LABORATORY “5”
Kinetic Modeling of Bisphenol E Cyanate
Ester Cure Behavior Using DSC
Mohammed Alzayer
Chris Clay
Xinhang Shen
Mat E 453
Lab Section 2
October 7, 2014
1
ABSTRACT
The polymerization of three different samples of bisphenol E cyanate ester (BECy) were
analyzed using differential scanning calorimetry (DSC). The BECy monomer were
heated at a constant rate. An exothermic peak was observed corresponding to the curing
of the monomer. Using data from these peaks and the Kissinger and Ozawa modeling
techniques, the activation energy (Ea) and the pre-exponential factor of the Arrhenius
relation (A) were determined. The samples had concentrations of 1%, 3%, and 5%
nanoclays. Heating rates of 2.5, 5, 10, and 15 K/mins were tested.
1. INTRODUCTION
1.1 DSC Background
Differential Scanning Calorimetry (DSC) is a thermal analysis technique that is widely
used to characterize polymeric materials. DSC measures the amount of heat flow required
to raise the temperature of a sample. It then compares the sample’s response to the heat
flow to that of an inert sample and plots the heat flux in watts as a function of time or
temperature. During a physical or chemical change, the DSC will give information on
whether the change is exothermic or endothermic depending on the amount of heat that
the sample takes in order to keep the temperature increasing at the same rate as the
reference pan [1].
The two major types of DSC are heat flux and power compensated. DSC with heat flux
model holds both the sample and reference pans in one furnace. The furnace, equipped
with highly sensitive thermocouples, can maintain the same temperature in both samples.
This is done by simply raising the furnace temperature, which brings the cooler pan to
2
equilibrium with the other pan [2]. Power compensated DSC, on the other hand, has two
separate furnaces for the sample and reference. The furnace with lower temperature will
receive an increase in electrical power leading to a higher temperature that matches the
one in the second furnace [2].
The material used in sample and reference pans is usually aluminum which is disposable
and inexpensive. When operating DSC, it is recommended to use an inert purge gas such
as helium or the less expensive nitrogen gas to get a highly efficient thermal environment
[2].
1.2 BECy Overview
The thermoset material
studied in this lab is
bisphenol E cyanate ester
(BECy, 1,1’-bis(4cyanatophenyl)ethane,), a
diisocyanate monomer that
Figure 1. BECy monomer strcutre with two phenyl rings in
the backbone. [2]
contains two phenyl rings as seen in Fig. 1. The presence of phenyl rings in BECy
structure helps keep the material rigid and inhibits any mobility in its chains [2]. It also
gives the material a high storage modulus and makes the polymerization process much
more efficient than many other polymers. Some of the properties that make BECy
attractive for industrial purposes include its low volatile emissions, long pot life, and its
low viscosity [2]. BECy’s high glass transition temperature of 270 ºC makes it a desirable
3
matrix material for applications that require light weight, high strength, and high
temperature [2].
1.3 Curing of Thermosets
DSC is commonly utilized to study the curing behavior of thermoset polymers such as
BECy, polyurethane, unsaturated polyester, vinyl ester, and epoxy. Thermosets usually
undergo chemical reactions when used which lead to an increase in their viscosity [1].
They eventually start to crosslink and lose their ability to dissolve or flow. This type of
crosslinking is referred to as curing, an exothermic process in which heat is generated.
During the process, as the molecular weight of the polymer is increasing, the number of
molecules decreases. Furthermore, the chains start to branch and grow leading to many of
these chains getting connected and forming networks with infinite molecular masses [1].
At the end of curing, the chains lose their mobility and the overall material becomes
rigid, cross linked, and insoluble [1].
1.4 Isothermal Measurements
Isothermal scanning is one of two approaches that are utilized to examine the kinetics of
cure behavior of thermosets. When doing isothermal measurements, the sample is kept at
a constant temperature for varying time intervals [1]. The degree of cure, α, also known
as extent of conversion, ranges between 0 (uncured) and 1 (fully cured) and is given by:
𝛼=
∆𝐻𝑇 −∆𝐻𝑟
∆𝐻𝑇
,
(1)
where
𝛼: extent of conversion,
∆𝐻𝑇 : total amount of heat at a certain heating rate for an unreacted sample.
4
∆𝐻𝑟 : the residual heat of the reaction for a cured sample for a specific period of time.
[1]
The enthalpy in this equation can be calculated using the DSC heat flux versus time
curve. Integrating the area under the exothermic peak yields a value for the enthalpy [1].
