LAB REPORT
DYNAMIC MECHANICAL ANALYSIS
DEPARTMENT OF POLYMER ENGINEERING
SPRING 2020
VISHAL TYAGI
1
TABLE OF CONTENTS
INTRODUCTION......................................................................................................................2
BACKGROUND……………………………………………………………………………………… 3
PROCEDURE..........................................................................................................................6
SAMPLE CALCULATIONS......................................................................................................9
RESULTS...............................................................................................................................10
CONCLUSION.......................................................................................................................13
REFERENCES.......................................................................................................................13
FIGURES
Figure 1. Representative applied sinusoidal load and measured sinusoidal response of the
specimen………………………………………………………………………….………………….03
Figure 2. Schematic plot of the occurrence of a glass transition process and its respective
classification…………………………………………………………………………………..……..05
Figure 3 . Experimental objective of determining activation energy of glass transition
process……………………………………………………………………………………...………..05
Figure 4. Dynamic mechanical analysis apparatus, TA Instruments Q800 DMA………..…..06
Figure 5. Schematic illustration of film tension clamp for Q800 DMA. ……………….………07
Figure 6 . Plot for determining activation energy………………………………………...………09
Figure 7 . Plot of cos(δ) Vs Temperature……………………………………………………………10
Figure 8 . Plot of sin(δ) Vs Temperature……………………………………………………........….11
TABLES
Table 1. Regression statistics for line of fit……………………………………………………....09
2
INTRODUCTION
Polymers, because of their viscoelastic nature, exhibit behavior during deformation which is
both temperature and time (frequency) dependent. For example, if a polymer is subjected to
a constant load, the elastic modulus exhibited by the material will decrease over a period of
time. This occurs because the polymer under a load undergoes molecular rearrangement in
an attempt to minimize localized stresses. Hence, modulus (stiffness) measurements
performed over a short time span result in higher values than longer term measurements. This
time dependent behavior would seem to imply that to accurately evaluate material
performance for a specific application, one needs to test the material under the actual
temperature and time conditions it will see in end-use. Fortunately, that type of tedious testing
is not necessary .Dynamic mechanical analysis (DMA) is a technique which measures the
modulus (stiffness) and damping (energy dissipation) properties of a material as the material
is deformed under periodic stress. It is one of the best thermal analysis techniques for using
this time/temperature predictive approach.
In dynamic mechanical analysis,Tg can either be defined as the temperature where the
maximum loss tangent or the maximum loss modulus is observed, or as the inflexion point at
which a significant drop of the storage modulus occurs. However,the respective peaks or
points usually occur at different temperatures which results in a broad transition region for
polymeric materials. In addition to the inherent chemical properties and the used criterion of
es-timating theTg value, factors related to instrument and test conditions, such as test
frequency, heating rate, sample size and clamping effects can also influence the measured
Tg value. It has been reported that increasing the test frequency or heating rate leads to a
shift of Tg to higher temperatures. The bond rotations and segmental motion associated with
temperature above glass transition are responsible for the rubbery state of polymers .The
energy associated with these phenomena is the activation energy.once the activation energy
barrier is crossed the polymer chains are free to move. Activation energy can be measured
using the arrhenius relation , If a DMA scan is performed with multiple frequencies, one may
get an estimate of the activation energy by plotting the tan delta maximum temperatures (1/T)
measured at different frequencies vs. log frequency.
3
BACKGROUND AND THEORY
Dynamic mechanical analysis (DMA) is a characterization tool that is used to determine the
viscoelastic properties of materials. DMA is sometimes referred to as a thermal analysis
technique as it can be used to detect temperature sensitive molecular phenomena such as
the glass transition and crystallization.
In DMA, the transient or dynamic viscoelastic properties can be measured. Transient
viscoelastic properties refer to tests such as creep or stress relaxation where either an
instantaneous stress or strain is applied to the specimen and the strain or stress monitored as
a function of time respectively. The dynamic viscoelastic properties refer to tests where the
specimen is under a sinusoidal (time-varying) deformation. DMA is able to differentiate the
elastic and viscous components of the viscoelastic response. In our experiment we will be
applying a sinusoidal strain to the sample at different rates (i.e frequencies).
Figure 1. Representative applied sinusoidal load and measured sinusoidal response of the
specimen.
For viscoelastic materials, the measured sinusoidal response is typically out of phase with the
input sinusoidal load. If the phase difference (also called phase angle), δ, is 0o the material is
purely elastic, and if δ is 90o then the material is purely viscous. Viscoelastic materials such
as polymers typically have 0o < δ < 90o. The elastic response of the material denotes the
tendency to store energy while the viscous response denotes the tendency to dissipate
energy.
