RHEOLOGY AND DYNAMIC MECHANICAL ANALYSIS – What They Are and Why They’re Important
Presented for University of Wisconsin - Madison
by Gregory W Kamykowski PhD TA Instruments May 21, 2019
TAINSTRUMENTS.COM Rheology: An Introduction
Rheology: The study of the flow and deformation of matter. Rheological behavior affects every aspect of our lives. Dynamic Mechanical Analysis is a subset of Rheology
TAINSTRUMENTS.COM Rheology: The study of the flow and deformation of matter
Flow: Fluid Behavior; Viscous Nature F F = F(v); F ≠ F(x)
Deformation: Solid Behavior F Elastic Nature
F = F(x); F ≠ F(v)
0 1 2 3 x
Viscoelastic Materials: Force F depends on both Deformation and Rate of Deformation and F vice versa.
TAINSTRUMENTS.COM 1. ROTATIONAL RHEOLOGY 2. DYNAMIC MECHANICAL ANALYSIS (LINEAR TESTING)
TAINSTRUMENTS.COM Rheological Testing – Rotational - Unidirectional
2 Basic Rheological Methods 10 1 10 0
1. Apply Force (Torque)and 10 -1
measure Deformation and/or 10 -2 (rad/s) Deformation Rate (Angular 10 -3
Displacement, Angular Velocity) - 10 -4 Shear Rate Shear Controlled Force, Controlled 10 3 10 4 10 5 Angular Velocity, Velocity, Angular Stress Torque, (µN.m)Shear Stress
2. Control Deformation and/or 10 5 Angular Displacement, Deformation Rate and measure 10 4
10 3
Force needed (Controlled Strain (Pa) ) Displacement or Rotation, 10 2 Controlled Strain or Shear Rate) ( 10 1 Torque, Stress Torque, 10 -1 10 0 10 1 10 2 10 3
s (s)
TAINSTRUMENTS.COM Steady Simple Shear Flow
Top Plate Velocity = V0; Area = A; Force = F
H y Bottom Plate Velocity = 0 x
vx = (y/H)*V0
. -1 γ = dvx/dy = V0/H Shear Rate, sec σ = F/A Shear Stress, Pascals . η = σ/γ Viscosity, Pa-sec These are the fundamental flow parameters. Shear rate is always a change in velocity with respect to distance. TAINSTRUMENTS.COM Representative Flow Curve
1.E+05 Newtonian Pseudoplastic Region Behavior 1.E+04 0 < n < 1 (Newtonian)
1.E+03 η η Transition Power Law = 0 Region Region
1.E+02
Viscosity (Pa-sec) 1.E+01 . η = m*γ (n-1)
1.E+00 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 η ∝ 3.4 0 MW Shear Rate (sec-1)
TAINSTRUMENTS.COM Simple Shear Deformation
Top Plate Displacement = X0; Area = A; Force = F
H y Bottom Plate x Displacement = 0
x = (y/H)*X0
γ = dxx/dy = X0/H Shear Strain, unitless σ = F/A Shear Stress, Pascals G = σ/γ Modulus, Pa These are the fundamental deformation parameters. Shear strain is always a change in displacement with respect to distance.
TAINSTRUMENTS.COM Stress Relaxation
Stress Relaxation of Soy Flour, Overlay
109
• Instantaneous Strain • Note the decrease in the modulus as a
) function of time.
108 G(t) ( [Pa] F
G(t) T=20°C T=30°C T=40°C T=50°C 107 1 2 100 10 10 103 time [s]
TAINSTRUMENTS.COM Creep Testing
Stress is held constant. Strain is the measured variable.
