Thermochimica Acta 582 (2014) 25–34
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Thermochimica Acta
journal homepage: www.elsevier.com/locate/tca
Development of a reaction mechanism for liquid-phase
decomposition of guanidinium 5-amino tetrazolate
N. Kumbhakarna, S.T. Thynell ∗
Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802, United States
a r t i c l e
i n f o
Article history:
Received 19 December 2013
Received in revised form 12 February 2014
Accepted 17 February 2014
Available online 25 February 2014
Keywords:
Guanidinium 5-amino tetrazolate
Reaction mechanism
Liquid phase
Continuum-based model
Sensitivity analysis
a b s t r a c t
The objective of this work is to formulate a detailed reaction mechanism of the decomposition of guanidinium 5-amino tetrazolate (GA) in the liquid phase using a combined experimental and computational
approach. The experimental information comes from data published in the literature. The computational
approach is based on using quantum mechanics for identifying species and determining the kinetic rates,
resulting in 55 species and 85 elementary reactions. In these ab initio techniques, various levels of theory
and basis sets were used. A continuum-based model for predicting species formation and mass loss of
a TGA experiment was also developed and solved numerically, accounting for reversible chemical reactions and mass transfer in simulations of the GA decomposition process. The model accounts for reactions
within the liquid phase and evaporation of several of the observed experimentally measured products.
Simulation results for species concentrations and heat release were obtained, and these results were
found to satisfactorily match the temporal experimental results previously published in literature for
the decomposition of GA. Important reaction pathways in the proposed reaction scheme were identified
based on a sensitivity analysis.
© 2014 Elsevier B.V. All rights reserved.
1. Introduction
Recently, research on nitrogen-rich energetic materials has
received significant attention for a variety of reasons. First, their
high positive heats of formation may release a large amount of heat
on combustion as dinitrogen (N2 ) is one of the major products [1].
Second, the formed molecular nitrogen may achieve a high specific
impulse without undesirable smoke or soot. Third, the molecular
nitrogen is an environmentally friendly final product. Tetrazoles,
with their heterocyclic ring structure, fall within this class of highnitrogen compounds [2]. Within tetrazole family of compounds,
the triaminoguanidinium azotetrazolate (TAGzT) [3] and guanidinium azotetrazolate (GzT) [4], are of interest due to their potential
applications as gas generators and burn rate modifiers for propellants. Similarly, the guanidinium 5-aminotetrazolate (GA), shown
in Fig. 1, is also of interest and possesses a much simpler molecular
structure.
The molecular and electronic structures of GA were reported by
Paoloni et al. [5]. Tao et al. characterized GA and several compounds
containing the amino-tetrazolate (ATz− ) anion based on infrared
∗ Corresponding author. Tel.: +1 814 863 0977.
E-mail address: [email protected] (S.T. Thynell).
http://dx.doi.org/10.1016/j.tca.2014.02.014
0040-6031/© 2014 Elsevier B.V. All rights reserved.
(IR), nuclear magnetic resonance (NMR), elemental analysis, thermal stability, phase behavior, and density [6]. Their conclusion
was that these compounds have good thermal and hydrolytic
stabilities. Neutz et al. described the synthesis and fundamental
properties of GA in their work [7]. They also applied thermogravimetric analysis (TGA), differential scanning calorimetry (DSC) and
evolved gas analysis (EGA) to investigate the thermal properties
and the decomposition behavior of GA. They found that GA is thermally quite stable and insensitive to friction and impact. They
also reported that it melts at ∼397 K, and its thermal decomposition has an onset temperature of 440 K. The decomposition is
suggested to involve five steps, producing nitrogen (N2 ), ammonia (NH3 ), cyanamide (NH2 CN) and hydrazoic acid (HN3 ), as well
as other unidentified species as the final products. It is mentioned
that HCN is also formed, but it could not be seen in the FTIR
spectroscopy results due to a detector lower limit of 750 cm−1 .
The presence of HCN is thought to be indicated by the time-offlight data due to the detected m/z = 26. However, the time-of-flight
data for m/z = 16 and m/z = 26 show the same temporal behavior
for temperatures above 640 K, suggesting that m/z = 26 is likely
caused by cyanamide. Furthermore, an examination of the results
from FTIR spectroscopy reveals that the P and R branches from a
band centered near 3310 cm−1 should be visible if HCN is formed.
