramp

γ(t) Time

η (σ ) = σ / γ& (σ )

An instantaneous viscosity can be calculated from the applied stress and the time derivative of the deformation

1000

1 0.1

η [Pa s] 100

Viscosity η [Pas]

The stress is increased from zero to a finite value and the deformation is measured as a function of time.

0.01

Strain 10

Yield stess at maximum = 5.4 Pa at intercept ) 11 Pa

1E-3 1E-4 1E-5

1

1E-6 1E-7 1

10

Strain (x10-6)

145

stress deformation

.

rate γ(t) [1/s]

Rate γ [1/s]

147

Nonthixotropic material Up and down ramps superpose – except the first one => Start up from zero

6

viscosity [Pas] stress [Pa]

100

Stress τ [Pa]

Thixotropic loop for 3 Mayonnaise emulsions

The maximum viscosity method allows a more representative and unique determination of the yield stress

100

Stress [Pa]

148

37

Solids Testing

Hookean Body

Modulus & Glass transition

8

10

7

10

6

G' ABS unannealed G' ABS annealed

-150

-100

-50

0

50

100

150

G=

Temperature T [°C]

149

0

20

40

60

80

1 00

-0 .1

-0 .2

γo

1

Tim e 0 0

20

40

60

80

1 00

-1

γˆo

150

General Solids Behavior

Newtonian Fluid

For most solids, response and excitation are not in phase.

σ o= G γ o

0 .2

forced oscillation

η = σo ˆ γ&o ˆ

1.5

T im e 0 .0 0

20

40

60

80

1 00

Viscoelasticity

-0 .1

0 0

-0 .2

go

1

Strain rate

For a Newtonian fluid, the response to a sinusoidal excitation is also sinusoidal and out off phase with the strain rate

Stress

0 .1

151

σˆ o

T im e 0 .0

Strain

Modulus G' [Pa]

Modulus 10

For a Hookean body, the response to a sinusoidal excitation is also sinusoidal and in phase with the excitation

At the transition from solid to fluid, the modulus changes over several decades

9

Stress

0 .1

Tg 10

σ o= G γ o

0 .2

forced oscillation

Injection molded ABS part

Time 0 0

20

40

60

80

100

In the linear regime, linear viscoelasticity, the ratio of strain and stress amplitude and the phase fully characterize the system

6.3

phase angle, δ -1.5

Angle

Stimulus (stress or strain) Response (strain or stress)

-1

152

38

Transition from Solid to Liquid

Solids and Melts testing

What does change? (atomic groups) (main chain) Glass

G

soft (chain segments) stiff

Transition Plateau

Solids testing

(polymer chain) Flow

Viscoelastic Solid

Viscoelastic Fluid Solid

Melts testing

Temperature Time

Strain Stress

0

phase δ -1

tan δ

0

phase δ

-1

0

20

40

60

80

100

0

Time

153

Liquid Strain Stress

1

Strain; Stress

Strain; Stress

1

20

40

60

80

100

Time

154

Viscoelastic Response of an Adhesive

Relaxation or Material Time

Typical PSA Temperature scan

8mm

10

10

9

10

G' tan δ

8

SUPER BALL

LOSS (G”)

TENNIS BALL

7

10

6

10

Modulus at use temperature

Tack

Shear Resistance

2

5

10

4

10

0

3

10

Lowest use temperature 2

10

-50

0

50 o

Temperature T [ C]

155

>2mm

4

100

Loss tan δ

Modulus G' [Pa]

10

Using parallel plates with small radius and large gap permits measurements from the solid into the liquid phase

LOSS (G”)

STORAGE (G’) STORAGE (G’)

τ = η/G

τ(Tennisball) < τ(Superball)

156

39

Material & Process Time

Photography

The material (re-arrangement) time of a material τ depends on temperature

tτ = De tobs

tτ = τ ≅ exp(EA/kT)

 If the material time is shorter De1 (solid behaviour)

The observation time is the process time or the end use time

tapp 157

Observation time long Blurred image

De>1 Solid behavior

De E=3G and η=3ηE

163

Material under test

164

41

Material Functions 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

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.