3x10 -3
HDPE
2x10 -3 Viscoelastic (1/Pa)
1x10 -3 Fluid Compliance Solid
0x10 0
0 5 10 15 20
Step time (min)
TAINSTRUMENTS.COM Geometry Options
Concentric Cone and Parallel Torsion Cylinders Plate Plate Rectangular
Very Low Very Low Very Low Solids to Medium to High Viscosity Viscosity Viscosity to Soft Solids Water to Steel
TAINSTRUMENTS.COM Examples for Common Configurations
Geometry Examples Coatings Beverages Concentric Cylinder Slurries (vane rotor option) Starch pasting Low viscosity fluids Viscosity standards Cone and Plate Sparse materials Polymer melts in steady shear Widest range of materials Adhesives Polymer melts Parallel Plate Hydrogels Asphalt Curing of thermosetting materials Foods Cosmetics Thermoplastic solids Torsion Rectangular Thermoset solids
TAINSTRUMENTS.COM Rheology – Speak
Machine Parameter Rheological Parameter Angular Velocity (rad/sec) Shear Rate (1/sec) Angular Displacement (rad) Shear Strain ( - ) Torque (µN-m) Shear Stress (N/m2, Pa)
TAINSTRUMENTS.COM Converting Machine to Rheological Parameters in Rotational Rheometry
Machine Parameters M x Kσ σ M: Torque = =η Ω : Angular Velocity Ω γ• θ : Angular Displacement xKγ Conversion Factors Kσ : Stress Conversion Factor Kγ : Strain (Rate) Conversion Factor σ Rheological Parameters MxKσ σ : Shear Stress (Pa) = = γ• : Shear Rate (sec-1) G η : Viscosity (Pa-sec) γ : Shear Strain θ xKγ γ G : Shear Modulus (Pa)
The conversion factors, Kσ and Kγ, will depend on the following: Geometry of the system – concentric cylinder, cone and plate, parallel plate, and torsion rectangular Dimensions – gap, cone angle, diameter, thickness, etc.
TAINSTRUMENTS.COM Shear Rate and Shear Stress Calculations
Geometry Couette Cone & Plate Parallel Plates Conversion Factor
Kγ Ravg/(Ro-Ri) 1/β R/h
2 3 3 Kσ 1/(2*πRi L) 3/(2πR ) 2/(πR )
TAINSTRUMENTS.COM Cone & Plate and Parallel Plate Geometric Considerations
Standard DHR Peltier 20mm 40mm 50mm plate geometry diameters
Shear Stress Shear Stress At given torque, Increase in diameter → Decrease in shear stress
Shear Rate At given angular velocity Increase in cone angle → Decrease in shear rate Increase in gap (parallel plate) → Decrease in shear rate
So, for low viscosity fluids, use the largest diameter cone or plate. For high viscosity fluids, use the smallest diameter cone or plate
TAINSTRUMENTS.COM Rheological Methods – Unidirectional Testing
. Flow . Stress/Rate Ramp . Stress/Rate Sweep Sweep . Time sweep/Peak Hold . Temperature Ramp . Creep (constant stress) Ramp
. Stress Relaxation (constant Stress, Shear Rate strain) Time . Axial Testing
TAINSTRUMENTS.COM Thixotropy: Up & Down Flow Curves
Toothpaste loop 600
400 (Pa)
thixotropy: 600.997 Pa/s
Stress 200
The area between the curves is an indication of the thixotropic nature of the material.
0
0 2 4 6 8 10
Shear rate (1/s)
TAINSTRUMENTS.COM Flow Stress Ramp on a Yielding Material
500
464 Pa-sec 400
300 319 Pa-sec (Pa)
Stress 200
EmulsionSample A (3) A 197 Pa EmulsionSample B (3) B
100 The yield stress was obtained just by visual means. A has a higher yield stress than B
0 0.0 0.2 0.4 0.6 0.8 1.0 1.2
Shear rate (1/s)
TAINSTRUMENTS.COM Steady State Flow at 25 C - Coatings
10 3
10 2
10 1 (Pa.s) G
10 0
These are rate sweeps. Equilibration occurs at each point. Concentric Cylinder geometry 10 -1
10 -2 10 -1 10 0 10 1 10 2 10 3
S (1/s)
TAINSTRUMENTS.COM Polymer Melt Flow Curve
1.E+06 Williamson Model . c η = η0/(1+(σγ) ) 1.E+05 Cone and Plate 1.E+04 Viscosity (Pa-sec) 1.E+03 0.01 0.1 1 10 η 3.4 0 = KMw Shear Rate (1/sec) Steady testing with cone and plate and Mw = 400,000 Mw = 250,000 Mw = 160,000 parallel plate geometries is The shear rate and shear stress are constant throughout the gap with the often limited to cone-and-plate geometry. Parallel plate data can be corrected with the Rabinowitsch correction. low shear rates.
TAINSTRUMENTS.COM Normal Force Measurements with Cone & Plate
Normal Stress Difference: • In steady flow, polymeric materials can exert a force that tries to separate the cone and the plate. • A parameter to measure this is the Normal Stress Difference, N1, which equals
σxx- σyy from the Stress Tensor. • N1 = 2F/(πR2), where F is the measured force. 2 • Ψ1 = N1/ This is the primary normal stress coefficient.