After examining the cure behavior of BECy with the DSC curve, it is crucial to model the
curing kinetics. The models that were developed to describe the behavior relate the rate
of cure to the degree of cure [1].
The rate of cure is dependent on two separable functions and is given by:
𝑑𝛼
𝑑𝑡
(2)
= 𝐾(𝑇)𝑓(𝛼),
where
𝑑𝛼
𝑑𝑡
: the rate of cure,
𝐾(𝑇): the temperature dependent rate constant,
𝑓(𝛼): corresponds to the reaction model. [1]
The temperature dependence of the rate of cure is usually governed by an Arrhenius
expression as follows:
𝐾(𝑇) = 𝐴𝑒𝑥𝑝 (
−𝐸𝑎
𝑅𝑇
(3)
),
where
𝐴: pre-exponential factor,
𝐸𝑎 : the activation energy,
𝑅: the universal gas constant,
𝑇: the absolute temperature. [1]
5
The conversion obtained at a given heat rate or temperature can only be predicted using
the equations above if the model is known. Some of the models that exist for this purpose
are either nth order or autocatalytic models. Table 1 describes a couple of these models.
Table 1. Examples of phenomenological reaction models. [1]
Model
𝒇(𝜶)
nth order
(1 − 𝛼)𝑛
Prout-Tompkins Autocatalytic
(1 − 𝛼)𝑛 𝛼 𝑚
1.4 Dynamic Measurements
In dynamic measurements, the sample is heated at a constant rate over a range of
temperatures. The first dynamic method used in this lab is Kissinger’s. This method is
interested in one data point for each heating rate and hence assumes a first order reaction
[1]. The Kissinger equation that relates this data point, which is the peak temperature, to
other parameters is given by:
𝛽
𝐴𝑅
𝑝
𝑎
𝐸
𝑙𝑛 (𝑇 2 ) = 𝑙𝑛 ( 𝐸 ) − 𝑅𝑇𝑎 ,
(4)
𝑝
where
𝛽: the heating rate (dT/dt),
𝑇𝑝 : the peak temperature. [1]
It is assumed that the maximum reaction rate dα/dt occurs at the peak temperature
𝛽
making d2α/dt2 zero. By plotting 𝑙𝑛 (𝑇 2 ) against 1/𝑇𝑝 , one can determine both the
𝑝
activation energy and pre-exponential factor by fitting a linear line with the form y = mx
6
+ b. The resulting slope multiplied by the gas constant represents the activation energy
while the pre-exponential factor is calculated by the equation:
𝐸𝑎 𝑒𝑥𝑝(𝑏)
𝑅
where b is the y-
intercept [1]. Another dynamic method that can calculate the activation energy and the
pre-exponential factor is called the Ozawa model. This model is different from
Kissinger’s in that it assumes that both the activation energy and the pre-exponential
factor are functions of degree of cure, meaning that they change throughout the reaction
[1]. Ozawa equation is given by:
𝑙𝑜𝑔(𝛽) = −
0.4567𝐸𝑎
𝑅𝑇𝑝
(5)
+ 𝐴′,
where
𝐴′: a constant for each degree of conversion. [1]
The constant A’ is given by:
𝐸 𝐴
𝑎
𝐴′ = 𝑙𝑜𝑔 [𝑔(𝛼)𝑅
] − 2.315,
(5)
where
𝑔(𝛼): conversion dependent function. [1]
The activation energy and the pre-exponential factor can be determined in a similar
fashion to that described for Kissinger’s method if g(α) is known. Plotting log β against
1/𝑇𝑝 and fitting a line to the points help determine these numbers. In this case, the
activation energy is given by 𝐸𝑎 = 𝑚𝑅⁄−0.4567 where m is the slope of the resulted
line [1].
7
2. EXPERIMENTAL PROCEDURES
2.1 Materials
BECy, sample pans, balance, pipette, Perkin Elmer Pyris 1
2.2 Sample Preparation
1. DSC container was filled with dry ice and allowed to equilibrate for 30 minutes.
2. The weight of five pans with lids were measured and recorded.
3. Four samples of BECy monomer with 1% nanoclay were weighed out to
approximately 10 mg.
4. The sample pans were closed using the sample press. The sample pans were placed on
the die and positioned under the press. The handle was pulled forward gently to seal the
pan. Repeated the procedure for each sample.
