Phenomenological kinetics of the thermal decomposition of sodium hydrogencarbonate

Article abstract of DOI:10.1021/jp2094017

Aiming to find rigorous understanding and novel features for their potential applications, the physico-geometrical kinetics of the thermal decomposition of sodium hydrogencar-bonate (SHC) was investigated by focusing on the phenomen-ological events taking place on a single crystalline particle during the course of the reaction. The overall kinetics evaluated by systematic measurements of the kinetic rate data by thermo-gravimetry under carefully controlled conditions were interpreted in association with the morphological studies on the precursory reaction, mechanism of surface reaction, structure of the surface product layer, diffusion path of evolved gases, crystal growth of the solid product, and so on. The precursory reaction was identified as the decomposition of impurity, taking place at the boundary between the surface of the SHC crystal and the adhesive small SHC particles deposited on the surface. In flowing dry N₂, the thermal decomposition of SHC proceeds by two-dimensional shrinkage of the reaction interface controlled by chemical reaction with the apparent activation energy of about 100 kJ mol^-1, after rapid completion of the surface reaction and formation of porous surface product layer. Atmospheric CO₂ and water vapor influence differently on the overall kinetics of the thermal decomposition of SHC. Added gas phase of CO₂ slightly inhibits the overall rate because of the increasing contribution of the surface reaction. Under higher water vapor pressure, the physico-geometrical mechanism of the surface reaction changes drastically, indicating the preliminary reformation of reactant surface and the formation of needle crystals of solid product on the surface. The mechanistic change and extended contribution of the surface reaction result in the deceleration of the surface reaction and acceleration of the established reaction. (Figure presented)

Full text of DOI:10.1021/jp2094017

ARTICLE
pubs.acs.org/JPCA
Phenomenological Kinetics of the Thermal Decomposition of
Sodium Hydrogencarbonate
Nobuyoshi Koga,*,† Shuya Maruta,† Tomoyasu Kimura,† and Shuto Yamada‡
†Chemistry Laboratory, Department of Science Education, Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama,
Higashi-Hiroshima 739-8524, Japan
‡Center for Research and Advancement in Higher Education, Kyushu University, 744 Motooka, Fukuoka 819-0395, Japan
S Supporting Information
b
ABSTRACT: Aiming to find rigorous understanding and novel
features for their potential applications, the physico-geometrical
kinetics of the thermal decomposition of sodium hydrogencar-
bonate (SHC) was investigated by focusing on the phenomen-
ological events taking place on a single crystalline particle during
the course of the reaction. The overall kinetics evaluated by
systematic measurements of the kinetic rate data by thermo-
gravimetry under carefully controlled conditions were inter-
preted in association with the morphological studies on the pre-
cursory reaction, mechanism of surface reaction, structure of the
surface product layer, diffusion path of evolved gases, crystal growth of the solid product, and so on. The precursory reaction was
identified as the decomposition of impurity, taking place at the boundary between the surface of the SHC crystal and the adhesive
small SHC particles deposited on the surface. In flowing dry N2, the thermal decomposition of SHC proceeds by two-dimensional
shrinkage of the reaction interface controlled by chemical reaction with the apparent activation energy of about 100 kJ molꢀ1, after
rapid completion of the surface reaction and formation of porous surface product layer. Atmospheric CO2 and water vapor influence
differently on the overall kinetics of the thermal decomposition of SHC. Added gas phase of CO2 slightly inhibits the overall rate
because of the increasing contribution of the surface reaction. Under higher water vapor pressure, the physico-geometrical
mechanism of the surface reaction changes drastically, indicating the preliminary reformation of reactant surface and the formation
of needle crystals of solid product on the surface. The mechanistic change and extended contribution of the surface reaction result in
the deceleration of the surface reaction and acceleration of the established reaction.
solid-state reaction,7,8 and for evaluating the calculation methods
1. INTRODUCTION
of kinetic analysis.9ꢀ11
Thermal decomposition of sodium hydrogencarbonate (SHC:
NaHCO3) is one of the most common reactions utilized even in
The overall process of the thermal decomposition of SHC is
characterized by the simultaneous evolutions of CO2 and water
our daily life. For the detailed understanding on the kinetics and
vapor to produce sodium carbonate (SC): 2NaHCO3 (s) f
mechanisms of the reaction, large efforts have been paid by a
number of specialists of the solid-state reaction for more than two
centuries. The experimental findings have contributed notably
Na2CO3 (s) + CO2 (g) + H2O (g).12 The overall kinetics has
extensively been studied by thermoanalytical measurements,
where the largely distributed values of apparent activation energy
Ea, about 32ꢀ139 kJ molꢀ1, have been reported.3ꢀ11,13ꢀ15 The
not only toward the provision of fundamental knowledge for the
theoretical foundation of the thermal decomposition of solids,1,2
distribution indicates that the overall rate behavior depends
but also toward the development and refinement of the applica-
tions of the thermal decomposition process of SHC. In addition
to relevant industrial importance in the Solvay process, the
thermal decomposition process has the potential for various
applications as is seen in the recently published articles of utilizing
the reversibility of the thermal decomposition of SHC for the
CO2 separation technology.3,4 On the basis of the findings accu-
mulated, the thermal decomposition of SHC has also been
applied as a kind of test process for developing the new experi-
mental techniques of thermal analyses,5,6 for testing the techni-
ques and conditions of measuring the kinetic rate data of the
largely on the procedural factors such as sample preparations, ex-
perimental techniques, measuring conditions, calculation methods,
and so on. By applying an instrument of controlled rate evolved gas
analysis coupled with thermogravimetry (CREGA-TG),16 we re-
vealed that the rate behavior of the thermal decomposition of SHC
is influenced sensitively by the very small change in the atmospheric
CO2 and water vapor concentrations in the level of self-generated
Received: September 29, 2011
Revised:
November 6, 2011
Published: November 08, 2011
r
2011 American Chemical Society
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gaseous atmosphere during the course of reaction,6 where opposite
behaviors of deceleration and acceleration of the overall reaction
rate were confirmed by the respective effects of atmospheric CO2
and water vapor. This indicates that careful control of the measur-
ing conditions for recording the kinetic rate data is essential to the
reliable kinetic analysis. This is also true for the estimation of the
kinetic model function, which describes the physico-geometrical
characteristics of the rate behavior. The rate behavior of the present
reaction has been described in many cases by the simple first order
model: f(α) = 1 ꢀ α.3,4,6ꢀ11 However, the contracting geometry
type model was also reported by some authors.8,13 Although the
fractional reaction α is considered theoretically on the basis of a
certain reactant body and matrix,17 the practical determination of
the value is, in many cases of the thermal decomposition reactions,
due to the overall mass-loss with respect to the total mass-loss of the
subjected reaction step. Accordingly, the degree of consistency
between the kinetic model derived theoretically on the basis of the
physico-geometrical characteristics of the single step reaction of a
certain reactant body and that estimated by the empirical curve fit-
ting of the thermoanalytical curves may change depending on the
sample property, sampling, and measuring conditions for the
thermoanalytical measurements.18,19
Detailed understanding on the physico-geometrical character-
istics of the reaction, as is formalized in the kinetic model, is re-
quired for describing the physicochemical significance of the
kinetic parameters evaluated by the macroscopic measurements
of thermal analysis and for applying the kinetic information to the
development and refinement of the practical applications. Micro-
scopic observations of the morphological changes of the reactant
solids during the course of reaction are the useful techniques for
revealing the physico-geometrical characteristics of the reaction
and the special events of solid-state reaction,20 as has been demon-
strated for the thermal dehydration of lithium sulfate mono-
hydrate.21ꢀ23 For the present reaction, Ball et al.13 reported the
drastic change of the surface texture at the very beginning of the
decomposition reaction through examining the scanning elec-
tron microscopic views of the partially reacted particles. Several
special textures of solid-state reaction, such as the reaction front,
porous surface product layer, effluorescent growths of the pro-
duct solid on the surface, formations of cracks and holes on the
surface, and so on, were clearly presented. In contradiction,
Guarini et al. reported15 that the reaction is not accompanied
by the significant change of surface textures through the optical
microscopic observations on heating the sample.
