Post on 23-Jan-2017
Study on thermal decomposition and oxidation kineticsof cation exchange resins using non-isothermal TG analysis
Hee-Chul Yang • Min-Woo Lee • Ho-Sang Hwang •
Jei-Kwon Moon • Dong-Yong Chung
Received: 1 November 2013 / Accepted: 7 May 2014
� Akademiai Kiado, Budapest, Hungary 2014
Abstract Kinetics of two successive thermal decomposi-
tion reaction steps of cationic ion exchange resins and oxi-
dation of the first thermal decomposition residue were
investigated using a non-isothermal thermogravimetric ana-
lysis. Reaction mechanisms and kinetic parameters for three
different reaction steps, which were identified from a FTIR
gas analysis, were established from an analysis of TG analysis
data using an isoconversional method and a master-plot
method. Primary thermal dissociation of SO3H? from divi-
nylbenzene copolymer was well described by an Avrami–
Erofeev type reaction (n = 2, g(a) = [-ln(1 - a)]1/2]), and
its activation energy was determined to be 46.8
±2.8 kJ mol-1. Thermal decomposition of remaining poly-
meric materials at temperatures above 400 �C was described
by one-dimensional diffusion (g(a) = a2), and its activation
energy was determined to be 49.1 ± 3.1 kJ mol-1. The oxi-
dation of remaining polymeric materials after thermal disso-
ciation of SO3H? was described by a phase boundary reaction
(contracting volume, g(a) = 1-(1 - a)1/3). The activation
energy and the order of oxygen power dependency were
determined to be 101.3 ± 13.4 and 1.05 ± 0.17 kJ mol-1,
respectively.
Keywords Cation exchange resin � Thermal
decomposition � Oxidation � Kinetic analysis �Reaction model
Abbreviation
Nomenclature
B Heating rate (K min-1)
E Activation energy (kJ mol-1)
f(a) Reaction model
k0 Pre-exponential factor (s-1 Pa-n)
n Power rate dependence index
PO2 Oxygen partial pressure (Pa)
p(y) Function of the temperature integral on the right
hand side of Eq. (2)
SD Standard deviation
T Temperature (K)
y Dimensionless variable (=-E/RT)
y0 Dimensionless variable at reference temperature
(T0)
yc Dimensionless variable at analysis temperature (Tc)
Z Defined by Eq. (2)
Greek letters
a Extent of a conversion (-)
Introduction
Ion exchange resins are insoluble solid granules which, when
in contact with a liquid containing ions in a solution,
exchange some of their constitutive ions with other ions [1].
Ion exchange resins are widely used in various separation,
purification, and decontamination processes. Commercial
nuclear industries utilize ion exchange resins to clean their
process and process water. Over time, these resins have to be
regenerated or replaced. When this happens, the spent ion
exchange resins have to be disposed of and, as such, spent ion
H.-C. Yang (&) � M.-W. Lee � H.-S. Hwang � J.-K. Moon �D.-Y. Chung
Korea Atomic Energy Research Institute, Dukjindong 150,
Yuseong, Daejeon 305-353, South Korea
e-mail: nhcyang@kaeri.re.kr
123
J Therm Anal Calorim
DOI 10.1007/s10973-014-3853-9
exchange resins are a major fraction of the combustible
organic waste from nuclear industries [2]. One effective
treatment option is pyrolyzing or incinerating the spent res-
ins to yield ash and gas. Chun et al. [3] studied pyrolysis as a
pre-treatment process of spent radioactive resins prior to
stabilization for final disposal . Brodda et al. [4] investigated
gaseous emission species from the thermal degradation of
ion exchange resins by means of foil pulse pyrolysis coupled
with gas chromatography-mass spectroscopy.
