Dd

ND

a

ARRAA

KGRLCS

1

rhoSinwntdalis

Pc

h0

Thermochimica Acta 582 (2014) 25–34

Contents lists available at ScienceDirect

Thermochimica Acta

j ourna l h om epage: www.elsev ier .com/ locate / tca

evelopment of a reaction mechanism for liquid-phaseecomposition of guanidinium 5-amino tetrazolate

. Kumbhakarna, S.T. Thynell ∗

epartment of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802, United States

r t i c l e i n f o

rticle history:eceived 19 December 2013eceived in revised form 12 February 2014ccepted 17 February 2014vailable online 25 February 2014

eywords:uanidinium 5-amino tetrazolateeaction mechanism

a b s t r a c t

The objective of this work is to formulate a detailed reaction mechanism of the decomposition of guani-dinium 5-amino tetrazolate (GA) in the liquid phase using a combined experimental and computationalapproach. The experimental information comes from data published in the literature. The computationalapproach 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 theoryand basis sets were used. A continuum-based model for predicting species formation and mass loss ofa TGA experiment was also developed and solved numerically, accounting for reversible chemical reac-tions and mass transfer in simulations of the GA decomposition process. The model accounts for reactions

iquid phaseontinuum-based modelensitivity analysis

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 werefound to satisfactorily match the temporal experimental results previously published in literature forthe decomposition of GA. Important reaction pathways in the proposed reaction scheme were identifiedbased on a sensitivity analysis.

© 2014 Elsevier B.V. All rights reserved.

. Introduction

Recently, research on nitrogen-rich energetic materials haseceived significant attention for a variety of reasons. First, theirigh positive heats of formation may release a large amount of heatn combustion as dinitrogen (N2) is one of the major products [1].econd, the formed molecular nitrogen may achieve a high specificmpulse without undesirable smoke or soot. Third, the molecularitrogen is an environmentally friendly final product. Tetrazoles,ith their heterocyclic ring structure, fall within this class of high-itrogen compounds [2]. Within tetrazole family of compounds,he triaminoguanidinium azotetrazolate (TAGzT) [3] and guani-inium azotetrazolate (GzT) [4], are of interest due to their potentialpplications as gas generators and burn rate modifiers for propel-ants. Similarly, the guanidinium 5-aminotetrazolate (GA), shownn Fig. 1, is also of interest and possesses a much simpler moleculartructure.

The molecular and electronic structures of GA were reported byaoloni et al. [5]. Tao et al. characterized GA and several compoundsontaining the amino-tetrazolate (ATz−) anion based on infrared

∗ Corresponding author. Tel.: +1 814 863 0977.E-mail address: thynell@psu.edu (S.T. Thynell).

ttp://dx.doi.org/10.1016/j.tca.2014.02.014040-6031/© 2014 Elsevier B.V. All rights reserved.

(IR), nuclear magnetic resonance (NMR), elemental analysis, ther-mal stability, phase behavior, and density [6]. Their conclusionwas that these compounds have good thermal and hydrolyticstabilities. Neutz et al. described the synthesis and fundamentalproperties of GA in their work [7]. They also applied thermogravi-metric analysis (TGA), differential scanning calorimetry (DSC) andevolved gas analysis (EGA) to investigate the thermal propertiesand the decomposition behavior of GA. They found that GA is ther-mally quite stable and insensitive to friction and impact. Theyalso reported that it melts at ∼397 K, and its thermal decompo-sition has an onset temperature of 440 K. The decomposition issuggested to involve five steps, producing nitrogen (N2), ammo-nia (NH3), cyanamide (NH2CN) and hydrazoic acid (HN3), as wellas other unidentified species as the final products. It is mentionedthat HCN is also formed, but it could not be seen in the FTIRspectroscopy results due to a detector lower limit of 750 cm−1.The presence of HCN is thought to be indicated by the time-of-flight data due to the detected m/z = 26. However, the time-of-flightdata for m/z = 16 and m/z = 26 show the same temporal behaviorfor temperatures above 640 K, suggesting that m/z = 26 is likely

caused by cyanamide. Furthermore, an examination of the resultsfrom FTIR spectroscopy reveals that the P and R branches from aband 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 / Thermo

Nomenclature

A pre-exponential constant for reaction ratecp specific heat at constant pressureG Gibbs free energyh mass specific enthalpyhP Planck constantH enthalpyk reaction rate constantkB Boltzmann constantm massN number of chemical speciesQ rate of external heat suppliedS entropyT temperaturet timey mass fraction of species� transmission coefficient� species mass fraction sensitivity coefficient to

chemical reactionω species generation rate in terms of mass fraction

(unit: 1/s)

Subscriptsb backward reactionevap evaporationf forward reactiong gas phasei,j subscripts denoting species i and j respectivelyl liquid phase

aG

(Cssuau[ulpaouo

Superscripts‡ transition state

ssume that HCN is not an important decomposition product ofA.

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.ompounds having structure similar to this ion have received con-iderable attention in literature. For example, Kiselev and Gristantudied the thermal decomposition of 5-aminotetrazole (5-ATz)sing quantum mechanics, including the G3 multilevel procedurend density functional theory. It was demonstrated that bimolec-lar reactions are important, especially in the condensed phase8]. Paul et al. employed quantum mechanics based calculationssing various levels of theory to identify the principal unimolecu-

ar decomposition pathways of 5-ATz in the gas phase [9]. They alsoredicted activation barriers for these pathways. Zhang et al. used

b initio methods to investigate the kinetics of the decompositionf 5-ATZ to HN3 and cyanamide [10]. They evaluated rate constantssing conventional and canonical variational transition-state the-ries covering temperatures ranging from 300 to 2500 K. Piekiel

Fig. 1. Guanidinium 5-amino tetrazolate.

chimica Acta 582 (2014) 25–34

and Zachariah, using a T-Jump/time-of-flight mass spectrometry,studied the thermal decomposition of several tetrazole contain-ing energetic salts under very high heating rate conditions [11].They found two different reaction pathways involving ring open-ing; one involving the expulsion of N2 and the other producingHN3. The pathway that was followed depended on the placementof functional groups on the ring.