No such band structure is evident. Thus it appears reasonable to
26
N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34
Nomenclature
A
cp
G
h
hP
H
k
kB
m
N
Q̇
S
T
t
y
ω̇
pre-exponential constant for reaction rate
specific heat at constant pressure
Gibbs free energy
mass specific enthalpy
Planck constant
enthalpy
reaction rate constant
Boltzmann constant
mass
number of chemical species
rate of external heat supplied
entropy
temperature
time
mass fraction of species
transmission coefficient
species mass fraction sensitivity coefficient to
chemical reaction
species generation rate in terms of mass fraction
(unit: 1/s)
Subscripts
b
backward reaction
evap
evaporation
forward reaction
f
g
gas phase
i,j
subscripts denoting species i and j respectively
l
liquid phase
Superscripts
transition state
‡
assume that HCN is not an important decomposition product of
GA.
The ATz− anion in GA consists of a tetrazole ring with an amino
( NH2 ) group attached to the carbon atom as shown in Fig. 1.
Compounds having structure similar to this ion have received considerable attention in literature. For example, Kiselev and Gristan
studied the thermal decomposition of 5-aminotetrazole (5-ATz)
using quantum mechanics, including the G3 multilevel procedure
and density functional theory. It was demonstrated that bimolecular reactions are important, especially in the condensed phase
[8]. Paul et al. employed quantum mechanics based calculations
using various levels of theory to identify the principal unimolecular decomposition pathways of 5-ATz in the gas phase [9]. They also
predicted activation barriers for these pathways. Zhang et al. used
ab initio methods to investigate the kinetics of the decomposition
of 5-ATZ to HN3 and cyanamide [10]. They evaluated rate constants
using conventional and canonical variational transition-state theories covering temperatures ranging from 300 to 2500 K. Piekiel
Fig. 1. Guanidinium 5-amino tetrazolate.
and Zachariah, using a T-Jump/time-of-flight mass spectrometry,
studied the thermal decomposition of several tetrazole containing energetic salts under very high heating rate conditions [11].
They found two different reaction pathways involving ring opening; one involving the expulsion of N2 and the other producing
HN3 . The pathway that was followed depended on the placement
of functional groups on the ring.
Knowledge of the decomposition behavior of ingredients used
in propellants is of significant interest for a wide variety of reasons. First, there is a long-term need to develop comprehensive
ignition and combustion models of rocket motors and gas generators in order to facilitate the engineering systems design.
Second, long-term storage of energetic materials requires a thorough understanding of the susceptibility to accidental ignition due
to slow cook-off, impact and electrostatic discharge. Finally, knowledge of initiation of decomposition within a molecule can provide
synthesis chemists a guide to the design of safer and more stable energetic materials. In most cases involving modeling of the
ignition and combustion of energetic materials, comprehensive
chemical reaction mechanisms are available only for the gas phase.
In the solid or liquid phase, global reactions are most frequently
used to simulate the ignition and combustion of energetic materials [30,31]. Current understanding of liquid-phase reactions is very
limited regarding several aspects: (i) identities of the intermediate
decomposition products, (ii) reaction pathways and (iii) rates of elementary reactions. Much additional work is needed regarding the
development of liquid-phase decomposition and reaction models
of energetic materials, which should improve the predictive capability of propellant ignition and combustion models. The present
work on GA is an attempt in this direction. As a result, the motivation of this work is to formulate a chemical reaction mechanism for
GA in the liquid phase by using molecular modeling ab initio methods and to compare the predicted results with the experimental
results obtained by Neutz et al. [7].
2. Molecular modeling
Quantum mechanics calculations provide an avenue for corroborating existing experimentally measured data and providing
information otherwise unavailable experimentally. The Gaussian
09 [12] suite of programs was utilized to this end. Molecular structures of species involved in the decomposition of GA were identified
from transition-state calculations. The search for transition states
was in most cases performed by using the B3LYP/6-31(d) level
of theory. The obtained optimized structures served as an initial
guess to higher-order methods, such as the MP2 perturbation theory. By using the MP2 method [13] and a triple split valence basis
set with additional polarized functions, 6-311++G(d,p), the calculations account for the significant charge delocalization in the ions
present. For cases in which convergence problems were encountered and the transition states could not be obtained using the
MP2 method, the CBS-QB3 compound method developed by Montgomery et al. [14] was used. This method was chosen because it
gives a good balance between accuracy and computational effort;
however, calculations were also done by other methods including M062X. M062X is a high-nonlocality functional developed by
Zhao and Truhlar for thermochemistry, thermochemical kinetics,
noncovalent interactions, and excited states [15]. The computed
structures were optimized and vibrational frequency calculations
were performed to ensure that local energy minima (in case
of reactants and products) and saddle points (in case of transition states) were achieved. Various thermodynamic properties of
species including heat of formation, enthalpy, entropy, free energy
and specific heat, which are required in the model describing the
decomposition, were estimated in the gas and liquid phases from
N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34
the optimized structures. The temperature-dependent thermodynamic properties obtained from these results were then curved
fitted in the form of fourth-order polynomials identical to those
employed in the ChemKin program package [16]. The polynomialfit coefficients obtained in such manner enabled the calculation of
thermodynamic properties in the numerical simulation. Transitionstate optimizations corresponding to all the proposed reactions
were also subjected to IRC (intrinsic reaction coordinate) calculations [17,18] using B3LYP/6-31G(d) to ascertain that the transition
state indeed connected the reactants to the products. The potential energy surface data for reactions thus obtained using Gaussian
09 were used to calculate the reaction rate constants for the formulated reactions with the application of conventional transition
state theory (TST) [19], which accounts for a special type of equilibrium between the reactants and activated complex. This approach
was used for calculation of reaction rate constants because it has
been previously reported that for low temperatures TST can provide
reliable values of rate constants [20,21]. Considering the values of
reaction rate constants for the temperature range of interest in the
present model, the use of TST is justified. Following TST, the forward and backward rate constants for all the elementary reactions
were calculated as
k=
kB T ((S‡ )/Ru ) ((−H ‡ )/(Ru T ))
e
e
hP
(1)
where S‡ and H‡ are, respectively, the activation entropy and
activation enthalpy. The units of k were appropriately determined
for each reaction by multiplying with a suitable conversion factor depending on the type of reaction for which it was calculated.
