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应用第一性原理可以计算含能材料0 K下的结构和物理性质, 但温度效应的缺失通常会导致计算数据与实验结果产生偏差. 同时, 与温度相关的热力学参数是含能材料在宏观和介观尺度下建模的关键输入. 为此, 本文以高能低感炸药1-氧-2, 6-二氨基-3, 5-二硝基吡嗪(LLM-105)为研究体系, 基于准简谐近似, 采用色散修正的密度泛函理论研究温度加载下LLM-105的分子间相互作用和热力学性质. 晶格参数和热膨胀系数的演化表明LLM-105分子间相互作用具有强烈的各向异性, 其中b轴方向(分子层间)的膨胀率远高于ac平面(分子层内). Hirshfeld表面及其指纹图分析进一步证实LLM-105的分子间相互作用主要取决于O···H构成的氢键. 结合Mulliken布居数和结构分析, 温度加载下氢键相互作用的变化可诱发硝基旋转, 并使得C—NO2键的强度明显减弱, 为高温分解反应的触发键提供了理论依据. 此外, 本文计算了等容和等压条件下的热容、熵以及等温和绝热条件下的体模量等基础热力学参数. 其中绝热条件下的体模量与实验值吻合, 同时体模量随温度的演化反映了LLM-105在温度加载下的软化行为. 上述理论研究可用于构建含能材料在介观和宏观尺度下的模型, 也为测量原子分子水平下的热力学性质提供了重要的参考价值.
2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) is a typical high-energy and low-sensitivity energetic material (EM), which has excellent detonation performance and thermal stability. In the quasi-harmonic approximation, the dispersion corrected density functional theory is used to study the intermolecular interactions and thermodynamic properties of energetic LLM-105 crystal. By introducing the zero-point energy and temperature effect corrections, PBE-D3 dispersion correction scheme can significantly improve the calculation accuracy of structural parameters at an experimental temperature (294 K). The temperature dependent lattice parameters and thermal expansion coefficients exhibit strong anisotropy, especially the thermal expansivity in b-axis orientation (intermolecular layers) is much higher than that in the ac plane (intramolecular layers). Through Hirshfeld surface and fingerprint analysis, it is found that the intermolecular interactions of LLM-105 are mainly O···H hydrogen bonding interactions. The change of intermolecular interactions will result in the rotation of nitro group, which can contribute to forming new hydrogen-bonding interaction pattern. Mulliken population analysis shows that the bond order of C—NO2 bond is more sensitive to the change of temperature, so this bond may be a trigger bond for the high-temperature decomposition reaction of LLM-105. The fundamental thermodynamic properties of EMs can not only provide key parameters for mesoscopic or macroscopic thermodynamic simulations, but also gain theoretical insights into the temperature effects of EMs. Specific heat capacity reflects the amount of heat to be supplied to heating the matter and it is important to make the risk assessment of EMs during storage or when exposed to external thermal stimuli. Herein, the basic thermodynamic parameters, such as heat capacity, entropy, bulk modulus and elastic constants under different conditions are predicted. Among them, the calculated heat capacity and entropy describe the nonlinear behaviors within a temperature range of 0 to 500 K, and the calculated isobaric heat capacity Cp(T) is in good agreement with the available experimental measurements. The elasticity of material describes the macroscopic response of crystal to external force, and the bulk modulus B0 of molecular crystal can be determined through the equation of state, which is an important parameter for evaluating material stiffness. The bulk modulus under adiabatic condition is in reasonable agreement with experimental value, and the evolution of bulk modulus with temperature reflects the softening behavior of LLM-105 at temperature. Furthermore, the complete set of second-order elastic constants (SOECs) of LLM-105 is calculated and 13 independent SOECs (C11, C12, C13, C15, C22, C23, C25, C33, C35, C44, C46, C55, C66) are predicted. With the increasing temperature, all elastic constants gradually decrease due to the weakening of intermolecular interactions of LLM-105. Overall, these results will fundamentally provide a deep understanding of temperature effects and serve as a reference for the experimental measurement of the thermodynamic parameters of EMs. -
Keywords:
- LLM-105 /
- thermodynamic properties /
- intermolecular interactions /
- quasi-harmonic approximation
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图 1 (a) 实验温度下, 不同泛函结合不同色散修正方案计算的F-V曲线; (b) PBE泛函结合D3色散修正方案、零点能效应和温度效应计算的LLM-105的晶胞体积以及与实验的误差
Fig. 1. (a) F-V curves calculated at experimental temperature using different functional and dispersion correction schemes; (b) PBE functional combined with D3 dispersion correction scheme, zero point energy effect and temperature effect calculation of LLM-105 cell volume and experimental error.