TAINSTRUMENTS.COM TAINSTRUMENTS.COM Creep Testing on US and UK Paints
Creep and recovery can be done on both DHR and ARES rheometers
Creep is a unidirectional way of getting viscoelasticity. It is often followed by creep recovery. Creep answers the question of how much deformation to expect when a material is subjected to a constant stress, such as gravity It is usually easier on a DHR, but the ARES sometimes works better when there are instances of creep ringing.
TAINSTRUMENTS.COM Stress Relaxation
10 6
10 5 PDMS
10 4
10 3 (Pa)
10 2
10 1 Stress relaxation is another unidirectional way of Modulus getting viscoelastic properties. 10 0 This works better on the ARES than on the DHR.
10 -1
10 -4 10 -3 10 -2 10 -1 10 0 10 1
Step time (min)
TAINSTRUMENTS.COM Flow Temperature Ramp – Printing Inks
1,000
Room Temperature
100
10 Viscosity (Pa-sec) Viscosity
Printing Press Temperature
1 20 25 30 35 40 45 50 Temperatue (C)
TAINSTRUMENTS.COM Dynamic Testing
STRAIN
ELASTIC RESPONSE 90o VISCOUS RESPONSE Response, Strain Response, VISCOELASTIC RESPONSE δo
Polymers are viscoelastic materials. Time Both components – viscosity and elasticity – are important.
TAINSTRUMENTS.COM Dynamic Rheological Parameters
Parameter Shear Elongation Units
Strain γ = γ0 sin(ωt) ε = ε0 sin(ωt) ---
Stress σ = σ0sin(ωt + δ) τ = τ0sin(ωt + δ) Pa
Storage Modulus G’ = (σ /γ )cosδ E’ = (τ /ε )cosδ Pa (Elasticity) 0 0 0 0
Loss Modulus G” = (σ /γ )sinδ E” = (τ /ε )sinδ Pa (Viscous Nature) 0 0 0 0
Tan δ G”/G’ E”/E’ ---
Complex Modulus G* = (G’2+G”2)0.5 E* = (E’2+E”2)0.5 Pa
Complex Viscosity η* = G*/ω ηE* = E*/ω Pa-sec
. . Cox-Merz Rule for Linear Polymers: η*(ω) = η(γ) @ γ = ω
TAINSTRUMENTS.COM Dynamic Testing
•Dynamic Stress or Strain Sweep •Dynamic Time Sweep •Dynamic Frequency Sweep •Dynamic Temperature Ramp •Dynamic Temperature Sweep
TAINSTRUMENTS.COM Linear Viscoelasticity
10 4 Linear Region: • Osc Stress is linear with Strain. • G’, G” are constant. This is typically the first test done on unknown materials.
Non-Linear Region G’ = f(γ) Stress v. Strain
End of LVR or
(Pa) Critical Strain γc
10 3 0.1 1 10 100
It is preferable to perform testing in the linear region because you are measuring R (%) intrinsic properties of the material, not material that has been altered. TAINSTRUMENTS.COM TAINSTRUMENTS.COM Cure of a "5 minute" Epoxy
TA Instruments
1000000 This is an isothermal 1000000 time sweep. G' 5 mins. 100000 100000
10000 G" 10000 G'' (Pa)
1000 1000 G' (Pa) Gel Point - G' = G" 100.0 T = 330 s 100.0
10.00 10.00
1.000 1.000 0 200.0 400.0 600.0 800.0 1000 1200 time (s)
TAINSTRUMENTS.COM Frequency Sweep on PDMS
High frequency – elasticity predominates. 10 5 Low frequency – viscosity predominates.
Most frequent test for 10 4 polymer melts: ASTM D4440 – Standard Test Method for Plastics: Dynamic Mechanical Properties: 10 3 Melt Rheology (Pa)
100 to 0.1 rad/sec
10 2 5 pts. per decade 0.1 1.0 10.0 100.0 3 minutes of equilibration Frequency sweep takes about (rad/s) 6.5 min.