Knowledge of the decomposition behavior of ingredients usedin propellants is of significant interest for a wide variety of rea-sons. First, there is a long-term need to develop comprehensiveignition and combustion models of rocket motors and gas gen-erators in order to facilitate the engineering systems design.Second, long-term storage of energetic materials requires a thor-ough understanding of the susceptibility to accidental ignition dueto slow cook-off, impact and electrostatic discharge. Finally, knowl-edge of initiation of decomposition within a molecule can providesynthesis chemists a guide to the design of safer and more sta-ble energetic materials. In most cases involving modeling of theignition and combustion of energetic materials, comprehensivechemical reaction mechanisms are available only for the gas phase.In the solid or liquid phase, global reactions are most frequentlyused to simulate the ignition and combustion of energetic materi-als [30,31]. Current understanding of liquid-phase reactions is verylimited regarding several aspects: (i) identities of the intermediatedecomposition products, (ii) reaction pathways and (iii) rates of ele-mentary reactions. Much additional work is needed regarding thedevelopment of liquid-phase decomposition and reaction modelsof energetic materials, which should improve the predictive capa-bility of propellant ignition and combustion models. The presentwork on GA is an attempt in this direction. As a result, the motiva-tion of this work is to formulate a chemical reaction mechanism forGA in the liquid phase by using molecular modeling ab initio meth-ods and to compare the predicted results with the experimentalresults obtained by Neutz et al. [7].

2. Molecular modeling

Quantum mechanics calculations provide an avenue for cor-roborating existing experimentally measured data and providinginformation otherwise unavailable experimentally. The Gaussian09 [12] suite of programs was utilized to this end. Molecular struc-tures of species involved in the decomposition of GA were identifiedfrom transition-state calculations. The search for transition stateswas in most cases performed by using the B3LYP/6-31(d) levelof theory. The obtained optimized structures served as an initialguess to higher-order methods, such as the MP2 perturbation the-ory. By using the MP2 method [13] and a triple split valence basisset with additional polarized functions, 6-311++G(d,p), the calcu-lations account for the significant charge delocalization in the ionspresent. For cases in which convergence problems were encoun-tered and the transition states could not be obtained using theMP2 method, the CBS-QB3 compound method developed by Mont-gomery et al. [14] was used. This method was chosen because itgives a good balance between accuracy and computational effort;however, calculations were also done by other methods includ-ing M062X. M062X is a high-nonlocality functional developed byZhao and Truhlar for thermochemistry, thermochemical kinetics,noncovalent interactions, and excited states [15]. The computedstructures were optimized and vibrational frequency calculationswere performed to ensure that local energy minima (in caseof reactants and products) and saddle points (in case of transi-

tion states) were achieved. Various thermodynamic properties ofspecies including heat of formation, enthalpy, entropy, free energyand specific heat, which are required in the model describing thedecomposition, were estimated in the gas and liquid phases from

hermochimica Acta 582 (2014) 25–34 27

tnfiefitswtst0msrwbrrpww

k

waftHaWsrp

cwbpmietouiitsswtutmtt

3

tpTa

N. Kumbhakarna, S.T. Thynell / T

he optimized structures. The temperature-dependent thermody-amic properties obtained from these results were then curvedtted in the form of fourth-order polynomials identical to thosemployed in the ChemKin program package [16]. The polynomial-t coefficients obtained in such manner enabled the calculation ofhermodynamic properties in the numerical simulation. Transition-tate optimizations corresponding to all the proposed reactionsere also subjected to IRC (intrinsic reaction coordinate) calcula-

ions [17,18] using B3LYP/6-31G(d) to ascertain that the transitiontate indeed connected the reactants to the products. The poten-ial energy surface data for reactions thus obtained using Gaussian9 were used to calculate the reaction rate constants for the for-ulated reactions with the application of conventional transition

tate theory (TST) [19], which accounts for a special type of equilib-ium between the reactants and activated complex. This approachas used for calculation of reaction rate constants because it has

een previously reported that for low temperatures TST can provideeliable values of rate constants [20,21]. Considering the values ofeaction rate constants for the temperature range of interest in theresent model, the use of TST is justified. Following TST, the for-ard and backward rate constants for all the elementary reactionsere calculated as

= �kBT

hPe((�S‡)/Ru)e((−�H‡)/(RuT)) (1)

here �S‡ and �H‡ are, respectively, the activation entropy andctivation enthalpy. The units of k were appropriately determinedor each reaction by multiplying with a suitable conversion fac-or depending on the type of reaction for which it was calculated.ere we have adopted the standard state of 1 mol L−1 for evalu-ting the solution-phase data. To account for the tunneling effect,igner correction factor [22] for each reaction was considered. A

imilar approach for development of condensed-phase chemicaleaction mechanism and calculation of rate constants has been usedreviously by other research groups [23,24].

Attempts were also made to calculate the reaction-rateonstants based on various generalized transition state theoriesith multidimensional tunneling using the Polyrate program [25],

ut such attempts were found to be prohibitive with regard to com-utational time for the considerably large molecules in the presentechanism. For all the quantum chemical calculations in Gauss-

an 09, the polarizable continuum model (PCM), using the integralquation formalism variant (IEFPCM) [26,27] was used to reflecthe assumption that the liquid-phase reactions can be treated asccurring in a solution phase. This model accounts for the contin-um solvation effects. The UFF (universal force field) radius, which

s the default option in Gaussian 09, was used to build the cav-ty in PCM. Acetonitrile (CH3CN) was specified as the solvent in allhe optimization, frequency and IRC calculations to represent theolution-phase medium. Fernandez-Ramos et al. reported that theolvent can significantly affect rates of some reactions [20]. Hencee used other solvents to ascertain the effect of solvent type on

he computed thermodynamic and chemical kinetic properties. Bysing acetone, methanol, nitromethane and water as the solvent,he differences in heats of reaction and activation enthalpies in

ost cases did not exceed by more than 0.25 kcal/mol comparedo the results obtained by using acetonitrile. This finding is similaro the conclusion reached by other investigators [28,29].

