Use of solid insertion probe mass spectrometry and constant rate thermal analysis in the study of materials: Determination of apparent activation energies and mechanisms of solid-state decomposition reactions

Article abstract of DOI:10.1021/jp991042g

Thermally induced reactions are of great importance in the manufacture and characterization of a very wide range of increasingly complex materials covering areas as diverse as ceramics and heterogeneous catalysts. Subsequently, there is a need for improved thermoanalytical methods that can provide enhanced resolution and a greater understanding of the energetics and mechanisms involved. This paper describes a new solid insertion probe mass spectrometer (SIP-MS) system that is designed to meet these needs by operating high vacuum with small sample masses. The SIP-MS system supports both conventional linear heating and a range of sample-controlled thermal analysis (SCTA) techniques including constant rate thermal analysis (CRTA). Its ability, in conjunction with the latter technique, to obtain reliable apparent activation energy measurements throughout a process under near-ideal experimental conditions is demonstrated. In addition, the system can discriminate between different reaction mechanisms and provide information on the often complex solid-state reactions found in calcination processes.

Full text of DOI:10.1021/jp991042g

6944
J. Phys. Chem. B 1999, 103, 6944-6949
Use of Solid Insertion Probe Mass Spectrometry and Constant Rate Thermal Analysis in
the Study of Materials: Determination of Apparent Activation Energies and Mechanisms of
Solid-State Decomposition Reactions
†
M. J. Tiernan, P. A. Barnes,* and G. M. B. Parkes
Centre for Applied Catalysis, Materials Research DiVision, UniVersity of Huddersfield,
Queensgate, Huddersfield HD1 3DH, U.K.
ReceiVed: March 26, 1999; In Final Form: June 17, 1999
Thermally induced reactions are of great importance in the manufacture and characterization of a very wide
range of increasingly complex materials covering areas as diverse as ceramics and heterogeneous catalysts.
Subsequently, there is a need for improved thermoanalytical methods that can provide enhanced resolution
and a greater understanding of the energetics and mechanisms involved. This paper describes a new solid
insertion probe mass spectrometer (SIP-MS) system that is designed to meet these needs by operating high
vacuum with small sample masses. The SIP-MS system supports both conventional linear heating and a
range of sample-controlled thermal analysis (SCTA) techniques including constant rate thermal analysis
(CRTA). Its ability, in conjunction with the latter technique, to obtain reliable apparent activation energy
measurements throughout a process under near-ideal experimental conditions is demonstrated. In addition,
the system can discriminate between different reaction mechanisms and provide information on the often
complex solid-state reactions found in calcination processes.
3
Introduction
of the reported values by Reading et al. indicated that a
relatively reproducible value was obtained when only those
Increasingly, materials manufactured by calcination have
complex formulations and it is important to be able to
understand, and quantify, the effects of the different components
on the thermal decomposition reactions involved. To achieve
these aims, high-resolution techniques are required to provide
meaningful fundamental data.
Kinetic parameters for solid-state decomposition reactions
have been widely investigated using methods based on the
general kinetic equation:
studies that employed appropriate experimental conditions and
calculation methods were considered. This led the authors to
suggest that the activation energy of the thermal decomposition
-
1
of CaCO3 is in the range 210 ( 10 kJ mol and that this value
is meaningful in terms of the conventional energy barrier model
of chemical reaction kinetics. Deviations from this value were
attributed to the existence of mass or thermal transport influences
under inappropriate experimental conditions with the measured
value being particularly sensitive to the concentration of product
2
,3,5
dR
dt
-E/(RT)
gas (CO2) in the vicinity of the reacting sample.
It has been
)
Af(R) e
(1)
suggested that it is possible to measure the true activation energy
for a solid-state decomposition provided care is taken to
where A is the preexponential factor, T is the absolute
temperature, t is the time, R is the fraction of sample
decomposed, E is the activation energy, R is the gas constant,
and f(R) is a function dependent on the reaction mechanism.
It is well-known that a number of factors are important in
solid-state reactions in addition to the usual energy factors that
relate to the chemistry involved. These include geometric
considerations as well as nucleation, autocatalytic, and diffusion
effects, all of which can produce significant deviations in the
3
minimize such experimental influences or by employing a
2
pressure correction term in the kinetic equation.