2. EXPERIMENTAL SECTION
2.1. Sample Characterization. Reagent grade sodium hydro-
gencarbonate (SHC: Sigma-Aldrich Japan, special grade) was
sieved to various fractions of particle size and supplied as the
sample without any further purification. Before subjecting to the
kinetic study of the thermal decomposition process, the sample
was characterized by powder X-ray diffraction (XRD: RINT
2200 V, Rigaku Co., monochrome Cu Kα, 40 kV, 20 mA), Fouri-
er transfer infrared spectroscopy (FT-IR: Shimadzu FTIR8400S,
diffuse reflectance method), and thermogravimetry-differential
thermal analysis (TG-DTA: Shimadzu DTG-50). The morphol-
ogy of the sample particles was observed by scanning electron
microscopy (SEM: JSM-6510, Jeol) after coating the sample with
Pt by sputtering (JFC-1600, Jeol, 20 mA, 60 s).
2.2. Characterization of the Thermal Decomposition Pro-
cess. The thermal decomposition process was characterized ini-
tially by TG/DTA-mass spectroscopy (MS) and high temperature
powder XRD measurements. Using an instrument of TG/DTA-
MS constructed by connecting TG-DTA (TG8120, Rigaku Co.)
to a quadrupole mass spectrometer (M-200QA, Anelva Co.), the
sample of 2.0 mg, weighed into platinum cell (5 mmϕ and 2.5 mm
in height), was heated at a heating rate β = 5 K minꢀ1 in flowing
He (200 cm3 minꢀ1, >99.99%, Japan Helium Center, introduced
after passing through the moisture absorbent column of silica gel)
for recording TG-DTA curves, where the mass spectra of evolv-
ed gases were recorded simultaneously in the range from 10 to
50 amu (EMSN, 1.0 A; SEM, 1000 V). In flowing N2 (100cm3 minꢀ1,
>99.9%, Iwatani Gas, introduced after passing through the moisture
absorbent column of silica gel), phase change of the sample, press-
fitted on a platinum plate, during stepwise isothermal heating up
to 393 K at β = 10 K minꢀ1 was traced by XRD using the above
instrument by equipping with a programmable heating chamber
(PTC-20, Rigaku Co.), where the sample temperature was kept
constant during the respective diffraction measurements for
15 min. Subsequently, the sample was heated isothermally at
398 K and the XRD measurements were started repeatedly at
every 15 min.
2.3. Measurements for the Precursory Reaction. For trac-
ing the precursory endothermic phenomena accompanied with
detectable mass-loss, differential scanning calorimetry (DSC:
DSC-50, Shimadzu Co.) was applied for the samples (10.00 (
0.05 mg) of different sieve fractions of particle size, weighed into
an aluminum cell (5 mmϕ and 2.5 mm in height), and covered
with an aluminum lid without sealing. The DSC measurements
were carried out at a heating rate β = 5 K minꢀ1 in flowing N2
(50 cm3 minꢀ1, introduced after passing through the moisture
absorbent column of silica gel). Temperature and enthalpy cali-
brations of the instrument were performed preliminary by the
melting point measurements for the pure metals (>99.99%) of
Ga, In, Sn, Pb, and Zn. For the sample of 280 mesh passed frac-
tion (<53 μm in aperture), DSC curves for the precursory
endothermic phenomena were recorded at different heating
rates 1 e β e 10 K minꢀ1 for the kinetic analysis. The sample
heated to the end of precursory endothermic phenomena was
cooled down to room temperature and observed by SEM.
2.4. Measurements for the Thermal Decomposition Pro-
cess. The samples (100ꢀ170 mesh sieve fraction: ca. 90ꢀ150 μm
in aperture) of 5.00 ( 0.01 mg, weighed into a platinum cell
(6 mmϕ and 3 mm in height), were used for the measurements
of kinetic rate data of the thermal decomposition process using a
hanging-type thermobalance (TGA-50, Shimadzu Co.). In this
The present study was undertaken to reveal the physico-
geometrical kinetics of the reaction by focusing on a single crystalline
particle of SHC. The overall kinetics was evaluated by systematic
measurements of the kinetic rate data under well-controlled re-
action conditions. The kinetic results were interpreted in asso-
ciation with the microscopic observations of the reaction mor-
phology. Influences of atmospheric CO2 and water vapor on the
physico-geometrical characteristics and the overall kinetics of the
reaction were also demonstrated. The consensus between the
theory of physico-geometrical kinetics of the thermal decompo-
sition of solids and the experimentally resolved phenomenolo-
gical features of the present reaction was carefully evaluated. It is
hoped that the present very fundamental research contributes
largely to the further development and refinement of the experi-
mental approaches to the kinetics of the thermal decomposition
of solids, together with the further detailed understanding on the
kinetics of the thermal decomposition of SHC.
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Figure 2. Typical TG-DTA curves for the thermal decomposition of
SHC (170ꢀ200 mesh) at β = 5 K minꢀ1 in flowing N2 (100 cm3 minꢀ1).
Figure 1. TypicalSEM images ofthereactant particles(100ꢀ170 mesh).
sampling condition, the sample particles spread on the bottom of
the platinum cell without forming significant layer. The mea-
sured temperature of the instrument was calibrated preliminary
by using the melting point of pure metal wires (>99.99%) of In,
Sn, Pb, and Zn and a series of magnetic standards of NiꢀCo
compounds.24 The measurements were carried out by three
different modes of temperature program, that is, isothermal,
linear nonisothermal, and controlled transformation rate (CRTG)25
modes, in flowing N2 or N2ꢀCO2 (5% N2ꢀ95% CO2, CO2
purity: >99.9%, Nakamura Sanso) at a rate of 100 cm3 minꢀ1
(introduced after passing through the moisture absorbent col-
umn of silica gel). Isothermal mass-loss traces were recorded at
different constant temperatures after heating up to the pro-
grammed temperature at β = 10 K minꢀ1. The linear non-
isothermal measurements were performed at different β from
1 to 5 K minꢀ1. By equipping with a self-constructed controller of
sample controlled thermal analysis26,27 to the above thermoba-
lance, the sample was heated at β = 2 K minꢀ1, where the mass-
loss rate during the thermal decomposition was regulated at
Figure 3. Mass chromatograms of m/z 18 and 44 for the evolved gas
during the thermal decomposition of SHC (280 mesh passed).
atmosphere were observed by SEM after cooling down to room
temperature.