G' G"

Output

Strain

Input

Oscillation Time Sweep

G' G"

0

Time

200

400

600

800

1000

1200

1400

Time

• Material parameters are defined by the test mode • For an elongation deformation, the stress is σE,, the deformation

AutoStrain and AutoTension are available in this mode

(rate) e(f), the compliance D(t), the modulus E(t), the viscosity ηE(t) 165

166

Structured Fluid: Pre-Testing A R E S a m p litu d e te s t o f a la te x p a in t

In a strain sweep, the strain is varied linear or logarithmic over the selected range. Strain, stress amplitude and phase shift are recorded.

3

10

3.

2

10

1%

12%

1%

0 .1 %

1

-2 0 0

Strain

10

s tra in 0 .1 %

0

0

200

400

600

800

NLM

1. 2.

20

strain γ [%]

Modulus G'; G'' [Pas]

G ' [P a ] G '' [P a ]

G' & G"

10

Oscillation Strain Sweep

1000 1200 1400 1600 1800

G' G" NLM

t im e t [ m in ]

• 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. 167

Time

0.01

0.1

1

10

100

Strain %

The non-linear monitor (NLM) senses the end of the linear viscoelastic range 168

42

Testing in the Linear Region - Strain Sweep Strain sweep of a cosmetic cream

In a frequency sweep, the frequency is varied linear or logarithmic over the selected range. Strain, stress and phase are recorded.

G' G''

Structured sample

10 G" G'

Estimate the yield stress from the on-set of linear behavior

G', G'', η*

τy=G'γ c 1

Strain

Modulus G', G'' [Pa]

Oscillation Frequency Sweep

critical strain γc

10

4

10

3

10

2

η*

10

0.1

Time 0.1

1

10

100

0

1

10

2

10

Frequency

1000

Strain γ [%]

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 170

Structured fluids: Frequency Dependence

10

10

10

4

• Represents the viscoelastic nature of a material in time • Provides . information about the material at different processing or application rates (ω~γ)

G’ C A G” η* [Pas]

3

2

0

10

1

10

2

10

Cosmetic lotion 10

Modulus G', G'' [Pa]

G' [Pa], G'' [Pa]; η* [Pas]

Polymers: Frequency Dependence

10

1

10

Frequency ω [rad/s]

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 171

2

1

G' [Pa] G'' [Pa] tan δ

tan δ = G''/G' > 0.5 to 1 gel like behaviour 0.1

1

frequency ω [rad/s]

10

0.1

• G’ and G” are virtually independent of frequency, as well as tan δ. tan δ

169

Control oscillation tests on strain

• Also the material behaves predominately elastic (G’>G”) => which stands for structure in the material, capable of storing energy

172

43

Oscillation Temperature Ramp

Thermo-Mechanical Characterization

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.

Viscoelastic & Thermo-mechanical characterization

G' G"

.

Rate γ

γ, T

Temperature

Time

Heat

. τ(γ)

In all temperature dependent test, the AutoTension function is available

173

174

Advanced solids testing - DMA

Temperature Ramp in Torsion

Modulus, Glass transition, ß-transition

PMMA Temperature Ramp 1Hz 3°min

Injection molded ABS part

10

Tg 9

1

Modulus G' [Pa]

Modulus 10

G' ABS unannealed G' ABS annealed

8

tan δ ABS unannealed tan δ ABS annealed 10

10

0.1

7

0.01

6

Tß -150

-100

-50

0

50

100

150

Loss tan δ

10

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

11

10

1

3 .5

Pea k(1 17 .9 8,1.65 43 )

3.0

10

10

0

(-CH 2-C-(CH 3)-(COOCH 3)-)n )

)

10

2.5

2]

m 9 /c 10 ( n y " G d [

2

Pe ak (1 7 .9 2,0 .0 7 41 3)

-1

10

[ ]

ta n _ d e lt a

2.0

(

]

1.5

m 108 /c n ( y ' G [d

)

Pea k(1 04 .1 ,0 .9 66 )

-2

1.0

10

7

10

ta n_ de lta = 0 .01 4 05 [ ] T emp = -92 .0 02 [°C]

10

0.5

6

-15 0 .0

10 -100.0

-50.0

0.0

50.0

T e mp [°C]

Temperature T [°C] 175

G', G"

t

.