Since ion exchange resins consist of a base polymer and
functional groups, and thermogravimetric (TG) analyses
provide important knowledge on the multi-step thermal
400
0
20
40
60
80
100
TG
/%
(a) RXN-1
Temperature/K
RXN-2
600 800 1000 1200 1400
DT
G/%
min
-1
–0.25
–0.20
–0.15
–0.10
–0.05
0.00 1
TG
/%
0
20
40
60
80
100(b)
Temperature/K
RXN-1
300 400 500 600 700 800
RXN-3
900
DT
G/%
min
-1
–4.0
–3.5
–3.0
–2.5
–2.0
–1.5
–1.0
–0.5
0.0
Fig. 1 Representative results of TGs under reducing atmospheres (a) and an oxidizing atmosphere (b), and three identified reaction steps
Fig. 2 SEM images of dried
resin (a), after processing of
RXN-1 reaction step (b) and
during the course of RXN-2
reaction step (after 70 % of
mass loss) (c)
1
0.5
1.0
0.00
0.05
0.020.00
–0.02
1
1.0
0.5
35004000 3000 2500
Wavenumber/cm–1
Wavenumber/cm–1
Abs
orba
nce/
a.u
Abs
orba
nce/
a.u
Reference FTIR peaks of SO2(g)
Reference FTIR peaks of CH4
Reference FTIR peaks of C6H6
FTIR peaks during first mass loss
Linked spectrum at 22.992 min.
Linked spectrum at 59.711 min.
Benzene,99 + %, A.C.S. spectrophotometric grade
Methane
Sulfur dioxide
Water vaper
(a)
(b) FTIR peaks during second mass loss
Reference FTIR peaks of H2O(g)
2000 1500 1000
35004000 3000 2500 2000 1500 1000 500
Fig. 3 Detected major gaseous
species in reaction steps RXN-1
and RXN-2
H.-C. Yang et al.
123
decomposition progress of ion exchange resins. Various
thermogravimetric analyses have thus also been performed
for various kinds of ion exchange resins [5–10]. The kinetic
analyses of the thermal decomposition of ion exchange res-
ins in these studies considered only reaction order models.
This study attempted to analyze more detailed kinetics for
reaction steps involved in both thermal decomposition and
oxidation of ion exchange resins at a wider temperature
range from 400 to 1,700 K. A non-isothermal TG analysis is
advantageous in that a wide range of temperature can be
covered with a single experiment. Non-isothermal kinetic
analysis of dehydration for wet resins was performed by
Chambre et al. [9]. However, non-isothermal kinetic analysis
on the thermal decomposition of a dehydrated ion exchange
resin has not yet been reported in the literature. This study
investigated the kinetics of thermal decomposition and oxi-
dation of cation exchange resins using a non-isothermal TG
analysis. The objectives of this study were to determine a
best-fitted kinetic model and kinetic parameters involved in
each reaction step of thermal decomposition and oxidation
reactions of strong acidic cation exchange resins with a
sulfonic acid functional group.
