Intermolecular interaction and mechanical properties of energetic plasticizer MN reinforced 2,4,6-trinitrotoluene/1,3,5-trinitrohexahydro-1,3,5-triazine molten-energetic-composite (MEC)

Abstract

Enhancing the mechanical properties is always an attractive challenge in the research area of energetic materials (EMs). In the present work, 1.5 wt% MN-plasticizers (mononitrotoluene compounds, a mixture of 2-nitrotoluene and 4-nitrotoluene) were applied for reinforcing a molten-energetic-composite (MEC) 2,4,6-trinitrotoluene (TNT)/1,3,5-trinitrohexahydro-1,3,5-triazine (RDX). Brazilian disk testing results show that the tensile modulus of reinforced MEC increases by 26%. In order to explore the reinforcement mechanism, quantum chemistry (QC) and molecular dynamics (MD) simulations were performed to study the structural and physical properties of the reinforced MEC. The basis set superposition error (BSSE) and the interaction energies of TNT, RDX and plasticizers were computed at the MP2/6-311++G** level. Compared with the weak interaction energy between RDX and TNT (−1.586 kJ mol⁻¹), the interaction energies of reinforced MEC increase massively after incorporating MN-plasticizer. The SEM images of fractured surfaces from MECs also reveal that MNs can form layered deposits in TNT and closely surround crystalline RDX due to the presence of strong intermolecular interaction. Besides, MD simulation results further explain that the tensile modulus of (100) TNT and (100) RDX increases when introducing MN plasticizer separately, which agree with the change trends of mechanical properties from the Brazilian disk test. This work provides a new path for studying reinforced energetic composites by combining microscopy, mechanical testing and theoretical simulations.

---

1 Introduction

Chemical energy is constantly stored in setting up certain high energy chemical bonds, which is rightly the main energy-storage mechanism in most energetic materials. Energetic materials (EMs) are generally defined as compounds with large amounts of stored chemical energy, which can be released under specific conditions such as heat, shock and electrostatic discharge. In the actual applications, physical properties of EMs directly affect or even determine whether the occurrence of detonation is premature, which may lead to the safety issue called initiation early.^1,2 In order to prevent the accident, the mechanical properties of EMs must be improved. Different from other composites such as polymer, ceramics and alloys, the reinforcement of energetic-composite is a new concept for EMs. However, lacking of the reinforcement-mechanism studies for EMs makes the selection of proper reinforcing-agent very difficult.

Since 2,4,6-trinitrotoluene (TNT) was synthesized by J. Willbrand in 1863,³ its excellent enthermal stability makes it suitable as a carrier for melt-loading more powerful explosives (e.g. RDX, HMX, CL-20). Despite many candidates have been developed such as DNAN, TNAZ, DNTF, MTNI, and DNP,^4–8 TNT is still widely used in civilian and military applications because of its mature process and low manufacturing cost. As a carrier, TNT has its own problems. TNT based molten-energetic-composites (MECs) exhibit poor mechanical properties, and show undesirable defects such as cracks, voids, irreversible growth and brittleness, which have negative effects on sensitivity and safety of munitions based on melt-cast loaded explosives.^9,10 D. L Smith et al.¹¹ first found that there were cracks in the formulation of RDX and TNT through SEM technology. Afterwards, Niu and Zhang et al.¹² testified that weak H-bonds interaction existed between TNT and RDX by DFT investigations. Though weak interaction has been found between TNT and RDX, the solutions for enhancing the interaction were less proposed.