Here we have adopted the standard state of 1 mol L−1 for evaluating the solution-phase data. To account for the tunneling effect,
Wigner correction factor [22] for each reaction was considered. A
similar approach for development of condensed-phase chemical
reaction mechanism and calculation of rate constants has been used
previously by other research groups [23,24].
Attempts were also made to calculate the reaction-rate
constants based on various generalized transition state theories
with multidimensional tunneling using the Polyrate program [25],
but such attempts were found to be prohibitive with regard to computational time for the considerably large molecules in the present
mechanism. For all the quantum chemical calculations in Gaussian 09, the polarizable continuum model (PCM), using the integral
equation formalism variant (IEFPCM) [26,27] was used to reflect
the assumption that the liquid-phase reactions can be treated as
occurring in a solution phase. This model accounts for the continuum solvation effects. The UFF (universal force field) radius, which
is the default option in Gaussian 09, was used to build the cavity in PCM. Acetonitrile (CH3 CN) was specified as the solvent in all
the optimization, frequency and IRC calculations to represent the
solution-phase medium. Fernandez-Ramos et al. reported that the
solvent can significantly affect rates of some reactions [20]. Hence
we used other solvents to ascertain the effect of solvent type on
the computed thermodynamic and chemical kinetic properties. By
using acetone, methanol, nitromethane and water as the solvent,
the differences in heats of reaction and activation enthalpies in
most cases did not exceed by more than 0.25 kcal/mol compared
to the results obtained by using acetonitrile. This finding is similar
to the conclusion reached by other investigators [28,29].
Fig. 2. Liquid sample of GA is heated in a pan at a predetermined heating rate for
TGA and DSC analysis.
rearrangements. The complete mechanism is given in Tables S1
and S2 in the supplementary data. It should be noted that a transition state for proton transfer within the liquid phase from the
guanidinium cation to the tetrazolate anion could not be identified.
As GA is a relatively new material, these reactions were formulated by using information available in the literature on chemical
processes involving relevant materials such as 5-aminotetrazole
(5-ATz) [8–10] and triazines [28] as well as experimental data
in reference [7]. We propose that for GA, reactions are initiated
between the ion pair guanidinium (Gu+ ) and amino-tetrazolate
(ATz− ) to proceed through multiple pathways involving various
intermediates. Initiation via direct ring opening to release N2 is not
an important pathway. A wide variety of reaction pathways was
investigated in detail.
Ab initio calculations are helpful in deciding which reactions to
exclude from the mechanism based on thermodynamic arguments.
If a reaction is found to be highly endothermic, or considerably more
endothermic than a competing pathway, then that reaction may be
safely omitted from the mechanism in most cases. TST estimates of
the rate constants can be used for making similar arguments. Thus
thermodynamic parameters and rate coefficient values were used
to eliminate certain reactions from this mechanism. The significance of individual reactions in the mechanism will be examined
later when the modeling and sensitivity results are discussed. The
computational approach adopted for developing the chemical reaction mechanism in this work is similar to that of Liu et al. [29];
in this work, however, we aim to analyze the overall decomposition behavior of GA by explaining the formation of product species
observed in the experiments.