One difficulty with conventional isothermal kinetics is that
many experiments are required and, before the activation energy
can be calculated, the reaction mechanism must be known or
assumed. Nonisothermal techniques (i.e., linear heating thermal
analysis) for the investigation of kinetic parameters have become
popular because these take less time than a series of isothermal
5
1
experiments at different temperatures. A relatively new devel-
measured values of A and E for a given reaction. In such
opment, constant rate thermal analysis (CRTA), when used in
combination with the “rate-jump” method, has been recom-
mended to provide measurements of the thermally activated step
of a decomposition. This yields results that are much less
dependent on experimental parameters than those obtained with
circumstances, it is not appropriate to interpret E in terms of
the usual energy barrier model of homogeneous chemical
reaction kinetics and, for this reason, we prefer the term
apparent activation energy.
One of the most widely investigated solid-state reactions is
3
,6,7
2
conventional techniques,
since the effects of heat and mass
the decomposition of calcium carbonate (CaCO3). Reviews of
8
the literature3
-5
transfer are minimized. Our use of solid insertion probe mass
spectrometer (SIP-MS) improves the experimental conditions
by further reducing the temperature and concentration gradients
within the sample, due to the low sample mass and high vacuum
conditions employed.
for this reaction have revealed significant
variations in the measured values of E ranging from 142 kJ
-1
-1
mol to as high as 3828 kJ mol . However, a critical analysis
†
School of Chemical Sciences, Dublin City University, Ireland.
1
0.1021/jp991042g CCC: $18.00 © 1999 American Chemical Society
Published on Web 08/03/1999

Solid-State Decomposition
J. Phys. Chem. B, Vol. 103, No. 33, 1999 6945
TABLE 1: Algebraic Expressions (f(r)) for Common Reaction Mechanisms Operating in Solid-State Reactions
mechanism
symbol
f(R)
one-dimensional diffusion
two-dimensional diffusion
three-dimensional diffusion (Jander equation)
three-dimensional diffusion (Ginstein-Brounshtein equation)
random nucleation; unimolecular decay law (first order)
phase-boundary-controlled reaction (contracting cylinder)
phase-boundary-controlled reaction (contracting sphere)
two-dimensional growth of nuclei (Avrami-Erofeyev equation)
three-dimensional growth of nuclei (Avrami-Erofeyev equation)
D1
D2
D3
D4
F1
R2
R3
A2
A3
(1/2)R
1/[-ln(1 - R)]
3(1 - R)2 /{2[1 - (1 - R)1/3]}
/3
-
1/3
(3/2)[(1 - R)
(1 - R)
- 1]
1/2
(1 - R)
(1 - R)2
/3
1
/2
2(1 - R)[-ln(1 - R)]
3(1 - R)[-ln(1 - R)]2
/3
Theory
experiments are carried out using different linear heating rates
and E is then calculated from the slope of a plot of log â vs 1/T
for a given value of R. E is calculated for a range of values of
R, thereby allowing any variations with the fraction of sample
reacted to be determined. This method combines the advantages
of allowing the calculation of E at various stages throughout
the reaction without requiring prior knowledge of the kinetic
Kinetic interpretation of thermal analysis data for solid-state
decomposition reactions is normally carried out using methods
based on eq 1. The aim is to determine the kinetic model that
gives the best description of the reaction being studied and
allows the calculation of meaningful values for the parameters
E and A.
5
,7
model.
9
The most frequently cited kinetic models, listed in Table 1,
With both the Kissinger and Ozawa methods, it is important
to ensure that the plots obtained are linear across the entire range
of heating rates employed. Furthermore, experimental conditions
should minimize temperature and pressure gradients during the
can be categorized as diffusion-controlled processes (D1, D2,
D3, D4), boundary-controlled or n-order reactions (F1, R2, R3),
or processes involving random nucleation and subsequent
growth of nuclei (A2, A3).1 It has been shown that the shape
of CRTA curves can be used to distinguish between each of
these three categories, but differences between similar models
within each group are small and difficult to select unambigu-
0,11
5
,7
reaction. These criteria require the use of low sample masses
and pressure gradients for which our SIP-MS system is ideal,
especially when using CRTA.