Intermolecular interactions such as hydrogen bonding (HB) and van der Waals (VdWs) interactions become important in condensed matter physics as well as in biological chemistry. The strongest intermolecular-interactions play a significant role in determining molecular conformation, crystal packing and chemical–physical properties. Nowadays, many means were carried out to enhance the intermolecular interaction, such as preparation of cocrystal,^13–15 surface-modified polymers with employing nano particles,^16,17 etc. Surface-modification is an extensive technique which is widely applied not only in composites but in EMs, such as polymer-bonded explosives (PBXs) and MECs. Polymer-based agent and energetic plasticizers are mostly used for surface-modification. Energetic plasticizers are a series of energetic organic chemicals with low melt-points. One of the advantages is that they can maintain or even improve the detonation performance of energetic-composites, reference to the polymer agent. In industrial chemistry, 2-nitrotoluene (o-NT) and 4-nitrotoluene (p-NT) were usually used as intermediates for synthesizing drugs, azo dyes, photographic chemicals, rubber, polyurethane foams, and textile auxiliary agent.^18–21 For EMs, they were found to be good energetic-plasticizers when mixing as mono-nitrotoluene plasticizers (MNs). In the present work, 1.5 wt% MNs were incorporated into TNT and RDX (mass ratio is 35 : 65) for modification experiments. Scanning electronic microscopy (SEM) was used for observing the interfacial-interaction and the Brazilian disk test was employed for obtaining the mechanical properties of unmodified and modified formulations. Moreover, quantum-chemical (QC) method was carried out to investigate the intermolecular-interaction between plasticizers and TNT together with RDX. In addition, molecular dynamics (MD) simulation was used for acquiring the elastic constants. The experimental results were testified by theoretical calculations and intermolecular-interaction analysis, and the reinforcement mechanism for MNs reinforced MEC was further explained.

2 Experimental and simulation methods

2.1 Materials and chemicals

TNT (purity 99%, laminar particles) was provided by Liaoning Qingyang Chemical Industry Co., Ltd. RDX (purity 99%, fine crystal with particle size of 20–45 μm, coarse crystal with particle size of 245–350 μm) was supplied by Gansu Yinguang Chemical Industry Co., Ltd. o-Nitrotoluene (o-NT) and p-nitrotoluene (p-NT) (purity 99%) were provided by Shanghai Puzhen Technology Co., Ltd.

2.2 Fabrication of reinforced MEC

Under the vigorous stirring, TNT (35 g) was first melted at 90–100 °C with steam in a jacketed vessel. Subsequently, RDX with fine and coarse particle sizes (65 g, mass ratio is 1 : 1) were successively added into TNT slurry in two steps, and lastly the MNs-plasticizers (1.5 g, molar ratio of o-NT and p-NT is 1 : 1) were slowly added. Keeping the temperature of 110 °C, the mixtures were sufficiently stirred until RDX and plasticizers dispersed homogeneously in the melted TNT slurry. The blends were subsequently concentrated in vacuum (approximately 0.5 MPa) to remove air bubbles, and poured into pre-heated moulds curing for 1 h at ambient temperature (Scheme 1).

Scheme 1 A brief representation of the fabrication for MNs-modified melt-cast energetic composite (MEC) by our improved method.

2.3 Characterization

The morphologies for the tensile fracture surface of the samples were examined by scanning electronic microscope (SEM; TM-1000, Hitachi, Japan) at an accelerating voltage of 12 kV. The prepared surfaces were coated with platinum/palladium in order to prevent charge build up on the specimen surfaces.

Brazilian disk test was conducted using a Universal Testing Machine (Instron® 5582, UK) following GJB-772A-97 standard method.²² Testing temperature is 20 °C, and the cross-head speed is 0.1 mm min⁻¹. Samples should be processed into the discs of 10 mm diameter and 5 mm thickness.

2.4 Methodology

Quantum chemical (QC) computations were performed with Gaussian 09 package²³ at Moller–Plesset perturbation theory (MP2)^24–27 with 6-311++G** basis set.^28,29 The geometric parameters were optimized and no constraints were imposed on molecular structure during optimization process.

The interaction energies (ΔE) of the dimers were calculated by the supermolecule approach using the eqn (1):

ΔE = E_dimer − (E_mol1 + E_mol2) (1)

where E_dimer, E_mol1 and E_mol2 are energies of the stacked/paired dimer, energy of the molecule 1 and energy of the molecule 2 respectively. The interaction energies were corrected for basis set superposition error (BSSE) using Boys and Bernardi's counterpoise (CP) method.³⁰

Molecular dynamics simulation was performed with COMPASS force field.³¹ The MD computations in this work were carried out using the software program Materials Studio from Accelrys Inc. (San Diego, CA, USA).³² Periodic simulation cells of TNT and RDX crystal, containing 144 TNT and 144 RDX molecules respectively, were selected for simulation model. 2 × 3 × 3 box of unit cells was cleaved along the crystalline surface (1 0 0). Recently, we used quantum mechanics (QM) MD simulation to examine the influences of polymer-based-modifiers on different crystalline surface of TNT and RDX, showing that (100) crystal-facets of TNT and RDX have comparatively stronger interaction with modifiers than the others.^33–35