3. RESULTS AND DISCUSSION
3.1. Characterizations of Sample and Its Thermal Decom-
position Process. Figure 1 shows typical SEM images of the
sample particles (100ꢀ170 mesh). The sample particles are col-
umnar crystals grown along to b-axis as usual,15 Figure 1a. Many
small particles in a size of several μm are deposited on the sur-
faces of columnar crystal, Figure 1b. The same feature of the
adhesive particles deposited on the main crystal body have been
seen in the previously reported SEM images of SHC.4,28 The
growth front of the columnar crystals are not smooth surfaces,
which are covered with a crystalline layer, Figure 1c, and ag-
gregates of crystalline particles, Figure 1d. As was shown in
Figures S1 and S2 in the Supporting Information, the powder
XRD pattern and FT-IR spectra of the sample are in good agre-
ement with those of SHC.3,29,30
Figure 2 shows typical TG-DTA curves for the sample (170ꢀ
200 mesh: ca. 75ꢀ90 μm in aperture). The thermal decomposi-
tion proceeds in a smooth mass-loss process, where the measured
mass-loss value of 37.0 ( 0.2% averaged over the samples of
different sieve fractions is comparable with the value, 36.9%,
calculated by assuming the reaction: 2NaHCO3 (s) f Na2CO3
(s) + CO2 (g) + H2O (g). It should be noted here that a small but
detectable endothermic peak is observed, at around 355ꢀ365 K,
different constant rates C from 7.5 to 15 μg minꢀ1
.
Influence of the atmospheric water vapor on the thermal
decomposition process was evaluated by TG-DTA measure-
ments under controlled water vapor pressure, p(H2O). By keep-
ing the sample of 5.00 ( 0.02 mg, weighed into platinum cell
(5 mmϕ and 2.5 mm in height), at 340 K in an instrument of TG-
DTA (TG8120, Rigaku Co.), a mixed gas of N2ꢀH2O with a
controlled p(H2O) was introduced into the reaction tube at a
rate of about 400 cm3 minꢀ1 from a programmable humidity
controller (HUM-1, Rigaku Co.). After stabilizing the reaction
system for 30 min, the sample was heated at β = 5 K minꢀ1 under
different p(H2O) from 0.8 to 10.3 kPa for recording TG-DTA
curves. By selecting two different p(H2O), that is, 0.8 and 10.3
kPa, TG-DTA curves under those p(H2O) were recorded at
different β from 1 to 5 K minꢀ1
.
The sample particles reacted to different fractional reaction α
under different conditions of temperature program and reaction
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Figure 5. Typical SEM images of the surface textures of the sample
particles (280 mesh passed) heated to the end of precursory reaction.
and evolved gases of the precursory reaction support circumstan-
tially the above-mentioned proposal by Dei and Guarini.28
Change in the XRD pattern of the sample during stepwise iso-
thermal heating up to 393 K and subsequent isothermal heating
at 393 K in flowing N2 was shown in Figure S3 in the Supporting
Information. It was confirmed from the monotonous attenuation
of the XRD peaks of SHC and the compensative growth of those
of SC that the main reaction is exclusively the thermal decompo-
sition of SHC to produce SC without forming any crystalline in-
termediate compounds.
3.2. Precursory Reaction. The precursory reaction was traced
by DSC, as shown in Figure 4. The area of DSC endothermic
peak increases with decreasing the particle size of the sample,
where no detectable change of the reaction temperature is ob-
served, Figure 4a. This behavior indicates that the precursory
reaction is associated with the reaction of surface groups, and the
rate behavior is not influenced by the size and geometry of the
main body of sample particle. Although Dei and Guarini detected
the formation of SC by FT-IR spectrum during the precursory re-
action for the sample, which indicates a remarkable DSC endo-
thermic peak,28 the clear evidence of the formation of SC during
the precursory reaction could not be detected in the present study
by the changes of FT-IR spectra and powder XRD. This may be
due to the smaller portion of the sample participated in the pre-
cursory reaction. As was listed in Table S1 in the Supporting
Information, the apparent enthalpy changes ΔH observed for the
present samples are smaller by 10ꢁ than that reported by Dei and
Guarini.28
Figure 4. DSC traces for the precursory reaction of the thermal
decomposition of SHC. (a) Comparison among the samples of different
sieve fractions of particle sizes. (b) For the sample particles of 280 mesh
passed at different β.
before the main reaction process of the thermal decomposition.
The area of endothermic peak increased with decreasing the par-
ticle size of the sample. The endothermic peak is accompanying a
detectable mass-loss in TG, that is, 0.07% for the sample of 100ꢀ
170 mesh and 0.15% for the sample of 280 mesh passed. The
similar precursory reaction can be seen in many reported thermo-
analytical curves for the thermal decomposition of SHC.5,7,11,15,28
Figure 3 shows the mass chromatograms of m/z 18 and 44 of
the evolved gases during the thermal decomposition of SHC. As
has been reported previously,5,6,12 the main part of the thermal
decomposition is characterized by the simultaneous evolutions of
CO2 and H2O. During the precursory reaction, evolutions of
CO2 and H2O are confirmed, where the excess amount of H2O
with respect to CO2 are evolved. The observed profiles of mass
chromatograms of CO2 and H2O for the precursory reaction is in
coincident with those reported by Tiernan et al.5 As a possible
reaction at this stage, Dei and Guarini28 proposed the thermal
decomposition of sodium sesquicarbonate dihydrate (SSC:
Na2CO3 NaHCO3 2H2O), produced on the surface of SHC
3
3
formed during prolonged aging. Under the reaction conditions
comparable with the above thermoanalytical measurements, the
thermal decomposition of SSC initiates at the temperature cor-
responding to that of the precursory reaction of the present
SHC.31,32 The thermal decomposition of SSC is described by:
2(Na2CO3 NaHCO3 2H2O) f 3Na2CO3 + CO2 + 5H2O,31,32
Figure 5 shows typical SEM images of the sample particles
(280 mesh passed) heated to the end of the precursory reaction.
The reaction sites of the precursory reaction can be identified at the
boundaries between the surface of reactant crystals and the
adhesive particles, Figure 5c,d, where no distinguished textural
change can be foundon the surfaces of reactantcrystals, Figure 5a,b.
The product solid of the precursory reaction is needle-like crystal-
lites irradiating in parallel to the surface of reactant crystal,
3
3
where an excess amount of H2O with respect to CO2 is evolved.
