English

• 1. INTRODUCTION

  The design of new energetic materials, encompassing propellants, explosives, and pyrotechnics is a long-standing tradition in chemical science. Current interest has been focused on the development of high-energy-density materials (HEDMs) with higher performance and/or decreased sensitivity to thermal shock and friction^{[1, 2]}. However, the requirements of insensitivity and high-energy-density are quite often contradictory to each other, making the development of new HEDMs a difficult and challenging problem. In the pursuit of new energetic materials, some small ring compounds have attracted considerable attention. The typical compounds have fascinating characteristics including large strain energy, high heats of formation, and so on^{[3, 4]}.

  A three-membered ring is the smallest unit in all ring-compounds. To our knowledge, some three-membered ring compounds have been studied widely. For example, the diazocyclopropanes and aminonitroacetylene were studied at high-level calculation by DW Ball^{[5, 6]}, and the frequency and thermodynamic property were analyzed by quantum chemistry. The result shows that many derivatives of cyclopropane have good stability and excellent energy density. In addition, Inagali also reported on the potential application of two oxadiaziridine isomers as HEDMs^[7]. They determined an energetic character using QCISD/6-31G(d) and Gaussian-3 technologies. Otherwise, the structure and properties of triaziridine have been studied by using different calculation methods^[8], and detonation performance and thermodynamics stability of its nitro derivatives were also calculated at the B3LYP/6-311G** and MP2/6-311G** levels^[9]. Up to now, many three-membered ring compounds have become the candidates of high-energy-density materials. Summarizing a large amount of literatures, oxirane promoted us for its excellent potential as the parent body of high-energy-density compounds. It can be prepared via ethylene with air oxidation and the silver catalytic in industry. Moreover, its derivatives (such as glycidyl nitrate and nitro oxirane) have been theoretically studied in detail^{[10, 11]}.

  On considering the obvious improvement of energetic density, azide group is introduced into oxirane skeleton to design novel high-energy-density compounds. Furthermore, the stability and detonation performance are studied in the quantum chemistry framework at the CCSD(T)/cc-PVDZ// MP2/cc-PVDZ level.

  2. COMPUTATIONAL METHOD

  All geometries were optimized at the Gaussian03 software package^[12] on a desktop computer. The calculation method was performed using second-order Moller-Plesses perturbation theory (MP2) along with the standard Gaussian basis set labeled cc-PVDZ. The single point energies of all compounds were calculated at the CCSD(T)/cc-PVDZ level. The heat of formation (HOF) is a necessary performance for calculating detonation performances. In this work, HOF can be obtained according to isodesmic reactions^[13]:

  $ {{\text{C}}_2}{\text{O}}{{\text{H}}_{{\text{4}} - n}}{{\text{(}}{{\text{N}}_3}{\text{)}}_n} + n{\text{C}}{{\text{H}}_4} = {{\text{C}}_2}{{\text{H}}_4}{\text{O}} + n{\text{C}}{{\text{H}}_3}{{\text{N}}_3} $

  (1)

  For isodesmic reaction (1), the heat of reaction ΔH₂₉₈ at 298 K can be calculated from the following equation (2):

  $ \Delta {H_{298}} = \Delta {H_{f, p}} - \Delta {H_{f, R}} $

  (2)

  Where $\Delta {H_{f, p}}$ and $\Delta {H_{f, R}}$ are the HOF of the reactants and products at 298 K, respectively. Therefore, the HOFs of the title compounds can be determined when the heat of reaction is known. Now, we need obtain $\Delta {H_{298}}$ firstly, which can be calculated using the following expression (3):

  $ \Delta H_{298}^{} = \Delta E + \Delta ZPE + \Delta {H_T} + \Delta nRT $

  (3)

  ΔE is the change in total energy between the reactants and products at 0 K. ΔZPE is the difference between the zeropoint energy of reactants and products. The ΔH_T is the thermal correction from 0 to 298 K, and ΔnRT is the work term, which equals zero here.

  The HOF in solid state $\Delta {H_f}(s)$ can then be estimated using equation (4):

  $ \Delta {H_f}(s) = \Delta {H_f}(g) - \Delta {H_{sub}} $

  (4)

  Where $\Delta {H_{sub}}$ is the sublimation enthalpy evaluated using equation (5) suggested by Rice and Politzer et al.

