2
Constant rate thermal analysis of a dehydrogenation reaction
Antonio Perejón
a,b,
*, Luis A. Pérez-Maqueda
a,
*, Pedro E. Sánchez-Jiménez
a
, José M. Criado
a
,
Nataliya Murafa
c
and Jan Subrt
c
a
Instituto de Ciencia de Materiales de Sevilla (C.S.I.C.-Univ. Sevilla). C. Américo Vespucio 49,
Sevilla 41092. Spain
b
Departamento de Química Inorgánica, Facultad de Química, Universidad de Sevilla, Sevilla
41071, Spain
c
Institute of Inorganic Chemistry AS CR, 250 60 Řež, Czech Republic
Abstract
Constant Rate Thermal Analysis (CRTA) procedure has been employed for the first time to
study the kinetics of MgH
2
dehydrogenation by thermogravimetry under high vacuum. CRTA
implies controlling the temperature in such a way that the decomposition rate is maintained
constant all over the process, employing the mass change as the experimental signal
proportional to the reaction rate. The CRTA curves present a higher resolution power to
discriminate the kinetic model obeyed by the reaction in comparison with conventional heating
rate curves. The Combined Kinetic Analysis has been applied to obtain the kinetic parameters,
which show that MgH
2
decomposition under high vacuum obeys first-order kinetics (F1). It has
been proposed that the dehydrogenation of MgH
2
under high vacuum takes place by
instantaneous nucleation in the border line of the bidimensional crystallites followed by the
growth of the nuclei.
Keywords: hydrogen absorbing materials, metal hydrides, kinetics, thermal analysis
3
1. Introduction
Solid-state hydrides, including metal, intermetallic and complex hydrides present the highest
volumetric capacities of hydrogen storage, and have recently attracted interest for thermal
energy storage applications.
1-6
Among all the solid-state hydrides, Mg-based is the most studied
family, due to the large hydrogen content of MgH
2
(7.6 mass%), the high hydrogenation-
dehydrogenation enthalpy and the ample abundance of magnesium in earth.
7-11
Nevertheless, the
kinetic and thermodynamic properties of Mg-based materials present several issues that have to
be overcome for its use in practical applications. Magnesium needs temperatures above 573 K
to absorb hydrogen, the dehydrogenation temperature of MgH
2
is even higher because of its
high thermodynamic stability, and finally, MgH
2
presents a high reactivity towards air and
oxygen.
3, 7, 12-13
Desorption temperature has been reduced and the hydrogenation-
dehydrogenation reactions have been fasten by mechanical milling and alloying, doping with
catalytic additives and employing cycles of hydrogenation-dehydrogenation.
11, 14-19
However,
the mechanism and kinetic parameters of these reactions, which are of the most interest for
practical applications, have been less thoroughly studied.
Thermogravimetry is one of the most used techniques to study the kinetics of absorption and
desorption of hydrogen from Mg related compounds.
20-23
Authors normally employ
conventional constant heating rate or isothermal experiments to collect the data. However, it has
been demonstrated that constant rate thermal analysis (CRTA) presents a higher resolution
power for the discrimination of the kinetic model followed by solid state reactions, because the
shape of CRTA curves is related to the kinetic model.
24-25
Moreover, it has been shown that
CRTA allows minimizing the influence of both heat and mass transfer phenomena in solid state
processes and, therefore, the experimental curves are representative of the reactions to be
studied. For these reasons, it has been used for the kinetic study of different types of solid-state
processes.
26-28
CRTA implies controlling the temperature in such a way that the decomposition rate is
maintained constant all over the process at a value previously selected by the user, employing an
experimental signal proportional to the reaction rate or reaction fraction as control parameter.
29-
30
The objective of this work is the application of the CRTA methodology for the first time to
study the dehydrogenation kinetics of MgH
2
in conditions far from equilibrium. The combined
kinetic analysis procedure will be used to obtain the kinetic parameters.
4
2. Experimental
Magnesium hydride was purchased from Aldrich, product number 683043. The samples were
studied as received, no activation procedures were carried out to avoid possible modification of
the samples.
A CI Electronic thermobalance with a sensitivity of 2×10
-7
g and a low thermal inertia furnace
were used to perform the experiments. The instrument is connected to a high-vacuum system
composed of a rotary and a turbomolecular pump which can reduce the pressure to ~5 × 10
-5
mbar.
24
The system was outgassed overnight at room temperature to reach a steady-state. The
sample size was ~70 mg. The powders were weighted inside a glove-box and the instrument
opened to place the samples and then immediately closed. Experiments were carried out in
conventional linear heating rate conditions, at 2.5 K min
-1
and in CRTA conditions, at reactions
rates of 10
-3
min
-1
and 3× 10
-3
min
-1
, respectively. The CRTA control system is constituted by a
Eurotherm programmer that received the analog output of the thermocouple and controls the
temperature of the sample placed in the thermobalance, at the heating rate previously selected.
