Assessment of two new nitrogen-rich tetrazine derivatives as high performance and safe energetic compounds

Abstract

This work introduces two novel nitrogen-rich derivatives of tetrazine, i.e. 1,2-bis(6-nitro-1,2,4,5-tetrazin-3-yl)diazene and 1,2-bis(6-nitro-1,2,4,5-tetrazin-3-yl)hydrazine, as high performance and safe energetic compounds. Reliable methods are used to study the physical, thermodynamic, sensitivity, detonation and combustion properties of these compounds, which include crystal density, condensed phase heat of formation, impact sensitivity, electric spark sensitivity, heat of detonation, detonation temperature, detonation of velocity, pressure detonation, specific impulse, melting point, brisance and power. The predicted properties are also compared with 2,4,6-trinitrotoluene (TNT) and 1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) as two well-known melt-castable and high performance explosives, respectively. It is shown that these compounds can be seen as interesting organic explosives with relatively high detonation velocity and pressure as well as low sensitivity, and can be used for important industrial applications. Since these new compounds have a relatively high crystal density and melting point as well as great combustion performance, they can also be considered as suitable energetic ingredients in solid propellants. Hydrophobic interactions of these compounds were also computed and compared using the B3PW91/6-31 g(d,p) level of theory as a method for quantum chemical calculations.

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1. Introduction

The prediction of physicochemical, sensitivity, combustion and detonation properties of energetic materials is one of great importance prior to their actual synthesis. An ideal energetic material must have high performance and thermal stability but low sensitivity to external stimuli. Velocity of detonation, detonation pressure, detonation temperature and heat of detonation are several important parameters for the assessment of the performance of high explosives. In addition, the specific impulse can be used as an important factor for the assessment of combustion performance of propellants. Among different types of energetic materials, nitrogen rich compounds are especially important because they are involved in various industries. For example, they are used as suitable ingredients in explosive formulations and low smoke propellant charges.^1–4 Due to the importance of studying new high-energy density materials (HEDMs) with high explosive performance and insensitivity, many efforts have been done to design and synthesize them over several decades. Thus, high-nitrogen compounds constitute a unique class of energetic materials because of their favourable insensitivity, good detonation performance, and environmental acceptability.^5–8

High-nitrogen compounds usually contain high positive heats of formation (HOFs), which can provide high heat of combustion⁹ and heat of detonation.¹⁰ For compounds containing high values of heats of combustion and detonation, it can be expected to have high combustion and detonation performance.^11,12 However, high-nitrogen compounds can store a large amount of energy, which can release upon combustion or detonation processes. Since high nitrogen compounds usually have high crystal density, they can also provide high values of detonation pressure and velocity.^13,14

Tetrazine based compounds are one of the famous category of high-nitrogen compounds. Many of their derivatives have been designed and synthesized in recent years.^15–24 3,3′-Azobis (6-amino-1,2,4,5-tetrazine) (DAAT) is one of the tetrazine derivatives, which has been synthezied by Kerth and co-worker.²⁵ Several tetrazines compounds with similar molecular structure have also been synthesized, which include N-oxides of 3,3′-azobis(6-amino-1,2,4,5-tetrazine),^25,26 5,5′-dinitro-3,3′-azo-1H-1,2,4-triazole (DNAT),²⁷ 3′-azobis(bis[6,6′-(4-bromo-3,5-dimethylpyrazol-l-yl)])-1,2,4,5-tetrazine and N,N′-bis-(1,2,4,5-tetrazine-3yl)-3,5(dimethylpyrazol)-hydrazine.⁶ Some theoretical efforts have been done to design new high nitrogen content energetic compounds or prediction of some properties of synthesized high nitrogen energetic materials through computational evaluation, which have been reviewed elsewhere.²⁸ Jaidann et al.²⁹ reported theoretical predictions of some properties of synthesized high-nitrogen compounds 3,6-diazido-1,2,4,5-tetrazine (DiAT), N-oxides of 3,3′-azo-bis(6-amino-1,2,4,5-tetrazine) (DAATO), 3,6-di(hydrazino)-1,2,4,5-tetrazine (DHT) and 3,3′-azo-bis(6-amino-1,2,4,5-tetrazine) (DAAT). Wei and co-worker have studied the heats of formation (HOFs) for a series of tetrazolo-[1,5-b]-1,2,4,5-tetrazine (TETZ) and 1,2,4-triazolo-[4,3-b]-1,2,4,5-tetrazine (TTZ) derivatives through using density functional theory.³⁰ Wilcox and co-authors have computed enthalpies of formation and standard state entropies for tetrazine, amino- and nitrotetrazines as well as four extended ditetrazines using the basic geometric structural features of the minimum energy states of the tetrazines.³¹