CRTA “Rate-Jump” Method. CRTA is a one of a family
of related techniques, given the generic name sample-controlled
thermal analysis (SCTA), where the heating rate is not
predetermined but rather governed by some function of the
measured reaction rate of the process being studied. In CRTA
the reaction is forced to proceed at a constant (and low) reaction
1
1,12
ously.
Other methods to determine f(R) include those based
on a prior determination of E, which can then be used to
determine the kinetic model and calculate the remaining kinetic
parameters.10
In the present study, activation energies for the decomposition
of sodium hydrogen carbonate (NaHCO3) were measured using
both conventional linear heating and CRTA rate-jump tech-
niques. This was done in order to contrast the different
experimental conditions used by each technique and to confirm
the validity of the latter. A further set of activation energies
were also obtained for the thermal decomposition of CaCO3.
The additional ability of CRTA to provide an insight into
the kinetic model (i.e., f(R)) for each decomposition is demon-
strated, and all results are discussed in relation to values, found
using a variety of techniques, reported in the literature.
Linear Heating Rate Methods. Two similar methods that
have been recommended10 for the determination of E from linear
heating rate experiments are those developed by Ozawa and
Kissinger.14 Data analysis for linear heating rate experiments
in the current study was based on these methods.
Kissinger Method. This uses the following equation derived
from the condition for the maximum rate on a thermoanalytical
curve:
8
rate by appropriate control of either the temperature or, for
certain systems, the concentration of a reactant gas.15 Thus,
rather than setting the heating rate at a predetermined value,
1
6
the reaction rate is predetermined. Adopting this approach
enables temperature and pressure gradients to be greatly reduced
throughout the sample, minimizing the effects of heat and mass
3
,8,17
transfer.
CRTA can be modified to give the “rate-jump” method for
determining kinetic parameters. Here, the rate of reaction is
made to alternate between two preselected values, while the
changes in sample temperature required to achieve this are
8
,18
monitored.
Provided the reaction rate is allowed to reach
1
3
equilibrium at the two successive rates, the corresponding
temperature measurements can be used to calculate a value of
E for the reaction using the following form of the Arrhenius
equation:
T1T2
C2
E ) R
ln
(4)
â
R
E
E
RTm
(
T2 - T1
) ( )
C
1
ln
) ln -f(R) A
-
(2)
2
(
)
(
)
Tm
where T1 and T2 are the temperature measurements correspond-
ing to the two preset reaction rates C1 and C2 at the same value
-
1
where â is the heating rate (K min ) and Tm is the temperature
7
,10
(K) of maximum reaction rate. E can be calculated from the
of R (extent of reaction).
2
slope of a plot of ln(â/Tm ) vs 1/Tm for various heating rates.
Although the first term on the right-hand side of eq 2 is only
constant for first-order processes, it has been claimed that the
error in the activation energy determined by this method for
other kinetic models does not exceed 5%.10
The “rate-jump” method has the great advantage that the
calculation of the apparent activation energy is independent of
any assumptions regarding the mechanism of the process.
However, as it assumes that any changes in f(R) during each
temperature jump are negligible, the time taken to execute each
jump must be as small as possible in comparison to the total
Ozawa Method. This is based on the following equation:
3
duration of the experiment.
E
RT
A typical rate-jump measurement is illustrated in Figure 1.
The temperature required to maintain a constant reaction rate
is found to vary with the extent of reaction, depending on the
log â ) -0.4567
+ C
(3)
(
)
where C is a constant. As for the Kissinger method, a series of

6946 J. Phys. Chem. B, Vol. 103, No. 33, 1999
Tiernan et al.
TABLE 2: Experimental Conditions Employed for CRTA
“Rate-Jump” Experiments
C
1
C
2
sample mass (mol CO
2
(mol CO
2
no. of
rate jumps
-
1
-1
run sample
NaHCO
CaCO
(mg)
min
)
min
)
-
-
7
-7
-7
A
B
3
10.0 ( 0.2 1.2 × 10
5.0 ( 0.2 1.3 × 10
1.5 × 10
1.6 × 10
50
24
7
3
fields is preferable to changing the accelerating potential, since
it avoids the mass discrimination effect inherent in the latter
technique. This simplifies the acquisition of accurate data, which
is invaluable when carrying out background subtraction. The
use of a laminated magnet gives a maximum scanning speed
of 100 ms/decade, providing the rapid response required for
accurate control of the reaction rates.
