2013 TA Instruments New Castle DE
Ten Steps to Better Rheological Measurements
Ten Steps to a Better
Rheological Measurement
2005 Rheology training
seminar
1.
Understand why you are doing the measurement.
2.
Understand your instrument
3.
Know your sample
4.
Selecting the correct test fixture
5.
Loading the sample
6.
Oscillation testing guidelines
7.
Transient testing guidelines
8.
Steady shear testing guidelines
9.
Some instrument limitations
10. Presenting the data
Flow of a Rheological Experiment
 Identify the purpose of the experiment
 Design, program & run test
 Evaluate data and 0ptimize (if necessary)
 Results
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
2.
Flow of a Rheological Experiment
 Identify the purpose of the experiment
• 1. Understand why you are doing the measurement
 Design, program & run test
• 2. Understand your instrument
• 3. Know your sample
Points 3 through 8 are
• 4. Selecting correct test fixtures
sample specific
• 5. Oscillation testing guidelines
•Polymers
• 6. Transient testing guidelines
•Structured Fluids
• 7. Steady shear testing guidelines
•Solids
• 8. Loading the sample
 Evaluate data and 0ptimize if necessary
• 9. Instrument limitations
 Results
• 10. Presenting the data
Understand Why Your Doing the Measurement
• A successful rheological experiment requires thought and careful
planning.
• The first step in any rheological experiment is to identify the
purpose of your experiment.
• Ask youself:
• What is the goal of the testing?
• What do you want to know about your material?
• Do you know what kind of experiment I should do?
• More specific questions will depend on reason the reason
• for the experiment!
1
2013 TA Instruments New Castle DE
Understand Why Your Doing the Measurement
Rheological Approach
Use rheometer to characterize flow and viscoelastic
properties to:
The first step in any rheological experiment is
to identify the purpose of your experiment
1. Understand structure
• Requires understanding of how structure affects rheological
properties
The 3 main reasons for rheological testing are:
• Characterization of structure
MW, MWD, formulation, state of flocculation, etc.
• Predicting process performance
Extrusion, blow molding, pumping, leveling, etc.
• Understanding end-use performance
Strength, use temperature, dimensional stability, settling stability,
etc.
2. Predict processing performance
• Requires understanding of what rheological properties are
desired for processing
3. Predict product performance
• Requires understanding of desired performance
characteristics and how they relate to rheological properties
Influence of MW and MWD on Viscosity
Influence of MW on G‘ and G‘‘
The G‘ and G‘‘ curves are shifted to lower frequency
with increasing molecular weight.
10
6
10
5
10
4
10
3
10
2
SBR Mw [g/mol]
130 000
230 000
320 000
430 000
The high
frequency
behavior
(slope -1) is
independent of
the molecular
weight
Zero Shear
Viscosity
10
6
10
5
Slope 3.08 +/- 0.39
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
10
3
SBR polymer melt
G' 310 000 broad
G" 310 000 broad
G' 320 000 narrow
G" 320 000 narrow
-3
10
4
10
3
10
2
10
1
SBR M w [g/mol]
G' 130 000
G'' 130 000
G' 430 000
G'' 430 000
G' 230 000
G'' 230 000
-2
10
-1
10
0
10
1
10
2
10
10
Frequency aT [rad/s]
The G‘, G‘‘ cross-over
point is another
measure of the
broadness of the
distribution
3
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
Strain  [%]
Molecular Structure and Processibility
Bolw Molding Polyethylene
2.0x10
5
1.5x10
5
1.0x10
5
5.0x10
4
T = 180° C
Shear viscosity () [Pa s]
10
4
10
9
The maximum in G‘‘ is a
good indicator of the
broadness of the
distribution
narrow
4
Modulus G'' [Pa]
Modulus G', G'' [Pa]
5
5
10
5
Influence of MWD on G‘ and G‘‘
10
10
M olecilar weight M w [Dalto ns]
-4
Frequency  aT [rad/s]
6
6
100000
10
10
10
broad
4
4
10
10
N1() M-1
N1() M-2
() M-1 CP
() M-2 CP
() M-1 Capillary
() M-2 Capillary
3
10
0,1
SBR G'' 320 000
SBR G'' 310 000 (broad)
0.0
10
-3
-2
10
-1
10
10
0
1
10
10
Frequency aT [rad/s]
2
3
10
1
10
3
Normal stress difference N1() [Pa]
7
Modulus G', G'' [Pa]
10
Zero Shear Viscosityo [Pa s]
Viscosity * [Pa s]
The zero shear viscosity increases with increasing molecular weight.
TTS is applied to obtain the extended frequency range
Sample M2 has a
much
higher
elasticity
i.e normal
force
10
100
Shear rate  [1/s]
4
10
Sample M-2 produces significantly heavier bottles!!!
2
2013 TA Instruments New Castle DE
Tack and Peel of Adhesives
Tack and Peel performance of a PSA
HDPE pipe surface defects
o
T = 220 C
5
10
4
10
5
4
10
peel
3
10
Modulus G' [Pa]
10
4
10
G' rough surface
G' smooth surface
3
10
* rough surface
* smooth surface
tack
0.1
1
10
0.1
1
10
3
10
Complex viscosity * [Pa s]
good tack and peel
Bad tack and peel
Storage Modulus G' [Pa]
Bond strength
is obained
from peel
(fast) and
tack (slow)
tests and can
be related to
the
viscoelastic
properties at
different
frequencies
Surface Defects during Pipe Extrusion
Surface
roughness
correlates
with G‘ or
elasticity =>
broader
MWD or tiny
amounts of
a high MW
component
100
Frequency  [rad/s]
Frequency  [rad/s]
Sample 1 shows a rough surface after extrusion
Tack and Peel have to be balanced for an ideal adhesive
Deflocculation Curves for A16G Alumina
Rheological Characterization of Slips
69 wt%
81 wt %
[Reed, J.S. Introduction to the Principles of Ceramic Processing J. Wiley & Sons Inc 1988]
J.M. Keller, R. Ulbrich & R. Haber, American Ceramics Bulletin (76) 3 pp 87-91
Automotive Paint: Breakdown - Rebuild
Rheological Characterization of Slips
100.0
New Sample - Milled for shorter time
Old Sample - Milled for longer time
PD36
D52
D36
G' (Pa)
10.00
1.000
Preshear: 1000 1/s for 60 sec
Stress = 0.1 Pa
Frequency = 6.28 rad/s
0.1000
0
J.M. Keller, R. Ulbrich & R. Haber, American Ceramics Bulletin (76) 3 pp 87-91
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
1000
time (s)
3
2013 TA Instruments New Castle DE
Automotive Paint : Creep Recovery Test
80.0
Old
1000
40.0
30.0
1000
G’
G'' (Pa)
50.0
G' (Pa)
% strain
60.0
10000
10000
New Sample - Milled for shorter time
Old Sample - Milled for longer time
70.0
Mayonnaise and “Miracle Whip”
100.0
G”
100.0
Mayonnaise
Miracle Whip
20.0
New
0
0.0
global time (s)
600
Why do the measurement?
•
•
•
•
•
•
•
•
•
•
Predict Processability
Predict End-Use Performance
Glass Transition and secondary transitions
Damping behavior
Determine working temperature range, impact
behavior, residual strain trapped in moldings, etc..
Degree of curing, post curing
Ageing
Compatibility, Dispersion, …
Morphology characterization, Crystallinity,
Fingerprint of materials
10.00
10.00
0.1000
10.00
1.000
100.0
ang. frequency (rad/sec)
Polymer Materials Change with Temperature
Storage Modulus G’ (Pa)
10.0
Low MW
Increased Crystallinity
Cross-linked
Amorphous
Increasing MW
Temperature T (oC)
Alternative Approach
Use rheometer to simulate processing or end use
conditions to determine suitability for application.
1. Requires definition of processing or end use conditions
such as shear rate, strain, stress, and temperature, in
order to translate test to rheometer or DMA.
2. Must understand instrument and instrument limitations
in order to determine if rheometer can simulate
processing or end use conditions.
Defining Shear Rate Ranges
Situation
Shear Rate Range
Examples
Sedimentation of fine powders in liquids
10-6 to 10-3
Medicines, Paints, Salad dressing
Leveling due to surface tension
10-2 to 10-1
Paints, Printing inks
Draining off surfaces under gravity
10-1 to 101
Toilet bleaches, paints, coatings
Extruders
100 to 102
Polymers, foods
Chewing and Swallowing
101 to 102
Foods
Dip coating
101
Confectionery, paints
Mixing and stirring
101 to 103
Liquids manufacturing
Pipe Flow
100 to 103
Pumping liquids, blood flow
Brushing
103 to 104
Painting
Rubbing
104 to 105
Skin creams, lotions
High-speed coating
104 to 106
Paper manufacture
Spraying
105 to 106
Atomization, spray drying
Lubrication
103 to 107
Bearings, engines
to
102
4
2013 TA Instruments New Castle DE
Pot Life of an Hot Melt
Formulation of Bitumen
Pot life of two hot melt adhesives
0
5
10
10
dispersion
polymer
crosslinking
sulf
er
bitumen
good
bad
4
10
3
10
0
200
400
600
800 1000 1200 1400
Viscosity (t) [Pa s]
Complex viscosity * [Pa s]
Viscosity
stability at
procees
temperature is
critical for hot
melt
adhesives.
The viscosity
builds up due
to oxidative
crosslinking
10
sulfer
Incorporation of polymer
-1
0.0
8x10
time t [s]
Time t [s]
4
• monitor the
formulation
process
• determine
product
performance
Open time of this polyamide resin depends on moisture
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand your instrument.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
Ranges of Rheometers and DMA’s
1.
2.
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
Understand Your Instrument First!
Two types of rotational rheometers and DMA‘s
• AR-Series Rheometer and Q800/2980 DMA
• Single/combined motor transducer
• ARES Series Rheometers and RSA III Solids Analyzer
• Dual head/separate motor transducer
Rotational Rheometers Designs
ARES – Separate
motor & transducer
Measured
Torque
(Stress)
Transducer
AR Series –
Combined motor &
transducer Displacement
Non-Contact
Drag Cup
Motor
Both techniques, depending on the configuration, have
different specification, different features and different
performance for different applications
Sensor
Measured
Strain or
Rotation
Applied
Torque
(Stress)
Applied
Strain or
Rotation
Direct
Drive
Motor
Static Plate
5
2013 TA Instruments New Castle DE
DMA Designs
RSA III – Separate
motor & transducer
How Rheometers and DMA’s Work
Q800 – Combined
motor & transducer
Force Rebalance
Transducer (FRT)
Measures Force
Sample
Displacement
Sensor
(Measures Strain)
Sample
Actuator
(motor)
Applies
deformation
Motor
Applies
Force
(Stress)
Important Rheometer Specifications
•
•
•
•
•
•
Torque Range
Angular Resolution
Angular Velocity Range
Frequency Range
Normal Force
Temperature System and Range
AR or CMT Instrument Specifications
AR Technical Specifications
Torque range CS
Torque range CR
Displacement Resolution
Angular Velocity Range CS
Angular Velocity Range CR
Angular Frequency Range
Normal/Axial Force Range
AR 2000
0.1 µN.m - 200 mN.m
0.03 µN.m - 200mN.m
0.04 µrad
1 E-8 - 300 rad/s
1E-4 - 300 rad/s
7.5 E-7 - 628 rad/s
0.005 - 50 N
AR 1000
0.1 µN.m - 100mN.m
0.1 µN.m - 100mN.m
0.62 µrad
1 E-8 - 100 rad/s
1E-3 - 100 rad/s
6.3 E-4 - 628 rad/s
0.01 - 50 N
AR 550/QCRII
1 µN.m - 50mN.m
1 µN.m - 50mN.m
0.62 µrad
1 E-8 - 100 rad/s
1E-3 - 100 rad/s
6.3 E-4 - 250 rad/s
0.01 - 50 N
Rheology is the science of flow and deformation of matter
or
the study of stress– deformation relationships.
Fundamentally a rotational rheometer or DMA will control or
measure:
1. Force or Torque
2. Displacement or Angular Displacement
3. Linear or Angular Velocity
4. Normal Force
5. Temperature
ARES or SMT Instrument Specifications
ARES Technical Specfications
Motor
Torque Range
Strain Amplitude
Angular Velocity Range
Angular Frequency
Norma/Axial Force Range
ARES Technical Specfications
Motor
Torque Range
Strain Amplitude
Angular Velocity Range
Angular Frequency
Norma/Axial Force Range
ARES-LS2
High Performance LS
2 µN.m - 200 mN.m
5 µrad - 500 mrad
2 E-6 - 200 rad/s
1 E-5 - 500 rad/s
0.002 - 20 N
ARES-LS1
High Performance LS
0.2 µN.m - 100 mN.m
5 µrad - 500 mrad
2 E-6 - 200 rad/s
1 E-5 - 200 rad/s
0.002 - 20 N
ARES-RFS
Standard HR
0.2 µN.m - 100 mN.m
5 µrad - 500 mrad
1 E-3 - 100 rad/s
1 E-5 - 200 rad/s
0.01 - 20 N
ARES-RDA
Standard HR
20 µN.m - 200 mN.m
5 µrad - 500 mrad
1 E-3 - 100 rad/s
1 E-5 - 500 rad/s
Qualitative
ARES
Standard HR
2 µN.m - 200 mN.m
5 µrad - 500 mrad
1 E-3 - 100 rad/s
1 E-5 - 500 rad/s
0.01 - 20 N
RSA III and Q800 Instrument
Specifications
Maximum Force
Minimum Force
Force Resolution
Strain Resolution
Modulus Range
Modulus Precision
Tan δ Sensitivity
Tan δ Resolution
Frequency Range
Dynamic Sample Deformation Range
Temperature Range
Heating Rate
Cooling Rate
Isothermal Stability
Time/Temperature Superposition
35 N
18 N
0.001 N
0.0001 N
0.0001 N
0.00001 N
1 nanometer
1 nanometer
10E3 to 3x10E12 Pa 10E3 to 3x10E12 Pa
+/- 1%
+/- 1%
0.0001
0.0001
0.00001
0.00001
2xE-5 to 80 Hz
0.01 to 200 Hz
+/- 0.5 to 1,500 μm +/- 0.5 to 10,000 μm
-150 to 600ºC
-150 to 600ºC
0.1 to 60ºC/min
0.1 to 20ºC/min
0.1 to 60ºC/min
0.1 to 10ºC/min
+/- 0.1ºC
+/- 0.1ºC
Yes
Yes
6
2013 TA Instruments New Castle DE
Selecting the Correct Test Fixture
• The measured quantity (angular deformation and torque) are
transferred into a material quantity (stress, strain, viscosity, etc.)
Calculated parameters :
Measured parameters :
stress (Pa)
θ(t)
angular displaceme nt (rad)  (t )  K M
γ(t)  K γθ
strain ( )
dθ  Ω(t) angular ve locity (rad/s)
dt
γ(t)  K γ dθ
strain rate (1/s)
M(t)
torque (N m)
dt
K and K relate the measured
instrument data with the
desired material parameter
η(t)  τ(t) 
γo
viscosity (Pa s)
G(t)  τ(t)
modulus (Pa)
γo
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
Polymers
 Identify the purpose of the experiment
• 1. Understand why your doing the measurement
 Design, program & run test
• 2. Understand your instrument
• 3. Know your sample
• 4. Selecting correct test fixtures
• 5. Oscillation testing guidelines
• 6. Transient testing guidelines
• 7. Steady shear testing guidelines
• 8. Loading the sample
 Evaluate data and 0ptimize if necessary
• 9. Instrument limitations
 Results
• 10. Presenting the data
Know your sample
1.
2.
Molding Polymers Pellets
Molding temperature:
10 - 20°C > than test
temperature
- apply pressure
(8 – 12 000 lbs)
- keep at elevated
temperature long
enough to let the
sample relax
- cool down slowly
under pressure to
avoid orientations
The best approach is to
mold a sample plate
(100x100 or
50x50mm).
Punch out a sample
disk 8, 25 or
50mm
• Polymer samples come in different forms (powder,
flakes, pellets) and are sensitive to environmental
conditions.
• Careful sample preparation techniques are required
to prepare good test specimens for reproducible
testing.
• Molding a sample...
• Handling powders, flakes...
• Controling the environment...
Molding Powders and Flakes
• Before molding at high temperature, the sample has to
be compacted cold to reduce the volume.
• The compacted
samples are transferred
to the mold.
• Follow steps for
molding pellets
procedure
Note: sample may need to be stabilized or dryed to avoid
degradation
7
2013 TA Instruments New Castle DE
Preparing Semi Solid Samples
How to Control the Environment
• PP and Polyolefines in general tend to degrade fast –
need to be stabilized by adding antioxidents
• Moisture sensitive materials such as polyamides and
polyester require drying in vacuum or at temperatures
around 80°C.
• Cut rectangular sheets of
prepreg or adhesive
(30x30mm)
• Alternate direction of layer;
approx. 5 layer on top of
each other (remove release
paper from PSA)
• Compress the stag of sample
layers in a press (4 – 5000
lbs)
• Punch out 25 mm disks
• Materials such as PS or
PMMA absorb moisture
also. In the melt phase,
the gas separates in
bubbles and the sample
foams => pre - drying in
vacuum prior to testing
is necessary.
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
2.
Parallel Plate
• For filled and unfilled polymer systems. This geometry
is predominately used for oscillation measurements in
the linear-viscoelastic range.
R
H
Strain Constant: K =
Stress Constant: K =
2M
(R)3
20
40
60
mm
Shear
Stress
Caution: the shear rate varies with the radius!
Parallel Plates
Advantages:
• variable sample thickness
(recommended 0.5 to 2mm)
• shear rate range adjustable, changing
gap H or plate diameter R
• temperature ramps / sweeps can be
carried out without Gap-adjustment
• easy sample loading for high viscosity
samples (pre-mold disks or pellets)
• small sample volume
• viscosities: - low to high
• wall slippage problems can be
overcome by using serrated,
roughened plates
Disadvantages:
• shear rate not
constant (can be
corrected)
• instabilities in
shear field can
occur at high rates
(liquid shear-field
breaks up and
liquid is lost due to
centrifugal force)
Cone and Plate
• For unfilled polymer melt systems. Primarily to be
used in transient and steady test modes, outside of
the linear viscoelastic range.
Strain Constant: K =
Stress Constant: K =
1