The purpose of the present work is to introduce two high performance derivatives of tetrazines, i.e. 1,2-bis(6-nitro-1,2,4,5-tetrazin-3-yl)diazene 1 and 1,2-bis(6-nitro-1,2,4,5-tetrazin-3-yl)hydrazine 2, which have similar molecular structures as DAAT (Fig. 1). Reliable methods are used to study various aspects of these compounds including crystal density, condensed phase heat of formation, impact sensitivity, electric spark sensitivity, heat of detonation, detonation temperature, velocity of detonation, detonation pressure, specific impulse, melting point, brisance and power. Density functional theory (DFT) calculations are also used to study their hydrophobia behavior, which are important properties for explosive users and chemical industries. 2,4,6-Trinitro toluene (TNT) and octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) are two well-known melt-castable and high performance explosives, respectively. Due to molecular structure of two new energetic compounds, they can be introduced as two novel high performance melt-castable explosives. Thus, the predicted results of two novel energetic compounds are also compared with TNT and HMX.

Fig. 1 Molecular structures of 1,2-bis(6-nitro-1,2,4,5-tetrazin-3-yl)diazene, 1,2-bis(6-nitro-1,2,4,5-tetrazin-3-yl)hydrazine, 3,3′-azobis(6-amino-1,2,4,5-tetrazine) (DAAT), 2,4,6-trintro toluene (TNT) and octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX).

2. Materials and method

Different physical, thermodynamic, combustion and detonation performance parameters were calculated for the compounds 1 and 2. Reliable correlations have been used to calculate the mentioned properties including crystal density, condensed phase heat of formation, heat of detonation, detonation temperature, velocity of detonation, detonation pressure, specific impulse, melting point, brisance and power detonation. Sensitivities of these new high performance energetic compounds with respect to impact and electric spark stimuli have also been calculated through suitable models. All these properties have been compared with corresponding experimental values of TNT and HMX, which were collected from different available open sources (Table 1).

Table 1 Comparison of various properties of the tetrazine derivatives 1 and 2 with corresponding experimental values of TNT and HMX

No.	Properties	1	2	TNT^a^,^b	HMX^a^,^b
a Experimental values of the listed properties for HMX and TNT were taken from the mentioned references.b The calculated values by corresponding correlations, where applicable, are given in parentheses.
1	Molecular formula	C4N12O4	C4H2N12O4	C7H5N3O6	C4H8N8O8
2	Crystal density (g cm^−3)	1.96	1.94	1.654 (ref. 67) (1.636)	1.89 (ref. 68)
3	Condensed phase heat of formation (kJ mol^−1)	785.42	473.20	63.2 (ref. 43) (56.0)	74.9 (ref. 47) (83.9)
4	Impact sensitivity (cm)	163	140	98 (ref. 69)	29 (ref. 69)
5	Spark sensitivity (J)	4.56	9.14	6.85 (ref. 70) (6.31)	2.89 (ref. 71)
6	Heat of detonation (kJ g^−1)	5.139	5.219	4.564 (ref. 43) (3.546)	6.197 (ref. 43)
7	Detonation temperature (K)	5894	5431	3410 (ref. 47) (3778)	3470 (ref. 47) (4406)
8	Velocity detonation (km s^−1)	10.0	9.7	7.2 (ref. 47) (7.22)	9.1 (ref. 47) (9.20)
9	Detonation pressure (kbar)	422	414	203 (ref. 47) (221)	374 (ref. 47) (378)
10	Specific impulse (N s g^−1)	2.716	2.508	2.102 (ref. 51) (2.196)	2.614 (ref. 51) (2.605)
11	Melting point (K)	516	510	355.1 (ref. 72) (348.6)	548 (ref. 72) (477.1)
12	BrisrelTNT	143	141	100 (ref. 73) (91)	125–155 (ref. 73) (144)
13	EP(%TNT)	140	140	100 (ref. 73) (107)	150 (ref. 73) (144)

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Computation of hydrophobia properties of 1 and 2 were done at B3PW91/6-31 g(d,p) level of theory using Gaussian-09 software package,³² which is one of the widely used density functionals for this purpose. The thermodynamic data and their changes upon complex formation were derived from statistical thermodynamics based on the frequencies.

3. Results and discussion

3.1 Crystal density

Crystal density of an energetic compound is an essential parameter for calculation of its detonation performance. However, the prediction of crystal density is of outmost importance for chemists who synthesize energetic materials. A suitable model has been introduced for evaluating the crystal density of nitroaromatic energetic compounds with general formula C_aH_bN_cO_d.³³ It is based on the core crystal density function (ρ₀) as:

ρ₀ = 10.57(a/M_w) + 0.1266(b/M_w) + 30.38(c/M_w) + 35.18(d/M_w) (1)

where ρ₀ is in g cm⁻³ and M_w is the molecular weight of desired nitroaromatic compound in g mol⁻¹. The value of ρ₀ can be revised for the presence of some functional groups or molecular fragments.³³ The predicted results are given in Table 1. As seen in eqn (1), the value of ρ₀ is generally increased by decreasing the molecular weight and increasing the number of nitrogen, oxygen, carbon and hydrogen atoms. Since the presence of double bond between two cycles can increase the value of crystal density, replacement of group () with group () has little effect in increasing the density. The density of 1 and 2 are more than the density of TNT because the number of nitrogen atoms and the ratio of nitrogen to carbon in tetrazine compounds are more than corresponding carbocyclic TNT. However, the densities of all of the compounds in Table 1 are as 1 > 2 > HMX > TNT.