2.3 DSC measurements using Perkin Elmer Pyris 1
1. Nitrogen cylinder was turned on to a delivery pressure of 35 psi.
2. Air cylinder was turned on to a delivery pressure of 40
psi.
3. Pyris Manager software was launched.
4. Sample name, operator’s name, pertinent comments and
sample weight were entered and saved.
5. The program parameters were set 40°C to 350°C at
2.5°C/min.
6. The air shield button was pressed to enable loading of
samples
7. Platinum covers were removed and sample pan were
placed on left side of the furnace and the reference pan
Figure 2. DSC sample pan on the left and
reference on the right side of the furnace [3]
on the right side of the furnace (Fig. 2).
8. The initial temperature was entered and the run was started.
8
9. After the run, the program tab was changed and another run was preformed:
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
11. This procedure was repeated for BECy samples with 3% and 5% nanoclay
2.4 Post-test
1. The nitrogen and air values were shut and the sample pans disposed of in the solid
waste container.
2. The data was saved and exported.
3. RESULTS
3.1 Isothermal Analysis
The cure temperatures and the corresponding reaction rate, k, are given in Table 2:
Table 2. BECy cure temperatures and the reaction rates at these temperatures
Cure Temp. (°C)
k*10-4/s-1
160
36
170
54
180
74
200
150
−𝐸
ln k was plotted against 1/T according to Equation 3: 𝐾(𝑇) = 𝐴𝑒𝑥𝑝 ( 𝑅𝑇𝑎) (Fig.3)
9
14.4
y = -7248.2x + 29.539
R² = 0.999
14.2
14
lnk
13.8
13.6
13.4
13.2
13
12.8
12.6
0.0021
0.00215
0.0022
0.00225
0.0023
0.00235
1/T (K^-1)
Figure 3. Autocatalytic isothermal modeling of BECy sample. The equation shown is
used to calculate the parameters of interest.
𝑙𝑛𝐾 = 𝑙𝑛𝐴 −
𝐸𝑎
𝑅𝑇
As a result, the slope of the equation is -7248.2 = -Ea/RT. Therefore, the activation
energy is 7248.2*8.314 = 60261.5 J/mol.
3.2 Dynamic Analysis
The BECy samples analyzed for this part have different amounts of nanoclay (1%, 3%,
and 5%). Appendix, Table A1 summarizes the DSC data used when utilizing the dynamic
models. The peak curing temperatures were obtained by the software finding the
maximum value for the heat flow (Appendix, Fig. A1 – A3). Using the described dynamic
models, two graphs were obtained for Kissinger’s and Ozawa (Fig. 4 and Fig. 5).
10
-8.5
ln(β/Tp2)
-9
y = -4720.6x - 0.2476
R² = 0.9994
-9.5
1% nanoclay
3% nanoclay
5% nanoclay
-10
y = -8840.5x + 6.2515
R² = 0.9929
y = -6976x + 3.5095
R² = 0.9891
-10.5
0.00165 0.0017 0.00175 0.0018 0.00185 0.0019 0.00195 0.002 0.00205 0.0021
1/Tp , K-1
Figure 4. Kissinger's model equations for different samples of BECy.
1.4
1.2
log(β)
1
0.8
1% nanoclay
0.6
3% nanoclay
5 % nanoclay
0.4
0.2
y = -4789.7x + 9.3273
y = -3979.6x + 8.1358
R² = 0.9955
R² = 0.9937
y = -3002.3x + 6.5082
R² = 0.9997
0
0.00165 0.0017 0.00175 0.0018 0.00185 0.0019 0.00195 0.002 0.00205 0.0021
1/ Tp , K-1
Figure 5. Figure 3 Ozawa model equations for different samples of BECy.
11
Kissinger’s model says that for the line plotted by ln(β/T2) vs 1/T
𝑆𝑙𝑜𝑝𝑒 =
−𝐸𝑎
𝑅
and
𝑌 − 𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = 𝑙𝑛 (
𝐴𝑅
)
𝐸𝑎
These relations can be used to calculate Ea and A. For example, for BECy with 1% nanoclay
heated at rate of 2.5 K/ min.
−𝐸𝑎
−8840.5 𝐾 =
8.314
𝐽
𝑚𝑜𝑙 𝐾
𝐸𝑎 = 73499.92 𝐽/𝑚𝑜𝑙
This activation along with the y-intercept can be used along with the y-intercept of the graph to
obtain the pre-exponential factor A
6.2514 = 𝑙𝑛 (
𝐴 ∗ 8.314
73499.92
)
𝐴 = 4586367
This same procedure was used to calculate the activation energies and pre-exponential factors for
the other samples and heating rates.