Although identifications of SSC and product SC were not suc-
cessful in the present study, the findings on the reaction temperature
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Table 1. Summary of the Kinetic Results for the Precursory Reaction
a
2 d
method
range of β
range of α
Ea/kJ molꢀ1
γ1
f(α)
kinetic exponents
A/sꢀ1
γ2 ,
Kissinger
Freidman
1 e β e 10
1 e β e 5
peak max.
114.1 ( 8.4
124.8 ( 7.0
ꢀ0.9999
ꢀ0.9978 ( 0.0035
0.1 e α e 0.9
JMA(m) b
SB(m, n, p) c
m = 2.30 ( 0.08
m = ꢀ0.21 ( 0.22
n = 1.66 ( 0.09
p = 1.13 ( 1.13
(3.57 ( 0.10) ꢁ 1016
(1.47 ( 0.03) ꢁ 1015
0.9014
0.9992
a Correlation coefficient of the linear regression analysis for the Kissinger and Friedman plots. b f(α) = m(1 ꢀ α)[ꢀln(1 ꢀ α)]1ꢀ1/m. c f(α) =
αm(1 ꢀ α)n[ꢀln(1 ꢀ α)]p. d Square of the correlation coefficient of the nonlinear regression analysis for the fitting of experimental master plot.
Figure 5c, and some of those are penetrating to the reactant
crystal, Figure 5d.
On the basis of the above findings, the kinetic behavior of the
precursory reaction was estimated by the formal kinetic analysis
of the DSC curves recorded at different β shown in Figure 4b.
The results of kinetic analysis were summarized in Table 1. The
methodologies and course of the kinetic analysis for the pre-
cursory reaction were described in detail in the Supporting Infor-
mation. The apparent activation energy Ea for the precursory re-
action was slightly higher than that for the thermal decomposition
of SHC, which will be described below. The value of Ea de-
termined by the Kissinger method,33 114.1 ( 8.4 kJ molꢀ1, is
closely corresponding to the value reported for the thermal de-
composition of SSC.34 From the shape of the experimental master
plot for the precursory reaction, one of the nucleation and growth
type model was estimated as the possible physico-geometrical re-
action model. Through the nonlinear fitting of the experimental
master plot by Johnson-Mehl-Avrami model,35 JMA(m): f(α) =
m(1 ꢀ α)[ꢀln(1 ꢀ α)]1ꢀ1/m, of the nucleation and growth type
reaction, the best value of the kinetic exponent was estimated as
m = 2.30 ( 0.08, which isalso indicatingthe close correspondence
to the reported rate behavior of the thermal decomposition of
SSC.31 However, in comparison with the nearly perfect fitting
by an empirical kinetic model of Sestak-Berggren,36 SB(m,n,p):
f(α) = αm(1 ꢀ α)n[ꢀln(1 ꢀ α)]p, the rate process cannot be de-
scribed satisfactorily by JMA(m) model.
Figure 6. Mass-loss traces and their time derivative curves for the main
From the above findings, it is probable that the precursory re-
action can be avoided by eliminating the adhesive particles on the
thermal decomposition of SHC (100ꢀ170 mesh, m0 = 5.0 mg) in
flowing N2: (a) under isothermal heating at different T and (b) under
surface of SHC crystal. Even if the precursory reaction took part
in the thermal decomposition, the influence on the overall kinetic
of the thermal decomposition of the main body of SHC crystal is
very limited.
linearly increasing temperature at different β.
of the temperature profile is also corresponding to a contracting
geometry type reaction.38,39
3.3. Thermal Decomposition of SHC. Figure 6 shows the
mass-loss traces at different constant temperatures (Figure 6a)
and under linear nonisothermal heating at different β (Figure 6b)
for the main reaction of the thermal decomposition in flowing N2,
together with their time derivative curves. In the isothermal mea-
surements, no distinguished behavior of induction period can be
found. The reaction decelerates as reaction advances in a manner
of the reaction controlled by the contracting geometry.37 The re-
action advances smoothly even under dynamic heating, where the
fractional reaction α at the maximum mass-loss rate varied sys-
tematically from αp = 0.70 at β = 1.0 K minꢀ1 to αp = 0.65 at β =
5.0 K minꢀ1. Figure 7 shows a typical record of the mass-loss data
under the controlled constant mass-loss rate at C = 10.0 μg minꢀ1
(Figure 7a) and the temperature profiles of the reaction at dif-
ferent C (Figure 7b). The mass-loss rate was controlled success-
fully during the course of reaction. After reaching at the program-
med C, the reaction temperature increases gradually as reaction
advances and rapidly at the final stage of the reaction. The shape
For analyzing the overall kinetics of the main thermal decom-
position of SHC, the following fundamental kinetic equation was
assumed.
ꢀ
ꢁ
dα
dt
Ea
¼ A exp
ꢀ
fðαÞ
ð1Þ
RT
where A, Ea, and f(α) are the Arrhenius pre-exponential factor,
apparent activation energy, and kinetic model function, respec-
tively. In the present study, all the kinetic rate data converted
from the mass-loss data under different temperature program
modes, that is, isothermal, linear nonisothermal, and CRTG
modes, were applied universally to the kinetic calculations based
on eq 1.37,40ꢀ43
The results of kinetic calculations are illustrated in Figure 8.
An isoconversional relationship between the overall reaction
rate, dα/dt, and temperature, T, is derived by taking logarithms
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Figure 7. Typical results of mass-loss measurements under con-
trolled mass-loss rate, C, for the main thermal decomposition of SHC
(100ꢀ170 mesh, m0 = 5.0 mg) in flowing N2. (a) A typical record at
C = 10.0 μg minꢀ1 and (b) the temperature profiles of the reaction at
different C.
of eq 1.44
ꢀ
ꢁ
dα
dt
Ea
ln
¼ ln½Af ðαÞꢂ ꢀ
ð2Þ
RT
When the overall kinetic behavior is fully satisfied with eq 1, the
plot of ln (dα/dt) against Tꢀ1 for the data points at a restricted
α, that is so-called Friedman plot,44 should be a straight line ir-
respective of the program modes for measuring the kinetic rate
data. The plots of ln (dα/dt) against Tꢀ1 at different α in steps
of 0.1 in the range 0.1 e α e 0.9 were shown in Figure 8a. At the
selected α, all the data points recorded under different modes of
temperature program line up on a straight line. Slopes of the plots
at different α are nearly constant, indicating the constant value of
Ea in the wide range of α, Figure 8b. The Ea value averaged over
0.1 e α e 0.9 was 101.8 ( 1.6 kJ molꢀ1, which is closely
corresponding to some of those reported previously.5,7ꢀ9,11,15
The dependence of the rate behavior on α was evaluated by
drawing an experimental master plot, Figure 8c. The hypothe-
tical reaction rate, dα/dθ, was calculated by extrapolating the
rate data at the respective α to infinite temperature, according
to37,40,41,43
Figure 8. Kinetic analysis for the thermal decomposition of SHC (100ꢀ170
mesh) in flowing N2. (a) The Friedman plots at different α from 0.1 to 0.9 in
steps of 0.1, (b) the values of Ea at various α, and (c) comparisons of the
experimental master plot with the theoretical curves of RO(n) and SB(m,n,p)
models.