4. Numerical simulation
In order to confirm the validity of our proposed liquid phase
reaction mechanism, we performed a numerical simulation of the
decomposition of GA as detected by Neutz et al. [7] using TGA, DSC
and EGA experiments. The simulated physical system is shown in
Fig. 2. As shown, GA is present in liquid form in a small sample pan
in the instrument. Usually, only a few milligrams or less are needed
in such slow decomposition experiments. The sample is heated at
a certain preprogrammed rate, and its mass and heat release with
respect to a reference are recorded with time. As the sample reacts
and products are formed with increasing temperature, some products escape into the gas phase due to evaporation and the mass
of the liquid in the pan diminishes with time. A control volume
analysis of this liquid mass was done and (i) liquid species, (ii)
gaseous species and (iii) total liquid mass conservation equations
were derived. The final forms of these equations are
The detailed chemical mechanism for liquid phase decomposition of GA derived through ab initio calculations as described in the
previous section consists of 55 species and 85 elementary reactions.
These reactions include unimolecular decomposition, bimolecular
and ion recombination, as well as proton transfers and isomeric
dyl,i
= ω̇l,i − yl,i kevap,i + yl,i
yl,j kevap,j
dt
Nspec
Liquid species :
3. Chemical kinetics mechanism
27
(2)
j=1
Gaseous species :
dmg,i
= ml yl,i kevap,i
(3)
dml
= −ml
yl,i kevap,i
dt
(4)
dt
Nspec
Total liquid mass :
i=1
28
N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34
Table 1
Important reactions in the decomposition of liquid GA with thermodynamic parameters computed at the CBS-QB3 lever of theory.
‡
‡
‡
‡
HR a
Hf b
Hb c
GR d
Gf e
Gb f
(R1)
11.2
27.7
16.5
−0.7
28.2
28.9
(R2)
−2.1
19.2
21.3
−4.0
18.4
22.4
(R3)
17.7
33.9
16.2
5.8
33.7
27.9
(R4)
5.6
36.0
30.4
−6.2
47.2
53.3
(R5)
4.2
25.3
21.1
4.3
38.2
33.9
(R6)
−4.5
30.6
35.1
9.7
44.0
34.3
(R7)
3.5
33.3
29.7
17.7
47.6
29.9
No.
a
b
c
d
e
f
Reaction
Enthalpy of reaction (kcal/mol).
Activation enthalpy in the forward direction (kcal/mol).
Activation enthalpy in the backward direction (kcal/mol).
Gibbs free energy of reaction (kcal/mol).
Gibbs free energy of activation in the forward direction (kcal/mol).
Gibbs free energy of activation in the backward direction (kcal/mol).
For all the above equations : kevap,i
= Aevap,i e(−Ea,evap,i /(Ru T )) for species i
(5)
Here, reactions are assumed not to occur in the gas phase
due to dilution and rapidly decreasing temperature due to diffusion. While considering evaporation, solid and liquid propellant
combustion models usually assume that products from liquidphase reactions are immediately collected in gas bubbles implying
infinitely fast evaporation [30,31]. In the present model, however,
we have assigned a rate constant kevap,i as given in Eq. (5) to each
species i which governs the evaporation of that particular species
[32]. We assume that out of the 55 species, most of which are
intermediates, only 5 species depart the liquid. They are NH3 , HN3 ,
nitrogen, NH2 CN and melamine (C3 H6 N6 ). Values of evaporation
rate parameters were assumed such that nitrogen evaporates most
rapidly among the 5 species. Melamine, on the other hand is a stable
and heavier species and its evaporation is slow as compared to the
other four. The mass production rate of i-th species in the liquid
phase ω̇l,i was calculated from the chemical reaction mechanism
and reaction rate data, assuming reversible reactions.
Governing equations given above were solved with the DVODE
solver developed by Brown et al. [33] which employs Gear’s method
for integrating stiff ordinary differential equations. At the start of
the simulation, i.e. at t = 0, 1 g of GA is present and temperature is
390 K. Simulations were carried out with heating rates matching
those in the experiments for comparison. Data for species evolution and liquid mass variation with time obtained from these
simulations were used to calculate the heat release rate for GA
decomposition with time. The equation for heat release rate after
applying energy conservation to the system under consideration
can be written as
Q̇ = ml
+ ml
kevap,i yl,i hg,i +
yl,i cp,i
dml
dt
yl,i hl,i
dyl,i
dT
+ ml
h
dt
dt l,i
(6)
All the terms on the right hand side of this equation can be
easily calculated from the data obtained by solving the governing
N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34
29
Fig. 3. Sensitivity of species mass fraction to reaction rates (heating rate = 10 K/min).
equations given above. The required thermodynamic properties hl,i
and cpl,i for liquid species and hg,i for gaseous species were obtained
by quantum chemical calculations as described in Section 2.
Because of the stiffness of the numerical model, a high order
of precision is required; hence it was solved in the extended
double-precision mode. A critical issue in integrating the ordinary
differential equations in this problem is controlling error in the
solution. It was observed that the species production rates ω̇l,i and
hence the heat release rate Q̇ were extremely sensitive to the tolerances specified in DVODE. In order to get the correct solution,
tolerances RTOL and ATOL had to be carefully chosen for each solution variable. The error control strategies given by Brenan et al.