Figure 1. Temperature and gas-phase concentration profiles for a
typical “rate-jump” experiment showing the construct used to obtain
T , T , C , and C for the calculation of the activation energy E.
1 2 1 2
The system utilizes software, developed by the authors and
running under Windows 95 (Microsoft), for data acquisition and
control, which provides a range of experimental techniques
including conventional linear heating and a wide variety of
16
SCTA methods such as CRTA. Voltages corresponding to the
relative concentration of the species being measured are acquired
from the MID unit via a 16-bit analog-to-digital converter (ADC,
Strawberry Tree Dyna-Res). These values, together with the
sample temperature, are processed and stored by a PC (P-II,
Figure 2. Schematic cross section of the solid insertion probe: A,
water-cooling coil; B, thermocoax heating element; C, Nichrome plug;
D, ceramic tip; E, thermocouple; F, sample cavity.
mechanism of the reaction. In some cases an initial gradual fall
is replaced by a slow increase at higher R values. For other
reactions, e.g., the thermal decomposition of NaHCO3, there is
a different relationship with a continual rise in the temperature
required to achieve a constant reaction rate. As a result of this
variation of T with R, it is necessary, in many cases when
performing rate-jump experiments, to estimate the temperature
corresponding to a given rate of reaction by extrapolating back
to the same value of R at which C1 was measured, as indicated
in Figure 1. In practice the extrapolation is performed using
best-fit curves drawn through the higher and lower levels of
successive “jumps” for both temperature and concentration.
Furthermore, when a number of such rate-jump measurements
are made, any variation in E throughout the reaction can be
2
33 MHz, Viglen) and the required heating rate (for CRTA
experiments) calculated, using a three-term PID algorithm to
ensure good control of the reaction rate, as a series of
temperature set points. These set point values are then sent to
the furnace programmer (Eurotherm 818P), connected to the
computer via an RS232C serial interface, which controls the
power applied to the SIP Thermocoax windings.
In the current application, two ions, m/z ) 18 (water) and
m/z ) 44 (carbon dioxide), were monitored alternatively for
5
1
00 ms each with the furnace temperature being modified every
000 ms.
The combination of small sample mass, which reduces
-
5
temperature gradients, and high vacuum (10 Pa), which
minimizes diffusion problems and the possibility of back
reaction between the solid product and the evolved gases, makes
the SIP-MS ideal for kinetic studies of calcination and decom-
position processes. These benefits are further increased when
used with SCTA, and CRTA in particular, which allow
measurements to be made in controlled pseudo-equilibrium
conditions, thereby improving the quality and fundamental
significance of the data obtained.
8
,12
quantified.
Experimental Section
Equipment. Samples were analyzed using the SIP-MS
system,1
9,20
which has been modified to provide improved
temperature measurement, and to incorporate computerized data
21
acquisition, and to control software capable of performing both
linear heating and a range of SCTA techniques, including CRTA
and rate-jump experiments.
Materials. NaHCO3 (BDH, AnalaR grade reagent) and
CaCO3 (Fisons, 99.9%) were used as supplied.
The SIP, shown schematically in Figure 2, comprises a
cylindrical microfurnace (12 mm × 5 mm) positioned at the
end of a water-cooled stainless steel rod that can be located,
via airlock valves, directly into the source chamber of a VG
Micromass 7070HS mass spectrometer. Temperature measure-
ment is via a thermocouple (type K, chrome-alumel) located
at the base of the sample holder to place it in virtually direct
contact with the sample itself. The SIP can be heated electrically
to a temperature of 1300 K via a Thermocoax winding. Samples
in the mass range 10 µg to 10 mg can be analyzed depending
on the density of the material under study.
Experimental Conditions. Linear heating experiments on
NaHCO3 were performed using 4 ( 0.2 mg of sample at a series
-
1
of heating rates of between 2 and 7 K min .