3 *M
(R)3
20
40
60
mm
Shear
Stress
Note: the shear rate is constant over the radius.
8
2013 TA Instruments New Castle DE
Limitations of the Cone & Plate
Truncation Heights:
1 degree ~ 20 - 30 microns
2 degrees ~ 60 microns
4 degrees ~ 120 microns
Cone and Plate
Disadvantages
• highly sensitive to the
relative position (gap) of
cone and plate
• gap depends on temperature
• sample loading for high
viscosity samples is difficult
• not suitable for dispersions
with solid particles
• instabilities in shear field can
occur at high rates (liquid
shear-field breaks up and
liquid is lost due to
centrifugal force)
Gap must be > or = 10 [particle size]!!
Advantages
• homogeneous shear,
shear rate and stress
in the gap
• small sample volume
(ca. 1ml)
• viscosities: - low to
high
• cleaning easy
• ideal for normal force
measurements
Choosing the Geometry Size
Ten Steps to Better Rheological Measurements
Cone & Plate
Truncation Height = Gap
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
• Assess the approximate viscosity or consistency of
your sample.
• When a variety of cones and plates are available,
select appropriate diameter
• geometry
• Medium viscosity (polyolefines MI>5, polyester,..) 40 or 50 mm geometry
• High viscosity (polyolefines MI<5) – 20 or 25 mm
• Examine data in terms of absolute instrument
variables [torque/speed/displacement] and modify
geometry choice to move test range into the optimum
instrument range if necessary.
1.
2.
Loading a Molded Disk
• Environmental
system to test
temperature.
• Load disk onto plate
• Close oven.
• Bring upper plate to
gap position.
• Watch Normal force
• Open oven
• Trim sample.
• Close oven.
sample trimming
• Adjust gap
Loading Pellets
• Mount Guard ring and
shim. Load pellets.
• Close oven.
• Heat to temperature.
• Compress sample.
• Open oven.
sample trimming • Remove guard ring.
• Set gap. Watch
normal force
set to final gap
To 100 to 2000  • Trim sample.
• Set final gap
set to final gap
To 100 to 2000 
ARES
guard ring
AR
9
2013 TA Instruments New Castle DE
Correct filling
Loading Prepreg and Adhesives
• Mount disposable
plate.
• Insert 3-5 layer
prepreg or adhesive
sample (minimum
0.1mm) between
plates.
• Close oven.
• Heat to temperature.
• Set gap. Watch
normal force.
• Use normal force
control if required.
Under Filling
Over Filling
Correct Filling
set to final gap
to 100 to 2000 
55
Normal Force Gap Closing
Normal Force During Loading PDMS
30
7000
100microns/sec
50microns/sec
25
Sample is still
relaxing even
after the
measurement gap
is reached
normal force (N)
20
15
• Set trim gap 5% greater then final gap to insure proper
filling.
• When using 25 mm cones, pressed disks 0.5 mm thick
makes loading faster and reduces excess sample.
• Use force controlled gap setting to avoid overloading
the normal force transducers.
5000
4000
10
3000
5
2000
0
0
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
1000
90.00
time (s)
57
Hints for Loading the Sample
6000
gap (micro m)
• Most sensitive as the sample itself determines how
fast the gap is closed
• Gap Closure is halted when a normal force > the
registered maximum value, and the sample is allowed
to relax before closure continues. This avoids
overload of the transducer when loading high
viscosity melts
• The greater the maximum registered value the faster
the close
• Closure may take some time for highly viscous
polymers. Loading at higher temperature will speed
the process up
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
2.
• Make sure that torque and normal force have decayed
to zero before starting the test.
10
2013 TA Instruments New Castle DE
Step #1: Testing Material Stability
Time Sweep
Oscillation Testing Review
Stimulus (stress )
Response (strain )
0
6.3
phase angle, 
-1.5
Time t, Period T
Frequency, strain or stress amplitude
Phase angle and ratio of strain and stress amplitude
5
225
10
200
4
175
-2
Elastic Modulus:
Viscous Modulus:
Tan :
Complex Viscosity:
stored energy or elasticity
dissipated energy
damping
resistance to flow
0
•
•
•
•
4
6
8
10
12
14
16
18
Determines if
properties are
changing over
the time of
testing
• Degradation
• Molecular
weight
building
• Crosslinking
Important, but often overlooked!
Testing in the Linear Region
100
10
Modulus G', G" [Pa]
Testing parameters
Time: Recommended starting point: 10 minutes
Temperature: Application Temperature
Angular Frequency 6.28 to 10 rad/s
Strain amplitude: 1 – 10%
2
Time t [min]
Hints for Time Sweep on Polymers
• Visually observe the material => Use Camera on new
ovens
• Is material degraded?
• Did color change
• Use N2 purge
250
Temperature T [°C]
10
0
Applied:
Measured:
Calculated:
275
Modulus G' [Pa]
Amplitude
strain, stress
Polyester Temperature stability
Temperature stability
good
poor
Linear Region
G is constant
100
1
0.1
Torque [mNm]
G' [Pa]
10
0.01
1E-3
Non-Linear
Region G= f()
Critical strain c
1E-4
1E-5
1E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
Torque M [mN m]
1.5
• In the LVR,
the dynamic
parameters
are independent of strain.
• Test results
must be
compared in
the LVR.
Strain Amplitude [rad ]
Outside of the LVR the material response is no longer sinusoidal!
• Need to define
linear region
accurately.
Linear Region Considerations
Low Frequency
High Temp
Liquid
Consider when
selecting the
strain for the
frequency scan
Increases
Frequency
LVE()
% strain
Decreases
Solid
Low Temp
High Frequency
Solid or Low Temp
G’
• The linear region
depends on:
• Frequency
• Temperature
• State of sample
– solid or liquid
End
of
LVR
G'
Linear Region Considerations
Liquid or High Temp
% strain
Consider
when
selecting the
strain for
temperature
scans
11
2013 TA Instruments New Castle DE
Frequency Dependence of LVR
Modulus G' [Pa]
Strain sweep at different frequencies for PDMS
PDMS at R T
10
62.8 rad/s
18.85 rad/s
6.283 rad/s
4
1E-5
1E-4
Deceasing
frequency
End of the
LVR
1E-3
0.01
0.1
1
Hints for Testing Linear Region
The LVR
region
decreases
with
increasing
frequency
• Determine linear region only after accessing stability
• Suggested tests and parameters
• ARES – Run strain sweep: 0.1 to 100%
• AR – Run stress sweep: 100x’s min torque to 2/3 max
torque
• Sweep mode: log 5 points/decade
=> Consider
when
selecting the
strain for the
frequency
scan
• Frequency: 6.28 to 10 rad/s
• Temperature/s: Depends on subsequent tests
• Run test, evaluate data in spreadsheet, remove any of data
outside specifications
• Plot G’ vs. Strain
strain 
• Use 5% rule to determine linear region
Linear region varies from 7 to 25 % strain.
10% strain would be too high for frequency sweep to 100 rad/s
Testing the Frequency Dependence
G' [Pa], G'' [Pa]; * [Pas]
4
10
Importance of Frequency Sweeps
• Tells about the material’s reaction to short or long
excitations (elastic or viscous or both)
• Provides a quantitative measurement of the elasticity
(reversible deformation) in a material
• Measurement of Viscosity
• Zero Shear viscosity a low frequency,
• Steady viscosity at larger frequencies (Cox-Merz)
• power law index,…
• The frequency dependence of viscosity and modulus
correlates with MW & MWD.
• Represents the
viscoelastic nature
of a material in time
• Provides
.
information about
the material at
different processing
or application rates
(~)
G’
C
A
G”
* [Pas]
3
10
2
10
0
1
10
10
2
10
Frequency  [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
• High to low
• Provides a sizable number of data points in short period
of time - test can be aborted when the terminal region is
reached – thus reduces test time.
• Collects more data with samples of limited stability
Temperature range: 180 to 230 deg C
5
10
4
10
3
Frequency Sweeps over
a range of Temperatures
G'
G' [Pa]
10
10
2
0
10
G'; G'' [Pa]
• No problem for stable sample Problem for sample with
limited stability
3.4
TTS to Extend the Frequency Range
Hints for Frequency Sweeps on Polymers
Testing parameters
• Determine the LVR first
• Run 100 - 0.1rad/s in log sweep; 5 pts/decade
• Choose Strain has to be in the LVR (determined in a
strain sweep)
• Can be run low to high or high to low
• Low to high
M 
G'
 w
(G" )2  M z 
0  M w3.4 and J e 
10
5
10
4
TTS is an empirical
relationship and works
only when the material
is “thermo-rheologically
simple”
G'
G ''
1
2
10
10
Frequency
 [rad./s]
10
3
10
2
10
-1
10
0
10
1
10
2
10
3
Freq ue ncy  /a T [ra d/s]
Extended freq. range
12
2013 TA Instruments New Castle DE
Thermosetting Polymers – Temperature Ramp
At start of test have a
material that starts as
liquid, paste, pressed
power Pellet, or prepreg
1.50E5
Cure on AR1000
5.3E6 Pa
1.000E6
250.00
G' (Pa)
Crosslinking
reaction causes
h and G’ to increase
1.000E5
100000.00
10000 200.00
1000
75000.00
10.00 100.00
50000.00
100.0
1.000
Material hits minimum viscosity
which depends on max
temperature, frequency, ramp
rate and may depend on strain
or stress amplitude
Time
1.000
0.010000
0
8
10
7
10
G'
G''
0.05
6
Gel point
G', G'' [Pa]
5
4
10
3
0.00
10
 = Lsample/L
 = 2.56 %
2
10
Lsample [mm]
10
10
1
10
0
10
-1
10
60
80
100
120
140
160
180
200.0
400.0
600.0
800.0
time (s)
1000
1200
0
0.01000
1400
Target Strain = 2.0%
Lower toque limit = 10 mN.m
Hints for Temp. Ramp for Thermosets
• Use Normal force control to adjust for shrinkage
(AutoTension) and/or thermal expansion in parallel
plates
• Use AutoStrain to keep the torque in specified limits
for ARES
Dimensions changes during cure of a filled epoxy
9
10
Temperature ramp 2 C/min
Test frequency 1 Hz
Parallel plates 8mm
Initial gap 1.2mm
0.1000
PP-112 Time Sweep at 150 degC
0.018 Pa
Dimension Change during Cure
10.00
25000.00
0.1000
As the temp increases
the viscosity of resin
decreases
10000
1000
150.00
100.0
50.000
Temp
1.25E5
1.000E5
% strain
Material fully cured
Maximum h or G’ reached

