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
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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)
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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
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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
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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