plot is correlated to the kinetic model function by37,40,41,43
dα
¼ AfðαÞ
ð4Þ
dθ
For describing the experimental master plot, the kinetic model
function of reaction order model, RO(n): f(α) = n(1 ꢀ α)1ꢀ1/n
,
was applied for evaluating the dimension of reaction interface
shrinkage n. For a comparison, an empirical kinetic model of
SestakꢀBerggren, SB(m,n,p): f(α) = αm(1 ꢀ α)n[ꢀln(1 ꢀ α)]p,
which fits to various physico-geometric types of reaction and
those deviated cases with nonintegral or fractal dimension of
reaction geometry, size distribution of reactant particles, and
so on,43,47,48 was also applied. The most appropriate kinetic ex-
ponents in these kinetic model functions and the value of A were
estimated simultaneously through the nonlinear regression analysis
ꢀ
ꢁ
ꢀ
ꢁ
Z
dα dα
Ea
Ea
¼
exp
with θ ¼ texp
ꢀ
ð3Þ
dθ
dt
RT
0
RT
where θ is Ozawa’s generalized time.45,46 The experimental
master plot of dα/dθ against α indicates the deceleration as re-
action advances, which is corresponding to one of the con-
tracting geometry type reaction.37 The experimental master
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Table 2. Summary of the Kinetic Results for the Main Reaction of the Thermal Decomposition of SHC (100ꢀ170 Mesh)
atmosphere
measurement
Ea/kJ molꢀ1
f(α)
kinetic exponents
A/sꢀ1
γ2, d
N2 (100 cm3 minꢀ1
)
controlled rate
isothermal
101.8 ( 1.6
RO(n) a
n = 2.18 ( 0.02
(2.59 ( 0.02) ꢁ 109
0.9961
(0.1 e α e 0.9)
(0.1eα e 0.9)
SB(m,n,p) b
nonisothermal
m = ꢀ2.69 ( 0.25
n = 1.61 ( 0.10
p = 2.63 ( 0.25
n = 1.99 ( 0.02
(4.89 ( 0.08) ꢁ 109
0.9988
(0.1 e α e 0.9)
CO2 (100 cm3 minꢀ1
)
controlled rate
isothermal
102.2 ( 1.1
RO(n) a
(2.47 ( 0.03) ꢁ 109
(4.26 ( 0.07) ꢁ 109
0.9906
0.9989
(0.1 e α e 0.9)
(0.1 e α e 0.9)
SB(m,n,p) b
nonisothermal
m=-3.35 ( 0.24
n = 1.86 ( 0.09
p = 3.31 ( 0.23
m = ꢀ5.92 ( 0.35
n = 2.32 ( 0.14
p = 5.73 ( 0.34
n = 2.34 ( 0.04
(0.1 e α e 0.9)
N2ꢀH2O (ca. 400 cm3 minꢀ1
p(H2O) = 0.8 kPa
)
nonisothermal
103.4 ( 0.5
SB(m,n,p) b
(1.59 ( 0.04) ꢁ 1010 0.9985
(0.1 e α e 0.9)
(0.1 e α e 0.9)
RO(n) a
(1.03 ( 0.02) ꢁ 1010 0.9921
(2.67 ( 0.03) ꢁ 1010 0.9814
(2.30 ( 0.03) ꢁ 1011 0.9985
(0.2 e α e 0.9)
JMA(m) c
m = 1.43 ( 0.02
(0.2 e α e 0.9)
SB(m,n,p) b
N2ꢀH2O (ca. 400 cm3 minꢀ1
p(H2O) = 10.3 kPa
)
nonisothermal
109.7 ( 5.4
m = ꢀ5.31 ( 0.18
n = 2.60 ( 0.07
p = 5.23 ( 0.18
n = 2.08 ( 0.05
(0.1 e α e 0.9)
(0.1 e α e 0.9)
RO(n) a (0.35 e α e 0.9)
JMA(m) c (0.35 e α e 0.9) m = 1.88 ( 0.02
(1.52 ( 0.02) ꢁ 1011 0.9826
(2.84 ( 0.03) ꢁ 1011 0.9950
a f(α) = n(1 ꢀ α)1ꢀ1/n]. b f(α) = αm(1 ꢀ α)n[ꢀln(1 ꢀ α)]p. c f(α) = m(1 ꢀ α)[ꢀln(1 ꢀ α)]1ꢀ1/m
.
d Square of the correlation coefficient of the
nonlinear regression analysis for the fitting of experimental master plot.
by applying the LevenbergꢀMarquardt optimization algorithm.49
As was shown in Figure 8c, the experimental master plot was
fitted satisfactorily by RO(n) model with n = 2.18 ( 0.02 and
A = (2.59 ( 0.02) ꢁ 109 sꢀ1 (γ2 = 0.9961), indicating two-
dimensional shrinkage of reaction interface controlled by chemi-
cal reaction.18,37,50 In addition, the fitting curve by RO(2.18)
is very close to that by the empirical SB(ꢀ2.69,1.61,2.63) with
A = (4.89 ( 0.08) ꢁ 109 sꢀ1 (γ2 = 0.9988). Although the
physico-geometrical meanings of the kinetic exponents in SB-
(ꢀ2.69, 1.61, 2.63) are difficult to evaluate at present, the com-
parable good fitting by the empirical SB(ꢀ2.69, 1.61, 2.63) and
physico-geometrical RO(2.18) models supports the validity of
RO(2.18) for describing the physico-geometrical characteristics
of the reaction. The results of above formal kinetic analyses are
summarized in Table 2.
Figure 9 shows typical SEM images of the sample at the initial
stage of the thermal decomposition in flowing N2. The reaction
initiates at the surface of the sample particles. Formation of
whiskers on the surfaces can be found as the special event of the
surface reaction, Figure 9a. In addition to the side surface of the
columnar crystals, the whiskers are formed on the base surfaces
and on the adhesive particles deposited on the surfaces of the col-
umnar crystals, Figure 9b. The reaction front of the surface re-
action is seen in Figure 9b,c. Erosion of the original surface in the
depth of submicrometer order can be observed, where the whis-
kers are formed in the eroded area. Length of the whiskers is 0.5ꢀ
1.0 μm, Figure 9d. Possible participation of liquid phase on the
surface reaction is expected from the erosion of original reactant
surface in the considerable depth and formation of whiskers in
the eroded area. The liquid phase may be produced at the initial
reaction sites as the aqueous solution of SHC and/or SC and
spread on the reactant surface by eroding the original reactant
surface. Vaporization of water and evolution of CO2 from the
intermediate liquid phase promote the growth of solid product,
SC, in the form of whisker. The SC whiskers formed on the side
surfaces of columnar crystal disappear before α = 0.1 by the crys-
tal growth of SC, forming the surface product layer of aggrega-
tes of SC particles in the size of several hundred nanometers,
Figure 9e. The surface product layer maintains interstices to be
possible channels for the diffusional removal of the gaseous pro-
ducts evolved at the internal reaction zone during the subsequent
established reaction. The whiskers produced on the base surfaces
of columnar crystals, growing in parallel to the long axis of the
sample crystal, tend to have the lifetime slightly longer than those
formed on the side surfaces, Figure 9f.