The experimental conditions used for CRTA “rate-jump”
experiments are shown in Table 2. Maximum and minimum
-1
heating and cooling rates of +10 and -10 K min , respectively,
were used with the rate being continuously varied under software
control between these limits in order to alternate between the
preselected CO2 evolution rates C1 and C2.
The mass spectrometer is a very sensitive and stable double-
focusing magnetic sector instrument with a resolving power of
Results and Discussion
Decomposition of Sodium Hydrogen Carbonate. The
decomposition reaction of NaHCO3 in the range 373-453 K is
represented by the equation
25 000. For the current work, the instrument was operated in
“
peak select” mode in conjunction with an MID (multiple ion
2
2
detector) unit using field switching, which allows direct
measurement of up to 64 selected m/z values to give evolved
gas profiles for each species selected. Switching the magnetic
2
NaHCO f Na CO + CO + H O
(5)
3
2
3
2
2

Solid-State Decomposition
J. Phys. Chem. B, Vol. 103, No. 33, 1999 6947
TABLE 3: Activation Energies for the Decomposition of
3
NaHCO Calculated from the Data Shown in from Figure 5
by the Ozawa Method
E
linear regression
coefficient
(kJ mol-1)
a
R
0
0
0
0
0
0
.1
.2
.3
.4
.5
.6
86
80
84
91
92
89
92
92
92
89
4.4
0.9999
0.9983
0.9889
0.9882
0.9852
0.9888
0.9909
0.9899
0.9936
0.9915
Figure 3. Decomposition of NaHCO
3
at a linear heating rate of 5 K
evolution profile (B). Note
that the MS signal is directly proportional to the rate of reaction.
0.7
0.8
0.9
average
SD
-
1
min : H
2
O evolution profile (A) and CO
2
a
For isoconversional lines in Figure 5.
decomposition, which confirms that the activation energy
calculated is independent of both R (at least for R > 0.3) and
â in the heating range investigated in the current study. Table
3
shows E values calculated from each of these straight lines
-
1
using eq 3. The average value is 89 kJ mol with a standard
-
1
5
deviation (SD) of 4.4 kJ mol . Ortega et al. reported that the
activation energy for NaHCO3 decomposition determined using
the Ozawa method was independent of both R and â (for linear
-
1
Figure 4. Decomposition of NaHCO
min , showing the degree of coincidence of the H
3
at a linear heating rate of 5 K
heating rates between 2 and 10 K min ). For R values of 0.3
and below, slightly lower values of E were determined.
However, this phenomenon was not apparent in CRTA “rate-
jump” results discussed below and may be associated with an
overlap of the initial and main decomposition processes in linear
heating experiments (see Figure 3). With the CRTA “rate-jump”
method, the two processes are more completely resolved and
the measurements are strictly associated with the main decom-
position process.
-
1
2 2
O (A) and CO (B)
profiles after normalization.
A typical decomposition profile obtained under linear heating
rate conditions is shown in Figure 3. [Note that the magnitude
of the peaks is directly proportional to the rate of the reaction.]
After a small initial peak, possibly associated with decomposi-
tion of surface groups, the evolution of CO2 and H2O occurs
2
3
simultaneously throughout the main decomposition process.
Figure 6 shows a “rate-jump” experiment (run A in Table 2)
on NaHCO3. The product gases, H2O and CO2, are again seen
to be evolved simultaneously and in phase throughout the main
decomposition step in confirmation of the linear heating results.
The temperature trace in Figure 6 shows how the sample heating
rate was varied by the computer program in order to alternate
between the two preselected target CO2 evolution rates through-
out the main decomposition process. E was calculated for each
individual jump (Table 4). It appears that, in agreement with
This can be seen more clearly if the two profiles are brought
exactly into coincidence by normalization (on a scale 0 and 1)
to allow for the difference in response of the mass spectrometer
to the two evolved species (Figure 4). The difference in the
signals for the small initial peak is attributed to the loss of
physically adsorbed water. Thereafter the two gases are evolved
simultaneously and exactly in phase, showing that differences
in phase found with other materials are not due to experimental
problems.