Temperature

Temperature

Temperature ramp

Strain

Torque

100.0

150.0

20 0 .0

-3

0 .0

D e lt [m a L m ( ]

)

• 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

176

44

TTS to Extend the Frequency Range

Thermoset Polymer - Temperature Ramp

Temperature range: 180 to 230 deg C

10

6

Moduli G', G'' [Pa]

10

G' G'' η*

approx. gel point 5

10

10

10

5

4

4

10

Minimum viscosity

3

10

10

80

100

120

140

Complex viscosity η* [Pas]

Temperature ramp 5 C/min

AutoStrain increases the strain to keep the torque within the instrument range in order to accurately measure the viscosity minimum

10

5

10

4

10

3

10

2

10

0

10

5

10

4

TTS is an empirical relationship and works only when the material is “thermorheologically simple”

G' G ''

10

1

10

2

Frequency ω [rad./s] 10 3

10

2

10

-1

10

0

10

1

10

2

10

3

F re que ncy ω /a T [rad /s]

3

160

Extended freq. range

Temperature T [C] 177

Frequency Sweeps over a range of Temperatures

G'

G'; G'' [Pa]

10

6

G' [Pa]

Cure cycle of an epoxy compund Gel point and minimum viscosity 7

178

TTS, Briefly

TTS, Briefly Oscillation Example

Higher frequencies experimentally inaccessible

G’

G’

Oscillation Example

200

200

frequency

frequency

45

TTS, Briefly

Oscillation Example

140

140

160

160

G’

G’

Oscillation Example

TTS, Briefly

180

200

180

200

frequency

frequency

TTS, Briefly Oscillation Example

TTS, Briefly Oscillation Example

G’

140 160

G’

140 160

180

200

180

200

frequency

frequency

46

TTS, Briefly Oscillation Example

TTS, Briefly Oscillation Example

140

140 160

G’

G’

160

180

200

180

200

frequency

frequency

TTS, Briefly Oscillation Example

TTS, Briefly Oscillation Example

140

140 160

G’

G’

160

180

200

180

200

frequency

frequency

47

TTS, Briefly Oscillation Example

TTS, Briefly Oscillation Example

140

140 160

G’

G’

160

180

200

180

200

frequency

frequency

TTS, Briefly Oscillation Example

TTS, Briefly Oscillation Example

140

140 160

G’

G’

160

180

200

180

200

frequency

frequency

48

TTS, Briefly Oscillation Example

TTS, Briefly Oscillation Example

140

Master-curve at 200

G’

G’

160

180

aT=180

200

frequency

frequency

TTS, Briefly

TTS, Briefly Oscillation Example

140

140

160

160

aT=160

G’

G’

Oscillation Example

180

200

aT=140

180

200

frequency

frequency

49

TTS, Briefly

TTS, Briefly

Oscillation Example

Oscillation Example

aT

aT

Arrhenius or WLF

0.0

0.0

140

160

180

140

200

Temperature

160

180

200

Temperature

TTS, Briefly

Transient Relaxation

Oscillation Example Arrhenius or WLF

In a relaxation test, a step strain is applied to the material and the stress is recorded over time.

(temperature dependence of VE properties)

5

10

strain 4

3

10

strain G(t)

G(t)

Strain

aT

Strain

10

2

10

1

10

Time

0.0

140

160

180

0.01

0.1

1

10

100

Time

The measured torque and deformation are used to calculate the Relaxation modulus

200

Temperature 200

50

Stress Relaxation

Transient Creep

LDPE Melt Relaxation

LDPE Melt Relaxation

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.

2.0 1.8

0.8 0.6

o

T=140 C strain 10% strain 20% strain 50% strain 100% strain 200% strain 400%

0.1

increasing strain

0.4

Recoverable strain strain

1

0.01

Recoverable strain

1.0

Strainm

1.2

Stress

Modulus G(t) [KPa]

1.4

Modulus G(t) [KPa]

T=140 C strain 10% strain 20% strain 50% strain 100% strain 200% strain 400%

1.6

increasing strain

10

o

0.2 0.0 0

10

20

30

40

0.01

50

0.1

1

10

100

The recoil test is the most sensitive test to determine aq material’s elasticity

• Fast visco-elastic characterization of a polymer • Results less accurate for short and for long times 201

Time

Time

Time t [s]

Time t [s]

202

Time and Temperature

Creep on PDMS 35

PDMS at RT 30

Recoverable25strain

σo/η

Strain γ [ ]

20

2.0

Re coverab le Strain

Non-recoverable 15 strain 10

1.5

1.0

0.5

5

R eco ve rab le S train

0.0 50

0

60

70

80

90

10 0

110

120

Tim e [s]

-5 0

20

40

60

Time t [s]

80

100

120

• The best test approach to measure long relaxation (retardation) times • Recovery is the most sensitive parameter to measure elasticity

(E' or G') (E" or G")

(E' or G') (E" or G")

log Frequency

Temperature

log Time

log Time

203

51

Transient Stress growth

Stress Growth of the NIST Ref 2490

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.

