Modelling kinetic cure behavior of thermosetting polymers using
differential scanning calorimetry
1. Purpose
Isothermal and dynamic thermal scanning programs can be used to determine the kinetic
factors associated with the cure behavior of thermosetting polymeric materials. The students will
analyze the heat exchange thermogram of the thermosetting monomer bisphenol E cyanate ester
(BECy, 1,1’-bis(4-cyanatophenyl)ethane,) collected with differential scanning calorimetry, using
known kinetic models to determine the activation energy, Ea, and the pre-exponential factor, A,
of the governing Arrhenius equation.
2.1 Differential Scanning Calorimetry
Differential scanning calorimetry (DSC) is used to measure the temperatures and heat
flow during thermal transitions of materials in a wide range of applications, including polymer
cure kinetics. The two prominent forms of DSC instruments are the heat flux and power
compensated models. Both models are governed by the principle of comparing the heat
exchange, absorption (endothermic) or dissipation (exothermic), by a material when compared to
a reference, often air.
The heat flux model houses both sample pan and reference pan within a single furnace,
Fig. 1, whose temperature is regulated by a feedback loop which collects data on the heat
exchange between the furnace and each of the pans by way of highly sensitive thermocouples.
Regulation of the furnace temperature maintains both samples at the same temperature by
increasing the temperature of the furnace and bringing the lower temperature pan to equilibrium
with the second pan. Power compensated DSC units have individual furnaces for the sample and
reference pans, whose temperatures are monitored as the reactions proceed. In the case of the
power compensated DSC, however, only the furnace whose temperature is lower receives a
surge of electrical current, which will raise the temperature of the pan to match the higher
temperature pan. (The Perkin-Elmer instruments found in the MSE teaching labs are examples
of power compensated DSC.)
Fig 1: Schematic representation of heat flux DSC sample cell, containing both reference and sample pans.
2.2 DSC Samples
The sample to be characterized is sealed in an aluminum pan and placed alongside an
empty aluminum reference pan in the DSC furnace. The sample and the reference pan are heated
at the same rate by a heating element in the furnace. Thermal transitions such as melting or
crystallization involve release or absorption of heat which leads to a difference in temperature
between the sample and reference. The DSC measures the difference in heat flow required to
maintain the sample and the reference at the same temperature. A purge gas such as helium or
nitrogen may be used to ensure thermal efficiency and to remove evolved volatiles.
2.3 Bisphenol E cyanate ester
Bisphenol E cyanate ester (BECy) is a diisocyanate
monomer containing two phenyl rings along the backbone of the
monomer, Fig. 2. The monomer exhibits attractive processing
Fig. 2: Monomer form of BECY
and structural properties, including low viscosity (0.09 – 0.12 Pa·s), long pot life and low
volatile emissions, while fully cured BECy has an onset glass transition temperature ca. 270°C
which makes it suitable for lightweight, high strength, and high temperature matrix applications.
The appeal of these chemical species is the highly efficient
polymerization process and the high storage modulus;
attributed in large part to the presence of the aromatic rings
which inhibit polymer chain mobility. Additionally, BECy
exhibits a range of attractive characteristics: resistance to
radiation, fire and moisture, mechanical and electrical
stability over a broad range of temperatures, and excellent
compatibility with metals and fiber reinforcing agents.
Fig. 3: Trimerization accounts for the high
thermo-mechanical properties of BECy.
2.4 Kinetic Behavior Models
Kinetic modeling refers to the use of DSC data to determine the parameters of a
reaction’s kinetics: reaction order (n), extent of conversion (), activation energy (Ea) and the
Arrhenius pre-exponential coefficient (A).
Isothermal tests provide enthalpy information which is analyzed to determine the degree of
conversion, , of monomer into polymer. The rate of conversion (d/dt) is written in terms of
Equation 1.
𝑑𝛼
𝑑𝑡
= 𝐴𝑒
−𝐸𝑎⁄
𝑅𝑇 (1
− 𝛼)𝑛 𝛼 𝑚
(1)
Where n and m are the reaction order factors of the autocatalytic model. The order of the
reaction (i.e. the various competing chemical pathways from reactants to products), n + m, can
be determined by performing least squares regression between the model and data.
Dynamic thermal scans generate data used to calculate the values Ea and A using
isoconversional models: Kissinger model, Ozawa model, and Friedman analysis.
The Kissinger model relates the increase in peak temperature (Tp) of polymerization to the
increase in heating rate (, Equation 2.
𝐴𝑅 𝐸
𝛽
ln ( ⁄𝑇 2 ) = ln⁡( 𝐸 ) 𝑅𝑇𝑎
𝑎
𝑝
𝑝
(2)
Plotting ln (/Tp2) vs. 1/T(K) for each heating rate
yields the Ea and A values of the reaction, Fig. 4.