5
previous results, E is independent of R in that, while there is
For the range of linear heating rates investigated, a Kissinger
plot of ln(â/Tm ) vs 1/Tm was found to be a straight line with a
linear regression coefficient (r ) of 0.9984. Using eq 2, E was
some scatter, there is no obvious trend. It is interesting to note
that, under the conditions employed, the CRTA rate-jump
experiments gave a lower standard deviation (2.5 vs 4.4) than
the Ozawa model.
2
2
-
1
calculated to be 104 kJ mol from the slope of this line.
The isoconversional Ozawa plots, obtained by plotting log â
vs 1/T at the same degree of conversion (R) for various values
of R, are shown in Figure 5. In general, the plots are parallel
straight lines yielding similar values for E throughout the entire
One of the most important criteria in determining the
significance and validity of measured E values for solid-state
decomposition reactions is the establishment of an independence
from experimental conditions such as atmosphere, sample mass,
Figure 5. Isoconversional Ozawa plots for the thermal decomposition of NaHCO
represent plots calculated for R values of 0.1-0.9 at intervals of 0.1.
3
at heating rates, â, of 2, 4, 5, and 7 K min-1. Curves 1-9

6948 J. Phys. Chem. B, Vol. 103, No. 33, 1999
Tiernan et al.
Figure 6. Decomposition of NaHCO
conditions (run A) with control on CO evolution: H
A); CO evolution profile (B).
3
under CRTA “rate-jump”
Figure 7. R vs temperature plot for the decomposition of NaHCO
under CRTA “rate-jump” conditions (run A).
3
2
2
O evolution profile
(
2
and decreasing the rate at which product gas is removed from
the sample with the result that sample reaction rate, and hence
temperature, must increase to maintain the same residual partial
pressure. In the present study, although the product gas pressure
is not controlled in this way, the magnitude of the change in
sample reaction rate is kept very small and, in combination with
the high-vacuum conditions prevailing, minimizes any back
reaction and diffusion-related problems.
TABLE 4: Activation Energies for the Decomposition of
NaHCO
3
Calculated from CRTA “Rate-Jump” Experiments
E (kJ mol-1)
a
R
run A
0
0
0
0
0
0
0
0
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
104
101
102
103
104
98
98
101
98
The decomposition of NaHCO3 has been reported to follow
a first-order kinetic model, labeled F1 in Table 1, under linear
5
,22,24
heating rate conditions in an inert atmosphere.
Figure 7
shows a plot of R vs temperature for the decomposition of
NaHCO3 under CRTA “rate-jump” conditions. The shape of
this plot indeed confirms that the decomposition mechanism
follows an “n-order” type of kinetic model (models F1, R2, and
R3 in Table 1), although distinguishing between these three
average
SD
101
2.5
a
For experimental details see Table 2.
3
11
heating rate, and experimental method. Table 5 compares our
results using the Ozawa, Kissinger, and CRTA rate-jump
methods (all using the SIP-MS) with other values found in the
literature. It can be seen that the various techniques give results
falling into two main groups. The methods of Ozawa and
models would require further work.
Decomposition of Calcium Carbonate. The decomposition
of CaCO3 (eq 6) has been widely investigated in thermal analysis
1,3,6,24
studies:
-
1
Friedman gave an average value of E of 90.3 kJ mol , which
is ca. 10% lower than that obtained from the Kissinger, Romero,
and CRTA rate-jump methods (average value of 100.0 kJ
CaCO f CaO + CO
(6)
3
2
-
1
The kinetics of this reaction have also been found to be highly
mol ). In view of the inherent advantages of both the SIP-MS
and CRTA, we contend that the latter values more closely
represent the chemical activation stage of the process.
Higher values of E have been reported when the atmosphere
used has contained CO2 (a product of the reaction), which makes
it more difficult for the reaction to proceed in the forward
direction.22 This emphasizes the importance of controlling
product gas concentrations in the vicinity of the sample in order
to make meaningful kinetic measurements.3
3
,4
sensitive to heat- and mass-transfer effects, and measured
values of E are found to be particularly sensitive to the
concentration of the product gas, CO2. Consequently, values of
3
,25-27
E reported in the literature
range from under 200 to over
-
1
9
50 kJ mol .