or
G’
1.000E7
1.000E6
G'' (Pa) osc. torque (micro N.m)
Thermosetting Polymers - Isotherm
1.000E7300.00
200
Testing parameters
• Strain
• Depends on sample consistancy at the start:
powder, paste, low viscosity liquid
• Frequency – Typically 6.28 to 10 rad/s or higher
with ARES (faster data acquisition)
• Ramp Rate – 1 to 5°C/min.
Temperature T [C]
Thermosetting Polymers - AutoStrain
Torque
Thermoset Polymer - Temperature Ramp
Upper torque limit
Cure cycle of an epoxy compund Gel point and minimum viscosity
7
6
10
10
Temperature ramp 5 C/min
6

or
G’
Lower
torque limit
Temp
Constant strain cure (SMT)
With AutoStrain.
Time
Moduli G', G'' [Pa]
10
G'
G''
*
approx. gel point
5
10
5
10
4
10
4
10
Minimum viscosity
Complex viscosity* [Pas]
Strain
AutoStrain
increases the
strain to keep
the torque
within the
instrument
range in order
to accurately
measure the
viscosity
minimum
3
3
10
10
80
100
120
140
160
Temperature T [C]
13
2013 TA Instruments New Castle DE
Thermosetting Polymers: Consideration
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
• Frequency considerations
1.
• ARES can run at higher frequencies to generate higher
torques without risk of inertia issues at near minimum
viscosity
• Higher Frequencies also means faster data acquisition
between points for capturing rapid material changes.
• AR can run into system inertia limitations at minimum
viscosity. Monitor raw phase
• AutoStrain considerations
2.
• AutoStrain only adjusts when torque is above or below limits.
Need to get adjustment factor right. 20% adjustment factor
works for almost all samples.
• The AR2000 uses a lower torque limit as opposed to Auto
Strain. Strains can get large. Keep an eye on Strain.
Types of Transient Tests
• Relaxation
• A step strain is applied and the stress recorded
Stress Relaxation Experiment
• AR series: Response time dependant on feedback
loop (Strain is applied to sample instantaneously
• Stress is monitored as a function of time (t).
• Creep and Creep Recovery
• A step stress is applied and the strain recorded
• The recoverable strain is recorded after removing
the stress
Strain
Log Stress
0
Stress Relaxation and Linear Region
LDPE Melt Relaxation
increasing strain
Modulus G(t) [KPa]
10
1
0.1
0.01
0.01
• Fast viscoelastic
characterization of a
polymer
• Results less
accurate for
short and for
long times
o
T=140 C
strain 10%
strain 20%
strain 50%
strain 100%
strain 200%
strain 400%
0.1
1
Time t [s]
10
100
Log time
For small deformations (LVR) the
ratio of stress to strain is a
function of time only.
The material property is the
STRESS RELAXATION
MODULUS, G(t)
G(t) = (t)/
Stress Relaxation Parameters
• Strain
• Small strains (LVR)
• G(t) is independent of strain
• Large strains
• G(t) depends on the strain and decreases with
increasing strain.
• The ratio G(t)/Go(t) is a measure of non linearity
(to calculate the damping function)
• Temperature
• As application or sample comparison dictates.
• Temperature steps are seldom used to extend the
time range (see freq. sweep)
14
2013 TA Instruments New Castle DE
Hints for Relaxation Tests on Polymers
• Never start with too high strain
• ARES – transducer overload; motor stopped
• AR –target strain at full torque is not hit
• Useful to run a single oscillation test at 1 rad/s to
estimate the materials’ modulus G(t). Estimate the
maximum strain for the maximum instrument torque.
• Use logarithmic sampling
• For materials with short relaxation times, oscillation is
preferred => torque relaxes too fast below the instrument
resolution
• Stress relaxation is used often for stiff samples, which
relax much slower.
• Very little used for t-T superposition studies today
Creep / Recovery Experiment
• ARES Response time dependant on feedback loop
and transducer zero
• Stress is applied to sample instantaneously at t1. The
strain is monitored as a function of time (t).
• The stress is set to zero at t2. The strain is monitored
as a function of time  (t ).
In the creep zone:
COMPLIANCE
Stress
t1
25
2.0
15
Recoverable Strain
Strain  [ ]
20
10
1.5
1.0
0.5
5
R ecoverable Strain
0.0
0
50
60
70
80
90
100
110
120
Time [s]
-5
0
20
40
60
80
100
120
Time t [s]
time
t2
Jr(t) = { u – (t)} / 
• The best test
approach to
measure long
relaxation
(retardation
times)
• Recovery is
the most
sensitive
parameter to
measure
elasticity
Creep Parameters
• Stress in creep zone
• In linear viscoelastic region J(t) will be independent
of the applied stress in LVR
• Select the highest stress in the LVR.
• Recovery Zone (Stress zero by definition)
• Start recovery only, after steady state creep has
been obtained.
• Select a recovery time, twice the creep time
• The recoverable compliance Je is a very sensitive
measure of the melt elasticity
• Temperature(s)
• As application or sample comparison dictates
LDPE Melt creep recovery
10
10
-1
-2
10
-3
10
-4
10
-5
-1
LDPE Melt
o
T=140 C
10 Pa
50 Pa
100 Pa
500 Pa
1000 Pa
5000 Pa
10
slope 1
-2
10
increasing
stress
-3
10
-4
10
Recoverable Compliance Jr(t) [1/Pa]
30
J(t)(t)/
In the recovery zone:
RECOVERABLE
COMPLIANCE
Recoverable
Strain
Creep and Recovery with Increasing Stress
Compliance J(t) [1/Pa]
PDMS at RT
Recovery  = 0
/
Creep on PDMS
35
Creep 0
Strain
Non linear
effects can
be detected
in recovery
before they
are seen in
the creep
(viscosity
dominates)
-5
10
0.1
1
10
100
1000
Time t [s]
Creep – ARES and AR series
• AR series
• Drag cup motor: Steps torque to programmed stress and
holds constant with time.
• Optical Encoder: Records displacement with time, during
creep and recovery.
• Limitation: torque resolution during creep and residual torque
during recovery.
• ARES series (LS Motor Only)
• Motor/Transducer Feedback control: Motor drives angular
velocity to control feedback from transducer to constant
torque (stress).
• Encoder measures motor strain and strain rate Limitation:
• Limitation
• Requires initial viscosity value to back calculate a starting
shear rate to initiate feedback loop.
• Offset between sample torque and transducer zero.
15
2013 TA Instruments New Castle DE
Ten Steps to Better Rheological Measurements
Hints for Creep Tests on Polymers
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
• Use only AR series rheometer for recovery
measurements on polymer melts
• Operate always at the highest stress in the LVR
• Recovery time zone must at least be twice the creep
time zone.
• Do not exceed one strain unit during creep (End of
LVR).
2.
Steady State Flow Experiment
Steady State Flow on Polymer Melts
• In polymer rheology, the steady state viscosity as a
function of shear rate is the most used material
function – referred to as viscosity function
• The steady state stress as a function of shear rate is
referred to as flow curve
• Rotational rheometers can only measure the steady
state viscosity and 1st normal stress coefficient at low
rates (<10 1/s) due to edge failures. Higher shear
rates may be obtained from oscillation measurements
using Cox Merz.
Deformation
Stress or rate is applied to
the sample. Viscosity
measurement is taken
Denotes
Measurement
when the material has
reached steady state flow.
time
The stress or rate is
increased (logarithDelay time
mically) and the process
is repeated yielding a
Steady State Flow viscosity or flow curve .
or   Constant