Ref 2490 Transient T=25°C 50mm cone 0.04 ARES

100

rate 200 1/s

step-rate

Viscosity η(t) [Pa s]

Strain time

Viscosity

strain rate

strain in step-rate

10

Rate: LV start up 0.001s-1 0.003 s-1 0.01 s-1 3 s-1 0.03 s-1 0.1 s-1

1

Time

0.1

0.01

Select the step rate test to measure the transient viscosity or normal stress difference 205

0.1

1

Time t [s]

10

0.3 s-1 1 s-1 10 s-1 30 s-1 300 s-1 100 s-1 100

• 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

206

DMA / Rheology Applications

Applications of Dynamic Mechanical Analysis of Solids

Material

Property

Composites, Thermosets

Viscosity, Gelation, Rate of Cure, Effect of Fillers and Additives

Cured Laminates

Thermoplastics

Elastomers Coating, Adhesives

Glass Transition, Modulus Damping, impact resistance, Creep, Stress Relaxation, Fiber orientation, Thermal Stability Blends, Processing effects, stability of molded parts, chemical effects Curing Characteristics, effect of fillers, recovery after deformation Damping, correlations, rate of degree of cure, glass transition temperature, modulus

52

Polymer Structure

Polymer Structure • The mechanical properties of a polymer are a consequence of

• Chemical Composition of the Polymer

Chemical

• Dictates where changes in mechanical properties occur

• Physical Molecular Structure of the Polymer • Dictates how changes in mechanical properties will occur

Composition

• 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).

Where 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).

Mechanical

Physical Molecular Structure How Changes Occur

Strength (DMA)

Physical Structure: Effects of Crystallinity, Molecular Weight, and Crosslinking How Changes Occur

In

general, transitions are associated with different localized or medium-to long-range cooperative motions of molecular segments.

log Modulus

Increasing Crystallinity

Amorphous

Molecular Motions/Transitions/Relaxations

Crystalline

MOLECULAR MOTIONS ARE REFERRED TO AS RELAXATIONS.

THESE

Cross-linked

3 decade drop in modulus at Tg Increasing MW

Tm

Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 486.

Temperature

53

LDPE: Primary and Secondary Transitions

The Glass & Secondary Transitions

Sample: Polyethylene in Tension Size: 8.4740 x 5.7500 x 1.0000 mm

–Glass

Transition - Cooperative motion among a large number of chain segments, including those from neighboring polymer chains

10000







[  ] Storage Modulus (MPa)

–Local











  



























10 -150

File: A:\Petmd.001 Operator: RRU Run Date: 27-Jan-99 13:56

DMA

10000

10000













119.44°C





0.15



1000





 





100







-55.49°C



-50



0

 







-100















100

0.05



0

0.10



-10.55°C

β -Relaxation Originates in amorphous phase Related to glass transition

-50

0.15









-118.12°C

1000



50

100

10 150 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.





-100

0.05





10 -150









100





0.10

[ ] Loss Modulus (MPa)



1000

[ ] Tan Delta

[  ] Storage Modulus (MPa)







Temperature (°C)

Sample: PET Film in Machine Direction Size: 8.1880 x 5.5000 x 0.0200 mm Method: 3°C/min ramp Comment: 1Hz; 3°C/min from -140° to 150°C, 15 microns,





γ -Relaxation An amorphous phase relaxation A local-mode, simple, non-cooperative relaxation process

Primary and Secondary Transition in PET Film

0.20

 

100

0.25



1000



Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 487.

96.33°C



[ ] Loss Modulus (MPa)

–Secondary

10000 α -Relaxation, Tg Cooperative Motion of Amorphous Phase

[ ] Tan Delta

Transitions 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 chain Internal 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.)