Table 6 shows the E values obtained in a “rate-jump”
experiment (run B in Table 2) in the current study. The
corresponding decomposition profile is shown in Figure 8. A
low rate of reaction was purposefully chosen, and again, the
change in reaction rate at each jump was minimized to limit
the effects of CO2 concentration. The average value of E from
measurements made for each of the “rate jumps” in Figure 8
,4
To the best of our knowledge, this is the first study that reports
both the use of an SIP-MS system for the study of calcination
processes and the application of the CRTA “rate-jump” method
to the kinetics of NaHCO3 decomposition.
7,11
-1
-1
In other studies, the switching of the reaction rate in “rate-
jump” techniques has been achieved by alternatively increasing
was 220.3 kJ mol (SD ) 5.9 kJ mol ). Dollimore and co-
workers measured values of E for this reaction of between 200
TABLE 5: Comparison of Activation Energies for the Decomposition of NaHCO
3
Found in This Work and in the Literature
E
sample mass
(mg)
heating rate
source
(kJ mol-1)
atmosphere
(K min
-1
)
method
Ozawa
Friedman
Ozawa
Romero
Ozawa
Kissinger
“rate-jump”
“rate-jump”
5
Oretega et al.
94
87
a
N
N
N
N
2
2
2
2
1.0-10.0
2.0-16.0
2.0-16.0
0.6-11.0
2-10
2
2
Heda et al.
15-25
15-25
10
4
4
8
4
91
Romereo et al.24
this work
this work
this work
this work
99
89
104
101
96
vacuum
vacuum
vacuum
vacuum
2-10
b
(10
(10b
a
Not reported. b Maximum and minimum heating rate limits.

Solid-State Decomposition
J. Phys. Chem. B, Vol. 103, No. 33, 1999 6949
TABLE 6: Activation Energies for the Decomposition of
Conclusions
CaCO
3
Calculated from CRTA “Rate-Jump” Experiment
Run B
We describe a SIP-MS system using low-mass samples that
are heated under high vacuum to provide near-ideal experimental
conditions for the measurement of apparent activation energies
and the study of mechanisms of solid-state decompositions that
produce a gas, or gases. These benefits are enhanced when
combined with SCTA techniques such as CRTA, which further
reduce errors caused by variations in the sample temperature
and the gas-phase concentration. However, many other factors
that are sample-dependent may influence the apparent activation
energy of thermal processes, for example, the grain size,
crystallinity, purity, and thermal history of the material.
The SIP-MS system was used with both linear heating and
CRTA techniques to study the decomposition of sodium
hydrogen carbonate and calcium carbonate. Apparent activation
E
kJ mol 1)
-
(
a
R
run B
0
0
0
0
0
0
0
0
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
220
227
229
228
219
218
213
217
212
220
average
SD
6.3
-1
-1
-1
a
energies of 101 kJ mol , SD ) 2.5 kJ mol , and 220 kJ mol ,
For experimental details see Table 2.
-
1
SD ) 6.3 kJ mol , respectively, were obtained from CRTA
rate-jump” experiments. The mechanisms of both reactions
“
were found to be described by an nth-order expression where
nucleation or diffusion are not the rate-controlling factors.
Acknowledgment. This work is funded by an Engineering
and Physical Sciences Research Council (EPSRC) Grant No.
GR/L66069.
References and Notes
(
1) Maciejewski, M. J. Therm. Anal. 1992, 38, 51.
(2) Criado, J. M.; Gonzalez, M.; Malek, J.; Ortega, A. Thermochim.
Figure 8. Decomposition of CaCO
3
under CRTA “rate-jump” condi-
Acta 1995, 254, 121.
3) Reading, M.; Dollimore, D.; Rouquerol, J.; Rouquerol, F. J. Therm.
Anal. 1984, 29, 775.
4) Reading, M.; Dollimore, D.; Whitehead, R. J. Therm. Anal. 1991,
7, 2165.
tions with control on CO evolution (run B).
2
(
(
3
(
(
5) Ortega, A. Thermochim. Acta 1996, 284, 379.
6) Dollimore, D.; Gamlen, G. A.; Rouquerol, J.; Rouquerol, F.;
Reading, M.; In Proceedings of the 2nd European Symposium on Thermal
Analysis; Heyden: London, 1981; p 99.