  $ \Delta {H_{sub}} = {\alpha _1}{(SA)^2} + {\beta _1}{(\upsilon {\sigma _{tot}}^2)^{0.5}} + {\lambda _1} $

  (5)

  Where SA is the area of the isosurface of 0.001 e·Bohr^-3 electron density of a molecule. The values of coefficients α₁, β₁ and λ₁ are taken from Ref.^[14].

  The bond dissociation energy (BDE) of the trigger bond is often a key factor in investigating the stability and pyrolysis mechanism for energetic compounds^[15]. The expressions for the homolysis of the A–B bond and for calculating its BDE are shown as follows:

  $ {\text{A}} - {\text{B(}}g{\text{)}} \to {\text{A(}}g{\text{)}} + {\text{B(}}g{\text{)}} $

  (6)

  $ BD{E_{({\text{A}} - {\text{B}})}} = \left[ {{E_{{\text{A}} \bullet }} + {E_{{\text{B}} \bullet }}} \right] - {E_{({\text{A}} - {\text{B}})}} $

  (7)

  The bond dissociation energy with zero-point energy (ZPE) correction can be calculated by equation (8):

  $ BD{E_{({\text{A}} - {\text{B}})}}_{ZPE} = \left[ {{E_{{\text{A}} \bullet }} + {E_{{\text{B}} \bullet }}} \right] - {E_{({\text{A}} - {\text{B}})}} + \Delta ZPE $

  (8)

  BDE_(A−B) is the BDE of the A−B bond; E_(A−B), ${E_{{\text{A}} \bullet }}$ and ${E_{{\text{B}} \bullet }}$ are the total energies of parent molecule and the corresponding radicals, respectively.

  The characteristic height (H₅₀) that can also reflect the impact sensitivity and stability of compounds was estimated using equation (9) suggested by Pospıil et al^[16]:

  $ {H_{50}} = {\alpha _2}{\sigma _ + }^2 + {\beta _2}\gamma + {\lambda _2} $

  (9)

  The azide-substituted derivatives are extensively applied in the field of rocket propellant, and more gas molecules produced in the detonation reactions, more propulsive force obtained. So, the specific impulse (I_s) is frequently-used to evaluate the potential as a propellant. In theory, the specific impulse can be expressed in terms of the absolute temperature in the combustion chamber T_c and the number of moles of gaseous produced per unit weight of explosive N (N = n/M, where n is the number of moles of gaseous produced by 1 molar explosive and M is the molecular weight of explosive) by the simplified relationship given as equation (10):

  $ {I_s}\sim {T_c}^{1/2}{N^{1/2}} $

  (10)

  In equation (10), T_c can be given according to eq (11).

  $ - \Delta {H_{comb}} = {C_{p, gases}}({T_C} - {T_0}) $

  (11)

  Where ΔH_comb is the enthalpy of combustion, C_{p, gases} represents the total heat capacity of the gaseous product, and T₀ and T_c are the initial and combustion temperature, respectively. In equation (11), ΔH_comb can be calculated from the heats of formation of the explosive compound and the gaseous products as follows:

  $ \Delta {H_{comb}} = \sum\limits_{products} {{N_{\text{i}}}} \Delta {H_{f, i}} - {N_{HEDC}}\Delta {H_{f, HEDC}} $

  (12)

  3. RESULTS AND DISCUSSION

  3.1 Heats of formation

  Title molecules are optimized and the final structures are shown in Fig. 1. Heat of formation is one of the thermochemical properties of energetic materials because it is related directly with detonation parameters. In addition, HOF is usually also taken as the indicator of "energy content" of a high-energy-density compound. Therefore, it is necessary that accurate HOF values are calculated. In this section, we design isodesmic reactions in which the numbers of all kinds of bonds remain invariable to decrease the calculation errors of HOF. Because the electronic circumstances of reactants and products are very similar in isodesmic reactions, the errors of electronic correction energies can be counteracted. Then the errors of the calculated HOF can be greatly reduced^{[17, 18]}.