Cox-Merz Rule for Linear Polymers: η*(ω) = η() @ = ω
TAINSTRUMENTS.COM ETC Application: TTS on Polymer Melt
Polystyrene Frequency Sweeps from 160°C to 220°C
1.000E6 1.000E6 Extended Frequency range with TTS Reference Temperature = 210°C
1.000E5 1.000E5
10000 10000 G” (Pa) G'' (Pa) G' (Pa) G' G’ (Pa) G’ 1000 1000
100.0 Experimental 100.0 Frequency range
10.00 10.00 0.01000 0.1000 1.000 10.00 100.0 1000 10000 1.000E5 angang.. frequency frequency (rad /s)(rad/s)
TAINSTRUMENTS.COM Shift Factors for TTS
PG 64-22 (3) - Copy
10 1
c1: 8.22555
c2: 132.585 K Tref: 63.9970 °C R²: 0.999997 10 0
Activation Energy: 136.026 kJ/mol aT (x variable) Tref: 63.9970 °C R²: 0.997433
10 -1
50 55 60 65 70 75 80
Temperature (°C)
TAINSTRUMENTS.COM Dynamic testing: Dependence on Mw and MWD
107 Molecular weight 130 000 Zero shear viscosity increases 106 230 000 320 000 with increasing MW 430 000 105 * [Pa s]
4 10 Zero Shear [Pa s]
o Viscosity 0 106 10
3 Viscosity 10 Slope 3.08 +/- 0.39 increasing MWD Zero Shear Viscosity
5 -1 10 10 2 100000 Molecilar weight M [Daltons] 10 w o
SBR polymer broad, -4 -3 -2 -1 0 1 2 3 4 5 -2 10 10 10 10 10 10 10 10 10 10*/ 10 narrow distribution Frequency a [rad/s] T *red 430 000 -3 10 *red 320 000 When shifting along an Viscosity *red 230 000 * 130 000 axis of -1, all the curves 10-4 red *red 310 000 can be superposed, unless *red 250 000 10-5 the width of the MWD is 101 102 103 104 105 106 107 108 109 1010 1011 1012 not the same. frequency aT o
TAINSTRUMENTS.COM MWD and Dynamic Moduli
Effect of MWD on the dynamic moduli • The storage and loss modulus of 106 a typical polymer melt cross over between 1 and 100 rad/s. • ωc ∝ 1/Mw . • G ∝ 1/MWD. 105 c
104 SBR polymer melt G' 310 000 broad Modulus G', G'' [Pa] 3 G" 310 000 broad 10 G' 320 000 narrow G" 320 000 narrow
10-3 10-2 10-1 100 101 102 103 104 Frequency aT [rad/s]
Higher crossover frequency = lower Mw Higher crossover Modulus = narrower MWD
TAINSTRUMENTS.COM Example of Cox-Merz Rule
10000
Linear Polyethylene Flow Data Linear Polyethylene Oscillation Data [Cox Merz] Pa.s ) 1000
viscosity ( viscosity Flow instability
100.0 1.000E-3 0.01000 0.1000 1.000 10.00 100.0 1000 shear rate (1/s)
TAINSTRUMENTS.COM Coatings Frequency Sweep
10 3
Note how 2o is leveling out. 6o is descending sharply.
10 2 (Pa)
10 1
10 0
0.1 1 10 100
(rad/s)
TAINSTRUMENTS.COM Dynamic Temperature Ramp - Torsion
10 10 10 2
The storage (Pa) 10 9 10 1 modulus curve indicates the temperature range over which the Tan(delta) 10 8 10 0 material can Loss modulus contribute mechanically.
Glass transition
10 7 10 -1 temperatures are observed by the (Pa) onset in the storage modulus 10 6 10 -2 curve and peaks in the loss modulus and tan delta curves.
Storage modulus 10 5 10 -3
-150 -100 -50 0 50 100 150 200 250
Temperature (°C)
TAINSTRUMENTS.COM THE RHEOMETERS
TAINSTRUMENTS.COM DHR Rotational Rheometer
DHR Single head or CMT Combined motor & transducer
Displacement Sensor
Measured Strain or Rotation Non-Contact Drag Cup Motor
Applied Torque Sample (Stress)
Controlled Stress Static Plate Single Head Static Plate CMT
TAINSTRUMENTS.COM DHR Accessories – Visual Display
You can see the updated list of accessories on our website, www.tainstrument.com.
TAINSTRUMENTS.COM DHR Accessories – Visual Display
For the current listing of accessories, go to https://www.tainstruments.com.