(
7) Ortega, A.; Akhouayri, S.; Rouquerol, F.; Rouquerol, J.
Thermochim. Acta 1994, 235, 197.
(
8) Rouquerol, J. Thermochim. Acta 1989, 144, 209.
(9) Sharp, J. H.; Brindley, G. W.; Narahari Acker, B. M. J. Am. Chem.
Soc. 1966, 49, 379.
10) Malek, J.; Sestak, J.; Rouquerol, F.; Rouquerol, J.; Criado, J. M.;
(
Ortega, A. J. Therm. Anal. 1992, 38, 71.
(11) Criado, J. M.; Ortega, A.; Gotor, F. Thermochim. Acta 1990, 157,
171.
Figure 9. R vs temperature plot for the decomposition of CaCO
3
under
CRTA “rate-jump” conditions (run B).
(
12) Laureiro, Y.; Jerez, A.; Rouquerol, F.; Rouquerol, J. Thermochim.
Acta 1996, 278, 165.
13) Ozawa, T. Bull Chem Soc. Jpn. 1965, 1881.
and 230 kJ mol-1 using various CRTA, linear heating, and
(
6
isothermal techniques, while Romero et al. reported a value of
(14) Kissinger, H. E. Anal. Chem. 1957, 29, 1702.
(15) Parkes, G. M. B.; Barnes, P. A.; Charsley, E. L. Thermochim.
Acta 1998, 320 (1-2), 297.
-
1
E of 209 kJ mol under linear heating conditions in a flowing
2
4
N2 atmosphere. Rouquerol et al. also reported a mean value
(16) Barnes, P. A.; Parkes, G. M. B.; Brown, D. R.; Charsley, E. L.
-
1
of 209 kJ mol
from a CRTA “rate-jump” experiment
Thermochim. Acta 1995, 269/270, 665.
performed under vacuum.18 Such values, along with that
determined in the current study, support the contention of
Reading et al. that the true activation energy for this decom-
position is about 210 kJ mol , SD ) 10 kJ mol , with good
agreement with values measured under near-equilibrium ex-
perimental conditions.
(17) Tiernan, M. J.; Barnes, P. A.; Parkes, G. M. B. J. Phys. Chem. B
999, 103, 338.
1
3
(18) Rouquerol, F.; Rouquerol, J. Thermal Analysis (Proceedings of the
rd ICTA, Davos); Widemann, H. G., Ed.; Birkhauer: Basel, 1972; p 373.
3
-
1
-1
(19) Barnes, P. A.; Parkes, G. M. B. J. Therm. Anal. 1993, 39, 607.
(20) Barnes, P. A.; Parkes, G. M. B.; Sheridan, P. J. Therm. Anal. 1994,
2, 841.
4
(
21) Parkes, G. M. B.; Barnes, P. A. In preparation.
Figure 9 shows the plot of R vs temperature obtained for the
decomposition of CaCO3 under CRTA “rate-jump” conditions.
The shape of this plot indicates that the decomposition mech-
anism follows an “n-order” type of kinetic model (models F1,
R2, and R3 in Table 1), although as mentioned above,
(22) Heda, P. K.; Dollimore, D.; Alexander, K. S.; Chen, D.; Law, E.;
Bicknell, P. Thermochim. Acta 1995, 255, 255.
(23) Paulik, J., Paulik, F., Eds. In Simultaneous Thermoanalytical
Examination by Means of the DeriVatograph; Wilson and Wilson’s
Comprehensive Analytical Chemstry XII; Elsevier: Amsterdam, 1981; p
1
12.
(24) Romero, A.; Garcia Calvo, E.; Leton, P.; Arranz, M. A.
Thermochim. Acta 1991, 182, 235.
distinguishing between these three models would require further
work. Previous studies2,24 have also reported that the reaction
(
(
25) Brown, M. E.; Galway, K. A. Thermochim. Acta 1979, 17, 507.
26) Salvador, A. R.; Calvo, E. G.; Aparicio, C. B. Thermochim. Acta
mechanism is described by an order type model, although the
apparent order obtained depended greatly on the experimental
1
989, 143, 339.
(27) Rao, T. R. Chem. Eng. Technol. 1996, 19 (4), 373.
4
conditions.