File: F:...\DMADATA\Peten.tr1 Operator: RRU Run Date: 18-Jan-99 16:10

DMA

Comment: 15 microns, 120% Autostrain, -150°C to 100°C



50

Temperature (°C)

100

150

200

10 250

Universal V2.5D TA Instruments

Nielsen, Lawrence E., Mechanical Properties of Polymers and Composites, Marcel Dekker, Inc., New York, 1974, p. 19.

54

E' Onset, E" Peak, and tan δ Peak

PSA: Glass Transition Measurement

E'

Onset: Occurs at lowest temperature - Relates to mechanical Failure

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.

tan

δ 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.

Reference: Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 980.

Effect of Orientation on Tensile Modulus and Damping Machine Direction

Storage Modulus (GPa)

Fiber Reinforced Vinyl Ester Composite Secondary Transition Measurements

Transverse Direction DMA Multi-Frequency - Tension Film

Temperature (°C)

55

Effect of % Crystallinity on Glass Transition 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. CRYSTALLINE PET AMORPHOUS PET xx x x xx

x x x x x x x xx x

x x x x

1.0

Tan δ

Tan δ

x

0.1 x x x x x x x

“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”

10 x

x x

x x x xx x

5 xx

65%

x

40%

0.1

1.0

40

x x

5

x

20

x

x

x x

0.01

x

x

1.0

10

Effect of % Crystallinity on Modulus

1.0

0.5

25%

0.5 0% Crystallinity (100% Amorphous)

0.1 60 80 100 120 140 160 Temperature (°C)

0.01

20

40

0.1 60 80 100 120 140 160 Temperature (°C)

M. P.

The Main Points 1. “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.”

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

Redrawn with permission from Thompson and Woods, Trans. Faraday Soc., 52, 1383 (1956)

Molecular Structure - Effect of Molecular Weight Glassy Region

Transition Region

 Blending may produce a polymer whose modulustemperature 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.

Rubbery Plateau Region

MW has practically no effect on the modulus below Tg

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.

Temperature

Blending of Amorphous Polymers

Increasing MW

Tobolsky, A.V., Properties and Structure of Polymers, John Wiley & Sons, Inc., New York, 1967, p.81.

Below Mc

56

Mixture of Two Styrene-butadiene Copolymers

Impact Resistance

MODULUS PROPORTIONALITY FACTOR

Mixture of two copolymers very different in styrene content (16% and 50%). Numbers on curve show % of polymer with the higher styrene content.

100

Higher Styrene

100 60

Two steps in modulus are characteristic of immicible two-phase system

50

10

40 30

1 20 Low Styrene

0

01 -60

-40 -20 TEMPERATURE (°C)

0

20

Nielsen, Lawrence E., Mechanical Properties of Polymers and Composites, Marcel Dekker, Inc., New York, 1974, p. 212.

Polymer Blend - Aerospace Coating

Immicible Blend - PS/SB Blending may produce a polymer whose modulus-temperature curve shows two transition regions (Tobolsky, A.V., Properties and Structure of Polymers, John Wiley & Sons, Inc., New York, 1967, p.81).

10

10

10000

–––––– Polymer A

– – – Polymer Blend: A + B –––– · Polymer B

8

10

7

1.0

6

0.10













Polymer Blend A+B





1000

Storage Modulus (MPa)

10

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).

9

Logarithmic decrement

Shear modulus, G, (Nm )

10

•If the polymers blended are completely compatible, then the blend behaves like an

100 % Polymer A 

























100



100% Polymer B









10









10

5

-50

0

50

Temperature (°C)

100





0.01 150



1 -25

0

25

50

Temperature (°C)

75

100

125 Universal V2.5D TA Instruments

57

Polymer Blend - Aerospace Coating 1.5

–––––– Polymer A

– – – Polymer Blend: A + B –––– · Polymer B

46.46°C



100 % Polymer B

Polymer Blend A+B



1.0



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

76.19°C

Tan Delta





89.77°C



100% Polymer A





0.5















0.0































 











-0.5 -25

0

25

50

Temperature (°C)

75

100

125 Universal V2.5D TA Instruments

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

58

‘Low’ Mw mono dispersed sample 1.000E6

Resulting MWD: ‘Low’ Mw

1.000E6

1.200

1.000E5

1.000

1.000E5

115k

0.8000 10000

10000

w(M)

G' (Pa)

G'' (Pa)

1000

0.6000

1000

0.4000

100.0

100.0

0.2000

10.00 1.000E-3

0.01000

0.1000 1.000 ang. frequency (rad/sec)