TAINSTRUMENTS.COM Open Boundary Rotational Rheometer - SMT
ARES G2
Measured Torque Transducer (Stress)
Sample
Applied Direct Drive Strain or Motor Rotation Controlled Strain SMT or DH SMT: Separate Motor & Transducer DH: Dual Head TAINSTRUMENTS.COM ARES-G2 Accessories
For the current listing of accessories, go to https://www.tainstruments.com.
TAINSTRUMENTS.COM 1. ROTATIONAL RHEOLOGY 2. DYNAMIC MECHANICAL ANALYSIS (LINEAR TESTING)
TAINSTRUMENTS.COM Tensile Deformation
Deformation Parameters Young’s L0 = Initial Length (m) Modulus L = Stretched Length (m) ε = Elongational Strain, (L/L0) – 1 (unitless) (Engineering Strain)
. Strain is the amount of deformation normalized for the type of deformation and the dimensions of the specimen.
Force Parameters Conversions: T = Tensile force (Newtons) Machine → Rheological w = Initial Width (m) 0 Displacement → Strain t0 = Initial Thickness (m) τ τ Force → Stress E = = Tensile Stress, T/(w0*t0) (Pa) ε . Stress is the amount of force normalized for the type of deformation and the dimensions of the specimen.
Elongational Properties E = τ/ε (Pa) Modulus D = ε/τ (1/Pa) Compliance
TAINSTRUMENTS.COM UNIDIRECTIONAL TYPES OF TESTS ON THE DMA
. TRANSIENT . Stress Relaxation . Deformation applied instantaneously ⇒ Force measured as a function of time F . Deformation (mm) converted to Strain (ε), Force (N) to Stress (τ) . Stress (τ)/Strain(ε) = Modulus (E) . Creep . Force applied instantaneously ⇒ Deformation measured as a function of time . Force to Stress (τ), Deformation converted to Strain (ε) F . Strain (ε)/Stress (τ) = Compliance (D)
. PRACTICAL . Strain Ramp . Strain increased linearly with time or, optionally, exponential with the RSA-G2 . Iso-Strain . Strain held constant as temperature is varied . Stress Ramp . Stress increased linearly or exponentially with time . Controlled Stress . Stress held constant as temperature is varied
TAINSTRUMENTS.COM Stress Relaxation: Material Response
Glassy Region Transition Region Rubbery Terminal Plateau Region Region
This would be the type of curve expected for an uncrosslinked polymer if given sufficient time.
TAINSTRUMENTS.COM Creep Testing
Creep τ > 0 Recovery τ = 0 (after steady state)
Recoverable Strain
Stress = τ The greater the Stress = 0 elasticity, the greater the recovery. t t 1 2 time
With uncross-linked systems, strain increases indefinitely. If you have reached steady state flow, you can calculate the viscosity and the recoverable compliance. With cross-linked systems, there is a limiting strain.
Reference: Mark, J., et.al., Physical Properties of Polymers ,American Chemical Society, 1984, p. 102. TAINSTRUMENTS.COM Polyethylene Stress Ramp (or Strain Ramp)
1x10 7
8x10 6
6x10 6 (Pa) A
4x10 6 Stress
2x10 6
0
0 20.0 40.0 60.0 80.0 100.0
Strain P (%)
TAINSTRUMENTS.COM Dynamic Testing
STRAIN
ELASTIC RESPONSE 90o VISCOUS RESPONSE Response, Strain Response, VISCOELASTIC RESPONSE δo
Polymers are viscoelastic materials. Time Both components – viscosity and elasticity – are important.
TAINSTRUMENTS.COM Dynamic Rheological Parameters
Parameter Shear Elongation Units
Strain γ = γ0 sin(ωt) ε = ε0 sin(ωt) ---
Stress σ = σ0sin(ωt + δ) τ = τ0sin(ωt + δ) Pa
Storage Modulus G’ = (σ /γ )cosδ E’ = (τ /ε )cosδ Pa (Elasticity) 0 0 0 0 Loss Modulus G” = (σ /γ )sinδ E” = (τ /ε )sinδ Pa (Viscous Nature) 0 0 0 0
Tan δ G”/G’ E”/E’ ---
Complex Modulus G* = (G’2+G”2)0.5 E* = (E’2+E”2)0.5 Pa
Complex Viscosity η* = G*/ω ηE* = E*/ω Pa-sec
We will be mainly concerned with the Elongation column in this table.