The above models established for the (100) TNT, (100) RDX, and their blends with MNs (one molecule of o-NT with p-NT), were allowed to evolve dynamically in isothermal–isobaric (NPT) ensembles with Andersen temperature control³⁶ using stochastic collision method and Parrinello–Rahman pressure control³⁷ fully relaxing all cell parameters at atmospheric pressure (0.0001 GPa) and temperature (298 K). In the following condensed phase simulation cases, the van der Waals interactions were truncated at 9.5 Å, and the electrostatic interactions were computed via Ewald summation. The equations of motion were integrated with a step of 1 fs. Equilibration runs of 1 ns duration were performed, followed by production runs of 1–3 ns, during which data were collected with 10 fs sampling interval for subsequent analysis. Fig. 1 shows the (100) TNT, (100) RDX, (100) TNT/MNs, and (100) RDX/MNs periodic simulation cells after MD simulation.

Fig. 1 (100) TNT, (100) RDX, (100) TNT/MNs, and (100) RDX/MNs solid molecular structures after MD simulation.

The equilibrium trajectory documents were selected to do the mechanical property calculations. Optimization process was done before the calculation. The elastic constants were obtained by the mechanical analysis, and then other mechanical parameters can be calculated. The generalized Hooke's law is usually written as:

σ_i = C_ijε_j (2)

where σ_i is the stress tensor (GPa), ε_j is the strain tensor (GPa), and C_ij is the 6 × 6 stiffness matrix of elastic constants. If the material is idealized as an isotropic material, the stiffness matrix of the stress–strain behavior can be fully described by specifying only two independent coefficients (Lamé coefficients) as Scheme 2, wherein λ and μ are referred to as the Lamé coefficients.

Scheme 2 Stiffness matrix described by Lamé coefficients.

Herein, the elastic constants such as Young's modulus (E, GPa), Bulk modulus (K, GPa), Shear modulus (G, GPa) and Poisson's ratio (γ), can be written in terms of the Lamé coefficients as follows:^38,39

3 Results and discussion

3.1 Morphologies

Scanning electronic microscopy (SEM) was employed for analyzing the interfacial interactions between explosives and plasticizers. Fig. 2 shows the SEM images of regular RDX/TNT binary composite and reinforced RDX/TNT/MNs composite, respectively. It is obviously that many crossing cracks in the fracture surface of regular system, while in reinforced composite lots of layer-deposits appear and closely surround the crystalline facet of RDX, suggesting the presence of strong intermolecular-interaction between TNT and MNs. These layer-deposits can prevent the debonding of RDX crystalline from TNT, and are most likely to be responsible for the increase in toughness. From the schematic 3D structures of TNT and MNs, it is clearly seen that not only H-bonds but also strong π–π interaction exist, which may lead to the formation of eutectic compounds among these poly/mono nitro-aromatic compounds.

Fig. 2 SEM photographs of RDX/TNT and RDX/TNT/MNs fractured surface: (a) RDX/TNT: 65/35, (b) RDX/TNT/o-NT/p-NT: 65/35/1.5.

3.2 Intermolecular interaction analysis

Quantum chemistry method has become a powerful tool for disclosing molecular electronic structures including intermolecular interaction and essence of hydrogen bond. In order to investigate further the intermolecular-interaction between MNs and MEC, the interaction energy was computed at MP2/6-311++G** level. The optimized structures of TNT/MNs and RDX/MNs dimers are presented in Fig. 3. BSSE and interaction energies of those dimers are listed in Table 1. It is obviously that weak interaction presents in TNT and RDX, the interaction energy is only −1.586 kJ mol⁻¹, which agree with the view of Niu and Zhang et al.¹² The interaction energies of TNT/o-NT and TNT/p-NT are −131.557 kJ mol⁻¹ and −95.640 kJ mol⁻¹, respectively, while those of RDX/o-NT and RDX/p-NT are individually −48.487 and −4.620 kJ mol⁻¹. The results indicate that MNs and TNT have the stronger interaction than that of MNs and RDX, both of which are more vigorous than that of TNT and RDX. The phenomenon can be attributed to the presence of H-bonds and π–π conjugation interaction together between TNT and MNs plasticizers, reference to dominant H-bonds interaction between RDX and MNs plasticizers.