图 2 计算和实验测量[11]的LLM-105晶胞体积(a)和晶格参数(b)随温度的演化; (c) LLM-105的热膨胀系数随温度的演化; (d) LLM-105的分子结构和层间堆垛示意图, 其中粉色代表氢原子, 棕色代表碳原子, 蓝色代表氮原子, 红色代表氧原子
Fig. 2. Calculated cell volume (a) and lattice parameters (b) at elevated temperature, compared with experimental values[11]; (c) variation of thermal expansion coefficient of LLM-105 with temperature increasing; (d) diagram of molecular structure and interlayer stacking of LLM-105, where the pink, brown, blue and red balls represent hydrogen, carbon, nitrogen and oxygen atoms, respectively.
图 3 LLM-105晶体的 Hirshfeld表面、指纹图及其分子间相互作用对表面的相对贡献, 灰色区域表示LLM-105 晶体的 Hirshfeld 表面及其映射的二维指纹图, 其中蓝色和红色区域分别表示原子周围的正、负静电势
Fig. 3. Hirshfeld, fingerprint, and intermolecular interactions of LLM-105 crystal, the gray area represents the Hirshfeld surface of LLM-105 crystal and its mapped two-dimensional fingerprint, where the blue and red areas represent the positive and negative electrostatic potential of the atoms, respectively.
图 4 (a) 0—500 K范围内, LLM-105晶体分子间相互作用的变化量; (b) 层间分子的质心距离随温度的变化; (c) LLM-105分子中化学键布居数随温度的变化; (d) 计算的硝基(—NO2)与C—N环平面所成二面角随温度的变化
Fig. 4. (a) Changes of intermolecular interactions of LLM-105 crystals at 0–500 K; (b) evolution of centroid distance of interlayer molecules under temperature; (c) variation of the bond population in LLM-105 molecules with temperature increasing; (d) calculated dihedral angle between nitro group (—NO2) and C—N ring plane with temperature increasing.
图 5 等容(黑色曲线)和等压(红色曲线)条件下LLM-105晶体的热容(a)和熵(b)随温度的变化
Fig. 5. Heat capacity (a) and entropy (b) of LLM-105 crystal as a function of temperature under constant-volume (black line) and constant-pressure (red line) conditions, respectively.
图 6 (a) 等温(Bt)和绝热(Bs)条件下LLM-105晶体的体模量随温度的变化; (b) LLM-105晶体的二阶弹性常数完全集及其随温度的变化
Fig. 6. (a) Variation of bulk modulus of LLM-105 crystal under isothermal (Bt) and adiabatic (Bs) conditions with temperature increasing; (b) the complete set of second-order elastic constants of LLM-105 crystal and its temperature dependence.
表 1 实验温度下色散修正方案(PBE-D2/D3)结合零点能和温度效应计算的LLM-105结构参数及其与实验值之间的偏差
Table 1. Structural parameters of LLM-105 calculated by dispersion correction scheme (PBE-D2/D3) combined with zero-point energy and temperature effects at experimental temperature. The deviation is given under each calculated value.
V/Å3 a/Å b/Å c/Å β/(°) Expt.[4] 748.16 5.716 15.850 8.414 101.041 PBE-D2 745.83 5.62 16.30 8.25 99.46 (–0.31%) (–1.60%) (2.82%) (–1.96%) (–1.57%) PBE-D3 748.26 5.74 15.81 8.39 100.39 (0.01%) (0.36%) (–0.25%) (–0.32%) (–0.65%) 
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[1] 王泽山 2006 含能材料概论 (哈尔滨: 哈尔滨工业大学出版社) 第4—8页
Wang Z S 2006 Introduction to Energetic Material (Harbin: Harbin Institute of Technology Press) pp4–8
[2] Zhang C Y, Wang X C, Huang H 2008 J. Am. Chem. Soc. 130 8359
Google Scholar
[3] Jiao F B, Xiong Y, Li H Z, Zhang C Y 2018 Cryst. Eng. Comm 20 1757
Google Scholar
[4] Gilardi R D, Butcher R J 2001 Acta Crystallogr. E 57 o657
Google Scholar
[5] Tarver C M, Urtiew P A, Tran T D 2005 J. Energ. Mater. 23 183
Google Scholar
[6] Averkiev B B, Antipin M Y, Yudin I L, Sheremetev A B 2002 J. Mol. Struc. 606 139
Google Scholar
[7] Li G, Zhang C Y 2020 J. Hazard. Mater. 398 122910
Google Scholar
[8] Miao M S, Sun Y H, Zurek E, Lin H Q 2020 Nat. Rev. Chem. 4 508