Figure 10 shows typical SEM images of sample particles at the
final stage of the reaction. No distinguished change of the surface
morphology of the reacting particles can be found during the
course of the established reaction. At α = 0.8, the surface product
layer is still maintaining the interstices in the aggregates of pro-
duct SC particles, Figure 10a. Whiskers of several micrometers in
the length, radiating from the interstices of the solid product
layer, are sometimes observed during the course of the establish-
ed reaction, Figure 10b. The whiskers seem to be the tracks of
spouting of liquid phase produced by the condensation of water
vapor and dissolution of product SC during the course of diffu-
sion through the solid product layer. Self-cooling due to the
endotherm by reaction itself51 and the local increase in the partial
pressure of evolved gases by the possible impedance of the diffu-
sion through the solid product layer52 can be possible causes of
the formation of the liquid phase. Comparing the surfacemorpho-
logies of the final products under isothermal and nonisothermal
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Figure 10. Typical SEM images of the surface textures of the sample
(100ꢀ170 mesh) at the final stage of the thermal decomposition in
flowing N2: (a, b) decomposed to α = 0.80 by heating isothermally at
393 K for 50 min, (c) decomposed to α = 1.00 by heating isothermally at
403 K for 150 min, and (d) decomposed to α = 1.00 by heating non-
isothermally at β = 5.0 K minꢀ1 to 473 K.
to that for the established reaction of the shrinkage of reaction in-
terface. The two-dimensional shrinkage of the reaction interface
controlled by the chemical reaction at the reaction interface es-
timated by the curve fitting of the experimental master plot is sup-
ported by the SEM observation of the reaction morphology, where
the interstices of the product layer on the side faces of columnar
reactant particle maintaining during the course of established
reaction is to be the diffusion channels of the gaseous products
produced at the reaction zone inside the particle. The contribution
of the surface reaction on the overall reaction may increase with
decreasing particle size of SHC crystal. The present physico-geo-
metrical description of the overall kinetics based on a single
reactant particle is not applicable when a distinguished size dis-
tribution of the reactant crystals exists and when a large amount of
sample particles were applied for the measurements of the kinetic
rate data. The former directly causes the distribution of α among
the reacting particles.53,54 Similarly, the distribution of α among the
reacting particles also results from the possible gradients of tem-
perature and partial pressure of the evolved gases within the sample
bed.18 When such a distribution of α among the reacting particles
existsduringthecourseofreaction,theshapeofthekineticratedata
tends to indicate superficially that similar to the nucleation and sub-
sequent growth as is described by JohnsonꢀMehlꢀAvrami model,
JMA(m).53,54 The differences in the sampling and measuring con-
ditions can be the possible causes of the discrepancy of the most
appropriate kinetic model function reported previously, that is,
RO(n) or JMA(m). Even in such cases of distribution of α among
the reacting particles, the apparent value of Ea evaluated by one of
the isoconversional methods is nearly constant, indicating the ap-
parent value for the advancement of the reaction interface.53,54
3.4. Influence of Atmospheric CO2. Figure 11 compares the
mass-loss traces and those derivative curves for the thermal
Figure 9. Typical SEM images of the surface textures of the sample
(100ꢀ170 mesh) at the initial stage of the thermal decomposition in
flowing N2: (aꢀd) decomposed to α = 0.04 by heating isothermally
at 378 K for 5 min and (e, f) decomposed to α = 0.10 by heating
isothermally at 383 K for 5 min.
conditions, Figure 10c,d, the larger particles of product SC are ob-
served for the product under nonisothermal condition due to the
heating to the higher temperature to complete the reaction.
Because the interstices of the surface product layer is maintaining
in both the product solids under isothermal and nonisothermal
conditions, the difference in the degree of crystal growth of pro-
duct SC may not influence largely on the overall kinetics under
the respective conditions.
From the above findings of the formal kinetic analysis and re-
action morphology for the reaction in flowing N2, the physico-
geometrical mechanism of the thermal decomposition is char-
acterized by the surface reaction and subsequent advancement of
the reaction interface, formed between the original reactant cry-
stal and the surface product layer, inward the reactant particle.
The possible existence of the intermediate liquid phase during
the surface reaction indicates that the kinetics of the surface re-
action depends largely on the reaction atmosphere applied and
self-generated by the reaction itself. In flowing N2, the surface
reaction completes in the early stage of the thermal decomposi-
tion before α = 0.1, so that the overall kinetics evaluated from the
thermoanalytical measurements in 0.1 e α e 0.9 is corresponding
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Figure 12. Typical SEM images of the surface textures of the sample
(100ꢀ170 mesh) decomposed in flowing CO2: (a) decomposed to
α = 0.15 by heating isothermally at 398 K for 5 min and (b) decomposed
to α = 1.00 by heating nonisothermally at β = 5.0 K minꢀ1 to 473 K.
was supported by the comparable good fitting by SB(ꢀ3.35,
1.86. 3.31) with A = (4.26 ( 0.07) ꢁ 109 sꢀ1 (γ2 = 0.9989). The
physico-geometrical mechanism estimated by the kinetic cal-
culation is unchanged by the effect of atmospheric CO2. The
deceleration effect by atmospheric CO2 is detected by the slight
decrease in the value of A. The results of kinetic analysis were
also summarized in Table 2.
Typical SEM images of the sample surface at the initial stage of
the reaction and of final product decomposed in flowing CO2 are
shown in Figure 12. At the initial stage of the reaction, the larger
numbers of whiskers are radiating on the surface of the reacting
particles in comparison with those in flowing N2, Figure 12a. The
size and thickness of the whiskers are also larger than those in
flowing N2, where largely grown bars of solid product can be fo-
und in several places. The growth of whisker seems to be due to
the diffusion and release of gaseous product, possibly interme-
diated by liquid phase, along with the surfaces of the whiskers
and to the slower release rate of CO2 and H2O by the effect of
chemical equilibrium with respect to CO2. Formation of the sur-
face product layer of sintered SC particles as was observed for the
reaction in flowing N2 is retarded until about α = 0.2ꢀ0.3.
Because the surface product layer with interstices provides the
channels for diffusion of gaseous products, retardation of the
formation may have an influence on the overall reaction rate to be
decelerated. Once the surface product layer was established, it
maintains the interstices during the latter course of reaction as in
flowing N2. Figure 12b shows the surface morphology of the pro-
duct solid produced by the thermal decomposition under linear
heating in flowing CO2. In comparison with those produced in
flowing N2 under otherwise identical reaction conditions, see
Figure 10d, sintering of the constituent product particles of the
surface product layer is more extensive, reducing slightly the in-
terstices of the surface product layer.