400 600 800 1000 1200 1400 16000
20
40
60
80
100
(b)
Temperature/KM
ass/
%
0.25 K min-1
0.5 K min-1
0.75 K min-1
1 K min-1
500 600 700 800 900 10000
20
40
60
80
100
5 K min-1
10 K min-1
15 K min-1
20 K min-1
25 % O2
Temperature/K
Mas
s/%
500 600 700 800 900 10000
20
40
60
80
100 50 % O2
5 K min-1
10 K min-1
15 K min-1
20 K min-1
Temperature/K
Mas
s/%
500 600 700 800 9000
20
40
60
80
100 75 % O2
5 K min-1
10 K min-1
15 K min-1
20 K min-1
Temperature/K
Mas
s/%
500 600 700 800 9000
20
40
60
80
100100 % O
2
5 K min-1
10 K min-1
15 K min-1
20 K min-1
Temperature/K
Mas
s/%
Fig. 4 Results of non-isothermal TGs under nitrogen atmosphere (a) and typical results of those under oxidizing atmospheres (b)
Study on cation exchange resins using non-isothermal TG
123
Experimental
Materials and experimental system
The ion exchange resin used in this thermal analysis study is a
strongly acidic cation exchange resin (Amberlite IRN-77)
which has a sulfonic acid group of SO3H? and a matrix of
styrene divinylbenzene (DVB) copolymer. The strong ion
exchange resins used in the present TG study were spherical
beads with a harmonic mean size of 0.6–0.7 mm. The prepared
spent resin particles contain a significant amount of water. They
were dried and stored in an oven at 110 �C for a long time prior
to carrying out thermogravimetric analysis. The experimental
system consists of a controlled gas feeding system, a TG ana-
lysis system (N-1500, Scinco), and a FTIR system (Nicolet
i-S10, Thermo-Scientific). The TG analysis system measures a
sample’s mass change in a controlled atmosphere as a function
of temperature or time. Inert or various oxidizing atmospheres
with various oxygen partial pressures are controlled by flowing
a high-purity nitrogen ([99.999 % N2) or a mixed gas. The
mixed gas with various oxygen partial pressures was prepared
and fed into TG furnace using electronic MFCs (mass flow
controllers) connected to canisters of high-purity nitrogen and
oxygen. The flowing gas carries evolved gas during the course
of sample destruction or vaporization. These gases are trans-
ferred into the FTIR system, and they are scanned by the
infrared beam in the gas cell, and the spectral data are recorded.
TG analysis methods
Preliminary TG analyses of the dried cation exchange resins
under oxidizing as well as under inert atmosphere were first
performed to divide reaction steps involved in the whole
thermal destruction process of sample resins. Speciation of
gases evolved during the course of each divided reaction step
was then performed to know reactions occurred in each
reaction step. Non-isothermal TG analyses were performed
to interpret the reaction kinetics of each divided reaction
step. The non-isothermal TG analysis test program consisted
of 40 tests, including two duplicates of one test condition.
Test variables were furnace atmosphere and heating rate.
The temperature of the furnace was programed to rise from
room temperature to 1,400 K with slow heating rates of 0.25,
0.5, 0.75, and 1 K min-1 at inert atmosphere and with rapid
heating rates of 5, 10, 15, and 20 K min-1 at oxidizing
atmosphere, respectively. At each heating rate condition
under inert atmosphere, four oxygen partial pressures were
tested: 25, 50, 75, and 100 % of oxygen and remainder
consisted of pure nitrogen ([99.999 %).
Results and discussion
Determination of reaction steps
Representative results of TGs under an oxidizing atmosphere as
well as under inert atmospheres are shown in Fig. 1. As shown
in Fig. 1a, thermal decomposition of dried cationic resins in the
absence of oxygen ([99.999 % N2) and in the presence of
oxygen was divided into two reaction steps, respectively. The
first thermal decomposition reaction, denoted as RXN-1 in
Fig. 1a, occurred at temperature below 350 �C. SEM images of
dried resin particles before and after RXN-1 step and during the
course of RXN-2 step are shown in Fig. 2. No significant
changes in the morphology excluding shrinkage of resin par-
ticles during the reaction steps. After RXN-1, resin particles
with a diameter of 520 lm shrank to smaller particles with a
diameter of 450 lm. They shrank to smaller particles as the
RXN-2 step proceeded, as shown in Fig. 2c.
Detected gaseous species in reaction steps RXN-1 and
RXN-2 are shown in Fig. 3. Detected gaseous species in
RXN-1 reaction step were only SO2 and H2O. No organic
species were detected in this first thermal decomposition
reaction step. In the second thermal decomposition reaction
step at higher temperatures above 400 �C, denoted as RXN-2
in Fig. 1a, C6H6 and CH4 were identified as major emission
species from the TG analysis furnace. Based on the results of
TG analysis and a FIIR gas analysis, thermal decomposition
reaction steps RXN-1 and RXN-2 can be described as the
following reaction schemes.