or
•

or
•

time
Steady State Flow Experiment
Steady State Flow
Shear
Thinning
Region
Shear Rate
HDPE viscosity curve
T= 210 °C
6
Viscosity; * [Pa s]
Viscosity s, Pa s
Whether steady state has been reached, by applying stress
or rate, has no influence on the final result. In the polymer
industry, the viscosity function is always shown as a
function of the shear rate; each steady viscosity value
giving a single viscosity data point:
10
viscosity in Pa s
5
10
Creep
Time
•
Shear Rate, 1/s
s 
Oscillation
1E-6
1E-5
1E-4
.
1E-3
0,01
0,1
Shear rate  [1/s] or Frequency  [rad/s]
1
• 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
16
2013 TA Instruments New Castle DE
Rate Controlled Steady-State Flow
Parameters
• Controlled Rate
• Initial and final shear rate
• Start at lowest settable rate
• Suggest final value – 100 to 1000 1/s
• Use your judgment
• Step time
• Stepped Flow
• 10 seconds
• Steady State Flow
• AR: use algorithm (see slide on topic)
• ARES: use guideline (see slide on topic)
• Temperature
• As defined by application
Default
values
shown
•
•
•
•
Hints for Steady State Flow on ARES
• Defining time required to reach equilibrium:
• Run ‘Single Point Test’ at lowest shear rate to determine
‘delay before measure’ for steady rate sweep. Use this
equilibrium time as ‘delay before measurement’.
• Higher shear rates will require less time to reach equilibrium,
ensuring all data acquired was collected under steady state
conditions
• May sequence tests to shorten experiment time
Transient viscosity function
steady state
10 1/s
5 1/s
1 1/s
0.5 1/s
0.1 1/s
0.01 1/s
steady state
10
4
soak time
0.1
1
.
10
AR: Steady State Algorithm Flow
100
During the test, the dependant variable (speed in controlled stress
mode or torque in controlled shear rate mode) is monitored with time
to determine when stability has been reached.
An average value for the dependant variable is recorded over the
Sample period.
When consecutive average values (Consecutive within tolerance)
are within the tolerance specified here, the data is accepted.
The software will also accept the point at the end of the Maximum
point time, should the data still not be at a steady state value.
Stress Controlled Steady-State Flow
Parameters
• Controlled stress
• Initial and final stress
• Suggest: Control Torque- use 10 times lowest settable
torque
• Suggest final value – use maximum
• Likely to get instrument over-speed message
• Can throw sample out; Use covers
• Step time
• Stepped Flow
• 10 seconds
• Steady State Flow
• Use algorithm (see slide on topic)
• Temperature
• As defined by application
Shear rate  [1/s]
Stress Controlled Steady State Flow Hints
• No guarantee that the sample reaches steady state at
maximum point time
• Can run in stress control enabling stress and flow
information in one test
• Easier to controlling shear stress can measure much
lower shear rates than controlling rate in CMT or SMT
with HR motor
Structured Fluids
 Identify the purpose of the experiment
• 1. Understand why your doing the measurement
 Design, program & run test
• 2. Understand your instrument
• 3. Know your sample
• 4. Selecting correct test fixtures
• 5. Oscillation testing guidelines
• 6. Transient testing guidelines
• 7. Steady shear testing guidelines
• 8. Loading the sample
 Evaluate data and 0ptimize if necessary
• 9. Instrument limitations
 Results
• 10. Presenting the data
17
2013 TA Instruments New Castle DE
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
Know Your Sample
1.
2.
• Structured fluids can range in consistency from low
viscosity such as milk to pasty like tooth paste.
Structured fluids are very sensitive to mechanical and
environmental conditions. Correct pre-conditioning
and loading into the rheometer is important.
• Structured fluids are time-dependent – how you treat
the sample may affect the test results!
Handling Low Viscosity Fluids
Dealing with Pastes and Slurries
• Fluid samples which pour freely are relatively easy to
handle prior to loading:
• Keep the flask closed to avoid evaporation of
solvent or the continuous phase
• Shake or stir may be necessary to concentration
gradients in suspensions
• Adequate shelf temperature may be required to
avoid phase separation in emulsions
• Never return used sample into original flask to avoid
contamination
• High viscosity pastes and slurries may suffer structure
changes with time.
• Food samples, for example Dough, changes
continuously. The test samples need to be prepared
very carefully and consistently for each experiment in
order obtain reproducibility
• Slurries that may settle build a cake. These samples
have to be tested before sedimentation.
Dealing with Gels
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
• Gels, especially chemical gels, may change
irreversibly when applying large deformations.
• Prepare (formulate) the sample and bring it into
the final shape required for the measurement
without deforming the sample (cut, punch,..)
• Prepare (formulate) the sample in situ (test fixture,
rheometer,.=> systemic rheology)
2.
18
2013 TA Instruments New Castle DE
Selecting the Correct Geometry
• Low viscosity fluids are best contained in a cup and
bob geometry, pastes are better loaded into parallel
plate or cone plate geometry, you may say – Is this
always correct?
• A typical bob (30x30 mm) generates the same
torque as a 50mm parallel plate – no advantage!
• Low viscosity fluid stays in a 500 micron gap due
to capillary forces and requires much less fluid –
this is an advantage!
• Evaporation is easier to eliminate in a concentric
cylinder system with a solvent layer.
• In general high viscosity systems are difficult to
load in a cup and bob.
Concentric Cylinder
• Use with low viscosity fluids and systems with volatile
components. Use low viscosity oil or the volatile
component itself on top of the sample to avoid
evaporation. Requires a large sample volume.
Strain Constant: K =
Stress Constant: K =
Special Cylinder Geometries
Disadvantages:
• shear rate constant for
small gaps only
• instabilities in shear
field can occur at high
rate (homogeneous
liquid shear-field
breaks up, wall-slip)
• large sample volume
(>20ml)
Avoiding Slip with Plate Geometries
L(R1)2
Note: the average shear rate is represented by the value in the
middle of the gap
Concentric Cylinders
Advantages:
• good for low viscosity
fluids easy loading
• allows high shear
rates (>103 s-1)
without losing liquid
due to centrifugal
force
• Sample evaporation
is easy to eliminate
with a solvent layer
2
1- (R1/R2)2
1
• Vane is ideal for avoiding slippage, sample
breaking during loading, etc..
• Starch rotor and Helical screw are ideal for
mixing and avoiding sedimentation, etc..
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
• Different surface treatments are used to avoid slipping
of gels, suspensions, etc..
• Crosshatched surface
• Serrated surface
• Sand blasted or roughened surface
• Porous surface
2.
19
2013 TA Instruments New Castle DE
Loading Low Viscosity Fluids
Loading Pastes and Slurries
Check volume requirements for testing geometry
Pastes and slurries
• Deposit fluid in the
• Fill cup, lower the
middle of the plate,
rotate plate while
setting the gap to
insure even filling
bob to the mark.
Deposit a layer of
solvent to avoid
evaporation if
necessary
•
• Deposit the paste with a spoon
•
solvent
• Set gap first
Meniscus due
to surface
tension
•
and deposit
fluid at the
rim. Capillary
forces suck in
the fluid
•
Linear Gap Closing
Gap
Closing the Gap
(syringe with cut-off tip for less
viscous systems) in the middle of
the plate.
Load 10-20% excess material to
insure complete filling
Close the gap automatically using
logarithmic speed or force gap
setting to minimize shear in the
sample
Trim sample and set final gap
• Linear speed profile after reaching the user defined
‘Compression Distance’
Rapid Close
Controlled
Close
~ 1000 - 2000 microns
from final gap
• Exponential speed profile after reaching the user defined
‘Compression Distance’
Time
• Normal Force set not to exceed a certain value of after
reaching the user defined ‘Compression Distance’
Gap closes
Effect of squeeze
is to shear sample
117
118
Comparison of Linear and Exponential Gap
Closing
Rapid Close
~ 1000 - 2000 microns
from final gap
250
Exponential
Close
200
Controlled
Close
G' (Pa)
Gap
Exponential Gap Closing
Time
150
Fast Linear
Close
100
50
0
Squeeze Flow effect
is less pronounced
0
200
400
600
800
1000
Time (s)
119
120
20
2013 TA Instruments New Castle DE
Ten Steps to Better Rheological Measurements
Loading Gels
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
• Prepare gel
•
•
sample with the
desired shape
Use crosshatched,
roughened plates
Form the gel
between the
plates
2.
• Insert vane
without
breaking
the sample
(yoghourt,
sour
cream)
Structured Fluids: Results of the Pre-Testing
Structured Fluid: Pre-Testing
A R E S a m p lit u d e t e s t o f a la t e x p a in t
1. 2.
10
• The pre-test may indicate the following:
3
G ' [P a ]
G '' [ P a ]
3.
20
2
10
s tr a in
0 .1 %
10
1%
12%
1%
• Effect loading observed by the change of G’ in
section 1
• Possible yield in the material observed by a
significant drop in G’ in the low and high strain
section.
• Possible thixotropy observed by the time require to
obtain equilibrium in section 3
• Reversibility of material structure observed by the
difference between equilibrium in section 1 and 3
strain  [%]
Modulus G'; G'' [Pas]
10
0 .1 %
1
0
-2 0 0
0
200
400
600
800
1000 1200 1400 1600 1800
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.
Need for Pre-Shearing
Testing Time Dependence -Time Sweep
Structure recovery after preshear
• Important, but often overlooked
• Simulation shear processes in applications
Goo
Modulus G', G'' [Pa]
• If pre-testing indicates irreversible structure, preshear and delay will be required to establish a known
history to insure reproducible test results
G'
G''
Go
 t 
G ' ( t )  ( G '  G 0' )( 1  exp   )
 