. Chemical kinetics mechanism

The detailed chemical mechanism for liquid phase decomposi-

ion of GA derived through ab initio calculations as described in therevious section consists of 55 species and 85 elementary reactions.hese reactions include unimolecular decomposition, bimolecularnd ion recombination, as well as proton transfers and isomeric

Fig. 2. Liquid sample of GA is heated in a pan at a predetermined heating rate forTGA and DSC analysis.

rearrangements. The complete mechanism is given in Tables S1and S2 in the supplementary data. It should be noted that a tran-sition state for proton transfer within the liquid phase from theguanidinium cation to the tetrazolate anion could not be identified.As GA is a relatively new material, these reactions were formu-lated by using information available in the literature on chemicalprocesses involving relevant materials such as 5-aminotetrazole(5-ATz) [8–10] and triazines [28] as well as experimental datain reference [7]. We propose that for GA, reactions are initiatedbetween the ion pair guanidinium (Gu+) and amino-tetrazolate(ATz−) to proceed through multiple pathways involving variousintermediates. Initiation via direct ring opening to release N2 is notan important pathway. A wide variety of reaction pathways wasinvestigated in detail.

Ab initio calculations are helpful in deciding which reactions toexclude from the mechanism based on thermodynamic arguments.If a reaction is found to be highly endothermic, or considerably moreendothermic than a competing pathway, then that reaction may besafely omitted from the mechanism in most cases. TST estimates ofthe rate constants can be used for making similar arguments. Thusthermodynamic parameters and rate coefficient values were usedto eliminate certain reactions from this mechanism. The signifi-cance of individual reactions in the mechanism will be examinedlater when the modeling and sensitivity results are discussed. Thecomputational approach adopted for developing the chemical reac-tion mechanism in this work is similar to that of Liu et al. [29];in this work, however, we aim to analyze the overall decomposi-tion behavior of GA by explaining the formation of product speciesobserved in the experiments.

4. Numerical simulation

In order to confirm the validity of our proposed liquid phasereaction mechanism, we performed a numerical simulation of thedecomposition of GA as detected by Neutz et al. [7] using TGA, DSCand EGA experiments. The simulated physical system is shown inFig. 2. As shown, GA is present in liquid form in a small sample panin the instrument. Usually, only a few milligrams or less are neededin such slow decomposition experiments. The sample is heated ata certain preprogrammed rate, and its mass and heat release withrespect to a reference are recorded with time. As the sample reactsand products are formed with increasing temperature, some prod-ucts escape into the gas phase due to evaporation and the massof the liquid in the pan diminishes with time. A control volumeanalysis of this liquid mass was done and (i) liquid species, (ii)gaseous species and (iii) total liquid mass conservation equationswere derived. The final forms of these equations are

Liquid species :dyl,i

dt= ωl,i − yl,ikevap,i + yl,i

Nspec∑

j=1

yl,jkevap,j (2)

Gaseous species :dmg,i = mlyl,ikevap,i (3)

dt

Total liquid mass :dml

dt= −ml

Nspec∑

i=1

yl,ikevap,i (4)

28 N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34

Table 1Important reactions in the decomposition of liquid GA with thermodynamic parameters computed at the CBS-QB3 lever of theory.

No. Reaction �HRa �H‡

fb �H‡

bc �GR

d �G‡f

e �G‡b

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

a Enthalpy of reaction (kcal/mol).b Activation enthalpy in the forward direction (kcal/mol).c Activation enthalpy in the backward direction (kcal/mol).

F

dscpiws[inrrao

d Gibbs free energy of reaction (kcal/mol).e Gibbs free energy of activation in the forward direction (kcal/mol).f Gibbs free energy of activation in the backward direction (kcal/mol).

or all the above equations : kevap,i

= Aevap,ie(−Ea,evap,i/(RuT)) for species i (5)

Here, reactions are assumed not to occur in the gas phaseue to dilution and rapidly decreasing temperature due to diffu-ion. While considering evaporation, solid and liquid propellantombustion models usually assume that products from liquid-hase reactions are immediately collected in gas bubbles implying

nfinitely fast evaporation [30,31]. In the present model, however,e have assigned a rate constant kevap,i as given in Eq. (5) to each

pecies i which governs the evaporation of that particular species32]. We assume that out of the 55 species, most of which arentermediates, only 5 species depart the liquid. They are NH3, HN3,itrogen, NH2CN and melamine (C3H6N6). Values of evaporation

ate parameters were assumed such that nitrogen evaporates mostapidly among the 5 species. Melamine, on the other hand is a stablend heavier species and its evaporation is slow as compared to thether four. The mass production rate of i-th species in the liquid

phase ωl,i was calculated from the chemical reaction mechanismand reaction rate data, assuming reversible reactions.

