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

E/kJ mol-1Pre-exponential factor,

ln k0/s-1 Pa-nPower dependency

of oxygen, n

RXN-1 (thermal dissociation

of –SO3H)

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RXN-2 (thermal gasification

of RXN-1 products)

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RXN-3 (thermal oxidation

of RXN-1 products)

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