10
0
100
200
300
Time t [s]
400
500
 is a
characteristic
restructuring
time
21
2013 TA Instruments New Castle DE
Hints for Time Sweep on AR & ARES Series
Suggestions for Strain or Stress Sweep
Testing
• Load new sample, pre-shear to breaking structure
(time from section 2 during the pre-test) and follow
structure building at low amplitude (section 3of the
pre-test) at 1 Hz i.e. 1rad/s
• Typically, the restructuring curve can be
approximated by an exponential function. In this
case a characteristic restructuring time can be
calculated
• Sometimes the structure recovery is more complex
f.example a fast initial recovery to 90% of Goo and
very slow recovery of the rest 10%
• Dispersions
• Is structure broken during loading ?
• May need to pre-shear and wait for structure to
build.
• If the above condition exists:
• Pre-shear at 10 1/sec for 30 sec
• Run time sweep to see when sample is stable,
then run strain or stress sweep
• When comparing samples, condition all with the
same pre-shear history.
Importance of Waiting for Structure Rebuild
Testing in the Linear Region - Strain Sweep
Sample time sweep
100.0
Pre-shear
conditions:
100 1/s for 30
25.00 50.00 75.00 100.0
seconds
time (s)
10.00
0
G'
G''
Structured sample
10
Estimate the yield
stress from the
on-set of linear
behavior
y=G' c
1
critical
strain  c
125.0
150.0
175.0
10.00
0.1000
0.1
1.000
10.00
100.0
Testing in the Linear Region - Stress Sweep
100.0
100.0
Hair gel: open symbols; Shower gel: filled symbols
1.000
10.00
100.0
10
100
1000
Hints for Strain Sweep: ARES & AR
G'' (Pa)
G' (Pa)
1000
1
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
• Useful for Stability predictions (stability as defined by yield)
1000
0.1
Strain  [%]
osc. stress (Pa)
• End of LVR is indicative of “Yield” or “Strength of Structure”
10.00
0.1000
Strain sweep of a cosmetic cream
Delay after pre-shear = 150 seconds
Delay after pre-shear = 0 seconds
Modulus G', G'' [Pa]
G' (Pa)
100.0
• Pre-shear and delay determined from time sweep
• Strain Range
• Initial strain: Lowest settable value
• Final Strain: Dispersion: 10% strain
• Frequency: 6.28 rad/s
• Sweep Mode
• Logarithmic for samples with linear regions with
wide linear region;10 pts/decade
• Linear mode for highly structured materials with
short linear regions, i.e. toothpaste
10.00
1000
osc. stress (Pa)
22
2013 TA Instruments New Castle DE
Hints for Frequency Sweeps
Cosmetic lotion
10
Modulus G', G'' [Pa]
• Pre-shear and delay determined from time sweep
• Oscillation Stress Range:
• Recommend to program Oscillation Torque
• Initial Torque: 10 times minimum torque
• Final Torque: 1/2 maximum torque
• Frequency: 6.28 rad/s
• Sweep Mode
• Logarithmic for samples with wide linear
regions; 10 pts/decade
• Linear mode for highly structured materials with
short linear regions, i.e. toothpaste
Testing the Frequency Dependence
2
10
1
1
10
G' [Pa]
G'' [Pa]
tan 
tan  = G''/G' > 0.5 to 1
gel like behaviour
0.1
1
frequency  [rad/s]
10
0.1
• G’ and G” are
virtually
independent of
frequency, as well
as tan d.
tan 
Hints for Stress Sweep : AR
• Also the material
behaves
predominately
elastic (G’>G”) =>
which stands for
structure in the
material, capable
of storing energy
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
•
•
•
•
Determine the LVR first
Pre-shear and delay determined from time sweep
Run 100 - 0.1rad/s in log sweep; 5 pts/decade
Strain has to be below the critical strain c,
determined in the strain sweep
2.
Continuous stress ramp
Transient Tests for Structured Fluids
• Transient test measures the instantaneous response
of a material as a function of time
• Stress ramp
• – this is a very common method to determine the
yield stress
• Rate ramp
• The rate on the sample is continuously increased
and the stress recorded. The rate ramp is a fast
method to measure a flow curve
• Thixotropic loop
• A rate ramp up is followed by a down ramp. The
difference between the flow curve during the up
and down segment relates to thixotropy
• A Stress changing at a constant rate is applied to
material
• Resultant strain is monitored with time.
Stress (Pa)
m =Stress
rate (Pa/s)
Shear Strain
time (s)
The stress ramp is
predominately used to
measure the yield
stress. The parameters
evaluated are either
the measured strain or
the instantaneous
viscosity
23
2013 TA Instruments New Castle DE
Yield Stress in a Stress Ramp
Yield stress of a cosmetic lotion
h
4.0
[Pas]
Yield stess (at maximum) = 5.4 Pa
1000
3.5
3.0
2.5
Strain
2.0
10
1.5
Strain (x10-6)
1.0
1
0.5
0.0
0
50
100
150
200
Stress [Pa]
Continuous Rate Ramp
• Controlled stress (AR series)
• Initial and final stress
• Can start at zero
• Suggest final value –Use your judgment
• Duration or Time of experiment
• Typically 1 to 3 min.
• Shorter duration can affect results (inertia effect or
thixotropy)
• Temperature
• As defined by application
• Controlled Stress (ARES series)
• Requires guess of viscosity
• Test parameter similar AR
Viscosity Function From a Rate Ramp
Children Advil suspension
• A constant changing shear rate is applied to the sample
• The resultant stress is recorded
Shear rate
Stress
m = rate
change (1/s2)
time (s)
Rate ramps are used
mostly as a fast method
to measure the flow
curve or the shear rate
dependent viscosity of
non thixotropic fluids
10
Viscosity  [Pa s]
Viscosity  [Pas]
100
The maximum
viscosity
method is
more
representative
and
reproducible
then the strain
tangent
method
Continuous Ramp Testing Parameters
T= Room Temperture
Viscosity
1
Slope -1
10
0
Rate ramp on ARES:
high to low
0.1
1
10
Shear rate  [1/s]
Continuous Ramp Testing Parameters
• Controlled rate (ARES series)
• Initial and final rate
• Can start at zero
• Suggest final value –Use your judgment
Thixotropy Loop Test
• Constant increasing rate is applied to material.
• Resultant stress is monitored with time.
• (Combination of up and •down stress ramps is a
pseudo-thixotropic loop)
• Duration or Time of experiment
• Typically 1 to 3 min.
• Shorter duration can affect results (thixotropy)
Stress (Pa)
• Temperature
• As defined by application
• Controlled Rate (AR series)
• Uses feedback control
• Test parameter similar ARES
Rate
The thixotropic loop was
the traditional method
frequently used with
viscometers to measure
thixotropy.
Time (s)
24
2013 TA Instruments New Castle DE
Thixotropic Loop
Thixotropic Loop
first ramp up
0
10
2
Stress [Pa]
Viscosity (t) [Pas]
4
peak at stress 1.3 Pa
0
0
2
4
6
.
rate (t) [1/s]
8
Nonthixotropic
material
Up and
down ramps
superpose –
except the
first one
=> Start up
from zero
Thixotropic loop for 3 Mayonnaise emulsions
80
60
20
0
0
.
300
400
500
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
2.
Structured Fluid: Flow Curve in Rate Mode
Steady State Experiment
Deformation

or
•
200
Ten Steps to Better Rheological Measurements
=> small change in stress
causes a large change in strain
rate
=> it is easier to control small
stresses than small rates
10
Flow cuve of an ink paste
10
Viscosity  [mPa s]

or
•
100
Rate [1/s]
• Why is a stress ramp preferred for yield
measurements? What is the difference?
• Whether steady
state has been
reached, by applying
Denotes
stress or rate, has
Measurement
no influence on the
time
final result.
• In order to obtain a
continuous curve on
Delay time
structured materials,
however it matters
Steady State Flow
or   Constant how the viscosity
function is obtained.
sample A up
sample A down
sample B up
sample B down
sample C up
sample C down
40
10
Stress and Rate Ramps - Comments
Thixotropic
material
Up and down
ramps do not
superpose
Area under
the curve is a
measure of
thixotropy
100
10
9
10
8
10
7
10
6
10
5
10
4
10
3
10
2
10
1
10
0
Stress
Viscosity
slope -1
0.009 Pa
Shear rate  [1/s]
10
1
10
0
10
-1
10
-2
Stress  [mPa]
6
viscosity [Pas]
stress [Pa]
Stress  [Pa]
Children Advil suspension
Stepped
rate test on
ARES
Shear rates
are stepped
at equal
intervals
=> smooth
curve

The viscosity decreases with a slope of -1 versus strain rate and
the stress becomes rate independent => material with yield stress
time
25
2013 TA Instruments New Castle DE
Structured Fluid: Flow Curve in Stress Mode
1000000
viscosity (Pa.s)
100000
10000
Slope -1
1000
100.0
10.00
1.000
0.1000
1.000E-5
1.000E-3
0.1000
10.00
10000
Stepped
stress test on
AR2000
Stress is stepped at equal
intervals, the
data are
represented
as a function
of rate
=> discontinuous
curve curve
Solids
 Identify the purpose of the experiment
• 1. Understand why your doing the measurement
 Design, program & run test
• 2. Understand your instrument
• 3. Know your sample
• 4. Selecting correct test fixtures
• 5. Oscillation testing guidelines
• 6. Transient testing guidelines
• 7. Steady shear testing guidelines
• 8. Loading the sample
 Evaluate data and 0ptimize if necessary
• 9. Instrument limitations
 Results
• 10. Presenting the data
Sample Considerations
• Deformation Mode:
• E : Tension, compression and bending modes DMA
• G: Torsion rectangular shear mode - Rheometer
• Stiffness:
Stiffness of sample related to its dimensions [l,w,t].
Stiffness may limit sample size.
• Shape:
Accurate/reproducible modulus depends on good
sample shape [consistent cross-section throughout
length.
Sample size cannot exceed clamp restrictions
[Stiffness takes precedence].
Flow Curve in Stress Mode - Comments
• At the yield point, the rate can vary over a few
decades for a small increment in stress.
• If the stress is stepped up or down, at equal
intervals, the rate dependence will show a
discontinuity in the viscosity curve
=> in this case you have to control on strain rate in
order to obtain a continuous flow curve or viscosity
curve.
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
2.
Sample Stiffness and Material Modulus
Thick and Thin
Samples Can Have
The Same Stiffness
F=1N
x = 10 mm
High Modulus Material
F=1N
x = 10 mm
Low Modulus Material
Thick and Thin Samples
That Have The Same
Modulus
F=1N
x = 10 mm
Low Stiffness Sample
F=1N
x = 2 mm
High Stiffness Sample
26
2013 TA Instruments New Castle DE
Changing Sample Stiffness
Clamp Type
Tension Film
Tension Fiber
Dual/Single Cantilever
Three Point Bending
Compression – circular
sample
Shear Sandwich
Torsion
To Increase Stiffness……
Decrease length or increase
width. If possible increase
thickness.
Decrease length or increase
diameter if possible.
Decrease length or increase
width. If possible increase
thickness.
Note: L/T  10
Decrease length or increase
width. If possible increase
thickness.
Decrease thickness or
Increase diameter.
Decrease thickness or
Increase length and width.
Increase thickness
Decrease length
To Decrease Stiffness…….
Increase length or decrease
width. If possible decrease
thickness.
Increase length or decrease
diameter if possible.
Increase length or decrease
width,, If possible decrease
thickness.
Note: L/T  10
Increase length or decrease
width. If possible decrease
thickness.
Increase thickness or
decrease diameter.
Increase thickness or
Decrease length and width.
Decrease thickness
Increase length
Preparation of Solid Thin Films
Preparation of Solid Test Specimen
• Uniform and well-defined
dimensions
• Shape could be fiber, film or
rod/rectangular bar
• If sample is received as
pellets, mold sheet first and
cut specimen of the desired
size for torsion or bending
experiments
• Rubber can be tested in bending or torsion (rectangular sample)
or in shear (disc)
• Compression molded samples are preferred over injection molded
samples because of the highly oriented nature of injection
molding. Orientation does not affect Tg but tan delta before Tg.
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
• Curling of films
• Electrostatic effects on thin films can cause
static attractions that make manipulation
frustrating
• Small residual stresses in the film from
processing can cause curling
• Thin brittle films are subject to cracking
• Cutting with razor blade, not with scissor
• Be careful while trying to flatten for loading
DMA Clamping Guide
2.
Solids Clamping Selection – Rigid Samples
• Rigid (Glassy, Crystalline) Samples in Bending
Sample
Clamp
Sample Dimensions
• Rectangular or cylindrical sample desired: L/T > 10
necessary for quantitative Young’s modulus, otherwise mixed
mode of deformation and modulus will be low.
3-point Bend
Dual/single Cant.
Torsion
L/T> 10 if possible
Unreinforced
thermoplastics or Single Cantilever,
Torsion
thermosets
L/T >10 if possible
• ASTM Forms - smooth edges for better gripping of samples
• Unusual shapes - cut into rectangular bars or run as formed
for qualitative information
High modulus
metals or
composites
• Use Dual/Single Cantilever or Three Point Bend Clamps
Brittle solid
(ceramics)
3-point Bend,
Dual Cant. Torsion
L/T>10 if possible
Elastomers
Dual Cantilever
Single Cantilever
Shear Sandwich
Tension
L/T>20 for T<Tg
L/T>10 for T<Tg
(only for T> Tg)
T<2 mm W<5 mm
• Rigid Samples in Torsion
Films/Fibers
Tension
L 10-20 mm
T<2 mm
• Films and Fibers
Supported
Systems
8 mm Dual
Cantilever
minimize sample, put foil
on clamps
• Rectangular or cylindrical samples desired.
• Samples up to 5 mm can be tested in torsion.
• Use Tension Film or Tension Fiber clamps
• Short span cantilever may work well for stiff films
27
2013 TA Instruments New Castle DE
Solids Clamp Selection - Elastomers
• For sub -Tg information use dual/single cantilever
clamp or Torsion
• To characterize through Tg and above, use single
cantilever or Torsion. If sample is sufficiently thin [low
stiffness] then tension can be used.
• Shear sandwich clamp or parallel plate
• Can be used to characterize material above Tg
• Can be used for curing (Vulcanizing) a rubber
Clamp Selection – Coatings and Resins
• Coatings
• Only qualitative data from supported samples
• Transitions of coatings on substrates are best
observed in bending
• Resins
• Use fiberglass braid, metal mesh or metal shims
as support for cure characterization in dual/single
cantilever
• Use 8 mm dual cantilever clamps for low stiffness
• Use parallel plates for rotational rheometers
Torsion Rectangular
• high modulus samples
• small temperature
gradient
• simple to prepare
• Not suitable for films
and fibers!
M
W
L
T