Governing equations given above were solved with the DVODEsolver developed by Brown et al. [33] which employs Gear’s methodfor integrating stiff ordinary differential equations. At the start ofthe simulation, i.e. at t = 0, 1 g of GA is present and temperature is390 K. Simulations were carried out with heating rates matchingthose in the experiments for comparison. Data for species evo-lution and liquid mass variation with time obtained from thesesimulations were used to calculate the heat release rate for GAdecomposition with time. The equation for heat release rate afterapplying energy conservation to the system under considerationcan be written as

Q = ml

∑kevap,iyl,ihg,i + dml

dt

∑yl,ihl,i

+ m∑

y cdT + m

∑ dyl,i h (6)

l l,i p,i dt l dt l,i

All the terms on the right hand side of this equation can beeasily calculated from the data obtained by solving the governing

N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34 29

on to r

eab

oddshett[im

5

ow4sFeNssfimtnt

Fig. 3. Sensitivity of species mass fracti

quations given above. The required thermodynamic properties hl,ind cpl,i for liquid species and hg,i for gaseous species were obtainedy quantum chemical calculations as described in Section 2.

Because of the stiffness of the numerical model, a high orderf precision is required; hence it was solved in the extendedouble-precision mode. A critical issue in integrating the ordinaryifferential equations in this problem is controlling error in theolution. It was observed that the species production rates ωl,i andence the heat release rate Q were extremely sensitive to the tol-rances specified in DVODE. In order to get the correct solution,olerances RTOL and ATOL had to be carefully chosen for each solu-ion variable. The error control strategies given by Brenan et al.34] were adopted for this purpose to obtain solutions which arendependent of the tolerances in the extended double precision

ode.

. Results and discussion

The TGA measurements of Neutz et al. [7] for a heating ratef 10 K/min showed a complete residue-free decomposition of GAith onset of decomposition at about 440 K. A mass loss of about

0% was observed in the first step. In the subsequent steps, theample residue was completely desorbed at about 960 K. Theirourier transform infrared (FTIR) spectroscopy and mass spectrom-try tests identified N2 (m/z = 14 and 28), NH3 (m/z = 15, 16 and 17),H2CN (m/z = 42) and HN3 (m/z = 43) as the products of decompo-

ition. They also presented DSC results for a heating rate of 1 K/minhowing five thermal effects at temperatures beyond 423 K. Therst decomposition step (approx. 423–523 K) displayed two ther-

al effects, an endothermic and a weak exothermic process. In

he temperature range of 523–623 K, two weak exothermic sig-als were detected. At the end of the last endothermic reaction atemperatures >723 K, no liquid remained. Simulation results within

eaction rates (heating rate = 10 K/min).

the framework formulated above corroborated these experimentalresults as will be subsequently discussed.

To gain insight into the chemical processes taking place duringGA decomposition it is essential to pinpoint and place priority onthose individual reactions that play a critical role. Reaction sensi-tivity analysis is a suitable tool for this purpose. For a given reactionwith A as its pre-exponential constant, the mass fraction sensitivitycoefficient �i for species i is given by

�i = A

yli

∂yli

∂A≈ A

yli

�yli

�A(7)

Sensitivity coefficients were calculated for Gu+, ATz−, and theproduct species which appear in the gas phase. The results fromsome of the sensitivity calculations are displayed in Fig. 3. Thechosen temperatures for these calculations coincided with themaximum molar generation rate of the respective species. Out ofthe 85 reactions in the proposed mechanism, only a few reactionsare revealed to be critical. These reactions along with the molecularstructures of species are listed in Table 1. Optimized structures oftransition states labeled in Table 1, corresponding to each of thesecritical reactions, are shown in Fig. 4. In the proposed reactionmechanism, the pathway that proceeds through the intermediateINT5 is most dominant because mass fractions of NH3, Gu+, HN3and melamine are found to be most sensitive to reaction R1 asseen 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 causesadditional Gu+ to decompose. Reaction R3, in which ring opening ofINT6 occurs, plays a major role in production of N2 and melamine.Simultaneous proton transfer and ring breaking in reaction R4 isseen to have the strongest effect on N2 formation although it is

slightly endothermic in the forward direction. Bimolecular reactionR5 between guanidine and NH2CN does not affect any speciesother 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

e GA

aTmrTftf

hmtoawtp

TTa

Fig. 4. Transition states corresponding to important reactions in th

nd explained on the basis of the important reactions listed inable 1. As the entire decomposition process was found to beost sensitive to reaction R1, thermodynamic parameters for this

eaction using various levels of theory and basis sets are given inable 2. It can be observed that with the exception of the resultsrom the use of the B3LYP/6-31G(d) level of theory, there appearso be only a relatively small variation in activation enthalpy andree energy calculated using various levels of theory.

Fig. 5 shows the variation of liquid mass with temperature for aeating rate of 10 K/min for both experiment and simulation. Theass of GA is initially 1 gram. We observe that thermal decomposi-

ion in the TGA test of Neutz et al. [7] starts at about 440 K and ratef decomposition in the model is observed to be slightly slowers compared to the TGA experiment up to about 600 K. First step

hich results in about 40% mass loss is mainly caused by reactions

hat consume the Gu+ and ATz− ions and the ones that result inroduction of HN3 along with the intermediate INT5a1b1 (struc-

able 2hermodynamic parameters for reaction R1 calculated using various levels of theorynd basis sets.

Reaction R1: INT5 = INT5a1 + NH3

Theory and basis set �HRa �H‡

fb �H‡

bc �GR

d �G‡f

e �G‡b

f

B3LYP/631G(d) 6.0 23.2 17.2 −6.2 23.7 29.8M062X/6-31+G(d,p) 13.4 27.0 13.7 1.4 26.9 25.5M062X/6-311+G(3df,2p) 10.6 26.9 16.3 −1.0 27.1 28.1MP2/6-31+G(d,p) 17.0 29.6 12.6 4.8 28.7 23.8MP2/6-311++G(d,p) 17.7 29.9 12.3 6.0 29.3 23.3CBS-QB3 11.2 27.7 16.5 −0.7 28.2 28.9G2(MP2) 11.6 28.0 16.4 −0.4 27.7 28.0G4(MP2) 11.5 28.2 16.7 −0.3 28.8 29.1

a Enthalpy of reaction (kcal/mol).b Activation enthalpy in the forward direction (kcal/mol).c Activation enthalpy in the backward direction (kcal/mol).d Gibbs free energy of reaction (kcal/mol).e Gibbs free energy of activation in the forward direction (kcal/mol).f Gibbs free energy of activation in the backward direction (kcal/mol).