Viscoelastic properties are dependent on temperature and time. Controlling the rate at which
the sinusoidal load is applied enables the study of time effects on viscoelastic properties. DMA
4
can be used to prescribe practical end-use applications as it forms the basis for predicting
polymer performance under load, temperature and time (or frequency). The measured stress
and strain values are functions of temperature, frequency and applied load. There are
basically two types of DMA measurement. Deformation-controlled tests apply a sinusoidal
deformation to the specimen and measure the stress. Force-controlled tests apply a dynamic
sinusoidal stress and measure the deformation. Dynamic load may essentially be achieved in
free vibration or in forced vibration.
Also, Molecular motion is impacted by the rate of deformation. The glass transition process is
a kinetically trapped non-equilibrium phenomenon and its manifestation can be impacted by
the rate of sample deformation as well. When frequency is increased, the respective relaxation
may only occur at higher temperatures and thus an apparent increase in Tg is observed.
The loading of a viscoelastic material with a sinusoidal strain is represented as,
ε∗ = ε0𝑒𝑥𝑝(𝑖𝜔𝑡)
Where ε0 is the strain amplitude, ω is the angular frequency (= 2f) of the strain oscillation and
t is the elapsed time. The stress response, 𝜎∗, of the viscoelastic material to the sinusoidal
strain is represented as,
𝜎∗ = 𝜎0𝑒𝑥𝑝[𝑖(𝜔𝑡 + 𝛿)]
where 𝛿 is the phase angle and 𝜎0 is the stress amplitude. The complex modulus E* can
therefore be represented in the form,
𝐸∗ = 𝜎∗/ε∗ = 𝐸′ + 𝑖 𝐸′′ = |𝐸∗|𝑒𝑥𝑝(𝑖𝛿)
where |E*| is the absolute modulus which is (𝐸′2 + 𝐸′′2 )0.5 The storage modulus, E’, is
defined as,
𝐸′ = |𝐸∗|𝑐𝑜𝑠(𝛿)
and the loss modulus, E’’, is defined as,
𝐸′′ = |𝐸∗|𝑠𝑖𝑛(𝛿)
The storage and loss modulus are related through,
𝑡𝑎𝑛(𝛿) =𝐸′′/𝐸′
Notice E’, E’’ and tan (δ) are functions of the angular frequency.
5
Temperature sweeps in DMA can be used to determine the glass transition temperature, Tg,
due to the sudden changes in E’ and E’’ as Tg occurs. The criteria for determining Tg is
typically a matter of resolution as E’, E’’ and tan δ can be used to determine Tg.
Conventionally, the temperature at which E’’ or tan δ go through a peak maximum is usually
considered as Tg. In this experiment tan δ was used to determine Tg.
Figure 2. Schematic plot of the occurrence of a glass transition process and its respective
classification.
When using tan δ to monitor Tg, the temperature at which the peak is maximum will vary as a
function of deformation frequency. Tg will shift to higher temperatures with increasing
frequencies. An Arrhenius relationship can be used to describe the relationship between
frequency and Tg,
𝑓 = 𝑓𝑜𝑒𝑥𝑝(−𝐸𝐴 /𝑅𝑇𝑔)
where f0 is a frequency coefficient (sometimes referred to as an activation frequency), R is the
universal gas constant and EA is the activation energy.
A plot of ln f versus 1/ Tg should yield a linear relationship if the system follows an Arrhenius
behavior. The activation energy can be calculated as the slope of line times the gas constant
R.
Figure 3 . Experimental objective of determining activation energy of glass transition
process.
6
EXPERIMENTAL
Material: Natural Rubber
For this experiment, a TA Instruments Q800 Dynamic Mechanical Analyzer (DMA) was
used.
Figure 4. Dynamic mechanical analysis apparatus, TA Instruments Q800 DMA.
In this equipment, oscillatory and static forces are enabled by a non-contact, direct drive motor
that is thermostated and has low compliance. A wide range of material properties can be
measured due to the rapid and reproducible forces that can be generated. Forces from the
drive motor are transmitted directly to an air bearing slide. Pressurized air flows to the bearing
and permits a near frictionless surface that makes the slide essentially float. Displacement is
measured by a linear optical encoder that uses light diffraction patterns through a stationary
and moveable grating which gives high resolution to measure very small amplitudes. A variety
of clamps are available for use on the Q800 DMA to enable different sample deformation
modes. For this experiment we used the film/fiber tension clamp geometry where the sample
is mounted between a fixed and moveable clamp, which is ideal for tensile studies on films
and fibers.
Figure 5. Schematic illustration of film tension clamp for Q800 DMA.