[34] were adopted for this purpose to obtain solutions which are
independent of the tolerances in the extended double precision
mode.
5. Results and discussion
The TGA measurements of Neutz et al. [7] for a heating rate
of 10 K/min showed a complete residue-free decomposition of GA
with onset of decomposition at about 440 K. A mass loss of about
40% was observed in the first step. In the subsequent steps, the
sample residue was completely desorbed at about 960 K. Their
Fourier transform infrared (FTIR) spectroscopy and mass spectrometry tests identified N2 (m/z = 14 and 28), NH3 (m/z = 15, 16 and 17),
NH2 CN (m/z = 42) and HN3 (m/z = 43) as the products of decomposition. They also presented DSC results for a heating rate of 1 K/min
showing five thermal effects at temperatures beyond 423 K. The
first decomposition step (approx. 423–523 K) displayed two thermal effects, an endothermic and a weak exothermic process. In
the temperature range of 523–623 K, two weak exothermic signals were detected. At the end of the last endothermic reaction at
temperatures >723 K, no liquid remained. Simulation results within
the framework formulated above corroborated these experimental
results as will be subsequently discussed.
To gain insight into the chemical processes taking place during
GA decomposition it is essential to pinpoint and place priority on
those individual reactions that play a critical role. Reaction sensitivity analysis is a suitable tool for this purpose. For a given reaction
with A as its pre-exponential constant, the mass fraction sensitivity
coefficient i for species i is given by
i =
A ∂yli
A yli
≈
yli ∂A
yli A
(7)
Sensitivity coefficients were calculated for Gu+ , ATz− , and the
product species which appear in the gas phase. The results from
some of the sensitivity calculations are displayed in Fig. 3. The
chosen temperatures for these calculations coincided with the
maximum molar generation rate of the respective species. Out of
the 85 reactions in the proposed mechanism, only a few reactions
are revealed to be critical. These reactions along with the molecular
structures of species are listed in Table 1. Optimized structures of
transition states labeled in Table 1, corresponding to each of these
critical reactions, are shown in Fig. 4. In the proposed reaction
mechanism, the pathway that proceeds through the intermediate
INT5 is most dominant because mass fractions of NH3 , Gu+ , HN3
and melamine are found to be most sensitive to reaction R1 as
seen in Fig. 3. Reaction R1 is one of the steps in the INT5 pathway.
A slight increase in the rate of ring opening reaction R2 causes
additional Gu+ to decompose. Reaction R3, in which ring opening of
INT6 occurs, plays a major role in production of N2 and melamine.
Simultaneous proton transfer and ring breaking in reaction R4 is
seen to have the strongest effect on N2 formation although it is
slightly endothermic in the forward direction. Bimolecular reaction
R5 between guanidine and NH2 CN does not affect any species
other than NH3 . Dimerization reaction R6 is seen to affect Gu+
only. In the following discussion, simulation results are presented
30
N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34
Fig. 4. Transition states corresponding to important reactions in the GA decomposition mechanism optimized using the CBS-QB3 method.
and explained on the basis of the important reactions listed in
Table 1. As the entire decomposition process was found to be
most sensitive to reaction R1, thermodynamic parameters for this
reaction using various levels of theory and basis sets are given in
Table 2. It can be observed that with the exception of the results
from the use of the B3LYP/6-31G(d) level of theory, there appears
to be only a relatively small variation in activation enthalpy and
free energy calculated using various levels of theory.
Fig. 5 shows the variation of liquid mass with temperature for a
heating rate of 10 K/min for both experiment and simulation. The
mass of GA is initially 1 gram. We observe that thermal decomposition in the TGA test of Neutz et al. [7] starts at about 440 K and rate
of decomposition in the model is observed to be slightly slower
as compared to the TGA experiment up to about 600 K. First step
which results in about 40% mass loss is mainly caused by reactions
that consume the Gu+ and ATz− ions and the ones that result in
production of HN3 along with the intermediate INT5a1b1 (struc-
Table 2
Thermodynamic parameters for reaction R1 calculated using various levels of theory
and basis sets.
Reaction R1: INT5 = INT5a1 + NH3
‡
‡
‡
‡
Theory and basis set
HR a
Hf b
Hb c
GR d
Gf e
Gb f
B3LYP/631G(d)
M062X/6-31+G(d,p)
M062X/6-311+G(3df,2p)
MP2/6-31+G(d,p)
MP2/6-311++G(d,p)
CBS-QB3
G2(MP2)
G4(MP2)
6.0
13.4
10.6
17.0
17.7
11.2
11.6
11.5
23.2
27.0
26.9
29.6
29.9
27.7
28.0
28.2
17.2
13.7
16.3
12.6
12.3
16.5
16.4
16.7
−6.2
1.4
−1.0
4.8
6.0
−0.7
−0.4
−0.3
23.7
26.9
27.1
28.7
29.3
28.2
27.7
28.8
29.8
25.5
28.1
23.8
23.3
28.9
28.0
29.1
a
b
c
d
e
f
Enthalpy of reaction (kcal/mol).