Fig. 3 Optimized geometries of TNT/RDX, TNT/o-NT, TNT/p-NT, RDX/o-NT, and RDX/p-NT dimers with hydrogen bond (N, O and C atom as donor) at MP2/6-311++G** level.

Table 1 Interaction energies for dimers of TNT/RDX, TNT/o-NT, TNT/p-NT, RDX/o-NT, and RDX/p-NT

Dimer structures	BSSE [kJ mol^−1]	Interaction energy [kJ mol^−1]
TNT/RDX	80.979	−1.586
TNT/o-NT	48.518	−131.557
TNT/p-NT	85.544	−95.640
RDX/o-NT	211.840	−48.487
RDX/p-NT	127.178	−4.620

---

3.3 Mechanical properties

Brazilian disk test (BDT) is a kind of indirect tensile test, which is suitable for characterizing the tensile mechanical performance of explosives since it is more secure than the direct-tensile test. It is reported that BDT was applied for the mechanical testing of brittle materials such as ceramics and resins, especially that it was used extensively in the Cavendish Laboratory to study polymer-bonded explosives (PBXs).^40–42 Due to the analogous components and physical properties with PBXs, the MECs can be tested by employing the same characterization. Fig. 4 is the schematic diagram of the Brazilian disk test.

Fig. 4 Schematic diagram of the Brazilian disk test (left one with flat anvils commonly used, right one with curved anvils used in this work).

The tensile stress at the center of the disc is given by the H. Awaji and S. Sato's model,⁴³ which is shown as follows:

here, P is the applied load, with D and t is the diameter and thickness of samples, respectively. b/R is the ratio of contact half width to the sample radius.

The testing results from Table 3 show that tensile modulus has a big increase from 4.86 GPa to 6.14 GPa when the MNs plasticizers are incorporated into TNT and RDX blends, which indicates that MNs plasticizer can reduce the brittleness of TNT and further enhance the modulus.

Table 2 Tensile modulus (E), Poisson's ratio (γ), bulk modulus (K), shear modulus (G), Cauchy pressure (C₁₂ − C₄₄) for (100) TNT, (100) RDX, (100) TNT/MNs, and (100) RDX/MNs. Unit for E, K, G, C₁₂ − C₄₄ is GPa

	(100) TNT	(100) TNT/MNs	(100) RDX	(100) RDX/MNs
C11	10.44	14.29	10.77	15.43
C22	8.46	13.58	10.68	13.34
C33	5.74	11.14	9.75	12.69
C44	5.71	6.24	3.56	3.69
C55	1.04	2.97	3.05	2.60
C66	2.72	2.77	1.64	3.30
C12	5.75	9.58	6.44	6.59
C13	1.64	4.94	5.82	6.10
C23	3.58	7.14	4.52	7.40
E	5.85	7.83	6.57	9.44
γ	0.31	0.35	0.34	0.32
K	5.18	9.15	7.14	9.07
G	2.23	2.88	2.44	3.55
K/G	2.32	3.17	2.92	2.55
C12 − C44	0.04	3.34	2.88	2.90

---

Table 3 Mechanical properties of TNT/RDX and TNT/RDX/MNs under the Brazilian disk test

Formula	Strain/%	Tensile modulus/GPa	Maximun loading/N
TNT/RDX-35 : 65	0.024	4.86	171
TNT/RDX/MNs-35 : 65 : 1.5	0.034	6.14	170