Ozawa also provides a model based on the heating
rate, but goes on to include a function of the
ln (/Tp2)
monomer conversion, g(). Equation 3 shows the
relationship between , Ea and A’. Equation 4
shows the relationship between A’ and g(.
log 𝛽 =
−0.4567𝐸𝑎
𝑅𝑇𝑖
+ 𝐴′
Fig. 4: Linear fit of dynamic thermal
program data collected with DSC. Line
slope corresponds to activation energy of
isoconversional model.
(3)
𝐴𝐸
𝑎
𝐴′ = 𝑙𝑜𝑔 [𝑔(𝛼)𝑅
] − 2.315
(4)
Once again a plot of log b vs. 1/T(K) yields a best fit line for each degree of conversion whose Ea
and A’ can be uniquely extrapolated.
The Friedman analysis also uses a conversional function, f(), and is written in the form of
Equation 6. As with the previous models the plot of ln (d/dt) vs. 1/T(K) yields values of Ea and
A for the various degrees of conversion.
𝑑𝛼
ln ( 𝑑𝑡 ) = 𝑙𝑛𝑓(𝛼)𝐴 −
3.
𝐸𝑎⁄
𝑅𝑇
(5)
Experimental Procedure
**Fill up DSC container with dry ice (CO2) and allow temp. to equilibrate ~30 min.
3.1
Sample and Reference Pans Preparation
1) Measure the weight of one empty reference pan with lid and four sample pans with lids;
record the mass.
2) Weigh out four samples of BECy monomer (yellow liquid) using the mg-scale balance,
~10mg each, by placing one pan and cover with lid at a time on the scale and using a
disposable pipette to add BECy one drop at a time.
3) To close the sample use the sample press, place the pan on the die and position it under
the press. Gently pull the handle forward to seal the pan. Repeat the sample preparation
procedure for each BECy sample. NOTE: Remember to keep track of sample mass in
each pan!
3.2 DSC measurements using Perkin Elmer Pyris 1
1) Turn on nitrogen cylinder along north wall. The delivery pressure should be 35 psi.
2) Turn on air cylinder along north wall. The delivery pressure should be 40 psi.
3) Click “Pyris” button to launch the software and use Pyris Manager to select the
instrument to connect to the program. The “Method Editor” window will open and
information can be entered into the fields under each tab.
4) In the “Sample Info” tab enter the sample name, operator’s name, pertinent comments
AND sample weight.
5) Click on the “file name” box, then the “browse” button to select the correct folder for
your data files. <C:\\Program Files\Pyris\Data\MatE 453 F14\group name>. Click on
save.
6) In the “Program” tab, use the buttons on the right side to “Add a Step”
a. Heat sample 1 from 40°C to 350°C at 2.5°C/min.
7) Set the initial temperature in the “Initial State” tab to 40°C and set the Yvalue to zero.
8) To load reference and sample pan, press the air shield button.
9) Remove the platinum covers with the suction-cup tool. Place the sample in the left
furnace and the reference in the right furnace. Replace lids and make sure these are flat
and level.
10) Enter the starting temperature on the right hand column and click on “go
to Temp” button. Once the temperature has stabilized start the run by
clicking on the “run experiment” button.
11) At the end of the run, the program will return to the starting temperature. Carry out the
data collection with each BECy sample. Change Program tab accordingly:
a. Heat sample 2 from 40°C to 350°C at 5°C/min.
b. Heat sample 3 from 40°C to 350°C at 10°C/min.
c. Heat sample 4 from 40°C to 350°C at 15°C/min.
Post-test:
1.
When runs are complete and DSC is cooled, close the nitrogen and air gas valves and
dispose of the samples in the solid waste.
2.
To export a text copy of your data, go to File/Export Data/ASCII Data and save a copy to
the same file as your original data.
3.
Pyris Analysis:
1. Open the file for the data collected located in your group folder:
< C:\\Program Files\Pyris\Data\MatE 453 F14\group name >
4.
After opening the data file use the analyze drop-down list to determine …
Assignment
1. Using the autocatalytic isothermal model, calculate the activation energy of the cured BECy
sample given the data in Table 1. Recall that the reaction rate, k, takes the form
𝑘(𝑇) = 𝐴𝑒
−𝐸𝑎⁄
𝑅𝑇
Cure Temp. (°C)
k*10-4/s-1
160
36
170
54
180
74
200
150
2. Use the dynamic scanning data collected for the BECy sample and the Kissinger model to
calculate Ea (J/mol K) and A for the 1%, 3% and 5% nanoclay samples cured at
2.5°K/min, 5°K/min, 10°K/min, 15°K/min. Plot ln(/Tp2) vs. 1/Tp and find the best
linear fit to show the relationship between the slope and activation energy values.
3. Using the Ozawa model, calculate the Ea (J/mol K) values for your BECy data set. How
do the activation energies for the different nanoclay loadings compare for the Kissinger
vs. Ozawa models.
4. Qualitatively discuss the meaning of the shoulder observed in your polymerization
thermograms, with respect to the order of the cure reaction.