3.2 Condensed phase heat of formation

The condensed phase heat of formation for an energetic compound is another important parameter for assessment of its combustion and detonation performance. It can be used to investigate its characteristics and chemical stability as well as the calculation of explosive and propellant properties such as detonation pressure, velocity, detonation temperature, heat of detonation and specific impulse through computer codes or empirical methods.^34–36 Eqn (2) introduces a reliable pathway for calculation of the condensed phase heat of formation of a C_aH_bN_cO_d nitroaromatic compound:³⁷

Δ_fH^θ(c) = Δ_fH^θ_EC + 105.0Δ_fH^θ_IEC − 106.6Δ_fH^θ_DEC (2)

where Δ_fH^θ(c) is the condensed phase heat of formation in kJ mol⁻¹; Δ_fH^θ_EC is the contribution of elemental composition in Δ_fH^θ(c), which is calculated as:

Δ_fH^θ_EC = 32.3a − 39.49b + 92.41c − 63.85d (3)

Δ_fH^θ_IEC and Δ_fH^θ_DEC are also increasing and decreasing energy content parameters of an energetic compound, respectively, which can be specified by the contribution of polar groups and some specific molecular fragments. The predicted results of 1 and 2 are given in Table 1.³⁷ As seen in eqn (2) and (3), increment of the number of carbon and nitrogen atoms as well as decreasing of the number of hydrogen and oxygen atoms can increase the value of Δ_fH^θ(c). Since the number of carbon, nitrogen and oxygen atoms for 1 and 2 are the same, the value of Δ_fH^θ(c) for 1 is significantly higher than 2 because the absence of hydrogen atom in later. The heat of formation of all compounds in Table 1 are as 1 > 2 > HMX > TNT. Since the trend of increasing of crystal density and Δ_fH^θ(c) are in the same direction, it will be shown that detonation velocity and pressure have the same trend.

3.3 Impact sensitivity

Impact sensitivity is one of the most commonly used measurements of many kinds of sensitivity, which can cause initiation of reaction of an energetic compound during many accidents accompanying with high pressure on sample.^38,39 The drop weight impact test is convenient and the most common method to assess sensitivity with respect to impact stimuli. This test typically involves dropping of a 2.5 kg mass from a predetermined height onto the striker plate. Impact drop height (h₅₀, cm) is the height from which a weight of 50% probability in causing an explosion (h₅₀) was measured when hit by a hammer with a standard weight. A suitable correlation has been used to predict impact sensitivity of tetrazine based energetic compounds with general formula C_aH_bN_cO_d as:⁴⁰

log h₅₀ = (46.29a/M_w) + (35.63b/M_w) − (7.701c/M_w) + (7.942d/M_w) + (44.42n_–CNC–/M_w) + (102.3n_–CNNC–/M_w) (4)

Where log h₅₀ is in cm; n_–CNC– and n_–CNNC– are the numbers of –CNC– and –CNNC– moieties in the molecule. The predicted impact sensitivities of 1 and 2 are given in Table 1. According to eqn (4), the impact sensitivities of 1 and 2 depend on their elemental composition and molecular weight as well as the number of –CNC– and –CNNC–. The impact sensitivity of 1 ismore than 2 because the number of –CNNC– for 1 is more than 2 and the molecular weight for 1 is less than 2. The impact sensitivities of all of the compounds given in Table 1 are as 1 > 2 > TNT > HMX. The calculated data confirm that the impact sensitivities of both 1 and 2 are high even though as compared to TNT with relatively high safety.

3.4 Electric spark sensitivity

The electric spark or electrostatic sensitivity (E_ES) of an energetic compound can be defined as the degree of sensitivity to the electrostatic discharge, which can be determined by subjecting the explosive to a high-voltage discharge from a capacitor. It is an important quantity that can be determined by the electrostatic discharge energy required for 50% probability of initiation.⁴¹ For prediction of sensitivity compounds 1 and 2 with respect to electric spark stimuli, the following correlation was used:⁴²

E_ES = 4.60 − 0.733a + 0.724d + 9.16b/a − 5.14C_R,OR (5)

where E_ES is in J; C_R,OR is 1.0 for the presence of certain groups such as alkyl (–R) or alkoxy (–OR) groups attached to an aromatic ring.⁴² The compounds 1 and 2 have the same number of carbon and oxygen as well as there is no hydrogen atom in 1. The predicted E_ES of all of the compounds given in Table 1 are as 2 > TNT > 1 > HMX. In contrast to impact sensitivity, the value E_ES of the compound 1 is lower than TNT. However, more cautions should be considered for using 1 where initiation of decomposition of energetic material by electric spark is more probable.