Figure 11. Comparisons of the mass-loss traces and those derivative
curves for the thermal decomposition of SHC (100ꢀ170 mesh, m0 =
5.0 mg) recorded in flowing N2 and CO2: (a) under isothermal
condition at T = 403 K and (b) under linear nonisothermal condition
at β = 5 K minꢀ1
.
decomposition of SHC (100ꢀ170 mesh) under isothermal and
nonisothermal conditions recorded in flowing N2 and CO2. De-
celeration effect by atmospheric CO2 can be detected by the
slight decrease in the mass-loss rate in the isothermal mass-loss
data and slight increase in the reaction temperature in the non-
isothermal mass-loss data in comparison with those in flowing
N2. When the mass-loss rate was controlled to be constant, the
reaction temperature increased slightly in flowing CO2. Although
we have reported that the rate of the thermal decomposition
is decelerated sensitively by atmospheric CO2 in the order of
10 ppm,6 the present results indicate that the deceleration effect
by atmospheric CO2 observed in the region of very low concen-
tration is not continuous and is saturated in the higher CO2 con-
centrations.
The same kinetic calculation, as is the above for the reaction in
flowing N2, was applied for the mass-loss data in flowing CO2
under three different modes of temperature program. The typical
kinetic rate data and detailed results of kinetic calculation for the
reaction in flowing CO2 were described in the Supporting
Information, together with typical figures in Figures S6, S7,
and S8. All the data points recorded under isothermal, noniso-
thermal, and CRTG modes of temperature program satisfied the
isoconversional relationship based on eq 2, representing the
straight line of the plots of ln(dα/dt) against Tꢀ1 at the selected
α. The values of Ea calculated from the Friedman plots were
nearly constant irrespective of α. The Ea value averaged over 0.1
e α e 0.9 was 102.2 ( 1.1 kJ molꢀ1, which is substantially the
same value with that for the reaction in flowing N2. The exper-
imental master plot of dα/dθ against α was fitted satisfactorily
by RO(n) model with n = 1.99 ( 0.02 and A = (2.47 ( 0.02) ꢁ
109 sꢀ1 (γ2 = 0.9906), where the validity of RO(1.99)
From the above observations, it is apparent that the atmo-
spheric CO2 influences mainly on the reaction behavior of the
surface reaction at the initial part of the thermal decomposition by
retarding the establishmentof the surface product layer. In spite of
such influences of atmospheric CO2 in heterogeneous character-
istics, the overall rate behavior of the established reaction, char-
acterized by two-dimensional shrinkage of the reaction interface
controlled by chemical reaction with Ea = ∼100 kJ molꢀ1, is not
influenced largely.
3.5. Influence of Atmospheric Water Vapor. Figure 13 shows
the influence of p(H2O) on the mass-loss data and those derivative
curves for the thermal decomposition of SHC (100ꢀ170 mesh)
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Figure 13. Influence of p(H2O) on the mass-loss traces and those de-
rivative curves for the thermal decomposition of SHC (100ꢀ170 mesh)
recorded under linearly increasing temperature at β = 5 K minꢀ1
.
recorded under linearly increasing temperature at β = 5 K minꢀ1
.
Even under the higher p(H2O), the precursory reaction was de-
tected as the endothermic process with detectable mass-loss. The
mass-loss data for the main thermal decomposition of SHC in-
dicatea complex behaviorbythe effectofatmosphericwatervapor.
With increasing p(H2O), the onset temperature of the derivative
curve shifts to higher temperature, whereas the peak top tempera-
ture shifts to lower temperature. From the observations, it is ex-
pected that the influences of p(H2O) on the surface reaction and
the subsequent established reaction are different. The apparent ac-
celeration effect of p(H2O) on the overall kinetics of the estab-
lished reaction is in coincident with that of our previous result.6
The enhancement of the overall decomposition rate with increas-
ing p(H2O) has been observedforthe thermal decompositionpro-
cess of several metal hydroxides.16,55ꢀ57
Selecting two different p(H2O), 0.8 and 10.3 kPa, the overall
kinetics under the respective p(H2O) were evaluated by using a
series of the mass-loss data recorded under linearly increasing
temperature at different β, 1 e β e 5 K minꢀ1. The typical
kinetic rate data under the respective measuring conditions were
shown in Figure S9 in the Supporting Information. The results of
kinetic calculation are illustrated in Figure 14. The Friedman
plots at selected α indicate fairly good linearity irrespective of
α and of p(H2O) applied, as was shown in Figure 14a for the re-
action under p(H2O) = 10.3 kPa. However, the slopes of the
Friedman plot change among different α, where the change is
more extensive for the reaction under higher p(H2O). The var-
iation of Ea with α was shown in Figure 14b. In the initial part of
the reaction, the higher value of Ea, ∼140 kJ molꢀ1, and its rapid
decrease to ∼100 kJ molꢀ1 are observed as the characteristic be-
havior by the effect of atmospheric water vapor. The shift of the
onset temperature of the reaction to the higher temperature with
increasing p(H2O) can be correlated to the change of Ea during
the initial part of the reaction. After the values of Ea were
stabilized at around α = 0.10, the Ea values for the reaction
under p(H2O) = 0.8 kPa remain the nearly constant values
during the later course of the reaction, giving the value of Ea =
103.4 ( 0.5 kJ molꢀ1 averaged over 0.1 e α e 0.9. Under
p(H2O) = 10.3 kPa, the values of Ea change during the later
course of the reaction, indicating a convex shape with the
maximum value of 116.4 ( 1.1 kJ molꢀ1 at α = 0.40. The value
Figure 14. Kinetic analysis for the thermal decomposition of SHC
(100ꢀ170 mesh) under controlled p(H2O). (a) The Friedman plots
at different α from 0.1 to 0.9 in steps of 0.1 for the reaction under
p(H2O) = 10.3 kPa, (b) the values of Ea at various α, and (c) com-
parisons of the experimental master plot with the theoretical curves
of RO(n) and SB(m,n,p) models.
Figure 14c shows the experimental master plots for the re-
actions under p(H2O) = 0.8 and 10.3 kPa. The plots indicate the
bends at α = 0.20 and 0.35 for the reactions under p(H2O) = 0.8
and 10.3 kPa, respectively. The bends indicate the possible change
of the reaction mechanism. In the part before the bend, the surface
reaction is likely contributing largely on the overall rate behavior,
where the region is extending with increasing p(H2O). In addition
to the above RO(n) model, a nucleation and growth type model of
JMA(m) was applied for fitting the experimental master plots
in the part after the bend, because JMA(m) model has been
estimated as one of the most appropriate kinetic model functions
for the present reaction.3,4,6ꢀ11 The fitting curves of RO(n) and
JMA(m) were compared in Figure 14c in the respective ranges of
0.2 e α e 0.9 and 0.35 e α e 0.9 for the reactions under
of Ea averaged over 0.1 e α e 0.9 was 109.7 ( 5.4 kJ molꢀ1
,
indicating the larger standard deviation due to the variation
during the course of reaction.