10.00 100.0

10.00

0 4

‘High’ Mw mono dispersed sample 1.000E6

1.000E6

1.000E5

1.000E5

5 Log [Molar mass (g/Mol)]

6

Resulting MWD: ‘High’ Mw 0.6000

0.5000

1150k

10000

10000

G'' (Pa)

G' (Pa)

0.4000

0.3000

w(M) 0.2000 1000

1000

0.1000

100.0 1.000E-5

1.000E-4

1.000E-3 0.01000 ang. frequency (rad/sec)

0.1000

100.0 1.000

0 4

5

6

7

Log [Molar mass (g/Mol)]

59

Blend of ‘Low’ and ‘High’ Mw 1.000E6

1.000E6

1.000E5

1.000E5

Resultant MWD: ‘Low’ and ‘High’ Mw 0.3000

0.2500

115k 1150k Blend

0.2000

10000

10000

G' (Pa)

0.1500

w(M)

G'' (Pa)

1000

1000

0.1000

100.0

100.0

0.05000

10.00 1.000E-5

1.000E-4

1.000E-3

0.01000 0.1000 1.000 ang. frequency (rad/sec)

10.00

0

10.00 1000

100.0

4

5

6

7

Log [Molar mass (g/Mol)]

G’ Comparison

η* Comparison

1.000E9 Molecular weight (WLF) n0: 1.365E8 Pa.s Mw: 1.164E6 g/mol

1.000E6

1.000E8

1.000E5

115k 1150k 115k 1150k Blend

1.000E7 115k 1150k 115k 1150k Blend

|n*| (Pa.s)

Molecular weight (WLF) n0: 2.020E7 Pa.s Mw: 6.613E5 g/mol

G' (Pa)

10000

1.000E6

1.000E5

1000

Molecular weight (WLF) n0: 1.691E5 Pa.s Mw: 1.606E5 g/mol

10000 100.0

1000 1.000E-5 10.00 1.000E-5

1.000E-4

1.000E-3

0.01000 0.1000 ang. frequency (rad/sec)

1.000

10.00

100.0

1.000E-4

1.000E-3

0.01000 0.1000 ang. frequency (rad/sec)

1.000

10.00

100.0

1000

1000

60

Effect of Plasticizer

MWD Comparison 1.200 115k 1150k 115k 1150k 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

1.000

w(M)

0.8000 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

0.6000

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

0.4000

0.2000

0 4

5

6 Log [Molar mass (g/Mol)]

Molecular Mobility Plasticization

7

 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

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.

61

Effect of Crosslinking

Thermosets

•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 J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, rise in the glass transition temperature. Cowie, Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991 p.262

 Temperature Ramp at constant frequency 

ISBN 0 7514 0134 X

Mc = MW between crosslinks



120



160

Viscosity dependence on temperature (i.e. minimum viscosity) Gel temperature Gel time

 Time sweep at constant temperature and frequency

300

 

Viscosity change with time Gel time

1500

 Or combination profile to mimic process

9000 30,000

Temperature

Sheet Molding Compound Cure in Shear Sandwich

Cure of a "5 minute" Epoxy

Comment: 1 Hz, 20 microns 100

100

Frequency = 1Hz Amplitude = 20 microns

TA Instruments 1000000

140

10

5 mins.

80 0.1

60 0.01

10000

G"

1000

1000

Gel Point - G' = G" T = 330 s

100.0

100.0

0.01

10.00

40

0.001

100000

10000 G' (Pa)

0.1

1 100

[ – – – – ] Loss Modulus (MPa)

[ ––––– · ] Temperature (°C)

1

100000

G'' (Pa)

Storage Modulus (MPa)

19.51MPa

120

1000000

G'

10

0

10

20

30

40

Time (min)

50

60

70

0.001

Universal V2.6D TA Instruments

10.00

1.000 0

200.0

400.0

600.0 time (s)

800.0

1000

1.000 1200

62

Automotive Industry Structural Adhesive Isothermal Cure at 25°C

"Baking" Cookie Dough TA Instruments

1.000E7

1.000E7

175.0

Cross-over points: 1 global time: 10970 s G': 1.474E6 Pa

Temp

125.0

100.0

100.0

75.0

1.000E6

1.000E6

Time = >3hrs

n*

1.000E5

1.000E5

10000

25.0 0

1000

2000 3000 global time (s)

4000

5000

1000 0

200.0

175.0

1.000E7

6000

8000

10000

•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’ Isothermal step run in controlled strain mode to ensure data taken within displacement resolution 0.01% Strain used in test shown.