TAINSTRUMENTS.COM Dynamic Oscillatory Testing Methods
• Frequency Sweep • Strain Sweep • Stress Sweep • Temperature Sweep • Temperature Ramp • Time Sweep • Temperature Sweep (Multifrequency) • Fatigue Test
Most common sequence • Strain sweep at 1 Hz to find the “sweet spot” for testing and the Linear Viscoelastic Region (LVR) • Temperature ramp at 1 Hz and 3 C/min using amplitude from strain sweep testing.
TAINSTRUMENTS.COM Dynamic Strain Sweep
PC Ambient Strain Sweep SC
10 10 0.8
0.6 Oscillation force
10 9 2.352e9 Pa (Pa) (Pa)
0.4 (N)
10 8 Loss modulus
Storage modulus 0.2
10 7 0.0 0 10 20 30 40 50 60
Oscillation displacement (um)
The material shows a nice Linear Viscoelastic Region (LVR). The oscillation force at 30 microns is about 0.4 N, which is definitely in the sweet spot for our DMA’s. We aim for a storage modulus of 2350 MPa at room temperature with polycarbonate.
TAINSTRUMENTS.COM Polycarbonate Testing on the DMA 850
DMA-PC
10 10 10 1
Mechanical E’ onset point Strength Tan Delta peak
10 9 2.322E9 Pa 10 0 E” peak
Single Cantilever Tan(delta)
(Pa) Rectangular Geometry (Pa) 3°C/min 10 8 30 µ amplitude 10 -1 1 Hz frequency
Loss modulus 10 7 10 -2 Storage modulus Dampening Testing polycarbonate is a good way Properties to check out the instrument and to instruct new people on the DMA850.
10 6 10 -3
20 40 60 80 100 120 140 160 180 200
Temperature (°C)
This is the main test performed on DMA instruments.
TAINSTRUMENTS.COM Polymer Structure-Property Characterization
• Glass transition • Secondary transitions • Crystallinity • Molecular weight/cross-linking • Phase separation (polymer blends, copolymers,...) • Composites • Aging (physical and chemical) • Curing of networks • Orientation • Effect of additives
Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 489.
TAINSTRUMENTS.COM The Glass Transition
. “The glass transition is associated with the onset of long- range cooperative segmental mobility in the amorphous phase, in either an amorphous or semi-crystalline polymer.”
. Any factor that affects segmental mobility will affect Tg, including… . the nature of the moving segment, . chain stiffness or steric hindrance . the free volume available for segmental motion
Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 508.
TAINSTRUMENTS.COM Glass Transition E' Onset, E" Peak, and Tan δ Peak
. Storage Modulus E' Onset: . Occurs at lowest temperature, relates to mechanical failure
. Loss Modulus E" Peak: .Occurs at middle temperature . Related to the physical property changes . Reflects molecular processes - the temperature at the onset of segmental motion
. Tan δ Peak: . Occurs at highest temperature; Used historically in literature . Measure of the "leatherlike" midpoint between the glassy and rubbery states . Height and shape change systematically with amorphous content.
Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 980.
TAINSTRUMENTS.COM The Glass & Secondary Transitions
–Glass Transition - Cooperative motion among a large number of chain segments, including those from neighboring polymer chains
–Secondary Transitions –Local Main-Chain Motion - intramolecular rotational motion of main chain segments four to six atoms in length Side group motion with some cooperative motion from the main 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 (e.g. plasticizer.)
Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 487.