decomposition mechanism optimized using the CBS-QB3 method.

ture shown in Table 1). Most of these reactions are found to beendothermic and typically having low activation energies whichmakes them active at low temperatures. The second step in themass loss beyond 600 K is mainly caused by reactions that producemelamine and CH2NH. Melamine evaporates and CH2NH is theonly stable species in the last remaining traces of liquid; here weassume that CH2NH remains in the liquid since no reference ismade to its appearance in the time-of-flight data of Neutz et al. [7].Quantum chemical calculations show that most of these reactionsare exothermic. From the sensitivity analysis discussed earlier, itis clear that reaction R1 is most critical of all the reactions in themechanism. In order to explore the mass loss behavior further,simulation was also run after modifying the original reactionmechanism by reducing the forward activation enthalpy of reac-tion R1 by 2 kcal/mol, which is relatively small amount and mostlikely less than the uncertainty associated with the calculationsusing the MP2/6-311++G(d,p) method. It was observed that themass loss profile with reaction R1 now occurring faster is in betteragreement with experimental results as displayed in Fig. 5. This isbecause with the modified mechanism NH3 is formed more rapidlyso its evaporation rate also increases causing the mass to decreasemore rapidly in the first step.

When comparing our predicted results with the experimentaldata acquired by Neutz et al., it is important to note that a contin-uous gaseous stream is sampled. The molecules contained in thisstream were formed a very short period of time earlier within theliquid sample. As a result, we choose to use the molar productionrate of the various relevant species for comparison purposes. Sincethe accumulation of N2, NH3, and HN3 must be very small in theliquid phase, which is equivalent to high evaporation rates, the con-centration of these species may reach a pseudo steady state in theliquid phase. Molar production rates of species evolution into thegas phase are plotted in Figs. 6–8, along with the mass spectrometry

(EGA) data of Neutz et al. [7] for comparison purposes. Molar pro-duction rates corresponding to the modified mechanism, in whichreaction R1 is enhanced as mentioned earlier, are also plotted. Itis clear from these figures that for HN3, NH3 and N2, although the

N. Kumbhakarna, S.T. Thynell / Thermochimica Acta 582 (2014) 25–34 31

F oss pr

cstlasNreaIttb

tsteosbae

Frr

ig. 5. Variation of liquid mass with temperature (heating rate = 10 K/min). aMass l

alculated species profiles closely match the mass spectrometerignals, peaks in the simulation are slightly delayed as comparedo experiment. The same phenomenon is also reflected in the massoss profile. In the EGA data, ion current peaks for m/z values 42nd 43 appear close to 900 K. These peaks could be from decompo-ition of melamine and subsequent evaporation of these products;H2CN and fragments could also be generated from the melamine

ing due to electron impingement ionization in the mass spectrom-ter. Neutz et al. [7] have identified the m/z = 26 signal in their datas HCN and have proposed gas-phase reactions for its formation.n our work, we consider reactions only in the liquid phase, andhus HCN is absent in our mechanism. Again it can be observedhat when reaction R1 has a slightly lower barrier the agreementetween the simulation and experiments is better.

Fig. 9 shows the variation of liquid species mole fractions withemperature, and Fig. 10 shows that of gaseous species masses. Ithould be noted that species profiles in these figures correspondo the modified chemical mechanism in which the reaction R1 isnhanced. In the proposed chemical reaction mechanism, initiallynly the ion pair, Gu+ and ATz− is present. These ions prefer to

tay separated in the liquid phase due to solvation effect. Same haseen reported for the ions in ammonium perchlorate (AP) by Zhund Lin [35]. Their calculation results suggest that a strong solventffect exists on the dissociation kinetics in solution. Gu+ and ATz−

ig. 6. Variation of HN3 molar evolution rate with temperature (heatingate = 10 K/min). aHN3 profile with the forward activation enthalpy of reaction R1educed by 2 kcal/mol.

ofile with the forward activation enthalpy of reaction R1 reduced by 2 kcal/mol.

are consumed early in the event through low energy pathways bycombining with each other to form various intermediates. Theseintermediates then undergo reactions such as R1 in Table 1 torelease NH3, which evolves into the gas phase at about 480 K asshown in Fig. 10. Significantly large amount of the species INT5a1b1appears in the liquid phase as shown in Fig. 9. This corroboratesthe earlier assertion that out of the various pathways for Gu+ andATz−, the one that proceeds through the intermediate speciesINT5 is favored most. This is expected because the combinationreaction of Gu+ and ATz− to form INT5 is exothermic and also hasvery low energy barrier. In the formation of INT5 the C atom of Gu+

attaches itself to the ring N atom adjacent to carbon. Next reactionin the INT5 pathway is R1 (Table 1) giving INT5a1 which undergoesring opening in Reaction R2 to form INT5a1b. There are multipleparallel reactions in the next step which involves the release HN3from INT5a1b1 via bimolecular H atom exchange with variousother intermediates. HN3 evolves into the gas phase at 460 K asshown in Fig. 10. INT5a1b1 evolution peaks at about 570 K in theliquid with simultaneous appearance of HN3 in the gas phase.