3-Point Bending
Sample
Stationary Fulcrum
Moveable
Clamp
• Best mode for measuring medium to high modulus
materials
• Conforms with ASTM standard test method for
bending
• Purest deformation mode since clamping effects are
eliminated
W = Width
L = Length
T = Thickness
Single Cantilever
Sample
• Best general
purpose mode
(thermoplastics)
Force
Dual Cantilever
Sample
Stationary
Clamp
Movable
clamp
• Preferred mode over dual cantilever for most neat
thermoplastics (un-reinforced) except elastomers
• Clamping torque is important
Movable
clamp
Stationary
Clamp
• Highly damped materials can be measured
• Best mode for evaluating the cure of supported
materials
28
2013 TA Instruments New Castle DE
Tensile
• Best mode for
evaluation of
thin films and
fibers (bundle or
single filaments)
• Small samples
of high modulus
materials can be
measured
Compression
Stationary
Clamp
Sample
(film, fiber,
or thin sheet)
• Good mode for
low to medium
modulus
materials
(gels, elastomers)
Movable Clamp
Sample
Stationary clamp
Movable clamp
• TMA constant force & force ramp measurements
(mini-tensile tester)
• Force Track & constant force control
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
• Materials must provide restoring force
(support necessary static load)
• Options for expansion & penetration measurements
Before Loading the Sample
1.
2.
Sample Dimension Errors
• Prepare homogenous sample of
constant thickness and width
• Make sure the test specimen has no air
bubbles enclosed or cracks
• Make precise measurement of the
sample dimensions
Avoid Clamping Effects
• When measurements on samples are inexact, the
moduli values are affected.
• Always use the same clamping torque for a
series of samples –
• Specimen with uneven surfaces or geometries will
not give consistent moduli.
• even if stress patterns affect absolute results, the
run to run variations will be minimal
• clamp the sample symmetrical
• Bear in mind that moduli are usually plotted in log
form, a slight change visually on the graph is a large
change in data.
• Transition temperatures and tan  will not be affected
by dimension errors .
• Do not apply too much torque on softer
samples, no squeezing
• re-clamping may be necessary in the glassy state
(thermal contraction)
29
2013 TA Instruments New Castle DE
Alignment in Tension Mode
Loading Films and Fibers - Comments
• Films and fibers are often more fragile requiring a
gentle treatment in loading and testing
• Production often involves tremendous stresses on the
material: drawing, orienting, annealing, extruding.
Internal stress causes rapid changes during and after
Tg, measuring system must compensate rapidly
• Uneven thickness are more problematic since aspect
ratio is extreme
• The Deformation for films and fibers is in tensile.
• Sample length is more variable than bending modes: clamp
geometry doesn’t interfere with size. Normal force control
keeps sample stretched.
Using Multiple Fibers
• In many cases, the testing needs to use bundled
fibers to represent real life
• Evenly distribute or wind the bundles
• Avoid kinking that would make some fibers longer
than others
• Approximate sample dimensions and do not use
absolute modulus values: run to run variations may
be significant
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
2.
ideal
inclined
sagging
variable thickness
Sample Buckling
• Buckling during loading
causes serious errors as
buckled areas do not “feel”
the force or deformation
• Buckling can be the result of
non-uniform stretching, or
crooked loading of a film.
• Observe film from edge while
oscillating to verify goodness
of load.
• If sample is buckling, reload
a new sample.
Procedure to Run a Solid Sample
1. Load sample at room temperature
2. Change temperature to the desired starting point
with Normal force control active (automatically adjust
gap to compensate sample and fixture’s thermal
expansion or contraction)
3. Run Strain Sweep or generate a stress-strain curve
to confirm the linear region
4. Run desired test modes like frequency sweep or
temperature step/ramp
30
2013 TA Instruments New Castle DE
Strain Sweep and Linear Region
Constant Deformation
In bending using dual cantilever
1.10
–––––– Filled Silicone Elastomer
–––––– General Purpose Polystyrene
1.05
Normalized Storage Modulus
1.00





0.95






• A deformation changing at a constant rate is applied to
material
• Resultant stress is monitored with time.

The constant deformation is
predominately used to
measure the linear
deformation range of
materials. The parameters
evaluated are the
measured stress (force) vs.
strain (displacement).
Stress

0.90



0.85


0.80
Critical Strain
Filled Silicone
Elastomer
0.75
0.70
0
20
m = Rate
(mm/s)
Critical Strain
General Purpose
Polystyrene
40
60
80
100
120
Amplitude (µm)
140
Universal V2.4D TA Instruments
Stress-Strain Curve - for Linear Region
time (s)
Stress/Strain Curves - for Linear Regions
In tension using the film fixture
Strain Rate Test at -125°C
In tension using the film fixture
2.0
6x10
5

5

1.5
5x10

stress(t) [dyn/cm
) 2]

Stress (MPa)



1.0

Linear
Region
0.5





5
3x10
5
2x10
5
1x10

0.0
Start-up
Typical of
Poor loading
Approx. 0.6 % strain

0.0
5
4x10
0.5
1.0
1.5
2.0
Strain (%)
2.5
3.0
Universal V2.6B TA Instruments
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
strain(t) [%]
Frequency Sweeps on Solids
10
8
Happy & Unhappy Balls
Hints for Frequency Sweep on Solids
Testing parameters
10
0
• Determine the LVR first
Modulus is the same
tan  is very different
• Run 100 - 0.1rad/s in log sweep; 5 pts/decade
107
E' (
)
[dyn/cm²]
-1
10
tan_delta (
[]
Unhappy ball
• Choose Strain has to be in the LVR (determined in a
strain sweep)
• Use appropriate Force Track/AutoTension to avoid
sample buckling if appropriate
)
106
Happy ball
10
5
10-1
100
101
10
-2
102
Freq [rad/s]
31
2013 TA Instruments New Castle DE
Temperature (°C)
Dynamic Temperature Ramp
time between
data points
Bundle of Hair in a Temperature Ramp
A linear heating
rate is applied.
The material
response is
monitored at a
constant
frequency and
constant
amplitude of
deformation.
m = ramp rate
(°C/min)
Denotes Oscillatory
Measurement
time (min)
Data is taken at user defined time intervals.
Temperature T [oC]
Temperature Step & Multi Frequency
 epoxy and
rubber
transition have
different T
dependence
tan (3.14 Hz)
tan d (0.314 Hz)
tan d (0.0314 Hz)
d
0.15
Soak Time
d
Step
Size
Time
transition Rubber modifyer
transition Epoxy resin
5
0.10
4
3
2
0.05
b
transition
ln v
Denotes Oscillatory
Measurement
tan
Temperature (oC)
0.20
a b
A step and hold
temperature
profile is applied.
The material
response is
monitored at one,
or over a range of
frequencies, at
constant
amplitude of
deformation.
Frequency Dependence of Modified Epoxy
1
0
a
0.00
-150
-100
transition
-50
Temperature T [°C]
-1
0
-2
50
-3
4.583
4.6285
4.7033
***
1/T [1/°C]
Hints for Normal Force Control
0
A
Force/Time Curves
OF
A
A = Oscillatory force amplitude
OF = Offset force (static force)
Clamps without offset force:
Single Cantilever
Dual Cantilever
Shear Sandwich
Clamps with offset force:
Tension Film
Tension: Fiber
3-Point Bend
Compression
Penetration
Force Offset Modes
Static force [General]
Used in tensioning clamps to prevent sample buckling
[tension], or loss of contact with the probe [compression]
during the test. Static force must exceed dynamic force at all
times during experiment
• Constant Force
• Applies same static force throughout experiment
• Can be used with highly crystalline or crosslinked
materials
to measure displacement for quantitative expansion
• Force Track
• Applies Static Force in Proportion to Sample Modulus.
Used to reduce stretching as specimen weakens
• Values from 125-150% work well for most samples
32
2013 TA Instruments New Castle DE
Normal Force Control - Parameters
Normal Force Control - Parameters
Static Force
Force Track
(autostrain)
Tension Film
0.01 N
120 to 150%
Tension Fiber
0.001 N
120%
Compression
0.001 to 0.01 N
125%
Three Point Bending
Thermoplastic Sample
1N
125 to 150%
Three Point Bending
Stiff Thermoset Sample
1N
150 to 200%
Can use constant static
force
AutoTension
1.Initial Static Force:_____
2.Static F >Dyn. Force: ______
3.Min. Static Force:______
4.AutoTension Sensitivity:_____
Ten Steps to Better Rheological Measurements
PMMA Temperature Ramp 1Hz 3°min
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
11
10
1
3.5
Peak(117.98,1.6543)
2.
3.0
10 10
0
10
-1
2.5
Peak(17.92,0.07413)
2.0
DeltaL (
[mm]
10 9
1.5
)
10 8
)
G' (
)
2
[dyn/cm ]
10
tan_delta (
[]
G" (
)
2
[dyn/cm ]
(-CH 2-C-(CH 3)-(COOCH 3)-)n
Peak(104.1,0.966)
10
10 7
10
-2
tan_delta = 0.01405 [ ]
Temp = -92.002 [°C]
10
-100.0
-50.0
1.0
0.5
6
-150.0
1. Initial Static Force:_____
2. ForceTrack: ______
3. Minimum dynamic Force:______
AutoStrain
5.Inc. strain if force drops
below:_____
6.Dec. strain if force goes
above:_____
7.Adjustment Factor:_____
Dimension Changes During Temperature Ramps
10
Q800 Program Parameters
RSA III Auxiliary
Control Program Parameters
Clamp Type
0.0
50.0
100.0
150.0
-3
0.0
200.0
Temp [°C]
• More than 90% of all solids testing on a DMA is in
oscillation
• Solids analyzer also perform time dependent or
steady measurements on solid materials; for
example:
• Creep on solid fibers
• Long term relaxation studies on solid specimen
• Tack test
Stress Relaxation Happy & Unhappy Balls
2x10
7
Happy ball has an
infinite relaxation time
107
E(t) (
)
[dyn/cm²]
Transient and Steady Testing on a DMA
Happy ball
Unhappy ball
2x10
6
10 -3
10-2
10-1
100
101
102
10 3
time [s]
33
2013 TA Instruments New Castle DE
Creep on Packaging Films
120000
Flow of a Rheological Experiment
 Identify the purpose of the experiment
• 1. Understand why your doing the measurement
 Design, program & run test
• 2. Understand your instrument
• 3. Know your sample
• 4. Selecting correct test fixtures
• 5. Oscillation testing guidelines
• 6. Transient testing guidelines
• 7. Steady shear testing guidelines
• 8. Loading the sample
 Evaluate data and 0ptimize if necessary
• 9. Instrument limitations
 Results
• 10. Presenting the data
 Poor Performance
 Good Performance
 Excellent Performance
Creep Compliance (µm^2/N)
100000
80000





