Activation enthalpy in the forward direction (kcal/mol).
Activation enthalpy in the backward direction (kcal/mol).
Gibbs free energy of reaction (kcal/mol).
Gibbs free energy of activation in the forward direction (kcal/mol).
Gibbs free energy of activation in the backward direction (kcal/mol).
ture shown in Table 1). Most of these reactions are found to be
endothermic and typically having low activation energies which
makes them active at low temperatures. The second step in the
mass loss beyond 600 K is mainly caused by reactions that produce
melamine and CH2 NH. Melamine evaporates and CH2 NH is the
only stable species in the last remaining traces of liquid; here we
assume that CH2 NH remains in the liquid since no reference is
made to its appearance in the time-of-flight data of Neutz et al. [7].
Quantum chemical calculations show that most of these reactions
are exothermic. From the sensitivity analysis discussed earlier, it
is clear that reaction R1 is most critical of all the reactions in the
mechanism. In order to explore the mass loss behavior further,
simulation was also run after modifying the original reaction
mechanism by reducing the forward activation enthalpy of reaction R1 by 2 kcal/mol, which is relatively small amount and most
likely less than the uncertainty associated with the calculations
using the MP2/6-311++G(d,p) method. It was observed that the
mass loss profile with reaction R1 now occurring faster is in better
agreement with experimental results as displayed in Fig. 5. This is
because with the modified mechanism NH3 is formed more rapidly
so its evaporation rate also increases causing the mass to decrease
more rapidly in the first step.
When comparing our predicted results with the experimental
data acquired by Neutz et al., it is important to note that a continuous gaseous stream is sampled. The molecules contained in this
stream were formed a very short period of time earlier within the
liquid sample. As a result, we choose to use the molar production
rate of the various relevant species for comparison purposes. Since
the accumulation of N2 , NH3 , and HN3 must be very small in the
liquid phase, which is equivalent to high evaporation rates, the concentration of these species may reach a pseudo steady state in the
liquid phase. Molar production rates of species evolution into the
gas phase are plotted in Figs. 6–8, along with the mass spectrometry
(EGA) data of Neutz et al. [7] for comparison purposes. Molar production rates corresponding to the modified mechanism, in which
reaction R1 is enhanced as mentioned earlier, are also plotted. It
is clear from these figures that for HN3 , NH3 and N2 , although the
N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34
31
Fig. 5. Variation of liquid mass with temperature (heating rate = 10 K/min). a Mass loss profile with the forward activation enthalpy of reaction R1 reduced by 2 kcal/mol.
calculated species profiles closely match the mass spectrometer
signals, peaks in the simulation are slightly delayed as compared
to experiment. The same phenomenon is also reflected in the mass
loss profile. In the EGA data, ion current peaks for m/z values 42
and 43 appear close to 900 K. These peaks could be from decomposition of melamine and subsequent evaporation of these products;
NH2 CN and fragments could also be generated from the melamine
ring due to electron impingement ionization in the mass spectrometer. Neutz et al. [7] have identified the m/z = 26 signal in their data
as HCN and have proposed gas-phase reactions for its formation.
In our work, we consider reactions only in the liquid phase, and
thus HCN is absent in our mechanism. Again it can be observed
that when reaction R1 has a slightly lower barrier the agreement
between the simulation and experiments is better.
Fig. 9 shows the variation of liquid species mole fractions with
temperature, and Fig. 10 shows that of gaseous species masses. It
should be noted that species profiles in these figures correspond
to the modified chemical mechanism in which the reaction R1 is
enhanced. In the proposed chemical reaction mechanism, initially
only the ion pair, Gu+ and ATz− is present. These ions prefer to
stay separated in the liquid phase due to solvation effect. Same has
been reported for the ions in ammonium perchlorate (AP) by Zhu
and Lin [35]. Their calculation results suggest that a strong solvent
effect exists on the dissociation kinetics in solution. Gu+ and ATz−
Fig. 6. Variation of HN3 molar evolution rate with temperature (heating
rate = 10 K/min). a HN3 profile with the forward activation enthalpy of reaction R1
reduced by 2 kcal/mol.