  Figure 1

  

  Figure 1.  Optimized structures of azide-oxirane in this paper

  DownLoad: Full-Size Img PowerPoint

  Table 1 lists the calculated data of azide-oxirane. Inspecting the values in Table 1, it is found that all azide-oxiranes have high and positive HOFs, which is popular characteristic as HEDMs. HOFs (ΔH_(g)) in gas state are bigger than HOFs (ΔH_(s)) in solid state. There is a good liner relationship between the HOF values and the numbers (n) of azide group: HOF = 146.4n – 9.705 (R² = 0.99, n = 1~4), which shows an increase of 146 kJ∙mol^-1 for each azide group on the oxirane ring, and azide group can play an important role in increasing HOF. We also should notice that the HOFs are affected by the position of azide group for isomeride. For example, the distance between two azide groups associated to the same C atom of B₂ is closer than that of B₁, resulting in larger HOF of B₂ than that of B₁.

  Table 1

  

  Table 1.  Sublimation Enthalpy (ΔH_sub), Heat of Formation in Gas State (ΔH_(g)), Heat of Formation in Solid State (ΔH_(s)), and Variance of Electrostatic Potential (σ_tot²) of Azide-oxirane at the MP2/cc-PVDZ Level

  DownLoad: CSV

  Compound	σtot2 (kJ/mol)2	ΔHsub (kJ/mol)	ΔH(g) (kJ/mol)	ΔH(s) (kJ/mol)
  A	244.66	18.65	152.28	133.63
  B1	218.30	20.53	294.87	274.34
  B2	177.16	13.60	312.91	299.31
  B3	185.63	14.65	385.32	343.41
  C	162.57	18.77	451.95	433.18
  D	147.91	24.02	596.93	572.92

  3.2 Molecular stability

  To predict the impact sensitivity of energetic materials, some work has been carried out at the molecular level. For example, Owens et al.^[19] first noted that there is a correlation between sensitivity and the electrostatic potential (ESP) at the midpoint of the C−NO₂ bond; Politzer and coworkers have established correlations between ESP surrounding an isolated molecule and several condensed-phase properties^[20]. The later work suggests that the dissociation energy of the weakest bond of the explosive molecule may play an important role in initiating the detonation reaction.

  In this work, the N−N was regarded as the trigger bond in explosive reaction. The trigger bond is estimated according to the principle of the smallest bond order^[21]. Table 2 lists the bond order, BDE and characteristic height. Inspecting the values in Table 2, we can find that all bond orders are less than 1.000, which shows to regard N−N as a trigger bond is reasonable. All azide-oxirane derivatives have large BDEs, which indicates that these molecules have good thermodynamics stability. Based on the bond orders, this trend of stability can be arranged in the sequence of A > B₁ > D > B₃ > C > B₂. Impact sensitivity is usually characterized through a drop hammer test. It is measured by the height from which a given weight hammer falling upon the compound to induce an explosion with 50% probability. In this paper, H₅₀ values are calculated according to equation (9) and listed in Table 2. It is found that the largest and smallest values are 54.13 and 20.30 cm, respectively. Compared with the H₅₀ values of two famous explosives RDX (29cm) and CL-20 (12cm), all compounds are absolutely less sensitive than that of CL-20, and A, B₁ and D are less sensitive than RDX.

  Table 2

  

  Table 2.  Bond Order (B_N-N), Bond Dissociation Energies with the Zero Point Energy Correction (BDE_ring-N), Bond Dissociation Energy without Zero Point Energy Correction (BDE_ring-N⁰) and Characteristic Height (H₅₀) Calculated at the MP2/cc-PVDZ Level

  DownLoad: CSV

  Compound	BN-N	BDEring-N (kJ/mol)	BDEring-N0 (kJ/mol)	H50 (cm)
  A	0.9735	567.79	544.79	54.13
  B1	0.9732	586.75	565.75	49.07
  B2	0.9575	580.92	556.92	20.30
  B3	0.9600	583.73	560.57	23.60
  C	0.9578	663.41	642.41	25.15
  D	0.9614	620.41	598.41	32.44

  3.3 Specific impulse

  The specific impulse is obtained according to the largest exothermic principle. All nitrogen atoms are assumed to go to N₂, carbon atoms to CO₂ (if oxygens are enough) or C, while oxygen atoms preferentially form H₂O (If hydrogens are available). The relevant data are listed in Table 3. I_s values indicate that the introduction of azide group raises the specific impulse. However, it is regrettable that all the I_s values of azide-oxirane are less than that (14.43) of octahydro-1, 3, 5, 7-tetranitro-1, 3, 5, 7-tetrazocine (HMX) because the carbon atoms can not be oxidized completely, and abundant energy can not be released in poor-oxygen system. So, the oxygen balance must be considered when the high-energy-density compounds are designed. However, on the consideration that the detonation performance of azide-oxirane is closer to that of RDX, it is reasonable that the azide-oxiranes can be regarded as the candidates of HEDMs.

