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