ATz− is also consumed by unimolecular decomposition to formother anions within the liquid. Gu+ reacts with anions, such as N3

−

and NH2CNN−, through bimolecular proton transfer reactions toform guanidine. However, only a small amount is formed as canbe seen in Fig. 9. Being ionic reactions, they have low barriers andare thermodynamically favored. Furthermore, a small amount ofN2 is also formed by tetrazole ring opening reactions from vari-ous species present as intermediates in the liquid phase. This isshown in Fig. 10 and in reaction R3 (Table 1). These ring-openingreactions typically have fairly high activation enthalpies and arethus not favored at these low temperatures. Also in Fig. 10, NH2CNappears in the gas phase later in the event as compared to N2, NH3and HN3, due to significant enthalpic barriers and endothermicity.When the temperature has increased sufficiently, these reactionpathways become active and NH2CN appears at 580 K.

The reactions that are active beyond 700 K are those producingCH2NH by hydrogen atom exchange between NH2CH and variousintermediates hence CH2NH is seen to be evolving in the liquid in

large quantity toward the end of the heating process. Melamine isproduced through a pathway which involves dimerization of theintermediate INT5a1b1 (reaction R6 in Table 1) and subsequentsteps 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/mi2 kcal/mol.

Frr

eoiM

Frv

510 K whereas it appears at about 470 K in the DSC test. This is in

ig. 8. Variation of N2 molar evolution rate with temperature (heatingate = 10 K/min). aN2 profile with the forward activation enthalpy of reaction R1educed by 2 kcal/mol.

limination of NH2CN. As evaporation of melamine is slower thanther species, it is seen to diminish in the liquid phase and emergen the gas phase at high temperatures as observed in Figs. 9 and 10.

elamine is a quite stable species and hence largely evaporates

ig. 9. Variation of liquid species mole fraction with temperature (heatingate = 10 K/min). All species profiles are plotted for the case in which forward acti-ation enthalpy of reaction R1 is reduced by 2 kcal/mol.

n). aNH3 profile with the forward activation enthalpy of reaction R1 reduced by

without decomposing in the liquid phase. It was observed to bestable even at 1073 K and 22 GPa by Ming et al. [36]. Yao et al. havealso reported that high pressure and high temperature conditionsare required for the decomposition of melamine [37]. This indicatesthat the activation energy of the ring-opening step of melamine isvery high.

Neutz et al. [7] also conducted DSC tests for GA, showing thevariation of differential heat release rate with temperature duringthe thermal decomposition process with respect to some referencesample. In the present model, heat release rate was computed withEq. (6) and 1 g of pure liquid GA was selected as the reference tocalculate the differential heat release rate. Qualitative comparisonof heat release rate calculation from the present model and the DSCdata is presented in Fig. 11 for both original and modified reactionmechanisms. Although both the computed and experimental datafollow the same general trend up to about 750 K, the endother-mic peak is seen in the simulation for the original mechanism at

tune with the slight discrepancy in the mass loss profile and molegeneration rate profiles shown earlier in Figs. 6–8. The exothermicpeak in the model also appears earlier than that observed in DSC.

Fig. 10. Variation of gaseous species masses with temperature (heatingrate = 10 K/min). All profiles are plotted for the case in which forward activationenthalpy of reaction R1 is reduced by 2 kcal/mol.

N. Kumbhakarna, S.T. Thynell / Thermo

Fp

TrBpeomtrrw

it(bcEiteogoNm

F(v

ig. 11. Variation of Heat flow with temperature (heating rate = 1 K/min). aHeat flowrofile with the forward activation enthalpy of reaction R1 reduced by 2 kcal/mol.

he predicted rates of exothermic reactions which dominate in thisegion are probably higher than those observed in the experiment.eyond 750 K, the DSC data show predominantly an endothermicrocess whereas the model predicts almost no heat release. Onexplanation for this discrepancy is that the model assumes thatnly melamine evaporates in this high temperature range. Theelamine formation, including ring closure, is exothermic and thus

he difference between the predicted and measured heat releaseates is not surprising. As a result, if one were to consider evapo-ation of intermediates to the melamine formation the agreementould improve.

In order to gain more insight in the heat release behavior dur-ng GA decomposition the total heat release rate was split into itshree components: (i) heat release due to evaporation of species,ii) net heat generation due to chemical reactions and (iii) sensi-le heat required to raise the temperature of the sample. All threeomponents are plotted in Fig. 12 for the modified mechanism.xamining the variation of heat rate due to chemical reactionst can be concluded that endothermic reactions dominate untilhe temperature reaches 540 K. For temperatures above 540 K, thexothermic pathways become more active. The evaporation partf heat release shows two endothermic peaks. On observing theaseous species profiles in Fig. 10, it becomes clear that the first

f these peaks is due to the evaporation of NH3, HN3, NH2CN and2, whereas the second one is mainly caused by the evaporation ofelamine.

ig. 12. Variation of different components of heat release rate with temperatureheating rate = 1 K/min). All profiles are plotted for the case in which forward acti-ation enthalpy of reaction R1 is reduced by 2 kcal/mol.

chimica Acta 582 (2014) 25–34 33

6. Summary

A detailed reaction mechanism for the decomposition of GA con-sisting of 55 species and 85 elementary chemical reactions wasformulated based on quantum chemical calculations with insightfrom experiments. Numerical simulation of the GA decompositionprocess was carried out by solving a system of ordinary differ-ential equations representing the mass loss, reversible reactionsand evaporation of stable species. Simulation results were foundto satisfactorily match the experimental data of Neutz el al. [7].Important reaction pathways were discussed and critical reactionswere identified that could be the subject of further studies. Withinthe present modeling framework and assumptions, the followingmajor conclusions were obtained:

1. Decomposition of GA begins with chemical interaction withinthe ion pair Gu+ and ATz−, where the carbon in Gu+ bonds to aring nitrogen next the carbon in 5ATz−, forming the intermediateINT5.

2. Pathway in which the intermediate species INT5 is formed is themost critical.

3. The first step observed in mass loss is caused by formation andevaporation of NH3, HN3, N2 and NH2CN whereas melamineevaporation 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 occurby the quantum mechanics calculations for the liquid phase.