3.5 Heat of detonation

Heat of detonation (Q_det) is one of the important detonation parameters that can be used as the energy available to do mechanical work and estimating potential damage to surroundings.^43,44 Though it may be measured experimentally or calculated from different theoretical approaches, theoretical calculations are useful in comparing the relative heat releasing of one explosive with respect to another. Moreover, it can also be used to assess detonation pressure and velocity of explosives via assumed different decomposition pathways.^44,45 Predicting fairly simple and accurate heats of detonation, by simple empirical methods, are desired to evaluate the performance of energetic compounds. Suitable method was used to estimate the heats of detonation of 1 and 2 as:⁴⁶

Q_det = 2.129 + 0.178c + 0.874d/a + 0.160b/d + 0.965C_SFG (6)

where Q_det is in kJ g⁻¹; C_SFG is the contribution of some specific functional groups in aromatic. The value of C_SFG equals −1.0 for aromatic energetic compounds that have some specific functional groups, namely –COOH, NH₄⁺, two –OH (or one –OH with one –NH₂) and three –NH₂.⁴⁶ The calculated values of Q_det for 1 and 2 are given in Table 1 and compared with the measured values of TNT and HMX. As seen in Table 1, the heat of detonation of 2 is close to 1 and higher than TNT. However, the values of four compounds in Table 1 are as HMX > 2 ≈ 1 > TNT.

3.6 Detonation temperature

Detonation temperature (T_det) is measured experimentally from the brightness of the detonation front as it proceeds towards the detector.⁴⁷ Since it is not known how much radiation is absorbed from detonation products by the shocked and partially decomposed explosive between the detector and the end of the reaction zone, accurate determination of T_det is difficult. A reliable model has been recently introduced for its prediction, which gives good results as compared to one of the best available equations of state, i.e. BKWC-EOS,⁴⁸ as:

T_det = 5136 − 190.1a − 56.4b + 115.9c + 148.4d − 466d/a − 700.8b/d − 282.9n_NHx (7)

where T_det is in K; n_NHx is the number of –NH₂ and NH₄⁺ in an C_aH_bN_cO_d energetic compound.⁴⁹ Since the number of carbon, oxygen and nitrogen atoms for two compounds are the same, negative contributions of the number of hydrogen atoms and the ratio of hydrogen to oxygen atoms can decrease detonation temperature of 2 as compared to 1. Moreover, both compounds 1 and 2 have lower hydrogen and higher nitrogen atoms in their molecular formula than HMX and TNT, which can provide higher detonation temperatures for the new compounds on the basis of eqn (7). Thus, detonation temperature of all compounds can be arranged as 1 > 2 > HMX > TNT.

3.7 Velocity and pressure of detonation

Detonation velocity and pressure are two important detonation performance parameters, which can be used for measuring the effectiveness of different explosives. Detonation velocity can typically be measured to within a few percent at various charge diameters and extrapolated to an infinite diameter for comparison with steady state calculation. Both detonation pressure and velocity of detonation depend strongly on crystal density of an explosive. Thus, these properties can be enhanced by increasing the value of the loading density.^34,50 They can be calculated by some computer codes such as BKW⁵¹ an RUBY⁵² and latter's offspring TIGER,⁵³ CHEQ⁵⁴ and CHEETAH⁴⁸ with an appropriate empirical equation of state such as Becker–Kistiakosky–Wilson (BKWEOS),⁵⁵ the Jacobs–Cowperth waite–Zwisler (JCZ-EOS)^56,57 and Kihara–Hikita–Tanaka (KHT-EOS).⁵⁸ Among different empirical methods for calculation of detonation velocity,⁵⁹ the following correlation is good because there is no need to use the condensed phase heat of formation of a C_aH_bN_cO_d explosive:⁶⁰

D = 1.64 + 3.59ρ₀ − 0.133a − 0.0034b + 0.121c + 0.0442d − 0.277n_–NRR′ (8)

where D is detonation velocity in km s⁻¹; ρ₀ is the loading density in g cm⁻³; and n_–NRR′ is the number of specific groups in the explosive in form –NH₂, NH₄⁺ or groups.⁶⁰ For calculation of detonation pressure, similar correlation of the following form was used:⁶¹

P = −22.32 + 104.04ρ₀² − 10.98a − 1.997b + 5.562c + 5.539d − 23.68n_–NHx − 154.1n⁰₁ (9)

where P is detonation pressure in kbar; n_–NHx is the number of –NH₂ or NH₄⁺ in the energetic compound; n⁰₁ has the value one for an energetic compound that follows condition d > 3(a + b) and for the other situations has zero value.⁶¹ The calculated detonation velocity and pressure are also given Table 1, which are 1 > 2 > HMX > TNT.