RXN-1
RXN-2
H.-C. Yang et al.
123
The dissociation of the functional group (SO3-H?)
from divinylbenzene copolymer first occurs at relatively
low temperature from about 200 �C. This first thermal
decomposition reaction RXN-1 was relatively fast in the
non-isothermal condition with a heating rate of
5 �C min-1 and it finished before the temperature
reached 350 �C, as shown in Fig. 1a. The reaction pro-
gress of the second thermal decomposition reaction step
RXN-2 was relatively slower when compared to that of
RXN-1, as shown in Fig. 1a. RXN-2 reaction step started
at about 400 �C and finished at about 1,200 �C, when
heated with a ramping rate of 5 �C min-1.
The mass loss pattern of the first reaction step under the
oxidizing atmosphere was similar to that under inert atmo-
sphere, as shown in Fig. 1. Its emission gaseous species were
also detected as SO2 and H2O, and no carbon dioxide was
detected. This indicates that the first reaction step under
oxidizing atmosphere was the same as that under the oxygen-
free atmosphere. No difference in the mass loss pattern with
different oxygen partial pressures was found in this first
(a)
1.7x10-3 1.8x10-3 1.8x10-3 1.9x10-3 2.0x10-3 2.1x10-3 2.2x10-3–13.4
–13.2
–13.0
–12.8
–12.6
–12.4
–12.2
–12.0
–11.8 Conversion, α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Temperature/K-1
ln(B
/T1.
8946
61)
(b)
7.50x10-4 9.00x10-4 1.05x10-3 1.20x10-3 1.35x10-3
–14.8
–14.6
–14.4
–14.2
–14.0
–13.8
–13.6
–13.4
–13.2
–13.0
–12.8Conversion,α
0.1 0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9
ln(B
/T1.
8946
61)
Temperature/K-1
(c)
9.8x10-4 1.0x10-3 1.1x10-3 1.2x10-3 1.3x10-3 1.3x10-3 1.4x10-3
–11.2
–11.0
–10.8
–10.6
–10.4
–10.2
–10.0
–9.8
–9.6
Po2 = 25kPa
Conversion, α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
ln(B
/T1.
8946
61)
Temperature/K-11.0x10-3 1.1x10-3 1.1x10-3 1.2x10-3 1.3x10-3 1.3x10-3 1.4x10-3
–11.2
–11.0
–10.8
–10.6
–10.4
–10.2
–10.0
–9.8
–9.6
Po2 = 50kPa
Conversion, α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9ln
(B/T
1.89
4661
)
Temperature/K-1
1.1x10-3 1.2x10-3 1.2x10-3 1.3x10-3 1.3x10-3 1.4x10-3–11.2
–11.0
–10.8
–10.6
–10.4
–10.2
–10.0
–9.8
–9.6
–9.4
Po2 = 75kPa
Conversion, α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9ln
(B/T
1.89
4661
)
Temperature/K-11.2x10-3 1.2x10-3 1.3x10-3 1.3x10-3 1.4x10-3 1.4x10-3
–11.2
–11.0
–10.8
–10.6
–10.4
–10.2
–10.0
–9.8
–9.6
–9.4
Po2 = 100kPa
Conversion, α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9ln
(B/T
1.89
4661
)
Temperature/K-1
Fig. 5 Slopes of the regression lines in the isoconversional plots for each reaction step: RXN-1 (a), RXN-2 (b), and RXN-3 (c)
Study on cation exchange resins using non-isothermal TG
123
reaction step, and the mass loss rate was nearly the same as
that under a N2 atmosphere. Denoted as RXN-3 in Fig. 1b,
the mass loss rates of remaining polystyrene beads shown in
Fig. 2b were greatly influenced by the oxygen partial pres-
sure. This suggests that thermal decomposition of remaining
polystyrene bead in the presence of oxygen can be described
as a gas–solid interfacial reaction, where the conversion rate
is greatly influenced by the oxygen partial pressure. This
second reaction step RXN-3 in the presence of enough
oxygen can be described as the following reaction scheme.