150.0

4000

1000 12000

Electronics Industry: Powder Resin Ramp and Hold Cure

1.000E8

1.000E7

2000

global time (s)

Electronics Industry: Powder Resin Ramp and Hold Cure 1.000E8

10000

COOKIE.04O-temp sweep COOKIE.05O-temp sweep COOKIE.06O-temp sweep COOKIE.07O-temp sweep

50.0

10.00

G'' (Pa)

n* (Pa.s)

1000

temperature (Deg C)

150.0

G' (Pa)

10000

200.0

175.0

1.000E7

150.0

G' (Pa)

|n*| (Pa.s)

100.0

G”

1.000E5

75.0

Gel Point global time: 787.3 s G': 1.963E5 Pa

1.000E5

50.0

10000 25.0 -250.0

G'' (Pa)

100.0

125.0 1.000E6

250.0

75.0

1.000E5

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

Temp

0

temperature (Deg C)

125.0 1.000E6

temperature (Deg C)

1.000E6

500.0

750.0 global time (s)

1000

1250

1500

10000 1750

50.0 Minimum Viscosity global time: 702.0 s |n*|: 15420 Pa.s

10000 0

250.0

500.0

750.0

1000

1250

1500

25.0 1750

global time (s)

63

Temperature Sweep - Rheometer - ABS 2.500

S a m p le : P o lyca rb o n a te S ize : 1 7 .5 0 0 0 x 1 1 .8 5 0 0 x 1 .6 2 0 0 m m M e th o d : ra m p 3 °C /m in C o m m e n t: A m p litu d e 3 0 µ m

1.000E10

117.6 °C 2.250

1.000E9

2500

2.000

2000

1.000E7

1 .5

1500

300

Tan Delta

1.000

Storage Modulus (MPa)

tan(delta)

G' (Pa)

1.000E8

G'' (Pa)

1.000E7

400 1 45.98°C

1.500

1.250

500

1.000E9

1.750

1.000E8

File : C :\T A \D a ta \D M A \D m a -p c.0 0 1 O p e ra to r: A p p s . L a b Ru n D a te : 0 2 -J a n -1 9 9 7 1 7 :0 3 In stru m e n t: 2 9 8 0 DM A V 1 .0 F

DMA

1 .0

1000

200

Loss Modulus (MPa)

1.000E10

Temperature Sweep-DMA-Polycarbonate

ABS -150degC 1Hz AR2000-0001o

ABS 0.025 % strain, 1Hz

0.7500

0 .5 1.000E6

0.5000

500

1.000E6

100

0.2500

0

0 20

1.000E5

0 0

50.0

100.0 temperature (°C)

150.0

200.0

60

Sample: PET Film in Machine Direction Size: 8.1880 x 5.5000 x 0.0200 mm Method: 3°C/min ramp Comment: 1Hz; 3°C/min from -140° to 150°C, 15 microns,

10000









119.44°C



1000



–T g



0.15



–β–Transition

1000

[ ] Tan Delta





 





100







-55.49°C





-100

-50

0













50













–Good



10

–DMA 2980 –Film Clamp –Temp Ramp@ 1 Hz



–Poor



  

0.1

150





200

10 250



–––––– Poor Performance

–––––– Good Performance –––––– Excellent Performance



100

180

–Excellent









Temperature (°C)

160

–85°C: Thermoforming Temperature



100

1



1 40

U niv ers a l V4 .1 D TA In stru m en ts

0.05





10 -150









100





0.10

[ ] Loss Modulus (MPa)



1000

Storage Modulus (MPa)



120

Temperature Ramp on Thermoforming Packaging Films

10000



100

T em perature (°C )

File: A:\Petmd.001 Operator: RRU Run Date: 27-Jan-99 13:56

DMA

10000



80

250.0

Primary / Secondary Transitions in PET Film

[  ] Storage Modulus (MPa)

40

1.000E5

-50.0

25

35

45

55

65

Temperature (°C)

75

85

95 Universal V3.4C TA Instruments

Universal V2.5D TA Instruments

64

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

How to develop a testing strategy

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

Testing strategy: Development steps

Considerations: • 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

• 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

65

Testing strategy: Development steps (cont’d)