3.8 Specific impulse

Specific impulse (I_sp) is a parameter to identify the energy efficiency of propellant combustion. It gives the effective time to generate thrust and sustain the propellant mass against the gravitational force through energy conversion,⁶² which can be defined as the integral of thrust, the recoil force, per unit weight of material over the time of combustion.⁶³ Some complicated computer codes are usually used to estimate the specific impulse, considering various equilibrium reactions as well as thermodynamic calculations of decomposition reactions.⁶⁴ The same computer codes are usually used to differentiate between propellants because comparison of the specific impulse calculations from different computer codes may not be useful.¹¹ For C_aH_bN_cO_d nitroarmatics, a suitable correlation of the following form has been recently introduced to predict specific impulse of an explosive when it is considered as monopropellant:¹¹

I_sp = 2.425 − 0.074a − 0.0036b + 0.0237c + 0.04d − 0.1001n_NHx − 0.1466(n_Ar − 1) (10)

where is I_sp in N s g⁻¹; n_NHx is the number of –NH₂ or –NH groups, and n_Ar is the number of aromatic rings in an aromatic explosive. The specific impulse of three energetic compounds 1, 2 and HMX are given in Table 1, which are close to each other and much higher than TNT.

3.9 Melting point

Melting point is one the fundamental physical properties for using in chemical identification, purification, and calculation of the other important physicochemical properties such as vapour pressure and aqueous solubility. Group contribution methods can be used to estimate the physical and thermodynamic properties of a pure energetic compound.⁶⁵ For calculation of melting points of 1 and 2, a new correlation of the following form was used:⁶⁶

T_m = 326.9 + 5.524T_add + 101.2T_non-add (11)

where T_m is melting point in K; T_add is additive part of melting point, which is based on a suitable combination of elemental composition; T_non-add is also non-additive part of melting point. T_add and T_non-add for an energetic compound is given as:

T_add = a − 0.5049b + 2.643c − 0.3838d (12)

T_non-add = T_PC − 0.6728T_NC (13)

where T_PC and T_NC are two variables, which can be obtained on the basis of molecular structures of pure energetic compounds. The predicted melting points of 1 and 2 are given in Table 1 that are close to each other. The positive and negative contributions of structural parameters in T_non-add are denoted as T_PC and T_NC, respectively. For the presence of some specific polar groups and structural moieties, the contribution of T_PC should be considered. The number of alkyl and alkoxy groups is used to estimate T_NC for nitroaromatic compounds. Since there is no contribution for T_PC and T_NC in compounds 1 and 2, the values of T_PC and T_NC are equal to zero for these compounds.

3.10 Brisance of an energetic material

Brisance is defined as the ability of an explosive to wreck a solid object in direct contact or in vicinity of the detonation wave impact. Very high pressure is created upon detonation of an explosive in its shock wave, which can shatter rather than displace any object in its path. Meanwhile, subsequent expansion of gases performs volume work. Since it is essentially the shattering power of an explosive, it is different from the total work capacity of explosives. However, the time with which the explosive reaches its peak pressure can be used to measure its brisance. Some works have been done to express the relationship between detonation velocity or detonation pressure and brisance.⁷³ Several test methods have been used for the determination of the brisance of energetic materials, which include lead block compression test, copper cylinder test, Quinan test and Hopkinson pressure bar method.⁷⁴ A new suitable correlation has been introduced recently for prediction of brisance of an energetic compound, which has the following form:⁷⁵

Bris_relTNT = 85.5 + Bris_corr − 35.98Bris⁻ + 19.69Bris⁺ (14)

where Bris_relTNT is the relative brisance with respect to TNT; Bris⁺ and Bris⁻ are correcting positive and negative functions for those values obtained on the basis of Bris_core; Bris_core is the core brisance, which is based on the number of nitrogen atoms and the distribution of oxygen atoms between carbon and hydrogen atoms as:

Bris_core = 4.812c + 2.556(d − a − b/2) (15)

The predicted brisance for compounds 1 and 2 are given in Table 1. As seen, brisance of all of the compounds are as 1 > 2 > HMX > TNT.

3.11 Power detonation

The power of an explosive is a measure of its ability to do useful work. It is the sum of all forms of the mechanical work during detonation process, which can be determined directly from field measurements but laboratory methods would be preferred. It is normally related to the performance of a standard explosive such as TNT. A suitable correlation of the following form was used to predict the power of new compounds relative to TNT:⁷⁶

EP(%TNT) = 113 − 5.16CEC − 46.18OCF (16)

where EP(%TNT) is explosive power related to TNT as a standard 100; CEC and OCF are the contribution of elemental composition to explosive power and overestimated correcting function, respectively.⁷⁷ The predicted power for compounds 1 and 2 are given in Table 1. As seen the predicted values of EP(%TNT) for 1 and 2 are close to experimental values of HMX.

3.12 Hydrophobia

It is important to study interactions of 1 and 2 with water. Fig. 2 shows the optimized geometries of 1 and 2 with water at the B3PW91/6-31 g(d,p) level of theory. Table 2 has summarized the optimized geometry compounds of the two types of complexes. According to the intermolecular distances and the change in bond length, the hydrogen bonding length of complex 2 in the state 2 is shorter than other states, so the state 2 of complex 2 is more hydrophilic than other states.