Ozawa’s model plots log(β) vs 1/T to obtain the expressions
𝑆𝑙𝑜𝑝𝑒 =
−0.4567 𝐸𝑎
𝑅𝑇𝑝
𝐸𝑎 𝐴
] − 2.315
𝑔(𝛼)𝑅
𝑌 − 𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = 𝑙𝑜𝑔 [
12
A similar procedure can to the one above can used to find the activation energies using the Ozawa
model. However, the pre-exponetial factor A cannot be determined as the function g(α) is not
known. A summary of the results of these calculations is shown in Table 3.
Table 3. Summary of results of activation energies and pre-exponential factors obtained
from different kinetic models.
Sample
Model
Ea (J/mol)
A
BECy w/
Kissinger
73499.92
4586367
1% nanoclay
Ozawa
87194.14
BECy w/
Kissinger
57998.46
3% nanoclay
Ozawa
72446.67
BECy w/
Kissinger
39247.068
5% nanoclay
Ozawa
54655.40
BECy
Autocatalytic
60261.53
233218.5
3685.241
29.54
4. DISCUSSION
The activation energies calculated were all on the sample order of magnitude (~104
J/mol). One interesting result of the modeling was that the Ozawa model consistently
predicted the activation energy to be about 15000 J/mol higher than the Kissinger model
predicted. This makes obtaining a real value for the activation energies difficult, but the
trend in the changes of energies with the change of nanoclay concentration can still be
observed. The activation energy for both Ozawa and Kissinger models showed that the
13
increased concentration of nanoclays decreased the curing temperature as well as the
activation energies. This indicates that nanoclays act as a catalyst for the curing of BECy.
The pre-exponential factor A determined by the Kissinger model also shows a trend of
decreasing as the nanoclay concentration increases. The pre-exponential factor cannot be
determined with Ozawa model because g(α) is not known. The g(α) function depends
upon the mechanism by which the curing process occurs.
Both the Ozawa and Kissinger models fit the data well, with R2 values always being
greater than 0.985. The Ozawa model generally fit slightly better than the Kissinger
model, with R2 values always being greater than 0.990.
For samples with the same nanoclay concentration, the peak curing temperature increases
as the heating rate increases. This agrees with expectations, as the faster a sample is
heated, the less time a sample has to react at any given temperature. The entire reaction
therefore takes longer, and the peak temperature is higher.
As the nanoclay concentration increases, the shoulders on the curing peaks seem to
increases, indicating that the reaction order n increases.
14
5. CONCLUSIONS
Differential scanning calorimetry can provide information about both the temperatures at
which chemical and physical process take place as well as how those process take place.
The increase in nanoclay concentration was shown to lower the curing temperature of
BECy monomer, as well as decreasing the activation energy. Both Ozawa and Kissinger
models were useful in the determination of the activation energy.
6. ACKNOWLEDGMENTS
The data was taken from a Mat E 453 group from a previous year.
7. REFERENCES
1. Hardis, Ricky. Cure kinetics characterization and monitoring of an epoxy resin for
thick composite structures. Iowa State University Digital Repository, 2012. Web.
2. Mendoza, J. D., Modelling kinetic cure behavior of thermosetting polymers using
differential scanning calorimetry, Iowa State University.
3. Differential Scanning Calorimetry. Web. http://www.fauske.com/chemicalindustrial/thermal-stability
15
8. APPENDIX
Table A1. DSC data for different samples of BECy. Each curing peak temperature and its
corresponding heating rate are listed.
BECy Sample
Tp (K)
Heating Rate (K/min)
1% nanoclay
537.69
2.5
553.27
5
574.6
10
588.72
15
514.35
2.5
536.39
5
554.68
10
573.47
15
491.02
2.5
517.32
5
545.46
10
562.5
15
3% nanoclay
5% nanoclay
16
Figure A1. DSC plots of 1% nanoclay in BECy at varying heating rates. The data for
2.5K/min was missing.
Figure A2. DSC plots of 3% nanoclay in BECy at varying heating rates
17
35
30
25
Heat Flow, W/g
20
2.5 K/min
15
5 K/min
10
10 K/min
15 K/min
5
0
0
50
100
150
200
250
300
350
400
-5
-10
Temperature, C
Figure A3. DSC plots of 5% nanoclay in BECy at varying heating rates
18