Kinetic analysis of each reaction step
Model-free analysis
The rate of thermal decomposition reaction under an oxi-
dizing or reducing atmosphere can be described with an
Arrhenius equation and a power law approach, respectively
[10]. The reaction rate is thus described as
dadt¼ k0ðPO2
Þn exp � E
RT
� �f ðaÞ; ð1Þ
where a is the extent of a conversion, k0 is the reaction rate
constant (s-1 Pa-n), PO2 is the oxygen partial pressure (Pa),
and n is the power dependency of the oxygen partial pressure.
The function f(a) is a reaction model that represents the
influence of the extent of conversion on the conversion rate.
In the case of a non-isothermal reaction, the applied heating
rates are constant, and the temperature can be expressed as
T = Bt ? T0 where the constant heating rate, B, is given as
dT/dt = B. Using this transformation of Eq. (1) followed by
a separation of the variables results in
daf ðaÞ ¼
k0
BðPO2Þnexp � E
RT
� �dT: ð2Þ
Integrating both sides of Eq. (2) gives
gðaÞ ¼ ZE
BRpðyÞ; ð3Þ
where g(a) is the result of an integral on the left hand side
of Eq. (2), Z ¼ k0ðPO2Þn, and p(y) is a function of the
temperature integral on the right hand side of Eq. (2):
p yð Þ ¼Zyc
y0
e�y
y2dy ¼ e�y
y2þZyc
y0
e�y
ydy; ð4Þ
where y = -E/RT [11–14]. A simple mathematical treat-
ment provides the activation energy of the reaction as [14]
E ¼ �R
1:001450
d lnðB=T1:894661Þdð1=TÞ
� �ð5Þ
All results of non-isothermal TG analyses under a
nitrogen atmosphere and typical results of those under
oxidizing atmospheres are shown in Fig. 4. The obtained
TG analysis data for the described reaction steps RXN-1,
RXN-2, and RXN-3 were analyzed to determine the
0.0 0.2 0.4 0.6 0.8 1.030
40
50
60
70RXN-1RXN-2
Act
ivia
tion
ener
gy/K
J m
ole
-1
Conversion, α
(a)
0.0 0.2 0.4 0.6 0.8 1.060
80
100
120
140
160
25 50 75100
PO2
/kPa(b)
Act
ivia
tion
ener
gy/K
J m
ole
-1
Conversion, α
Fig. 6 Plot of activation energy of reaction steps RXN-1 and RXN-2 (a), and RXN-3 (b), as a function of conversion
RXN-3
H.-C. Yang et al.
123
activation energy for a different level of conversion using
Eq. (5). Slopes of the regression lines in the conversional
plots for each reaction step, which are shown in Fig. 5,
were used to calculate the activation energy at each con-
version degree.
The activation energies for three different reaction steps
determined using Eq. (5) are shown in Fig. 6. The activa-
tion energies for RXN-1 and RXN-2 reaction steps were
not significantly changed with respect to the level of a
conversion. The mean value of activation energy was
determined as 46.8 and 49.1 kJ mol-1 for RXN-1 and
RXN-2 reaction steps, respectively. In the case of the
reaction step RXN-3, where oxygen partial pressure
influences on the conversion rate, the level of activation
energy was significantly different according to the oxygen
partial pressure. However, at a given oxygen partial pres-
sure condition, no significant change with respect to the
conversion rate was found. It should be noted that the
determined activation energies shown in Fig. 6 were
obtained in the absence of any knowledge of the reaction
model f(a).