Fig. 2 Optimized structures of 1/H₂O and 2/H₂O.

Table 2 Optimized bond lengths for 1 and 2 with H₂O (Å)

Bond	Compound 1		Bond	Compound 2
	State 1	State 2		State 1	State 2
1C–2N	1.41418	1.41469	1C–19N	1.33721	1.33383
2N–3N	1.24857	1.24870	19N–20H	1.01477	1.04988
3N–4C	1.41271	1.40881	19N–21N	1.37187	1.37016
4C–10N	1.34059	1.34118	21N–22H	1.01400	1.01458
10N–11N	1.31422	1.31276	21N–10C	1.34121	1.34216
11N–20C	1.32768	1.32913	10C–12N	1.35772	1.35970
20C–12N	1.32689	1.32556	12N–13N	1.30056	1.30039
12N–9N	1.31421	1.31450	13N–11C	1.33683	1.33572
9N–4C	1.34328	1.34453	11C–14N	1.32385	1.32431
20C–13N	1.48059	1.48111	14N–15N	1.31044	1.31058
13N–14O	1.21711	1.21699	15N–10C	1.35133	1.35308
13N–15O	1.21648	1.21619	11C–16N	1.47928	1.47851
1C–8N	1.34005	1.33678	16N–17O	1.21808	1.21884
8N–5N	1.31152	1.31620	16N–18O	1.21816	1.21860
5N–19C	1.32699	1.32545	1C–4N	1.36015	1.36580
19C–6N	1.32507	1.32892	4N–3N	1.29889	1.29866
6N–7N	1.31270	1.31172	3N–9C	1.33709	1.33602
19C–16N	1.47616	1.48096	9C–2N	1.32414	1.32581
16N–17O	1.22139	1.21654	2N–5N	1.30837	1.30693
16N–18O	1.21489	1.21720	5N–1C	1.35437	1.35795
17O–22H(H2O)	2.43145	—	6N–8O	1.21874	1.21935
2N–22H(H2O)	—	2.53230	6N–7O	1.22110	1.21839
			7O–24H(H2O)	2.27184	—
			20H–23O(H2O)	—	1.67306

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4. Conclusions

The properties of two new tetrazines derivatives 1 and 2 as high nitrogen explosives were evaluated and compared with corresponding experimental values of TNT and HMX. It was shown that both of them have relatively high performance, low sensitivity and good thermochemical properties. The results of this work can help designing or developing ideal energetics. The compound 1 has higher crystal density, condensed phase heat of formation, detonation temperature, velocity of detonation, detonation pressure and specific impulse than the compound 2, HMX and TNT. Thus, the compound 1 can be introduced as novel explosive with high detonation and combustion performance. Although impact sensitivity of 1 is high but its sensitivity with respect to external electric spark is lower than TNT, which shows that some cautions should be considered for synthesis and applications of 1 to prevent decomposition of 1 in the presence of this stimuli. The values of melting point, Bris_relTNT and EP(%TNT) of 1 are close to 2 and HMX as well as much higher than TNT. The bond length of complex 2 in the state 2 for tetrzines is shorter than other states, which confirms it has higher hydrophilic characteristics than other states. According to the reported results in this research, the suggested tetrazine derivatives can be introduced as high performance safe explosives with respect to well-known HMX.

Acknowledgements

We would like to thank the research committee of Malek-ashtar University of Technology (MUT) for supporting this work as well as Dr Mehdi Zamani and Mr Ahmad Zamani.