Google Scholar
[9] Gump J C, Stoltz C A, Mason B P, Freedman B G, Ball J R, Peiris S M 2011 J. Appl. Phys. 110 073523
Google Scholar
[10] Stavrou E, Riad Manaa M, Zaug J M, et al. 2015 J. Chem. Phys. 143 144506
Google Scholar
[11] Xu Z L, Su H, Zhou X Q, et al. 2019 J. Phys. Chem. C 123 1110
Google Scholar
[12] Xu Z L, Chen Q, Li X D, et al. 2020 J. Phys. Chem. C 124 2399
Google Scholar
[13] Manaa M R, Kuo I F, Fried L E 2014 J. Chem. Phys. 141 064702
Google Scholar
[14] Wang J K, Xiong Y, Li H Z, Zhang C Y 2018 J. Phys. Chem. C 122 1109
Google Scholar
[15] Wang X, Zeng Q, Li J S, Yang M L 2019 ACS Omega 4 21054
Google Scholar
[16] Wu Q, Yang C H, Pan Y, Xiang F, Liu Z C, Zhu W H, Xiao H M 2013 J. Mol. Model. 19 5159
Google Scholar
[17] Zong H H, Zhang L, Zhang W B, Jiang S L, Yu Y, Chen J 2017 J. Mol. Model. 23 275
Google Scholar
[18] Yuan W S, Hong D, Luo Y X, Li X H, Liu F S, Liu Z T, Liu Q J 2023 Spectrochim. Acta A 303 123170
Google Scholar
[19] Yu Q, Zhao C D, Li J S 2022 J. Therm. Anal. Calorim. 147 12965
Google Scholar
[20] Li J Y, Zhang H B, Wen M P, Xu J J, Liu X F, Sun J 2016 J. Energ. Mater. 34 170
Google Scholar
[21] Ma R, Sun W C, Picu C R 2021 Int. J. Solids Struct. 232 111170
Google Scholar
[22] Menikoff R, Sewell T D 2002 Combust. Theor. Model. 6 103
Google Scholar
[23] Chen J, Qiao Z Q, Wang L L, Nie F D, Yang G C, Huang H 2011 Mater. Lett. 65 1018
Google Scholar
[24] Yu Q, Zhao C D, Liao L Y, Li H Z, Sui H L, Yin Y, Li J S 2020 Phys. Chem. Chem. Phys. 22 13729
Google Scholar
[25] Jiang J, Liu J Y, Chen Y H, Wu Q H, Ju Z Y, Zhang S H 2021 Mol. Simulat. 47 678
Google Scholar
[26] Xiao Q, Sui H L, Hao X F, Chen J, Yin Y, Yu Q, Yang X L, Ju X 2020 Spectrochim. Acta A 240 118577
Google Scholar
[27] Dovesi R, Orlando R, Erba A, et al. 2014 Int. J. Quantum Chem. 114 1287
Google Scholar
[28] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
Google Scholar
[29] Grimme S 2011 Wires. Comput. Mol. Sci. 1 211
Google Scholar
[30] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
Google Scholar
[31] Fischer T H, Almlof J 1992 J. Phys. Chem. 96 9768
Google Scholar
[32] Fan J Y, Su Y, Zheng Z Y, Zhao J J 2021 J. Phys. Condens. Mat. 33 275702
Google Scholar
[33] Parwani A V 2009 CrystEngComm 11 19
Google Scholar
[34] Spackman M A, McKinnon J J 2002 CrystEngComm 4 378
Google Scholar
[35] Weese R K, Burnham A K, Turner H C, Tran T D 2007 J. Therm. Anal. Calorim. 89 465
Google Scholar
[36] Ma H X, Song J R, Zhao F Q, Gao H X, Hu R Z 2008 Chin. J. Chem. 26 1997
Google Scholar
[37] Drebushchak V A 2020 J. Therm. Anal. Calorim. 142 1097
Google Scholar
[38] Hooks D E, Ramos K J, Bolme C A, Cawkwell M J 2015 Propell. Explos. Pyrot. 40 333
Google Scholar
[39] Fan J Y, Su Y, Zhang Q Y, Zhao J J 2019 Comp. Mater. Sci. 161 379
Google Scholar
[40] 位付景, 张伟斌, 董闯, 陈华 2023 物理学报 72 096201
Google Scholar
Wei F J, Zhang W B, Dong C, Chen H 2023 Acta Phys. Sin. 72 096201
Google Scholar
[41] Stevens L L, Velisavljevic N, Hooks D E, Dattelbaum D M 2008 Propell. Explos. Pyrot. 33 286
Google Scholar
[42] Nye J F 1985 Physical Properties of Crystals: Their Representation by Tensors and Matrices (New York: Oxford University Press) pp131–148
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