7
The stages involved in a DMA measurement are as follows:
1.choose a load appropriate to the problem, and a clamping device,
2.prepare specimen (geometry, degree of plane-parallelism)
3.clamp the specimen
4.choose measuring parameters
Factors exerting an influence on the apparatus and specimen are:
1. Clamps
2. Specimen geometry
3. Frequency
4. Type of load
5. Temperature program
6. Tightening torque Influential factors
PROCEDURE:
1.The average length and thickness of tensile testing specimens was measured and
provided as input into the sample geometry section in the TA Thermal Advantage software.
2.When loading the sample, care should be taken to ensure proper vertical alignment.
3.Frequency was held constant while the temperature was ramped from -80ºC to 0ºC at a
rate of 2ºC/min.
4.The equipment was run in strain-controlled mode at a strain value of 0.1%.
5.A pre-load force of 0.01 N was applied to the fiber to keep the specimen taut prior to the
start of the experiment to establish a baseline length. A force track value of 125% was
enabled to ensure the specimen stays taut during the experiment.
6.Prior to the start of the experiment, the specimen was equilibrated at -80 oC for two
minutes.
7.The temperature sweep data was collected.
7.The same process was repeated for frequencies 1, 2, 3, 5 10, 15, 20, 30 and 50 Hz.
8
SAMPLE CALCULATIONS
1.calculation of activation energy
𝑓 = 𝑓𝑜𝑒𝑥𝑝(−𝐸𝐴 /𝑅𝑇𝑔)
Taking log on both sides we obtain
ln(𝑓)= ln(𝑓𝑜) - 𝐸𝐴 /𝑅𝑇𝑔
This is a form of general equation of a straight type
Y= mX + C
Where m = slope of straight line
Comparing the slope from the plot we get
m= - 𝐸𝐴 /𝑅
⇒𝐸𝐴 = - (Slope) x R = -(-20133) X 8.314= 167386 J
Calculation of storage and loss modulus from tan
Tan(𝛿) = 0.04457015
⇒(𝛿) = 𝑡𝑎𝑛−1 (0.04457015)= 2.551992
Loss modulus
Sin (𝛿) = sin (2.551992) = 0.044525
Storage modulus
Cos (𝛿) = cos (2.551992) = 0.9990
9
RESULTS AND DISCUSSIONS
Activation energy measurements
Ln(f) Vs 1/T
4.5
4
3.5
3
Ln(f),Hz
2.5
2
y = -20160x + 90.804
1.5
1
0.5
0
0.00425
-0.5
0.00430
0.00435
0.00440
0.00445
0.00450
0.00455
1/T (1/k)
Figure 6 . Plot for determining activation energy
Regression Statistics
Multiple R
0.990307
R Square
0.980709
Adjusted R
Square
0.977953
Standard Error
0.195149
Observations
9
Table 1. Regression statistics for line of fit.
Using the Arrhenius relation, the activation energy was calculated and was observed to be 167386
J..the line of fit has a R Square value of 0.980709 which implies that it fits approximately 98 % of the
values.
10
All semi crystalline and amorphous Polymers exhibit a glass transition. The glass transition is the
property of the amorphous part of the polymer. As the temperature is decreased polymers turn from
an amorphous state of low viscosity to a supercooled liquid with very high viscosity. This transition
is characterized by the glass transition temperature (Tg).
Glass transition is a kinetically trapped non-equilibrium phenomenon and at temperatures above the
glass transition range they have sufficient kinetic energy to move enhancing the mobility of chains in
amorphous regions . The bond rotations and segmental motion associated with temperature above glass
transition are responsible for the rubbery state of polymers .the energy associated with these phenomena
is the activation energy.once the activation energy barrier is crossed the polymer chains are free to
move.
relationship between storage modulus and temperature.
storage modulus Vs Temperature
1.2
f=30
0.8
f=50
0.6
f=20
f= 10
0.4
f= 15
f=5
0.2
f=3
f=2
0
-78.670166
-72.556816
-65.86232
-61.962753
-58.532787
-55.570564
-53.655613
-52.556305
-50.934338
-50.008686
-48.967857
-48.274677
-46.766956
-44.499016
-42.399815
-40.59029
-38.779922
-36.561817
-34.343792
-30.668474
-27.169353
-23.146387
-18.367353
-13.996313
-10.673899
-6.362862
-2.2854843
storage modulus
1
temperature (C)
Figure 7 . Plot of cos(δ) Vs Temperature
f= 1
11
relationship between loss modulus and temperature.