A second programmer was employed for programming the profile of the analog output supplied
by the thermobalance (the sample mass) as a function of the time. Thus, the control of the
reaction rate is achieved by connecting the control relay of the second programmer to the digital
input of the temperature programmer. CRTA control is carried out in such a way that the
temperature increases if the output signal is higher than the programmed setpoing and decreases
if it is lower that the setpoint.
31
The reacted fraction or conversion, α, has been expressed with
respect to the mass change using the equation:
1
where
0
is the initial mass,
f
the final mass and the sample mass at an instant time t. The
reaction rate is obtained differentiating the reacted fraction with respect to the time.
Temperature dependent X-ray diffraction patterns were recorded in vacuum in a Philips X’Pert
Pro diffractometer equipped with a high temperature Anton Par camera working at 45 kV and
40 mA, using CuKα radiation and equipped with an X’Celerator detector and a graphite
diffracted beam monochromator.
The microstructure of the starting MgH
2
sample was analyzed by scanning electron microscopy
(SEM) and high-resolution transmission electron microscopy (HRTEM). SEM micrographs
were taken in a Hitachi S-4800 microscope, while HRTEM measurements were carried out
using a 300 kV JEOL JEM 300 UHR electron microscope with a LaB
6
electron source.
5
3. Theoretical
The kinetic analysis has been carried out from the following general kinetic equation:
2
where dα/dt is the reaction rate, A is the preexponential factor of Arrhenius, E is the activation
energy, T is the absolute temperature and f(α) is a function representing the kinetic model
obeyed by the reaction. If the α-T (or α-t) plot is obtained at a constant decomposition rate (C =
dα/dt), equation (2) can be rearranged, after taking logarithms, in the form:
ln
ln
3
It has been previously shown that CRTA permits to discriminate the kinetic model obeyed by
the reaction from the analysis of a single α-T plot, which is not possible if this plot is obtained
from conventional rising temperature experiments.
32-33
Figure 1 presents α-T curves simulated
using the Runge-Kutta method and different kinetic models. Values of the activation energy of
150 kJ mol
-1
and the pre-exponential factor of 5×10
15
min
-1
were employed for the simulation,
and a constant reaction rate of 2×10
-3
min
-1
. It is clear in the figure that the shape of the CRTA
curves is different for each kinetic model. Thus, for reactions controlled by random nucleation
and nuclei growth (like A2) the α-T profile presents an initial increase in temperature and then it
backs on itself until reaching a value of the reacted fraction at with the rise in temperature is
resumed.
Figure 1. Reacted fraction versus temperature curves simulated for four kinetic models considering
CRTA conditions
(reaction rate of 2×10
-3
min
-1
) and the following kinetic parameters: E = 150 kJ mol
-1
and A =
5×10
15
min
-1
.
6
On the other hand, the α-T profiles for interphase boundary controlled reactions (like F1 and
R3) are concave, and have a sigmoidal shape for reactions controlled by diffusion (like D3).
Thus, the shape of the α-T plots permits to have an idea of the kinetic model obeyed by the
process before performing any numerical analysis.
The plot of the left hand side of equation (3) as a function of 1/T leads to a straight line, whose
slope leads to the activation energy and the intercept to the preexponential factor of the
Arrhenius expression of the process, only in the case that the proper f(α) function were selected,
except if the kinetic model were represented by the function f(α) = (1- α)
n
(i.e. R2, R3 and F1
models, frequently referred as “n order” reactions). In such a case, equation (3) becomes:
ln
1
1
1
ln
4
and E and n cannot be simultaneously determined from a single experiment unless one of these
two parameters were known from other source.
32
The combined kinetic analysis methodology allows determining the kinetic parameters without
any assumptions regarding the kinetic model, which overcomes the problem of selecting a
model from a list.
34-35
The combined kinetic analysis determine the kinetic model by comparison
of the shape of the resulting f(α) function with those of the ideal models, and therefore can be
applied for studying real systems that could not be directly fitted with ideal models due, for
example, to broad particle size distribution or heterogeneities in the samples. This method is
based on taking logarithms to the general kinetic equation (2). Rearranging terms in equation (2)
and considering f(α) as the Sestak-Berggren equation (
1
), the following
expression is obtained:
/
1
ln
5
This is a differential expression that does not require any integration of the kinetic equation that
could provide some errors in the resulting kinetic parameters.
36-38
The entire set of experimental
data (T, α and dα/dt) corresponding to different temperature schedules are substituted into
equation 5 and the left-hand side of the equation versus the inverse of temperature is plotted.
The values of the parameters n and m that provide the best linearity to the straight line obtained
are determined by and optimization procedure. Then, the values of E and cA can be calculated
from the slope and the intercept, respectively.
The main advantage of using the Sestak-Berggren equation is that is able to fit all the ideal
kinetic models proposed in the literature including its deviations. Thus, the use of this equation