---

3.4 Radial distribution function (RDF) and reinforcement mechanism

In order to investigate the reinforcement mechanism, molecular dynamics (MD) simulation was carried out. To quantify the distributions of MNs molecules around TNT and RDX, the radial distribution function (RDF) g(r) and the distance (r) of different representative atoms were calculated from the simulation trajectory, which are shown in Fig. 5. Though the peak positions of CHON atoms in TNT (100) are basically the same with TNT (100) and MNs, due to their nitrotoluene moieties the RDF may hardly show the structures change after the incorporation of MNs. In contrast, the difference between methyl and nitro group distributions in RDX (100) and MNs is visible. Two new peaks are formed between 1 and 2 Å, which apparently belong to methyl and nitro groups from MNs. It is interesting that the peaks of nitrogen atoms decrease but peaks of oxygen atoms increase, which may indicates that the methyl of MNs can interact with N–NO₂ of RDX (100). Seen from RDX (100) to RDX (100)/MNs, it can be inferred that the incorporation of MNs plays a significant role in the enhancement for the intermolecular-interaction of MEC.

Fig. 5 The radial distribution function g(r) based on the trajectory documents after MD simulations.

The elastic parameters were obtained based on the equilibrium trajectory documents from dynamics simulation, which were presented in the Table 2. Results indicate that tensile modulus, bulk modulus and shear modulus of (100) TNT increase after the incorporation of MNs, the same as (100) RDX. These characteristics indicate that MNs can contribute to the increase of mechanical properties of TNT and RDX. Cauchy pressure (C₁₂ − C₄₄)⁴⁴ and K/G⁴⁵ are related to the brittleness and ductibility of composites. The higher the Cauchy pressure is, the more ductile the materials are. From the results in Table 2, it is found that (100) TNT is brittle and the (100) TNT/MNs shows the ductibility, and (100) RDX has slight enhancement after modification which agrees with the results of interaction-energy calculated. The trends of K/G values are little different from the Cauchy pressure since the quotient K/G empirically indicates the extent of the plastic range of a material, which is related to the manufacture performance of a material. Though K/G value of (100) TNT/MNs increases, that of (100) RDX/MNs presents a small decrease, which may suggest that the (100) RDX/MNs could show brittleness reference to (100) RDX.

4 Conclusions

In this work, MNs-energetic-plasticizers were introduced into the MEC for reinforcement, and for the first time, the intermolecular-interaction of this system was investigated by both experiments and theoretical computations. Compared with weak intermolecular-interaction between RDX and TNT (−1.586 kJ mol⁻¹), interaction energy of TNT/o-NT and TNT/p-NT was enhanced to −131.557 and −95.640 kJ mol⁻¹, respectively. Besides, molecular dynamics simulation results show that tensile modulus of (100) TNT/MNs increases by 33.8% compared with (100) TNT, and that of (100) RDX/MNs increases by 43.6%. As is evident, the Brazilian disk test testifies that the tensile elastic modulus of TNT/RDX/MNs (6.14 GPa) increases compared with the regular formula TNT/RDX (4.86 GPa), which agrees with the trends of MD simulation results. Analyzing the related mechanism, it is manifest from the microscopy that the reinforcement of MEC by MNs-plasticizers mainly depends on the intermolecular interaction between TNT and MNs. Meanwhile, the QC and MD simulation results further reveal that the increasing interaction energies between MEC and MNs-plasticizers is the main factor for the remarkable enhancement of mechanical properties. On the other hand, MNs-plasticizers (o-NT and p-NT) have the same mononitrobenzene moieties with TNT, which might be the reason having more interaction with TNT and arising the reinforcement effect. This study also provides a significant method of investigating small-molecule energetic plasticizers reinforced MECs by combining microscopy, mechanical test and theoretical calculations.

Acknowledgements

The authors wish to express their gratitude to the NSAF Foundation of National Natural Science Foundation of China and China Academy of Engineering Physics (Grant no. 11076002) and the NSFC Foundation of National Natural Science Foundation of China (Grant nos 11402237 and 51373159) for financial support.