References

1. P. F. Pagoria, G. S. Lee, A. R. Mitchell and R. D. Schmidt, Thermochim. Acta, 2002, 384, 187–204.
2. V. E. Zarko, Combust., Explos. Shock Waves (Engl. Transl.), 2010, 46, 121–131.
3. Y.-H. Joo and J. N. M. Shreeve, Angew. Chem., Int. Ed., 2010, 49, 7320–7323.
4. M.-H. V. Huynh, M. A. Hiskey, E. L. Hartline, D. P. Montoya and R. Gilardi, Angew. Chem., Int. Ed., 2004, 43, 4924–4928.
5. D. E. Chavez, M. A. Hiskey and R. D. Gilardi, Angew. Chem., 2000, 112, 1861–1863.
6. M. B. Talawar, R. Sivabalan, N. Senthilkumar, G. Prabhu and S. N. Asthana, J. Hazard. Mater., 2004, 113, 11–25.
7. D. Badgujar, M. Talawar, S. Asthana and P. Mahulikar, J. Hazard. Mater., 2008, 151, 289–305.
8. A. Vij, W. W. Wilson, V. Vij, F. S. Tham, J. A. Sheehy and K. O. Christe, J. Am. Chem. Soc., 2001, 123, 6308–6313.
9. M. H. Keshavarz, B. E. Saatluo and A. Hassanzadeh, J. Hazard. Mater., 2011, 185, 1086–1106.
10. M. H. Keshavarz, Thermochim. Acta, 2005, 428, 95–99.
11. M. H. Keshavarz, Propellants, Explos., Pyrotech., 2008, 33, 360–364.
12. M. H. Keshavarz, J. Hazard. Mater., 2009, 166, 1296–1301.
13. M. H. Keshavarz and A. Zamani, Cent. Eur. J. Energ. Mater., 2015, 12, 13–33.
14. M. H. Keshavarz, A. Zamani and M. Shafiee, Propellants, Explos., Pyrotech., 2014, 39, 749–754.
15. T. M. Klapötke and C. M. Sabaté, Chem. Mater., 2008, 20, 3629–3637.
16. P. F. Pagoria, G. S. Lee, A. R. Mitchell and R. D. Schmidt, Thermochim. Acta, 2002, 384, 187–204.
17. T. Wei, W. Zhu, X. Zhang, Y.-F. Li and H. Xiao, J. Phys. Chem. A, 2009, 113, 9404–9412.
18. H. Wei, H. Gao and J. N. M. Shreeve, Chem.–Eur. J., 2014, 20, 16943–16952.
19. P. He, J.-G. Zhang, K. Wang, X. Yin and T.-L. Zhang, J. Org. Chem., 2015, 80, 5643–5651.
20. S. Deswal, V. D. Ghule, T. R. Kumar and S. Radhakrishnan, Comput. Theor. Chem., 2015, 1054, 55–62.
21. B. Tan, M. Huang, H. Huang, X. Long, J. Li, F. Nie and J. Huang, Propellants, Explos., Pyrotech., 2013, 38, 372–378.
22. T. Wei, J. Wu, W. Zhu, C. Zhang and H. Xiao, J. Mol. Model., 2012, 18, 3467–3479.
23. Q. Wu, W. Zhu and H. Xiao, J. Chem. Eng. Data, 2013, 58, 2748–2762.
24. T. M. Klapötke and T. G. Witkowski, Propellants, Explos., Pyrotech., 2015, 40, 366–373.
25. J. Kerth and S. Lobbecke, Propellants, Explos., Pyrotech., 2002, 27, 111–118.
26. M. B. Talawar, R. Sivabalan, N. Senthilkumar, G. Prabhu and S. N. Asthana, J. Hazard. Mater., 2004, A113, 11–25.
27. D. L. Naud, M. A. Hiskey and H. H. Harry, Energ. Mater., 2003, 21, 57–62.
28. B. M. Rice, E. F. Byrd and W. D. Mattson, in High Energy Density Materials, Springer, 2007, pp. 153–194.
29. M. Jaidann, S. Roy, H. Abou-Rachid and L.-S. Lussier, J. Hazard. Mater., 2010, 176, 165–173.
30. T. Wei, W. Zhu, J. Zhang and H. Xiao, J. Hazard. Mater., 2010, 179, 581–590.
31. C. F. Wilcox, Y.-X. Zhang and S. Bauer, J. Energ. Mater., 2002, 20, 71–92.
32. M. Frisch, G. Trucks, H. Schlegel, G. Scuseria, M. Robb, J. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. Knox, H. Hratchian, J. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. Stratmann, O. Yazyev, A. Austin, R. Cammi, C. Pomelli, J. Ochterski, P. Ayala, K. Morokuma, G. Voth, P. Salvador, J. Dannenberg, V. Zakrzewski, S. Dapprich, A. Daniels, M. Strain, O. Farkas, D. Malick, A. Rabuck, K. Raghavachari, J. Foresman, J. Ortiz, Q. Cui, A. Baboul, S. Clifford, J. Cioslowski, B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Martin, D. Fox, T. Keith, M. Al-Laham, C. Peng, A. Nanayakkara, M. Challacombe, P. Gill, B. Johnson, W. Chen, M. Wong, C. Gonzalez and J. Pople, Gaussian 09 (revision A. 02), Gaussian, Inc., Wallingford, 2009.
33. M. H. Keshavarz, J. Hazard. Mater., 2007, 145, 263–269.
34. J. P. Agrawal, High energy materials: propellants, explosives and pyrotechnics, John Wiley & Sons, 2010.
35. A. K. Sikder, G. Maddala, J. P. Agrawal and H. Singh, J. Hazard. Mater., 2001, 84, 1–26.
36. M. H. Keshavarz, H. Motamedoshariati, R. Moghayadnia, H. R. Nazari and J. Azarniamehraban, J. Hazard. Mater., 2009, 172, 1218–1228.