are consumed early in the event through low energy pathways by
combining with each other to form various intermediates. These
intermediates then undergo reactions such as R1 in Table 1 to
release NH3 , which evolves into the gas phase at about 480 K as
shown in Fig. 10. Significantly large amount of the species INT5a1b1
appears in the liquid phase as shown in Fig. 9. This corroborates
the earlier assertion that out of the various pathways for Gu+ and
ATz− , the one that proceeds through the intermediate species
INT5 is favored most. This is expected because the combination
reaction of Gu+ and ATz− to form INT5 is exothermic and also has
very low energy barrier. In the formation of INT5 the C atom of Gu+
attaches itself to the ring N atom adjacent to carbon. Next reaction
in the INT5 pathway is R1 (Table 1) giving INT5a1 which undergoes
ring opening in Reaction R2 to form INT5a1b. There are multiple
parallel reactions in the next step which involves the release HN3
from INT5a1b1 via bimolecular H atom exchange with various
other intermediates. HN3 evolves into the gas phase at 460 K as
shown in Fig. 10. INT5a1b1 evolution peaks at about 570 K in the
liquid with simultaneous appearance of HN3 in the gas phase.
ATz− is also consumed by unimolecular decomposition to form
other anions within the liquid. Gu+ reacts with anions, such as N3 −
and NH2 CNN− , through bimolecular proton transfer reactions to
form guanidine. However, only a small amount is formed as can
be seen in Fig. 9. Being ionic reactions, they have low barriers and
are thermodynamically favored. Furthermore, a small amount of
N2 is also formed by tetrazole ring opening reactions from various species present as intermediates in the liquid phase. This is
shown in Fig. 10 and in reaction R3 (Table 1). These ring-opening
reactions typically have fairly high activation enthalpies and are
thus not favored at these low temperatures. Also in Fig. 10, NH2 CN
appears in the gas phase later in the event as compared to N2 , NH3
and HN3 , due to significant enthalpic barriers and endothermicity.
When the temperature has increased sufficiently, these reaction
pathways become active and NH2 CN appears at 580 K.
The reactions that are active beyond 700 K are those producing
CH2 NH by hydrogen atom exchange between NH2 CH and various
intermediates hence CH2 NH is seen to be evolving in the liquid in
large quantity toward the end of the heating process. Melamine is
produced through a pathway which involves dimerization of the
intermediate INT5a1b1 (reaction R6 in Table 1) and subsequent
steps involving rearrangement within the molecule and a step of
32
N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34
Fig. 7. Variation of NH3 molar evolution rate with temperature (heating rate = 10 K/min). a NH3 profile with the forward activation enthalpy of reaction R1 reduced by
2 kcal/mol.
Fig. 8. Variation of N2 molar evolution rate with temperature (heating
rate = 10 K/min). a N2 profile with the forward activation enthalpy of reaction R1
reduced by 2 kcal/mol.
elimination of NH2 CN. As evaporation of melamine is slower than
other species, it is seen to diminish in the liquid phase and emerge
in the gas phase at high temperatures as observed in Figs. 9 and 10.
Melamine is a quite stable species and hence largely evaporates
Fig. 9. Variation of liquid species mole fraction with temperature (heating
rate = 10 K/min). All species profiles are plotted for the case in which forward activation enthalpy of reaction R1 is reduced by 2 kcal/mol.
without decomposing in the liquid phase. It was observed to be
stable even at 1073 K and 22 GPa by Ming et al. [36]. Yao et al. have
also reported that high pressure and high temperature conditions
are required for the decomposition of melamine [37]. This indicates
that the activation energy of the ring-opening step of melamine is
very high.
Neutz et al. [7] also conducted DSC tests for GA, showing the
variation of differential heat release rate with temperature during
the thermal decomposition process with respect to some reference
sample. In the present model, heat release rate was computed with
Eq. (6) and 1 g of pure liquid GA was selected as the reference to
calculate the differential heat release rate. Qualitative comparison
of heat release rate calculation from the present model and the DSC
data is presented in Fig. 11 for both original and modified reaction
mechanisms. Although both the computed and experimental data
follow the same general trend up to about 750 K, the endothermic peak is seen in the simulation for the original mechanism at
510 K whereas it appears at about 470 K in the DSC test. This is in
tune with the slight discrepancy in the mass loss profile and mole
generation rate profiles shown earlier in Figs. 6–8. The exothermic
peak in the model also appears earlier than that observed in DSC.
Fig. 10. Variation of gaseous species masses with temperature (heating
rate = 10 K/min). All profiles are plotted for the case in which forward activation
enthalpy of reaction R1 is reduced by 2 kcal/mol.
N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34
33
6. Summary
A detailed reaction mechanism for the decomposition of GA consisting of 55 species and 85 elementary chemical reactions was
formulated based on quantum chemical calculations with insight
from experiments. Numerical simulation of the GA decomposition
process was carried out by solving a system of ordinary differential equations representing the mass loss, reversible reactions
and evaporation of stable species. Simulation results were found
to satisfactorily match the experimental data of Neutz el al. [7].