Notes and references

1. P. W. Cooper and W. Paul, Explosives Engineering, John-Wiley, New York, USA, 1996.
2. J. P. Agrawal and R. D. Hodgson, Organic Chemistry of Explosives, John-Wiley, London, UK, 2007.
3. J. Akhavan, The Chemistry of Explosives, The Royal Society of Chemistry, Thomas Graham House, Cambridge, UK, 2nd edn, 2004.
4. J. W. A. M. Janssen, H. J. Koeners, C. G. Kruse and C. L. Habraken, Pyrazoles. XII. The preparation of 3(5)-Nitropyrazoles by Thermal Rearrangement of N-Nitropyrazoles, J. Org. Chem., 1978, 38, 1777–1782.
5. S. Nicolich, J. Niles, P. Ferlazzo, D. Doll, P. Braithwaite, N. Rausmussen, M. Ray, M. Gunger and A. Spencer, Recent developments in reduced sensitivity melt pour explosives, The 34th International Annual Conference of ICT, Karlsruhe, Germany, 24–27 June 2003, p. 135.
6. D. S. Watt, and M. D. Cliff, Evaluation of 1,3,3 trinitro azetidine (TNAZ), A High Performance Melt-Castable Explosive, DSTO-TR-1000, Defence Science and Technology Organisation, Adelaide, Australia, 2000.
7. F. Zhao, P. Chen, R. Hu, Y. Luo, Z. Zhang, Y. Zhou, X. Yang, Y. Gao, S. Gao and Q. Shi, Thermochemical Propertiesnand Non-Isothermal Decomposition Reaction Kinetics of 3,4-Dinitrofurazanfuroxan (DNTF), J. Hazard. Mater., 2004, A113, 67–71.
8. S. Singh, R. Damavarapu, R. Surapaneni and P. Samuel, An insensitive melt-cast energetic material: 1-methyl-2,4,5-trinitroimidazole: MTNI, The 38th International Annual Conference of ICT, Karlsruhe, Germany, 30 June–3 July 2007, p. 147.
9. Q. Ma, Y. J. Shu, G. Luo, L. Chen, B. Zheng and H. Li, Toughening and elasticizing route of TNT based melt-cast explosives, Chin. J. Energ. Mater., 2012, 20, 618–629.
10. P. Ravi, D. M. Badgujar, G. M. Gore, S. P. Tewari and A. K. Sikder, Review on Melt Cast Explosives, Propellants, Explos., Pyrotech., 2011, 36, 393–403.
11. D. L. Smith and B. W. Thorpe, Fracture in the high explosive RDX/TNT, J. Mater. Sci., 1973, 8, 757–759.
12. X. Q. Niu, J. G. Zhang, X. J. Feng, P. W. Chen, T. L. Zhang, S. Y. Wang, S. W. Zhang, Z. N. Zhou and L. Yang, Theoretical investigation on intermolecular interactions between the ingredients TNT and RDX of composition B, Acta Chim. Sin., 2011, 69, 1627–1638.
13. A. D. Bond, What is a co-crystal?, CrystEngComm, 2007, 9, 833–834.
14. N. Blagden, D. J. Berry, A. Parkin, H. Javed, A. Ibrahim, P. T. Gavan, L. L. De Matos and C. C. Seaton, Current directions in co-crystal growth, New J. Chem., 2008, 32, 1659–1672.
15. D. Spitzer, B. Risse, F. Schnell, V. Pichot, M. Klaumünzer and M. R. Schaefer, Continuous engineering of nano-cocrystals for medical and energetic applications, Sci. Rep., 2014, 4, 6575.
16. B. B. Johnsen, A. J. Kinloch, R. D. Mohammed, A. C. Taylor and S. Sprenger, Toughening mechanisms of nanoparticle-modified epoxy polymers, Polymer, 2007, 48, 530–541.
17. E. Manias, Nanocomposites: Stiffer by design, Nat. Mater., 2007, 6, 9–11.
18. R. A. Finnegan and D. Knutson, Photochemical studies. VI. Photochemistry of nitrobenzoate esters and related nitroaromatic compounds. Some novel reduction and esterification reactions, J. Am. Chem. Soc., 1968, 90, 1670–1671.
19. M. J. Strauss, The nitroaromatic group in drug design. Pharmacology and toxicology (for nonpharmacologists), Int. Eng. Chem. Prod. Res. Dev., 1979, 18, 158–166.
20. J. H. Tocher and D. I. Edwards, The interaction of nitroaromatic drugs with aminothiols, Biochem. Pharmacol., 1995, 50, 1367–1371.
21. G. Booth, Nitro compounds, Aromatic, Ullmann's Encyclopedia of Industrial Chemistry, Wiley-VCH, Berlin, Germany, 2000.
22. National Military Standard of China, Experimental methods of sensitivity and safety GJB/772A-97, 1997, in Chinese.