TAINSTRUMENTS.COM THE DMA’S
TAINSTRUMENTS.COM DMA 850
DMA 850 Controlled Stress CMT – Combined Motor & Transducer
Sample
Displacement Sensor (Measures Strain)
Motor Applies Force (Stress)
TAINSTRUMENTS.COM RSA-G2
RSA G2 Controlled Strain SMT – Separate Motor & Transducer
Force Rebalance Transducer (FRT) (Measures Stress)
Sample
Actuator Applies deformation (Strain)
TAINSTRUMENTS.COM DMA Specifications
DMA 850 RSA G2 ARES G2 DHR DMA DMA (optional) Max Force 18N 35N 20N 50N
Min Force 0.0001N 0.0005N 0.001N 0.1N
Frequency 0.01 to 1250 1e-5 to 628 6.3e-5 to 100 6.3e-5 to 100 Range rad/s rad/s rad/s rad/s (1.6e-3 to 200 (1.6e-6 to 100 (1.0e-5 to 16 (1.0e-5 to 16 Hz) Hz) Hz) Hz) Dynamic +/- 0.5 to +/- 0.05 to +/- 1 to 50 +/- 1 to 100 Deformation 10,0000mm 1,500mm mm mm Range Control Control Stress Control Strain Control Control Stress Stress/Strain (CMT) (SMT) Strain (CMT) (CMT) Heating Rate 0.1oC to 0.1oC to 0.1oC to 0.1oC to 20oC/min 60oC/min 60oC/min 60oC/min
Cooling Rate 0.1oC to 0.1oC to 0.1oC to 0.1oC to 10oC/min 60oC/min 60oC/min 60oC/min
TAINSTRUMENTS.COM Clamps for DMA 850
S/D Cantilever Film/Fiber Tension 3-Point Bending Compression
Shear Sandwich Submersible Tension Submersible Bending Submersible Compression
The standard size S/D cantilever clamp is included with the purchase of the DMA 850. TAINSTRUMENTS.COM Clamps for RSA G2
Film/Fiber 3-Pt Bending Shear Sandwich
Compression Cantilever Contact Lens
TAINSTRUMENTS.COM DMA Clamping Guide
Sample Clamp Sample Dimensions
High modulus 3-point Bend metals or Dual Cantilever L/T> 10 if possible composites Single Cantilever Unreinforced thermoplastics or Single Cantilever L/T >10 if possible thermosets Brittle solid (ceramics) 3-point Bend L/T>10 if possible Dual Cantilever Elastomers Dual Cantilever L/T>20 for T
TAINSTRUMENTS.COM Primary and Secondary Transition in PET Film
Sample: PET Film in Machine Direction File: A:\Petmd.001 Size: 8.1880 x 5.5000 x 0.0200 mm DMA Operator: RRU Method: 3°C/min ramp Run Date: 27-Jan-99 13:56 Comment: 1Hz; 3°C/min from -140° to 150°C, 15 microns, 10000 10000
119.44°C 0.15 Β The peak is often 1000 associated with good 1000 impact properties 0.10
Delta [ ] Tan [ ] Loss (MPa) Modulus
100 100
[ ] Storage (MPa) Modulus -55.49°C 0.05
10 10 -150 -100 -50 0 50 100 150 200 250 Temperature (°C) Universal V2.5D TA Instruments
TAINSTRUMENTS.COM Molecular Structure - Effect of Molecular Weight
Glassy Region Rubbery Transition Plateau Region Region
MW has practically no effect on the modulus below Tg
High Low Med. MW MW MW
Temperature
TAINSTRUMENTS.COM Effect of Crosslinking
M = MW between c crosslinks
120
160
300
1500
9000
30,000
Temperature
TAINSTRUMENTS.COM Effect of Crystallinity
65%
40%
25%
0% Crystallinity (100% Amorphous) M.P .
Temperature
TAINSTRUMENTS.COM Effect of Filler on Modulus
60% mica Effects 40% mica • Concentration • Type of filler 60% asbestos 40% asbestos 20% mica
20% asbestos 20% calcium carbonate
polystyrene control
20 40 60 80 100 120 140 160 TEM P. (°C) Nielson, L. E., Wall, R. A., and Richmond, P. G., Soc. Plastics Eng. J., 11, 22 (1966)
TAINSTRUMENTS.COM Polymer Blend - Aerospace Coating
1.5 –––––– Polymer A 46.46°C – – – Polymer Blend: A + B –––– ∙ Polymer B 100% Polymer B 1.0 Polymer Blend 76.19°C A + B 89.77°C 0.5
Tan DeltaTan
0.0
100 % Polymer A
-0.5 -25 0 25 50 75 100 125 Temperature (°C) Universal V2.5D TA Instruments
TAINSTRUMENTS.COM Isothermal Cure of Tire Compound: Effect of Curing Temperature
TAINSTRUMENTS.COM Iso-Force Temp Ramp- Shrinkage of Oriented Film
Sample Length Decreases
Static Force is Held Constant
TAINSTRUMENTS.COM Humidity Option
This is the temperature/humidity chamber that was used to control the environment for this testing.