60000

40000




20000

0
0



1
2
3
4
5
6
7
8
Time (min)
9
10
Universal V2.1A TA Instruments
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
2.
Radial Compliance
1E+10
Storage Modulus G' [Pa]
1E+09
1E+08
1E+07
1E+06
1E+05
1E+04
1E+03
1E+02
1E+01
1E+00
1E-01
-50
0
50
100
150
The following are important key issues that may limit the
range of operation. It is critical that these items are
understood:
• Instrument Compliance which can affect data when the
sample becomes much stiffer than the instrument.
• More of a concern in dual head design
• Secondary flows or edge effects can limit the high
strain and strain rates.
• Instrument Inertia may dominate measurements of low
stiffness/low viscosity materials. This limits the
maximum frequency in single head rheometers and
DMA’s.
Instrument Compliance
• How do you see and compensate for compliance in
dual head instrument
• Look at actual and commanded strain in the
spreadsheet.
• If actual strain is < 80% of the commanded strain,
then sample geometry should be changed to
reduce stiffness of sample
compliance effects with parallell


































































plates below approx. +120°C




Torsion Bar









-100°C to +160°C


































G'
Torsion
Bar
Tan













G'
–
Paral.
Plate
Tan




25mm Parallel Plates





+90°C to +280°C





























































 













































































1E-02
-100
Instrument Limitations
200
250
• Refer to stiffness chart above.
300
Temperature [°C]
• All TA Instruments include compliance calibrations/corrections.
34
2013 TA Instruments New Castle DE
Edge Failure – Secondary Flows
Inertial Effects
torque, M
gap,
H
angular velocity, 
effective diameter
Large normal
stress
difference leads
to crack
formation at
free surface
• Results in apparent drop in viscosity
• Remedy: decrease gap to increase stabilizing
influence of surface tension
• What is Inertia?
• Definition: That property of matter which manifests
itself as a resistance to any change in momentum
of a body
• Angular motion: M = I d /dt
• M is the torque (Nm)
•  is the angular velocity (rad / s)
• I is the moment of inertia (Nm s² kg m²)
• I =  mr²
• m is the mass at distance r from the axis of
rotation
Inertial Effects in Oscillation for the AR Series
Correction for Inertia in Oscillation for AR
Negligible correction at low frequencies
1.000E6
70.00 70.00
1.000E5
1.000E5
G'' (Pa)
10000
60.00 60.00
50.00 50.00
40.00 40.00
30.00 30.00
delta (degrees)
Pdms-ar-04o
raw phase (degrees)
1.000E6
G' (Pa)
• During one cycle in oscillation, the material is
accelerated to maximum speed and then decelerated
to zero speed => inertia effects are always present
• Concern in oscillation experiments is particularly at
high frequency with low viscosity fluids
• Minimize correction by lowering the inertia of the
moving parts (test geometries)
• Inertia effects the measured phase. Plot raw
phase. If raw phase is above 150° then inertia is
dominating your test results
10000
20.00 20.00
Increasing correction at higher frequencies
10.00 10.00
1000
1000
0.01000
Effect of Inertia on Amplitude and Raw Phase
0
0.1000
1.000
Frequency (Hz)
0
100.0
10.00
Effect of Inertia on G’and G”
0.10
210.0
180 o
10000
10000
1000
1000
100.0
100.0
1.0E-5
1.0E-6
0
0.1000
1.000
10.00
100.0
ang. frequency (rad/sec)
7cm plate, inertia: geometry = 42.69, total = 57.01 µNm s²
4cm plate, inertia: geometry = 7.90, total = 22.22 µNm s²
G'' (Pa)
1.0E-4
G' (Pa)
1.0E-3
displacement (m)
raw phase (deg)
0.01
1.0E-7
1000
10.00
0.1000
1.000
10.00
100.0
ang. frequency (rad/sec)
10.00
1000
7cm plate
4cm plate
2cm plate
2cm plate, inertia: geometry = 1.109, total = 15.43 µNm s²
35
2013 TA Instruments New Castle DE
Ten Steps to Better Rheological Measurements
Understand why you are doing the measurement.
Understand the instrument first.
3. Know your sample.
4. How to select the correct test fixture
5. Loading the sample
6. Oscillation testing guidelines
7. Transient testing guidelines
8. Steady shear testing guidelines
9. Some instrument limitations
10. Presenting the data
1.
2.
Presenting the Data
• Accurate data interpretation, model fitting, and comparisons of
rheological data require selection of appropriate parameters and
plot scaling.
• Meaningful information can be masked if the data are not
presented the right way.
• After running experiment, always check and make sure the data
you are presenting are within instrument specifications, and
unaffected by artifacts.
• It is a good practice to include notes on plots that display
information pertinent to how the data was run and important to
the interpretation, such as pre-shear rate and time, temperature
in a frequency sweep, frequency in a temperature sweep, clamp
type or geometry, etc.
Presenting the Data
• Don’t overload plots with unnecessary parameters.
Better to make two plots rather then confuse the
interpretation.
• Legends
• Colors/symbols/lines
• Stamp critical points and fits such as end of linear
region, cross-over frequency, transition peaks,
onsets, etc.
Oscillation Tests
• Frequency Sweeps
• X-axis: Plot frequency  on log scale
• Y-axis: Plot G’, G”, tan  & * on log scale
• Temperature Sweeps and Ramps
• X-axis: Plot temperature on linear scale
• Y-axis: Plot G’& G” on log scale
• Y-axis: tan  can be plotted on log or linear scale
• A single transition over a temperature range is often best
observed on a linear scale.
• When multiple transitions are present, weaker secondary
transition peaks may not be obvious when tan is plotted
on linear scale.
Oscillation Tests
• Time Sweeps
• X-axis: Plot time on linear scale
• Y-axis: Plot G’ or * on log scale
• Strain Sweeps
• X-axis: Plot  same as sweep mode – log or lin
• Y-axis: Plot G’& G” on log scale
• Stress Sweeps
• X-axis: Plot  or  same as sweep mode – log or lin
• Y-axis: Plot G’ & G” on log scale
Data Presentation: Time Sweep on Polymer
What’s missing?
100.0
Aging Process
Melt
10.00
1.000
0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
time (s)
36
2013 TA Instruments New Castle DE
Data Presentation: Time Sweep on
Polymer
Data Presentation: Time Sweep on
Structured Fluid
That’s Better!
100.0
New Sample - Milled for shorter time
Old Sample - Milled for longer time
Polyester Temperature stability
275
Temperature stability
good
poor
10.00
250
225
200
4
10
G' (Pa)
Modulus G' [Pa]
10
Temperature T [°C]
5
175
-2
0
2
4
6
8
10
12
14
16
NOTES
Preshear: 1000 1/s for 60 sec
Stress = 0.1 Pa
Frequency = 6.28 rad/s
Temperature = 25 deg C
Geometry: 40 mm PP SST ST
1.000
0.1000
18
0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
1000
time (s)
Time t [min]
Remember to Check Specifications
Label Important Information
1.000E5
100000.0
LLDPE at 150°C and 1 Hz (6.28 rad/s)
10000.0
900.0
G’
800.0
500.0
400.0
300.0
200.0
G' (Pa)
Ignore
out of
spec
data
100.0
Critical Strain = 12%
10.0
torque
100.0
0
0.010000
0.10000
1.0000
10.000
100.00
1000.0
10000
1.0000E-3
0.010000
% strain
0.10000
1.0000
10.000
1.0
100.00
% strain
Label Important Information
Good Use of Colors, Symbols, & Legend
PSA: Glass Transition Measurement
Effect of Branching on LLDPE [150°C]
TA Instruments
1000000
FMLLDPE1.35O-freq step
GMLLDPE2.35O-freq step
G'
100000
HMLLDPE3.34O-freq step
IMLLDPE4.39O-freq step
100000
10000
10000
g' = 0.84-0.86
n* (Pa.s)
G' (Pa)
G' (Pa)
600.0
osc. torque (micro N.m)
1000.0
700.0
1000
100.0
n*
g' = 0.75-0.76
10.00
0.01000
1000
0.1000
1.000
10.00
ang. frequency (rad/sec)
100.0
1000
37
2013 TA Instruments New Castle DE
Good Use of Colors, Symbols, & Legend
Presenting Stress Relaxation & Creep Data
Polymer Blend - Aerospace Coating
1.5

100%
Polymer B
• In Creep, Strain, Creep compliance, and recoverable compliance
can be plotted
• Linear – linear
• Linear – log
• Log – log
Polymer Blend
A+B

1.0
• Stress relaxation results are typically always presented on a loglog scale.
–––––– Polymer A
 – – – Polymer Blend: A + B
–––– · Polymer B
46.46°C

76.19°C


89.77°C

Tan Delta



0.5







0.0























• The selection of scaling will depend on the time scale of interest.







• In general, linear scales work better for looking at the longer time
response of a material and log scales help to expand differences
on shorter time scales.