Kinetic model determination
If the activation energy determined from the isoconver-
sional method varies with the conversion level, the further
(a)
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
2.5
Conversion, α
0.25 K min-1
0.5 K min-1
0.75 K min-1
1 K min-1
p (y )
/p(y
0.5)
g(α)
/g( α
0.5)
0.0
0.5
1.0
1.5
2.0
2.5
A3/2
P3A3
A2
(b)
0.0 0.2 0.4 0.6 0.8 1.00
1
2
3
4 0.25 K min-1
0.5 K min-1
0.75 K min-1
1 K min-1
0
1
2
3
4F3/2
D1
R3
F1
g(α)
/g( α
0.5)
Conversion, α
p(y )
/p(y
0.5)
(c)
0.0 0.2 0.4 0.6 0.8 1.00
1
2
3
Po2 = 25kPa
5 K min-1
10 K min-1
15 K min-1
20 K min-1
R3
F1
P4
A3/2R1
R2g(α)
/g( α
0.5)
Conversion, α
p(y )
/p(y
0.5)
0
1
2
3
0.0 0.2 0.4 0.6 0.8 1.00
1
2
3
Po2 = 50kPa
5 K min-1
10 K min-1
15 K min-1
20 K min-1
R3
F1
P4
A3/2R1
R2 p (y)
/ p(y
0.5)
Conversion, α
g(α)
/g( α
0.5)
0
1
2
3
0.0 0.2 0.4 0.6 0.8 1.00
1
2
3
Po2 = 75kPa
5 K min-1
10 K min-1
15 K min-1
20 K min-1
R3
F1
P4
A3/2R1
R2 p(y)
/ p( y
0.5)
Conversion, α
g(α)
/ g( α
0.5)
0
1
2
3
0.0 0.2 0.4 0.6 0.8 1.00
1
2
3
Po2 = 100kPa
5 K min-1
10 K min-1
15 K min-1
20 K min-1
R3
F1
P4
A3/2R1
R2 p(y )
/p(y
0.5)
Conversion, α
g(α)
/ g( α
0.5)
0
1
2
3
Fig. 7 Theoretical master plots for common reaction models (lines) and experimental values by the averaged value of activation energy [RXN-1
(a), RXN-2 (b) and RXN-3 (c)]
Study on cation exchange resins using non-isothermal TG
123
process to interpret solid-state reaction model is mathe-
matically incorrect [15]. This is the case here. However,
the principal objective of this study is to determine a
conversion model equation that may be practically useful
for the design and optimization of a spent resin pyrolysis
system. For this reason, a conversion model for each
reaction step was determined by means of a master-plot
method using the averaged values of the activation energy.
Assuming a complex multi-step process with varying
activation energy as a single-step one, experimental master
plots were constructed according to Eq. (3) using the aver-
aged values of the activation energy E for all the different
conditions, and they are shown in Fig. 7. The theoretical
master plots of the most common mechanisms in solid-state
reactions are also plotted as solid lines in Fig. 7 [16].
The plots related to different heating rates for RXN-1
and RXN-2 are practically identical. RXN-1 and RXN-2
reaction models were determined as an Avrami-Erofeev
type reaction (n = 2, g(a) = [-ln(1 - a)]1/2]) and a one-
dimensional diffusion (g(a) = a2), respectively, from a
comparison of experimental master plots with the theoret-
ical plots. However, the plots related to different heating
rates for RXN-3 under various oxygen partial pressures are
significantly different at a high level of conversion
(a C 0.8).