Important reaction pathways were discussed and critical reactions
were identified that could be the subject of further studies. Within
the present modeling framework and assumptions, the following
major conclusions were obtained:
Fig. 11. Variation of Heat flow with temperature (heating rate = 1 K/min). a Heat flow
profile with the forward activation enthalpy of reaction R1 reduced by 2 kcal/mol.
The predicted rates of exothermic reactions which dominate in this
region are probably higher than those observed in the experiment.
Beyond 750 K, the DSC data show predominantly an endothermic
process whereas the model predicts almost no heat release. One
explanation for this discrepancy is that the model assumes that
only melamine evaporates in this high temperature range. The
melamine formation, including ring closure, is exothermic and thus
the difference between the predicted and measured heat release
rates is not surprising. As a result, if one were to consider evaporation of intermediates to the melamine formation the agreement
would improve.
In order to gain more insight in the heat release behavior during GA decomposition the total heat release rate was split into its
three components: (i) heat release due to evaporation of species,
(ii) net heat generation due to chemical reactions and (iii) sensible heat required to raise the temperature of the sample. All three
components are plotted in Fig. 12 for the modified mechanism.
Examining the variation of heat rate due to chemical reactions
it can be concluded that endothermic reactions dominate until
the temperature reaches 540 K. For temperatures above 540 K, the
exothermic pathways become more active. The evaporation part
of heat release shows two endothermic peaks. On observing the
gaseous species profiles in Fig. 10, it becomes clear that the first
of these peaks is due to the evaporation of NH3 , HN3 , NH2 CN and
N2 , whereas the second one is mainly caused by the evaporation of
melamine.
Fig. 12. Variation of different components of heat release rate with temperature
(heating rate = 1 K/min). All profiles are plotted for the case in which forward activation enthalpy of reaction R1 is reduced by 2 kcal/mol.
1. Decomposition of GA begins with chemical interaction within
the ion pair Gu+ and ATz− , where the carbon in Gu+ bonds to a
ring nitrogen next the carbon in 5ATz− , forming the intermediate
INT5.
2. Pathway in which the intermediate species INT5 is formed is the
most critical.
3. The first step observed in mass loss is caused by formation and
evaporation of NH3 , HN3 , N2 and NH2 CN whereas melamine
evaporation results in the second step.
4. Decomposition at first proceeds through endothermic reactions,
but is later replaced by exothermic reactions producing the N2 ,
NH3 , and HN3 .
5. Proton transfer between Gu+ and 5ATz− is not predicted to occur
by the quantum mechanics calculations for the liquid phase.
7. Concluding remarks
The work presented herein represents our attempt to combine results from experiments with theory to explain the thermal
decomposition behavior of an ionic compound. It is not complete, but the hope is that the work establishes a framework for
future work in the area of examining the condensed-phase thermal decomposition behavior of materials. There are opportunities,
however, for further improvements both in terms of experiments
and the theoretical treatment of the decomposition of GA.
In the area of experiments, it would be very useful to have
further details about the species that evolves at temperatures
above 650 K. These types of experiments would involve both FTIR
spectroscopy and time-of-flight mass spectrometry. Such data
would help guide the ab initio calculations in their use for identifying additional species and reactions. From a combustion point
of view, however, at the temperatures above 700 K, oxidation
of the evolved species would be of more interest than further
recombination reactions among the GA decomposition products.
In the area of the theoretical treatment, several areas could be
further improved. First, since reaction R1 involves hydrogen transfer, a quantum mechanical tunneling correction according to the
Eckhart model could further improve the accuracy of the kinetic
rates. This is particularly important at the lower temperatures,
where an increase in the tunneling correction is expected compared to the use of the Wigner expression. Second, no consideration
has been given to estimate or compute the activity coefficients. It is,
however, a complex task to ascertain the dependency of the activity
coefficient of each species, which is dependent on the concentration of that species as well as the concentration of other species
in the mixture. The dependency, however, may be less significant
as reaction R1 is a unimolecular reaction in the forward direction
[38]. Third, many reactions involve significant reactant and product
wells, and consideration of such an effect could be handled by the
Polyrate [25] or similar programs that are available. Here, however,
34
N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34
the number of atoms can be large and it appears unfeasible for our
group to pursue such a computational approach.
Acknowledgements
The authors acknowledge the support from the Air Force Office
of Scientific Research under grant number FA9550-13-1-0004. Also,
this material is based upon work supported by, or in part by, the
U. S. Army Research Laboratory and the U. S. Army Research Office
under grant number W911NF-08-1-0124.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.tca.2014.02.014.
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