TAINSTRUMENTS.COM Q800: DMA-RH Operating Range
TAINSTRUMENTS.COM Analysis of Nylon 6: Isohume-Temperature Scans
TAINSTRUMENTS.COM Dynamic Humidity Ramp
Acrylic-based TiO2 - Rm Temp Hum Ramp to 90% 20 Hz
10 10
10 9 (Pa) (Pa)
10 8 Loss modulus Storage modulus
10 7
0 20 40 60 80 100
Relative Humidity (%)
TAINSTRUMENTS.COM NEW AND MORE SPECIALIZED TESTING
TAINSTRUMENTS.COM SER2 for DHR Rheometers
This is an interesting application of using the rotational rheometer to determine elongational viscosity
TAINSTRUMENTS.COM Extensional Viscosity Measurements
Fix drum connected to transducer
Rotating drum connected to the motor: . rotates around its axis . rotates around axis of fixed drum
TAINSTRUMENTS.COM Extensional Viscosity
• Extensional rheology is very sensitive to polymer chain entanglement. Therefore it is sensitive to LCB • The measured extensional viscosity is 3 times of steady shear viscosity
ηΕ = 3 x η0 • LCB polymer shows strain hardening effect
Linear Branched
TAINSTRUMENTS.COM TAINSTRUMENTS.COM ARES-G2 DMA Mode
TAINSTRUMENTS.COM Orthogonal Superposition – 2 Modes
Only on ARES-G2
TAINSTRUMENTS.COM 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
TAINSTRUMENTS.COM UV Cure Profile Changes with Intensity
TAINSTRUMENTS.COM DETA on DHR and ARES-G2
TAINSTRUMENTS.COM Test Geometries
•Wide variety of test geometries: .Standard parallel plate .Disposable parallel plate .Annular Ring .Surface Diffusion .Rectangular Torsion •Innovative geometries for RH: true humidity-dependent rheology, not dominated by diffusion •True Axial DMA: .Film Tension .Three-point Bending
TAINSTRUMENTS.COM Paint Drying at Different Humidity Levels
TAINSTRUMENTS.COM Interfacial Accessories
Double Wall Ring
DuNouy Ring
Bicone
TAINSTRUMENTS.COM Surface Concentration Effects on Interfacial Viscosity
TAINSTRUMENTS.COM SPAN65® Layer Spread on Water
Interfacial properties Span65 layer on water T=20o C ω =1rad/s Span 65 [molecul/nm2] s s 0.1 4.3 0.36 G" G' 1.8 0.0 1.08 0.01 Both dynamic and
steady flow tests can be performed with the interfacial
1E-3 geometry. This is an example of a
1E-4 dynamic strain sweep. subphase base line
1E-5 Storage Loss & Modulus [N/m]
1E-4 1E-3 0.01 0.1 1 Strain [ ]
TAINSTRUMENTS.COM TAINSTRUMENTS.COM DHR Peltier Tribo-rheometry Accessory
Ring on Plate Ball on 3 Plates Ball on 3 Balls 3 Balls on Plate
TAINSTRUMENTS.COM Tribology of Lubricated Systems
Boundary Mixed Hydrodynamic Lubrication Lubrication Lubrication
1 Friction, µ Coefficient of Coefficient
(ηoilΩ)/FL
• In lubricated systems, the ‘Stribeck curve’ captures influence of lubricant viscosity(ηoil), rotational velocity (Ω) and contact load (FL) on µ • At low loads, the two surfaces are separated by a thin fluid film (gap, d) with frictional effects arising from fluid drag (Hydrodynamic Lubrication) • At higher loads, the gap becomes smaller and causes friction to go up (Mixed Lubrication) • At extremely high loads, there is direct solid-solid contact between the surface asperities leading to very high friction (Boundary Lubrication)
TAINSTRUMENTS.COM Rheo-Raman Accessory
Rheo-Raman on a hand lotion
TAINSTRUMENTS.COM Mimic of Heat Deflection Test on the DMA
Mimic of Heat Deflection Test
0.20 10 3
0.15 Stress (%)
0.10 (kPa) Strain
0.05
0.00 10 2
10 20 30 40 50 60 70
Temperature (°C)
TAINSTRUMENTS.COM Thank You
The World Leader in Thermal Analysis, Rheology, and Microcalorimetry
I hope you have enjoyed this presentation on rheology and DMA.
TAINSTRUMENTS.COM