Loss modulus Vs Temperature
0.8
0.7
f= 50 Hz
0.5
f=30 Hz
0.4
f=20 Hz
0.3
f=15 Hz
f=5 Hz
0.2
f= 10 Hz
0.1
f= 3 Hz
0
-78.670166
-72.556816
-65.86232
-61.962753
-58.532787
-55.570564
-53.655613
-52.556305
-50.934338
-50.008686
-48.967857
-48.274677
-46.766956
-44.499016
-42.399815
-40.59029
-38.779922
-36.561817
-34.343792
-30.668474
-27.169353
-23.146387
-18.367353
-13.996313
-10.673899
-6.362862
-2.2854843
Loss modulus
0.6
f=2 Hz
f=1 Hz
Temperature (C)
Figure 8 . Plot of sin(δ) Vs Temperature
Use of Tan δ to represent Tg
Tan δ represents the ratio of the viscous to elastic response of a viscoelastic material or in another word
the energy dissipation potential of a material. To make it simple, assume that one applies a load to a
polymer, some part of the applied load is dissipated by the energy dissipation mechanisms (such as
polymer chain segmental motion) in the bulk of polymer, and other part of the load is stored in the
material that will be release upon removal of the load (such as the elastic response of a spring). Tanδ
also relates to vibration damping. For vibration damping (or energy dissipation) you need high tanδ.
Tanδ can provide information on the overall flexibility and the interactions between the components of
a composite material. The height and area under the tanδ curve give an indication of the total amount
of energy that can be absorbed by a material. A large area under the tanδ curve indicates a great degree
of molecular mobility, which translates into better damping properties, meaning that the material can
better absorb and dissipate energy better. So, for the design of a material that can absorb impact better,
we like to increase the area under the tanδ curve.
12
Increasing tanδ indicates that material has more energy dissipation potential so the greater the tanδ, the
more dissipative the material is. On the other hand, decreasing tanδ means that material acts more elastic
now and by applying a load, it has more potential to store the load rather than dissipatin g it. For
example, in case of nano-composites (and filled polymers), increasing the nano-particle content
diminishes the value of tanδ as nano-particles impose restrictions against molecular motion of polymer
chains (due to the adsorption of polymer chain on the surface of the particles) resulting in more elastic
response of the material.
Since the measurement of glass transition temperature from the maximum loss factor is fairly easy than
measuring the glass transition temperature from loss modulus (which requires construction of tangents
and determining their intersection point) it is favorable to determine glass transition temperature from
the maximum loss factor.
Also, Glass transition temperature can also be described using:
1. Onset of the drop in storage modulus(E')
2. peak in loss modulus (E")
From the plots it can be seen that the drop in storage modulus and peak in loss modulus also occur at
approximately the same temperature at which the peak in the tan delta vs temperature curve is
observed.
Effect of frequency on glass transition temperature
The Tg value for epoxy resins based on the tanδ peak is significantly influenced by the test frequency.
When characterizing a material by DMA, the time of the deformation is related to the frequency as
frequency is the inverse of time (frequency = 1/time). Therefore, high frequencies are analogous to short
times and low frequencies to long times.The glass transition is a molecular relaxation that involves
segmental motion whose rate will depend on temperature. Therefore, as the frequency of the test
increases, the molecular relaxations can only occur at higher temperatures and Consequently , the Tg
increases with increasing frequency.
13
CONCLUSION
In the experiment, temperature was ramped from -80°CC to 0°C at a rate of 2°C/min. The frequencies
used to explore the thermal characteristics were 1, 2, 3, 5 10, 15, 20, 30 and 50 Hz.The temperature at
which tan (δ) showed a maximum was interpreted as the glass transition temperature (Tg).It was
observed that Tg increases with increase in test frequency.
Using the Arrhenius relation, the activation energy was calculated and was observed to be 167386 J.
Also,Data for the storage (E’) and loss (E’’) modulus as well as tan (δ) was reported in graphical form
as a function of temperature, T. The temperature at which tan (δ) showed a maximum was interpreted
as the glass transition temperature (Tg).
REFERENCES
1. E. Turi, ed.,Thermal Characterization of Polymeric Materials, Academic Press,Boston, Mass., 1981;
2. H. Barnes, J. Hutton, and K. Walters,An Introduction to Rheology, Elsevier SciencePublishing, Co.,
New York, 1989
3. G. Martin, A. Tungare, and J. Gotro,Polymer Characterization, ACS, WashingtonD. C., 1990
4.S. Rosen,Fundamantal Principles of Polymeric Materials, Wiley Interscience, NewYork, 1993, pp.
53–77 and 258–259.
5. E. Turi, ed., Thermal Analysis in Polymer Characterization, Heydon, London, 1981.