Limitations • 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

Typical example: Polymers

Rubber compund with different types of Carbon Black 10

5

G' Eta

o

Temperature:40 C Test frequency: 1Hz

-5

G' [Pa]; η* [Pas]

• 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

Storage Modulus G'x10 [Pa]

• 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

Linear viscoelastic range 10

10

4

1

10

Bad dispersion Medium dispersion Godd dispersion

3

10

-1

10

0

10

STRAIN %

1

2

10

0.1

1

Strain γ [%]

• Determine the critical strain γc • Note: sometimes not possible, because no strain independent plateau can be found (filled materials, blends)

66

Polymers: Strain sweep cont’d…

Polymers: Frequency sweep

Stress t [Pa]

10

6

10

5

10

4

10

3

1E-6

10

-1

0

10

10

1

2

10

10

3

10

4

5

10

Frequency sweep at 0.15 strain units

5

10

G' vs. stress 0.1 Hz 0.3 Hz 1 Hz 3 Hz 10 Hz

100000

G' G''

4

10

increasing frequency

3

10

G' vs. strain 0.1 Hz 0.3 Hz 1 Hz 3 Hz 10 Hz

G' [Pa]

G' [Pa]

-2

7

G', G'' [Pa]

10

10

10000

2

10

1000

1

1E-5

1E-4

1E-3

0.01

0.1

10 10

1

Strain γ

0.1

1

10

100

• ...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

Frequency ω [rad/s]

• 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 266

10

3

10

2

10

0

10

1

Frequency ω [rad/s]

2

10

Upper frequency is limited by the instrument, the low frequency is typically 0.1 rad/s, a practical limit is 0.01 rad/s

• …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 ( master curve • If t-TS not possible, make a 3D plot to extract significant information • Below Tg => solids testing torsion measurements, DMA

5

10

150 160 170 180 190 200

10

Frequency w/aT [rad/s]

frequency w [rad./s]

[rad/

s]

10

Complex fluids: Pre-testing

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: results of the pre-testing • The pre-test provides the following information:

Ketchup pre-test with manual strain switching 700

G' [Pa] G'' [Pa]

600

G', G'' [Pa]

500

400

300

200

100 50

100

150

200

250

300

350

400

time t [s]

• 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.

• 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)

68

Complex fluid: time sweep after pre-shear

Complex fluids: strain sweep

• 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

• 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

G' G' G''G''

G', G'' [Pa]

10

τy=G'*γc 1

critical strain γ c 0.1 0.1

1

10

Strain γ [%]

100

1000

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

Structure recovery after preshear

Goo

τ is a characteristic restructuring time

τ 10 0

100

300

400

500

Complex fluids: Stability- Shelf live

• How to continue testing, depends on the testing objective

Frequency sweep of a cosmetic cream

100

Modulus G', G'' [Pa]

Product stability => frequency sweep Classical yield stress measurement => stress ramp Flow curve required => rate or stress sweep Temperature stability => steady or dynamic Temperature ramp

200

Time t [s]

Complex fluids: What next?

• • • •

t G ' (t ) = (G∞' − G0' )(1 − exp  ) τ 

G' G' G'' G''

Go

G', G'' [Pa]

Strain sweep of a cosmetic cream

10

G' G' G'' G'' η* ETA

1

0.1

1

10

Frequency ω [rad/s]

100

• tan δ must be between 1 - 1.5 for best stability • tan δ 1.5: purely viscous behaviour, no interparticle forces prevent coagulation

69

Complex fluids: Yield

Complex fluids: Flow curve Flow cuve of an ink paste

Yield stress of a cosmetic lotion 3.5 3.0 2.5

Strain 2.0 10 1.5 1.0 1 0.5

Strain (x10-6)

Viscosity η [Pas]

100

The maximum in viscosity is more representative and reproducible then the extrapolation of the strain

0.0 0

50

100

150

10

10

9

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10

1

10

0

Stress Viscosity

slope -1

10

1

10

0

10

-1

10

-2

0.009 Pa

200

Stress [Pa]

Rate [1/s]

Stress τ [mPa]

Yield stess (at maximum) = 5.4 Pa

1000

10

Viscosity η [mPas]

4.0

h [Pas]

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.

Any Questions ????

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

Thanks for Attending

280

70