37. M. H. Keshavarz, J. Hazard. Mater., 2011, 190, 330–344.
38. C. Storm, J. Stine and J. Kramer, Chemistry and Physics of Energetic Materials, Kluwer, Dordrecht, The Netherlands, 1990.
39. M. H. Keshavarz, Propellants, Explos., Pyrotech., 2013, 38, 754–760.
40. M. H. Keshavarz, H. R. Pouretedal and A. Semnani, J. Hazard. Mater., 2007, 141, 803–807.
41. S. Zeman, J. Hazard. Mater., 2006, 132, 155–164.
42. M. H. Keshavarz, J. Hazard. Mater., 2008, 153, 201–206.
43. B. M. Rice and J. Hare, Thermochim. Acta, 2002, 384, 377–391.
44. M. J. Kamlet and S. Jacobs, J. Chem. Phys., 1968, 48, 23–35.
45. M. H. Keshavarz and H. R. Pouretedal, Thermochim. Acta, 2004, 414, 203–208.
46. M. H. Keshavarz, J. Hazard. Mater., 2007, 143, 549–554.
47. M. Hobbs and M. Baer, presented in part at the Proc. of the 10th Symp. (International) on Detonation, ONR, 1993.
48. L. E. Fried, W. M. Howard and P. C. Souers, CHEETAH 2.0 User's Manual, Livermore, CA, 1998.
49. M. H. Keshavarz, J. Hazard. Mater., 2006, 137, 1303–1308.
50. T. M. Klapötke, Chemistry of high-energy materials, Walter de Gruyter, 2012.
51. C. L. Mader, Numerical Modeling of Explosives and Propellants, CRC Press, 2nd edn, 1998.
52. H. B. Levine and R. E. Sharples, Operator's Manual for RUBY, University of California Lawrence Radiation Laboratory, 1962.
53. W. H. Z. M. Cowperthwaite, TIGER Computer Program Documentation, Stanford Research Institute, 1973.
54. A. Nichols and F. Ree, CHEQ 2.0 User's manual, UCRL-MA-106754, Lawrence Livermore National Laboratory, Livermore, CA, 1990.
55. C. L. Mader, Detonation properties of condensed explosives computed using the Becker-Kistiakowsky-Wilson equation of state, Los Alamos Scientific Lab., N. Mex., 1963.
56. S. J. Jacobs, Proceedings of the 12th International Symposium on Combustion, Combustion Institute, Pittsburgh, PA, 1969, p. 502.
57. W. H. Z. M. Cowperthwaite, Proceedings of the 6th International Symposium on Detonation, Office of the Chief of Naval Operations, Coronado, CA, Washington, DC, 1976, p. 167.
58. K. Tanaka, Office of the Chief of Naval Operations, Washington, DC, New Mexico, 1985, p. 548.
59. M. Keshavarz, Explosive Materials: Classification, Composition and Properties, Nova Science Publishers, Inc, 2011.
60. M. H. Keshavarz, R. T. Mofrad, R. F. Alamdari, M. H. Moghadas, A. R. Mostofizadeh and H. Sadeghi, J. Hazard. Mater., 2006, 137, 1328–1332.
61. M. H. Keshavarz, J. Hazard. Mater., 2007, 147, 826–831.
62. N. Kubota, Thermochemical Aspects of Combustion, 2002.
63. D. M. R. G. P. Sutton, Rocket Propulsion Elements, New York, 5th edn, 1976.
64. C. L. Mader, CRC Press, Florida, 2nd edn, 1998.
65. W. Qiang, M. Peisheng and N. Shifeng, Chin. J. Chem. Eng., 2009, 17, 468–472.
66. M. H. Keshavarz, F. Gharagheizi and H. R. Pouretedal, Fluid Phase Equilib., 2011, 308, 114–128.
67. C. M. Tarver, J. Chem. Eng. Data, 1979, 24, 136–145.
68. R. Meyer, J. Köhler and A. Homburg, Explosives, John Wiley & Sons, 2008.
69. B. M. Rice and J. J. Hare, J. Phys. Chem. A, 2002, 106, 1770–1783.
70. S. Zeman, Thermochim. Acta, 1980, 41, 199–212.
71. S. Zeman and J. Kočí, Hanneng Cailiao, 2000, 8, 18–26.
72. P. J. Linstrom and W. Mallard, NIST Standard Reference Data Base Number 69, which can be accessed electronically through the NIST Chemistry Web Book, http://webbook.nist.gov/chemistry/, references for individual molecules are given therein.
73. O. E. S. B. T. Fedoroff, G. D. Clift and E. F. Reese, PATR 2700, Picatinny Arsenal, Dover, 1962, vol. 2.
74. O. E. S. B. T. Fedoroff, G. D. Clift and E. F. Reese, PATR 2700, Picatinny Arsenal, Dover, NJ, 1962, p. 2.
75. M. H. Keshavarz, F. Seif and H. Soury, Propellants, Explos., Pyrotech., 2014, 39, 284–288.
76. M. H. Keshavarz and F. Seif, Propellants, Explos., Pyrotech., 2013, 38, 709–714.
77. A. N. Afanasenkov, Combust., Explos. Shock Waves (Engl. Transl.), 2004, 119–125.

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