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different from those observed in flowing N2 and CO2. Before ini-
tiating the reaction, the surfaces of the sample particles are re-
forming as is typically seen for the accommodation of the small
deposited particles into the surface of the main crystal body, see
Figure 15a. This indicates the interaction between the sample
surface and atmospheric water vapor. The needle crystals of surface
product growing in parallel to the direction of the long axis of the re-
actant crystal can be distinguished as the characteristics of the
surface reaction under high p(H2O), Figure 15b,c. The needle cry-
stals are platelet and construct the stacking structure, Figure 15d.
Formation of the similar surface product at the beginning of the re-
action has been reported by Ball et al. as “exfoliated layer”.13 The
preliminary reformation of SHC crystal surface and formation of
SC needle crystals during the surface reaction are likely to result
from dissolution-recrystallization mechanisms. Formation of the
surface product layer as was observed for the reaction in flowing
N2 is retarded with increasing p(H2O), where the formation was con-
firmed at around α = 0.3ꢀ0.4 under p(H2O) = 10.3 kPa. Although
the acceleration mechanism of the established reaction by the
atmospheric water vapor could not be revealed in the present study,
the structural change of the surface product layer can be sugges-
ted as one of the possible causes from the viewpoint of the reaction
morphology. At the same time, the increasing contribution of the
liquid phase during the course of reaction is also to be a possible
cause. The surface texture of the completely reacted sample is com-
parable with those obtained by the reactions in flowing N2 and
CO2, Figure 15e. The constituent product particles in the surface
product layer are smaller apparently than those produced under
comparable heating conditions in flowing N2, compare Figure 10d
and Figure 15f. This may be due to the retarded formation of the
surface product layer. The above observations of surface textures
during the reaction under p(H2O) = 10.3 kPa support the ex-
planations of the characteristics of thermoanalytical curves and the
interpretation of the kinetic results by the extended contribution of
the surface reaction on the overall kinetics.
Figure 15. Typical SEM images of the surface textures of the sample
(100ꢀ170) decomposed under controlled p(H2O) = 10.3 kPa: (aꢀd)
decomposed to α = 0.05 by heating nonisothermally at β = 5.0 K minꢀ1
to 373 K and (e, f) decomposed to α = 1.00 by heating nonisothermally
at β = 5.0 K minꢀ1 to 473 K.
4. CONCLUSIONS
The overall kinetics of the thermal decomposition of SHC was
investigated in view of the physico-geometrical characteristics of
the reaction taking place on a single crystalline particle. The re-
action is really heterogeneous in nature, exhibiting various char-
acteristic behaviors of the solid-state reaction. The precursory
reaction, which has been observed in many reported thermoana-
lytical data, is identified as taking place at the boundary between
the surface of the SHC crystal and the adhesive small particles de-
posited on the surface. From several circumstantial evidence, the
thermal decomposition of SSC is proposed as the possible ori-
gin of the precursory reaction. In flowing dry N2, the thermal
decomposition of SHC crystals initiates on the surface. Erosion
of crystal surface and formation of whiskers are the characteristic
events of the surface reaction, where possible existence of liquid
phase in the process of surface reaction is expected from those
textural observations. The surface reaction is completed in the
early stage of the reaction, α < 0.1, by the formation of surface
product layer. The surface product layer is the sintered aggre-
gates of the SC particles of several hundred nanometers, where
the interstices are to be the possible channels of the diffusion
of evolved gases. The established reaction proceeds by the
advancement of reaction interface inward. The overall kinetics
of the established reaction is described by the two-dimensional
shrinkage of the reaction interface controlled by the chemical
p(H2O) = 0.8 and 10.3 kPa, together with those of SB(m,n,p)
in the range 0.1 e α e 0.9. Under p(H2O) = 0.8 kPa, the
experimental master plot is fitted satisfactorily by RO(2.34) with
A = (1.03 ( 0.02) ꢁ 1010 sꢀ1 (γ2 = 0.9921) and JMA(1.43) with
A = (2.67 ( 0.03) ꢁ 1010 sꢀ1 (γ2 = 0.9811). Similarly, RO(2.08)
with A = (1.52 ( 0.02) ꢁ 1011 sꢀ1 (γ2 = 0.9826) and JMA(1.88)
with A = (2.84 ( 0.03) ꢁ 1011 sꢀ1 (γ2 = 0.9950) were evaluated
as the most appropriate kinetic model functions of the respective
types for fitting the experimental master plot under p(H2O) =
10.3 kPa. Under p(H2O) = 0.8 kPa, the RO(n) model is still in-
dicating the better fitting than that by JMA(m), although the
kinetic exponent n = 2.34 is slightly larger in comparison with that
evaluated for the reaction in flowing N2 and CO2. At the higher
p(H2O) = 10.3 kPa, the fitting by JMA(m) model is more ap-
propriate than that by RO(n). The apparent fitting to JMA(m)
under p(H2O) = 10.3 kPa are likely due to the extended con-
tribution from the surface reaction and the acceleration of the
established reaction enhanced by the atmospheric water vapor.
Typical SEM images of the surface textures of the sample
during the thermal decomposition under p(H2O) = 10.3 kPa
were shown in Figure 15. Under a high p(H2O), the surface
textures of the sample at the initial part of the reaction are quite
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reaction, that is, contracting cylinder model, with the apparent
Ea of ∼100 kJ molꢀ1. Formation of whiskers of SC irradiating
from the interstices of the surface product layer also indicates the
possible existence of the liquid phase during the established
reaction.
(9) Jankovic, B.; Adnadevic, B. Int. J. Chem. Kinet. 2007, 39 (8),
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(10) Ortega, A. Thermochim. Acta 1996, 284 (2), 379–387.
(11) Heda, P. K.; Dollimore, D.; Alexander, K. S.; Chen, D.; Law, E.;
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Atmospheric CO2 and water vapor influence differently on the
overall kinetics of the thermal decomposition of SHC. The atmo-
spheric CO2 decelerates slightly the overall kinetics due to the
increasing contribution of the surface reaction on the overall re-
action and to the retardation of the formation of surface product
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’ ASSOCIATED CONTENT
S
Supporting Information. Powder XRD pattern and
b
FT-IR spectra of the sample. Changes of the powder XRD pattern
during the thermal decomposition. The enthalpy change during
the precursory reaction. Detailed descriptions of the kinetic ana-
lyses for the precursory reaction and the main decomposition
reaction in flowing CO2. The typical mass-loss traces for the
reaction under controlled p(H2O). This material is available free
of charge via the Internet at http://pubs.acs.org.
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’ AUTHOR INFORMATION
Corresponding Author
*Tel\Fax: +81-82-424-7092. E-mail: nkoga@hiroshima-u.ac.jp.
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’ ACKNOWLEDGMENT
The present work was supported partially by the grant-in-aid
for scientific research (B; 21360340 and 22300272) from Japan
Society for the Promotion of Science.
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