The comparison of the experimental master plots with
the theoretical plots for the reaction RXN-3 showed that
none of the existing theoretical master plots matched the
experimental plots perfectly. For this reason, a relatively
acceptable kinetic model for RXN-3 was selected based on
the standard deviation (SD):
SD ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPnj
Pmi gkðaiÞ=gkð0:5Þ � pjðyiÞ=pjðy0:5Þ� �2
ðn� 1Þðm� 1Þ
s; ð6Þ
where m and n are the numbers of points and heating rates,
respectively [17]. The phase boundary reaction model
(spherical symmetry, g(a) = 1-(1 - a)1/3) appeared to be
Table 1 Standard deviations between theoretical master data and experimental ones
O2 partial pressure Heating rate/K min-1 Reaction model
A3/2 R1 R2 R3 P4 F1
25 kPa 5 1.465 1.882 0.85 0.52 1.465 1.882
10 1.733 2.15 1.076 0.684 1.733 2.15
15 1.691 2.108 0.999 0.618 1.691 2.108
20 1.652 2.069 0.947 0.572 1.652 2.069
50 kPa 5 1.673 2.089 0.975 0.511 1.673 2.089
10 1.607 2.032 0.998 0.577 1.607 2.032
15 1.556 1.972 0.898 0.475 1.556 1.972
20 1.509 1.926 0.817 0.383 1.509 1.926
75 kPa 5 1.369 1.786 0.669 0.286 1.369 1.786
10 1.263 1.68 0.578 0.238 1.263 1.68
15 1.227 1.644 0.543 0.227 1.227 1.644
20 1.188 1.605 0.51 0.221 1.188 1.605
100 kPa 5 1.065 1.482 0.388 0.227 1.065 1.482
10 1.107 1.524 0.446 0.148 1.107 1.524
15 1.172 1.589 0.478 0.118 1.172 1.589
20 1.335 1.752 0.621 0.188 1.335 1.752
Sum 22.612 29.288 11.793 5.994 14.148 18.357
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
5g(α)/g(α
0.5) values determined from varied activation energy
RXN 1 RXN 2 RXN 3 (P
O2 = 50kPa)
p(y)/p(y0.5
) plots of reaction model
determined by averaged activation energy RXN 1 RXN 2 RXN 3 p (
y)/p
(y0.
5)
Conversion, α
g(α
)/g
(α0.
5)
0
1
2
3
4
5
Fig. 8 Theoretical master plots for reaction models determined by
Fig. 7 (lines) and experimental values determined by activation
energy values shown in Fig. 6 (symbols)
H.-C. Yang et al.
123
an appropriate model for describing the reaction, because
they had smallest SD values as shown in Table 1, when
compared to other models.
The best-fitted reaction models determined from the
master plots, which are shown in Fig. 7, were based on the
averaged activation energy values for each reaction step.
However, activation energy for each reaction step signifi-
cantly changed with the conversion level, as shown in
Fig. 6. This may result in significant errors in further dis-
cussion of the reaction model. In order to understand the
significance of these errors, the theoretical master plots for
the reaction models by the averaged activation energy
values were compared with experimental values by varying
the activation energy values, and the results are shown in
Fig. 8. The comparison reveals that the model master plots
determined by averaged activation energy did not match
the experimental plots at all. This indicates that an inter-
pretation of reaction models may result in significant errors
if the activation energy varies with the degree of conver-
sion, as recently discussed in detail by Simon et al. [15].