23. 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, T. Keith, R. Kobayashi, J. Normand, 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, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Gaussian 09 C.01, Wallingford CT, Gaussian, Inc., 2010.
24. C. Møller and M. Plesset, Note on an approximation treatment for many-electron systems, Phys. Rev., 1934, 46, 618–622.
25. S. Sæbø and J. Almlöf, Avoiding the integral storage bottleneck in LCAO calculations of electron correlation, Chem. Phys. Lett., 1989, 154, 83–89.
26. M. J. Frisch, M. Head-Gordon and J. A. Pople, A direct MP2 gradient method, Chem. Phys. Lett., 1990, 166, 275–280.
27. M. J. Frisch, M. Head-Gordon and J. A. Pople, Semi-direct algorithms for the MP2 energy and gradient, Chem. Phys. Lett., 1990, 166, 281–289.
28. A. D. Becke, Density-functional thermochemistry. II. The effect of the Perdew–Wang geralized-gradient correlation correction, J. Chem. Phys., 1992, 97, 9173–9177.
29. A. D. Becke, Density functional thermochemistry. III. The role of exact exchange, J. Chem. Phys., 1993, 98, 5648–5652.
30. S. F. Boys and F. Bernardi, The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors, Mol. Phys., 1970, 19, 553–566.
31. H. Sun, COMPASS: an ab initio force-field optimized for condensed-phase—Overview with details on alkane and benzene compounds, J. Phys. Chem. B, 1998, 102, 7338–7364.
32. Accelrys Software Inc., Materials studio release notes, release 6.0, San Diego, USA, 2011.
33. W. Qian, Y. Shu, H. Li, Q. Ma and S. Wang, Simulation Study on the GAP-based comb-like ployurethane modifier used for TNT-based composite explosives, Proceedings of the 17th Seminar on New Trends in Research of Energetic Materials, Pardubice, Czech Republic, 9–11 April 2014, p. 390.
34. W. Qian, Y. Shu, H. Li and Q. Ma, The effect of HNS on the reinforcement of TNT crystal: a molecular simulation study, J. Mol. Model., 2014, 20, 2461.
35. J. J. Xiao, S. Y. Li, J. Chen, G. F. Ji, W. Zhu, F. Zhao, Q. Wu and H. M. Xiao, Molecular dynamics study on the correlation between structure and sensitivity for defective RDX crystals and their PBXs, J. Mol. Model., 2013, 19, 803–809.
36. H. C. Andersen, Molecular dynamics simulations at constant pressure and/or temperature, J. Chem. Phys., 1980, 72, 2384–2393.
37. M. Parrinello and A. Rahman, Polymorphic transitions in single crystals: A new molecular dynamics method, J. Appl. Phys., 1981, 52, 7182–7190.
38. J. P. Watt, G. F. Davies and R. J. O'Connell, The elastic properties of composite materials, Rev. Geophys. Space Phys., 1976, 14, 541–563.
39. J. H. Weiner, Statistical Mechanics of Elasticity, John-Wiley, New York, 1983.
40. International Society of Rock Mechanics (ISRM), Suggested methods for determining tensile strength of rock materials, Int. J. Rock. Mech. Min. Sci. Geomech. Abst., 1978, 15, 99–103.
41. M. Mellor and I. Hawkes, Measurement of tensile strength by diametral compression of discs and annuli, Eng. Geol., 1971, 5, 173–225.
42. S. G. Grantham, C. R. Siviour and W. G. Proud, High strain rate Brazilian testing of an explosive stimulant using speckle metrology, Meas. Sci. Technol., 2004, 15, 1867–1870.
43. H. Awaji and S. Sato, Combined mode fracture toughness measurement by the disk test, J. Eng. Mater. Technol., 1978, 100, 175–182.
44. D. G. Pettifor, Theoretical predictions of structure and related properties of intermetallics, Mater. Sci. Technol., 1992, 8, 345–349.
45. S. F. Pugh, Relations between the elastic moduli and the plastic properties of polycrystalline pure metals, Philos. Mag. A, 1954, 45, 823–843.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra03666f

---