7. Concluding remarks

The work presented herein represents our attempt to com-bine results from experiments with theory to explain the thermaldecomposition behavior of an ionic compound. It is not com-plete, but the hope is that the work establishes a framework forfuture work in the area of examining the condensed-phase ther-mal decomposition behavior of materials. There are opportunities,however, for further improvements both in terms of experimentsand the theoretical treatment of the decomposition of GA.

In the area of experiments, it would be very useful to havefurther details about the species that evolves at temperaturesabove 650 K. These types of experiments would involve both FTIRspectroscopy and time-of-flight mass spectrometry. Such datawould help guide the ab initio calculations in their use for iden-tifying additional species and reactions. From a combustion pointof view, however, at the temperatures above 700 K, oxidationof the evolved species would be of more interest than furtherrecombination reactions among the GA decomposition products.

In the area of the theoretical treatment, several areas could befurther improved. First, since reaction R1 involves hydrogen trans-fer, a quantum mechanical tunneling correction according to theEckhart model could further improve the accuracy of the kineticrates. This is particularly important at the lower temperatures,where an increase in the tunneling correction is expected com-pared to the use of the Wigner expression. Second, no considerationhas been given to estimate or compute the activity coefficients. It is,however, a complex task to ascertain the dependency of the activitycoefficient of each species, which is dependent on the concentra-tion of that species as well as the concentration of other speciesin 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 productwells, and consideration of such an effect could be handled by thePolyrate [25] or similar programs that are available. Here, however,

3 hermo

tg

A

otUu

A

t

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

4 N. Kumbhakarna, S.T. Thynell / T

he number of atoms can be large and it appears unfeasible for ourroup to pursue such a computational approach.

cknowledgements

The authors acknowledge the support from the Air Force Officef Scientific Research under grant number FA9550-13-1-0004. Also,his material is based upon work supported by, or in part by, the. S. Army Research Laboratory and the U. S. Army Research Officender grant number W911NF-08-1-0124.

ppendix A. Supplementary data

Supplementary data associated with this article can be found, inhe online version, at http://dx.doi.org/10.1016/j.tca.2014.02.014.

eferences

[1] R.P. Singh, H. Gao, D.T. Meshri, J.M. Shreeve, Nitrogen-rich heterocycles, in:P. Day, X. Duan, T.J. Meyer, G. Parkin, H.W. Roesky, J.-P. Sauvage (Eds.),Structure and Bonding, vol. 125, Springer-Verlag, Berlin, Heidelberg, 2007,pp. 35–83.

[2] H. Gao, J.M. Shreeve, Azole-based energetic salts, Chem. Rev. 111 (11) (2011)7377–7436.

[3] B.C. Tappan, A.N. Ali, S.F. Son, T.B. Brill, Decomposition and ignition of thehigh-nitrogen compound triaminoguanidinium azotetrazolate (TAGzT), Pro-pell. Explos. Pyrot. 31 (3) (2006) 163–168.

[4] R.S. Damse, N.H. Naik, M. Ghosh, A.K. Sikder, Thermoanalytical screening ofnitrogen-rich compounds for ballistic requirements of gun propellant, J. Propul.Power 25 (1) (2009) 249–256.

[5] L. Paoloni, G. La Manna, G. Camilletti, Molecular and electronic structure ofthe salt of guanidine with 5-amino-tetrazole, J. Mol. Struct 20 (1) (1974)135–139.

[6] G.-H. Tao, Y. Guo, Y.-H. Joo, B. Twamley, J.M. Shreeve, Energetic nitrogen-richsalts and ionic liquids: 5-aminotetrazole (AT) as a weak acid, J. Mater. Chem 18(45) (2008) 5524–5530.

[7] J. Neutz, O. Grosshardt, S. Schäufele, H. Schuppler, W. Schweikert, Synthe-sis, characterization thermal behaviour of guanidinium-5-aminotetrazolate(GA) – a new nitrogen-rich compound, Propell. Explos. Pyrot. 28 (4) (2003)181–188.

[8] V.G. Kiselev, N.P. Gritsan, Theoretical study of the 5-aminotetrazole thermaldecomposition, J. Phys. Chem. A 113 (15) (2009) 3677–3684.

[9] K.W. Paul, M.M. Hurley, K.K. Irikura, Unimolecular decomposition of5-aminotetrazole and its tautomer 5-iminotetrazole: new insight from isopo-tential searching, J. Phys. Chem. A 113 (11) (2009) 2483–2490.

10] J.-G. Zhang, L.-N. Feng, S.-W. Zhang, T.-L. Zhang, H.-H. Zheng, The mechanismand kinetics of decomposition of 5-aminotetrazole, J. Mol. Mod. 14 (5) (2008)403–408.

11] N. Piekiel, M.R. Zachariah, Decomposition of aminotetrazole based energeticmaterials under high heating rate conditions, J. Phys. Chem. A 116 (6) (2012)1519–1526.

12] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman,G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato,X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada,M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda,O. Kitao, H. Nakai, T. Vreven, J.A. Montgomery Jr., J.E. Peralta, F. Ogliaro, M.Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Nor-mand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N.Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo,R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W.Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador,

J.J. Dannenberg, S. Dapprich, A.D. Daniels, Ö. Farkas, J.B. Foresman, J.V. Ortiz, J.Cioslowski, D.J. Fox, Gaussian 09, Revision D.01, Gaussian Inc., Wallingford, CT,2009.

13] M. Head-Gordon, J.A. Pople, M.J. Frisch, MP2 energy evaluation by direct meth-ods, Chem. Phys. Lett. 153 (6) (1988) 503–506.

[

[

chimica Acta 582 (2014) 25–34

14] J.A. Montgomery, M.J. Frisch, J.W. Ochterski, G.A. Petersson, A complete basisset model chemistry. VI. Use of density functional geometries and frequencies,J. Chem. Phys. 110 (6) (1999) 2822–2827.