Determination of kinetic parameters
Determination of a pre-exponential factor (k0) and the
oxygen power dependency (n) for determined reaction
models by averaged activation energy was determined to
complete equation (1) for each reaction step. The curves of
7.0x10-4 1.4x10-3 2.1x10-3 2.8x10-3 3.5x10-3 4.2x10-30.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.25 K min-1
0.5 K min-1
0.75 K min-1
1 K min-1
g(α
) =
[–ln
(1–
α )]1/
2
(E/BR)p(y)
(a)
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
(E/BR)p(y)
(b)
0.25 K min-1
0.5 K min-1
0.75 K min-1
1 K min-1
g( α
) =
α2
0.00 1.50x10-6 3.00x10-6 4.50x10-6 6.00x10-60.0
0.1
0.2
0.3
0.4
0.5
0.6
(E/BR)p(y)
PO2
= 100 kPa 5 K min-1 10 K min-1
15 K min-1 20 K min-1
PO2
= 75 kPa
5 K min-1
10 K min-1
15 K min-1
20 K min-1
PO2
= 50 kPa
5 K min-1
10 K min-1
15 K min-1
20 K min-1
PO2
= 25 kPa
5 K min-1
10 K min-1
15 K min-1
20 K min-1
g(α
) =
1–
(1–α
)1/3
(c)
Fig. 9 Plots of determined g(a) against (E/BR)p(y) for all the
different conditions of RXN-1 (a), RXN-2 (b), and RXN-3 (c)
Table 2 Results of linear regression of the plots of g(a) against (E/
BR)p(y)
PO2/kPa Z/min-1 r
25 87521.7 0.99864
50 138756.5 0.99662
75 237512.0 0.99207
100 388985.5 0.99691
3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.811.0
11.2
11.4
11.6
11.8
12.0
12.2
12.4
12.6
12.8
13.0
Ln Z
Ln PO2
/kPa
Linear fitting slope ( = n) : 1.05 intercept ( = ln k0) : 7.90
Fig. 10 Plot of ln Z against ln PO2 for determination of the oxygen
power dependency n and the pre-exponential factor k0 of the
combustion reaction (RXN-3)
Study on cation exchange resins using non-isothermal TG
123
determined g(a) against (E/BR)p(y) for all the different
conditions are plotted in Fig. 9. The determined Z values
obtained by linear regressions of all the data for RXN-3 are
shown in Table 2. All the plots were fitted well linearly,
and all the linear regression coefficients were over 0.99.
These results indicate that determined kinetic models by
averaged activation energies are in close agreement with all
the experimental data. In the case of reaction steps RXN-1
and RXN-2, the determined Z value must be the same as
the pre-exponential factor, k0, since Z = k0(PO2)n and
n = 0. In the case of oxygen-influencing combustion
reaction (RXN-3), from the averaged Z values for the
corresponding oxygen partial pressures, the plots of ln
Z against ln PO2 are constructed in Fig. 10. The oxygen
power dependency n and the pre-exponential factor k0 for
the reaction RXN-3 were determined from the slope and
the intercept of the linearly fitted line in Fig. 10. The
reaction models and the kinetic parameters involved in the
reaction steps were finally determined, and the results are
shown in Table 3.
Conclusions
Two different reaction steps were identified for thermal
decomposition under both oxidizing and reducing atmo-
spheres. The primary thermal decomposition reaction,
which dissociates the functional group of sulfonic acid,
SO3H?, from divinylbenzene copolymer, was proven to be
a pure devolatilization reaction of which the reaction rate
was not influenced by the surrounding oxygen. Activation
energies of three reaction steps could be determined from a
model-free analysis of TG analysis data. Since the activa-
tion energy values varied with the conversion level, the
averaged activation energy values were used to interpret
kinetic models for each reaction step. Kinetic models for
each reaction step could be determined from the master
plots method. The primary thermal decomposition reaction,
which dissociates the functional group of sulfonic acid,
SO3H?, from divinylbenzene copolymer, was described by
an Avrami–Erofeev type reaction (n = 2). Thermal
decomposition of remaining divinylbenzene copolymer in
the absence of oxygen was described by one-dimensional
diffusion. The combustion of remaining divinylbenzene
copolymer in the presence of oxygen was described by a
phase boundary reaction (spherical symmetry).
Acknowledgements This work was supported by the National
Research Foundation of Korea (NRF) Grant funded by the Korea
government (MSIP) (No. 2012-M28A5025658) and by the main
project of Korea Atomic Energy Research Institute (KAERI) (No.
527260-13).
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Reaction step Temperature
range/K
Reaction
model, g(a)
Activation energy
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ln k0/s-1 Pa-nPower dependency
of oxygen, n
RXN-1 (thermal dissociation
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RXN-2 (thermal gasification
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RXN-3 (thermal oxidation
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