  Table 3

  

  Table 3.  Combustion Enthalpy (ΔH_comb), Thermal Capacity at Constant Pressure (C_p), Combustion Temperature (T_c), and Specific Impulse (I_s) of Azide-oxirane According to Idealized Stoichiometric Decomposition Reactions

  DownLoad: CSV

  Compound	ΔHcomb (kJ/mol)	Cp (J/mol·K)	Tc (K)	Is
  A	−375.46	107.68	3784.96	11.17
  B1	−516.17	128.44	4316.91	11.75
  B2	−541.14	128.44	4511.32	12.01
  B3	−564.02	129.48	4428.95	11.85
  C	−652.47	170.50	4124.95	11.67
  D	−769.68	204.78	4056.53	12.08

  4. CONCLUSION

  On the basis of the above calculations, the following conclusions are drawn: All oxirane derivatives have high and positive HOFs, which are affected by the position of substituent group. In addition, there is a good liner relation-ship between HOF and the number of azide groups. All compounds have high bond dissociation energies and H₅₀. Absolutely, all title compounds are more stable than CL-20, and A, B₁ and D are less sensitive than RDX. This trend of impact sensitivity can be arranged in the sequence of A < B₁ < D < B₃ < C < B₂. All I_s values of azide-oxirane are less than that of HMX, but the detonation performance of azide-oxirane is closer than that of RDX. Therefore, it is possible that the azide-oxiranes can be regarded as candidates of high-energy-density compounds.

  
  
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• 

  Figure 1  Optimized structures of azide-oxirane in this paper

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  Table 1.  Sublimation Enthalpy (ΔH_sub), Heat of Formation in Gas State (ΔH_(g)), Heat of Formation in Solid State (ΔH_(s)), and Variance of Electrostatic Potential (σ_tot²) of Azide-oxirane at the MP2/cc-PVDZ Level

  Compound	σtot2 (kJ/mol)2	ΔHsub (kJ/mol)	ΔH(g) (kJ/mol)	ΔH(s) (kJ/mol)
  A	244.66	18.65	152.28	133.63
  B1	218.30	20.53	294.87	274.34
  B2	177.16	13.60	312.91	299.31
  B3	185.63	14.65	385.32	343.41
  C	162.57	18.77	451.95	433.18
  D	147.91	24.02	596.93	572.92

  下载: 导出CSV

  Table 2.  Bond Order (B_N-N), Bond Dissociation Energies with the Zero Point Energy Correction (BDE_ring-N), Bond Dissociation Energy without Zero Point Energy Correction (BDE_ring-N⁰) and Characteristic Height (H₅₀) Calculated at the MP2/cc-PVDZ Level

  Compound	BN-N	BDEring-N (kJ/mol)	BDEring-N0 (kJ/mol)	H50 (cm)
  A	0.9735	567.79	544.79	54.13
  B1	0.9732	586.75	565.75	49.07
  B2	0.9575	580.92	556.92	20.30
  B3	0.9600	583.73	560.57	23.60
  C	0.9578	663.41	642.41	25.15
  D	0.9614	620.41	598.41	32.44

  下载: 导出CSV

  Table 3.  Combustion Enthalpy (ΔH_comb), Thermal Capacity at Constant Pressure (C_p), Combustion Temperature (T_c), and Specific Impulse (I_s) of Azide-oxirane According to Idealized Stoichiometric Decomposition Reactions

  Compound	ΔHcomb (kJ/mol)	Cp (J/mol·K)	Tc (K)	Is
  A	−375.46	107.68	3784.96	11.17
  B1	−516.17	128.44	4316.91	11.75
  B2	−541.14	128.44	4511.32	12.01
  B3	−564.02	129.48	4428.95	11.85
  C	−652.47	170.50	4124.95	11.67
  D	−769.68	204.78	4056.53	12.08

  下载: 导出CSV
•