100 % Polymer A
-0.5
-25
0
25
50
75
100
Temperature (°C)
• Some examples are as follows.
125
Universal V2.5D TA Instruments
Linear and logarithmic Plots
Creep Compliance with Increasing Stress
Log-linear scale provides perspective of LVE for complex fluid
LDPE Melt Relaxation
LDPE Melt Relaxation
2.0
100.0
1.8
1.0
0.8
0.6
increasing strain
0.4
1
o
T=140 C
strain 10%
strain 20%
strain 50%
strain 100%
strain 200%
strain 400%
0.1
0.01
0.2
0.0
0
10
20
30
40
0.01
50
0.1
1
10
100
Time t [s]
Time t [s]
Data curves may look very different in the logarithmic
representation!!
compliance (m^2/N)
1.2
Modulus G(t) [KPa]
Modulus G(t) [KPa]
1.4
10.0
1.0
Log-log scale provides different LVE perspective for polymer
LDPE Melt creep recovery
-2
-1
LDPE Melt
o
T=140 C
10 Pa
50 Pa
100 Pa
500 Pa
1000 Pa
5000 Pa
10
slope 1
-2
10
increasing
stress
10
-3
10
-4
10
10
-5
10
0.1
-3
10
-4
-5
1
10
Time t [s]
100
Log scale expands the scale initially
0.010
1.0E-3
0
50.00
150.0
200.0
250.0
Creep Recovery Curve on Polymer Melt:
Linear Scales for Long time Equilibrium
Parallel Plates LLDPE at 150°C
Data Fit to Straight Line Model to get slope of
Creep Compliance at equilibrium: Slope = 1/
Slope from fit = 2.451E-5 so  = 1/2.415E-5 = 40,799.6 Pa.s
2.5000E-3
a: y-intercept: 4.691E-5
b: slope: 2.4511E-5
regression: 0.99998
standard error: 0.3606
2.0000E-3
Initial
effects are
expanded
in time
100.0
time (s)
2.2500E-3
Recoverable Compliance Jr(t) [1/Pa]
Compliance J(t) [1/Pa]
10
-1
Log scale compresses the data
for higher values
0.10
Creep and Recovery with Increasing Stress
10
Stress = 0.3, 0.4 & 0.5 Pa
increasing strain
10
o
T=140 C
strain 10%
strain 20%
strain 50%
strain 100%
strain 200%
strain 400%
1.6
1.7500E-3
1.5000E-3
Creep Compliance = Jc
1.2500E-3
Equilibrium Recoverable
Compliance = Joe
1.0000E-3
7.5000E-4
Recoverable Compliance = Jr
5.0000E-4
2.5000E-4
1000
0
0
50.00
100.0
150.0
200.0
250.0
300.0
global time (s)
350.0
400.0
450.0
500.0
38
2013 TA Instruments New Castle DE
Presenting Steady State and Transient
Flow Data
Characteristic Flow Diagrams on Linear-Linear
Plot
• Multiple ways of plotting steady shear data.
• Shear stress vs. shear rate
• Viscosity vs. shear rate
• Viscosity vs. shear stress
Flow on linear-linear Plot
Bingham (Newtonian w/yield
stress)
Shear Stress, 
Bingham Plastic
(shear-thinning w/yield stress)
• Make use of log and linear scales
• Use viscosity models
Shear Thinning (Pseudoplastic)
Newtonian
y
Shear Thickening (Dilatent)

Shear Rate, 
Characteristic Diagrams for Shear Thinning
Fluids
Scaling Makes a Difference
Automotive Paint Samples: Data fit to Herschel-Bulkley Model
105
Ideal Yield Stress
(Bingham plastic)
, Pa
103
10000
101
1000
10-6 10-4 10-2 100
s
Pa.s
104
103
101
105
Pa.s
Log-log
Plots
105
10-1
102
s
103
viscosity (Pa.s)
10-1
101
Old Sample
a: yield stress: 5.207 Pa
b: viscosity: 0.2909 Pa.s
c: rate index: 0.8426
standard error: 5.983
New Sample
a: yield stress: 6.582 Pa
b: viscosity: 0.3777 Pa.s
c: rate index: 0.8319
standard error: 10.83
100.0
10.00
New Sample - Milled for shorter
time
Old Sample - Milled for longer time
1.000
0.1000
10-1
10-6
10-4
10-2
100
102
104
10-1
10-0
s
10-1
102
103
100.0
150.0
200.0
250.0
300.0
Ink Flow Curves: Shear Stress vs. Shear Rate
Automotive Paint Samples: Viscosity vs. Shear Stress
10000
50.00
shear stress (Pa)
Scaling Makes a Difference
viscosity (Pa.s)
0.01000
0
, Pa
1000
New Sample - Milled for shorter time
Old Sample - Milled for longer time
1000
100.0
100.0
1 Pa Change in Stress
10.00
10.00
1.000
0.1000
0.01000
1.000
10.00
100.0
shear stress (Pa)
1000
1.000
1.000E-5
1.000E-3
0.1000
10.00 100.0 1000 10000
shear rate (1/s)
39
2013 TA Instruments New Castle DE
Ink Flow Curves: h vs. Shear Stress
Ink Flow Curves: h vs. Shear Rate
1000000
Yield stress develops below which there
is no real macroscopic flow
1000000
100000
100000
viscosity (Pa.s)
viscosity (Pa.s)
10000
1000
100.0
10.00
Low shear viscosity limit often
disappears with higher concentration
10000
1000
100.0
10.00
1.000
1.000
0.1000
0.1000
1.000E-5
1.000E-3
0.1000
shear rate (1/s)
10.00
10000
1.000
10.00
100.0
shear stress (Pa)
1000
Margarine Data: Cross Model
Fitting the Right Model
Predicts the shape of the complete Flow Curve
1.000E6
=(K ) m

1.000E5
10000
viscosity (Pa.s)
Sub-sets of the Cross Equation which predict portions of the
complete Flow Curve
 n 1
Power Law
 = K1
Sisko
 =  + K1 n-1
1000
100.0

10.00
1.000

0.1000
1.000E-4
 = o - K1 n 1
Williamson
Cross
a: zero-rate viscosity: 4.426E5 Pa.s
b: infinite-rate viscosity: 0.08264 Pa.s
c: consistency: 2274 s
d: rate index: 0.9863
standard error: 2.428
thixotropy: 0 Pa/s
normalised thixotropy: 0 1/s
End condition: Finished normally
viscosity at 19.00 1/s: 11.94 Pa.s
0.01000
1.000
shear rate (1/s)

Flow Curve on Polymer Melt
Parallel Plates, LLDPE at 150°C
1.000E5
10000
Yield stress in a stress ramp
1.000E5
Yield stress of a cosmetic lotion
h
Data Fit to Williamson Model
Zero Shear Viscosity = 41,350 Pa.s
4.0
[Pas]
Yield stess (at maximum) = 5.4 Pa
1000
3.5
10000

3.0
100.0
shear stress (Pa)
a: zero-rate viscosity: 41350 Pa.s
b: consistency: 0.8478 s
c: rate index: 0.5729
standard error: 32.84
Viscosity  [Pas]
100
1000
viscosity (Pa.s)
100.0
2.5
Strain
2.0
10
1.5
Strain (x10-6)
Cross
0 - 
 - 
The maximum
viscosity method
is more
representative
and reproducible
then the strain
tangent method
1.0
1
0.5
10.00
Stress
0.0
0
50
100
150
200
Stress [Pa]
10000
1.000E-5
1.000E-4
1.000E-3
0.01000
0.1000
1.000
1.000
shear rate (1/s)
40
2013 TA Instruments New Castle DE
Structured fluid: Flow Curve in Rate Mode
Thixotropic loop
Flow cuve of an ink paste
10
9
10
8
10
7
10
6
10
5
10
4
10
3
10
2
10
1
10
0
10
Stress
Viscosity
slope -1
1
10
0
10
-1
10
-2
0.009 Pa
Shear rate  [1/s]
Stepped rate
test on
ARES
Shear rates
are stepped
at equal
intervals
=> smooth
curve
Thixotropic loop for 3 Mayonnaise emulsions
80
60
sample A up
sample A down
sample B up
sample B down
sample C up
sample C down
40
20
0
0
The viscosity decreases with a slope of -1 versus strain rate and
the stress becomes rate independent => material with yield stress
first ramp up
2
peak at stress 1.3 Pa
0
4
6
.
rate (t) [1/s]
300
400
500
8
100000
viscosity (poise)
4
Nonthixotropic
material
Up and
down ramps
superpose –
except the
first one
=> Start up
from zero
Stress [Pa]
Viscosity (t) [Pas]
viscosity [Pas]
stress [Pa]
2
.
1000000
6
0
200
Equilibrium Flow & Thixotropy Loops
Children Advil suspension
0
100
Rate [1/s]
Thixotropic loop
10
Thixotropic
material
Up and down
ramps do not
superpose
Area under
the curve is a
measure of
thixotropy
100
Stress  [Pa]
10
Stress  [mPa]
Viscosity  [mPa s]
10
10000
Equilibrium Flow
Thixotropy Loop
10
1000
1.000E-4
1.000E-3
0.01000
0.1000
1.000
10.00
100.0
shear rate (1/sec)
Tip #11: Take advantage of all of the
training opportunities available to you!
Tip #11: Take advantage of all of
the training opportunities
available to you!
• It is extremely important to us for our customers to get
the best out of their instruments
• While we’ve always offered multiple training
opportunities, we’ve dramatically increased this
offering over the past several years
• We will use this last presentation to make sure you
are aware of what is available
• Our web site is a good place to start to see what
training is available
• www.tainstruments.com
41
2013 TA Instruments New Castle DE
•
•
•
•
•
•
TA Instruments Corporate Website
Training Web page
Training Opportunities from TA
Initial Training at Installation
Initial Training at Installation
e-Training Courses
Theory & Applications Training Courses
Hands-On Training Courses
Custom Onsite Training Courses
Special Courses
e-Training Courses
• Preformed by Service Engineer during installation
• They will show you how to:
• Calibrate your instrument
• Use software to set up experimental run
• Prepare a sample for analysis
• Create & run a method
• Analyze the data
e-Training Courses
• Variety of courses that can be taken off our website
• These course include:
• QuickStart Courses that tell you how to get started
running your instrument – These are Free!!
• Advanced Courses build on the basics and talk
about advanced features and options
• These are available as recorded courses that you can
take 24/7
• Also available “Live” (see website for details)
42
2013 TA Instruments New Castle DE
Theory & Applications Training Courses
Example of Training Calendar
• One day lecture based courses for each technique
• Covers; theory, instrumentation, calibration, method
development, operating conditions, and applications
• Given at our corporate headquarters in New Castle,
DE (also in CA –see special courses)
Hands-On Training Courses
• A two day course that consists of running the
instruments, sample preparation, method
development, and data interpretation
• Attendance is limited per course to maximize the
benefit
• Courses are scheduled in DE, and our Chicago area
office
Custom Onsite Training Courses
• These courses are taught at your facility, with your
instruments, and your samples
• Can be Hands-On, Lecture, or a combination of both
• Typical agenda might be:
• Theory & Instrumentation (Lecture)
• Applications (Lecture)
• Calibration (Hands-on)
• Running your samples (Hands-on)
• Analyzing your data (Hands-on)
Special Courses
Special Courses
• This section will list new specialized courses that we
will be giving from time to time
• Current offerings:
• Theory & Applications Course in CA – Back by
popular demand
• Scheduled the week of September 12, 2005 at
Caltech in Pasadena (the week before NATAS in
nearby Universal City, CA)
• Rheology, DMA, TGA, DSC, MDSC®
• These are the same lecture based courses that we
give in DE
• DSC Certified User Training Course - Back by
popular demand
• October 19, 2005 as part of a “DSC Week”, which
includes Theory & Applications courses for DSC &
MDSC®, and Hands-on DSC & TGA training
• Course is designed to take users to the next level.
Covers theory, calibration & maintenance, method
development, and data interpretation
43
2013 TA Instruments New Castle DE
Special Courses
Lastly
• Rheology Certified User Training Courses – First
time offered
• A separate course for both AR & ARES users.
Scheduled on October 25 (AR) & 26 (ARES), 2005
as part of a “Rheology Week”, which also includes
the Rheology Theory & Applications course,and
Hands-on training courses for the AR & the ARES
• Course is designed to take users to the next level.
Covers theory, calibration & maintenance, method
development, and data interpretation
• Always let us know if you desire training that is not
listed. We are always open to suggestions, and
feedback.
• For more information on any and all of these options,
go to our website, or email
training@tainstruments.com
• Thank you for coming and for your interest in TA
Instruments
44