15] Y. Zhao, D. Truhlar, The M06 suite of density functionals for main group thermo-chemistry, thermochemical kinetics, noncovalent interactions, excited states,and transition elements: two new functionals and systematic testing of fourM06-class functionals and 12 other functionals, Theor. Chem. Acc. 120 (1–3)(2008) 215–241.

16] R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-II. A Fortran Chemical KineticsPackage for the Analysis of Gas-Phase Chemical Kinetics, Report No. SAND89-8009, Sandia National Laboratories, 1989.

17] K. Fukui, The path of chemical reactions – the IRC approach, Accounts Chem.Res. 14 (12) (1981) 363–368.

18] H.P. Hratchian, H.B. Schlegel, Accurate reaction paths using a Hessian basedpredictor-corrector integrator, J. Chem. Phys. 120 (21) (2004) 9918–9924.

19] K.J. Laidler, M.C. King, Development of transition-state theory, J. Phys. Chem.87 (15) (1983) 2657–2664.

20] A. Fernandez-Ramos, J.A. Miller, S.J. Klippenstein, D.G. Truhlar, Modeling thekinetics of bimolecular reactions, Chem. Rev. 106 (11) (2006) 4518–4584.

21] P. Pechukas, Transition state theory, Ann. Rev. Phys. Chem. 32 (1) (1981)159–177.

22] P.R.P. Barreto, A.F.A. Vilela, R. Gargano, A simple program to determine thereaction rate and thermodynamic properties of reacting system, J. Mol. Struct.Theochem. 639 (2003) 167–176.

23] S. Raman, R.W. Ashcraft, M. Vial, M.L. Klasky, Oxidation of hydroxylamine bynitrous and nitric acids. Model development from first principle SCRF calcula-tions, J. Phys. Chem. A 109 (38) (2005) 8526–8536.

24] R.W. Ashcraft, S. Raman, W.H. Green, Ab initio aqueous thermochemistry:application to the oxidation of hydroxylamine in nitric acid solution, J. Phys.Chem. B 111 (41) (2007) 11968–11983.

25] J. Zheng, S. Zhang, B.J. Lynch, J.C. Corchado, Y.-Y. Chuang, P.L. Fast, W.-P. Hu, Y.-P. Liu, G.C. Lynch, K.A. Nguyen, C.F. Jackels, A. Fernandez Ramos, B.A. Ellingson,V.S. Melissas, J. Villà, I. Rossi, E.L. Coitino, J. Pu, T.V. Albu, R. Steckler, B.C. Garrett,A.D. Isaacson, D.G. Truhlar, POLYRATE – version 2008, University of Minnesota,Minneapolis, 2008.

26] J. Tomasi, B. Mennucci, E. Cances, The IEF version of the PCM solvation method:an overview of a new method addressed to study molecular solutes at the QMab initio level, J. Mol. Struct. 464 (1–3) (1999) 211–226.

27] C.J. Cramer, D.G. Truhlar, Implicit solvation models: equilibria, structure, spec-tra, and dynamics, Chem. Rev. 99 (8) (1999) 2161–2200.

28] K. Yang, Y.H. Park, S.G. Cho, H.W. Lee, C.K. Kim, H.-J. Koo, Theoretical studieson the formation mechanism and explosive performance of nitro-substituted1,3,5-triazines, J. Comp. Chem. 31 (13) (2010) 2483–2492.

29] W.-G. Liu, S. Wang, S. Dasgupta, S.T. Thynell, W.A. Goddard III, S. Zybin, R.A.Yetter, Experimental and quantum mechanics investigations of early reactionsof monomethylhydrazine with mixtures of NO2 and N2O4, Combust. Flame 160(5) (2013) 970–981.

30] Y.-C. Liau, V. Yang, Analysis of RDX monopropellant combustion with two-phase subsurface reactions, J. Propul. Power 11 (4) (1995) 729–739.

31] E.S. Kim, V. Yang, Combustion, Ignition of nitramine propellants: aspects ofmodeling, simulation, and analysis, in: R.W. Shaw, T.B. Brill, D.L. Thompson(Eds.), Overviews of Recent Research on Energetic Materials, Advanced Series inPhysical Chemistry, vol. 16, World Scientific Publishing Co. Pte. Ltd., Singapore,2005, p. 369.

32] J.F. Brennan, J.S. Shapiro, E.C. Watton, Evaporation of liquids: a kinetic approach,J. Chem. Educ. 51 (4) (1974) 276.

33] P.N. Brown, G.D. Byrne, A.C. Hindmarsh, VODE A variable coefficient ODE solver,SIAM J. Sci. Stat. Comput. 10 (1989) 1038–1051.

34] K.E. Brenan, S.L. Campbell, L.R. Petzold, Numerical Solution of Initial-ValueProblems in Differential-Algebraic Equations, Society for Industrial and AppliedMathematics, Philadelphia, USA, 1996, pp. 131.

35] R.S. Zhu, M.C. Lin, A computational study on the decomposition of NH4ClO4:comparison of the gas-phase and condensed-phase results, Chem. Phys. Lett.431 (2006) 272–277.

36] F. Lei-Ming, C. Xi-Ping, H. Ohfuji, T. Irifune, S. Guang-Ai, C. Bo, P. Shu-Ming,Formation of diamond powders from melamine under high pressure and hightemperature, Chinese Phys. C 37 (8) (2013) 088002.

37] L.D. Yao, F.Y. Li, J.X. Li, C.Q. Jin, R.C. Yu, Study of the products of melamine(C3N6H6) treated at high pressure and high temperature, Phys. Stat. Sol. A 202(14) (2005) 2679–2685.

38] K.J. Laidler, Chemical Kinetics, Harper & Row Publishers Inc., New York, USA,1987, pp. 189.