混合溶剂对β-HMX结晶形貌影响的分子动力学模拟

陈 芳 刘圆圆 王建龙 苏宁宁 李丽洁 陈红春

(1中北大学化工与环境学院，太原 030051；2中北大学理学院，太原 030051；3北京理工大学材料学院，北京 100081)

混合溶剂对β-HMX结晶形貌影响的分子动力学模拟

陈 芳1,＊刘圆圆1王建龙1苏宁宁2李丽洁3陈红春1

(1中北大学化工与环境学院，太原 030051；2中北大学理学院，太原 030051；3北京理工大学材料学院，北京 100081)

为了解释混合溶剂对β-HMX结晶形貌的影响，采用分子动力学方法系统地研究了β-HMX晶体表面与混合溶剂(丙酮/γ-丁内酯和二甲基甲酰胺/水)的相互作用，体积比从1 : 3到3 : 1。使用修正的附着能模型预测了β-HMX在混合溶剂中的生长习性。结果表明：β-HMX晶体的(020)面与溶剂分子的相互作用最弱，混合溶剂对β-HMX不同晶面的作用变化，可以显著地改变β-HMX的晶体形态。通过比较β-HMX在不同体积比混合溶剂作用下结晶形貌的纵横比，发现混合溶剂为二甲基甲酰胺/水，其体积比为1 : 3时，有利于β-HMX晶体球形化。

β-HMX；晶体形貌；混合溶剂；分子动力学模拟；附着能

1 Introduction

HMX (cyclotetramethylenetetranitramine) is widely used not only for military purposes but also in industrial applications. HMX exists in four solid-phase polymorphs: α-, β-, γ-, and δ-phases. β-HMX is the most stable thermodynamically and mechanically1. The thermal decomposition mechanisms of β-HMX at various densities and at 2500 K were studied using ReaxFF reactive molecular dynamics simulations2. The effects of NO2, OH and OH-on the initial pyrolysis3and the influence of H+and NH4+on the N-NO2bond dissociation energy4of β-HMX were investigated using the density functional theory. The crystal morphology of energetic material is crucial factor for sensitivities and packing density of explosive. The growth habit of explosive is determined by both the internal structure and the external conditions. Among them, solvent has been found to be one of the most important external factors determining the morphology5. Moreover, one of the significant ways to modify and control crystal morphology is the use of solvents1,6-10or mixed solvents11-13in the crystallization process. Experimental approaches and computational simulations are the main methods which are used to research the crystal morphology. However, the former are expensive and time consuming. Molecular dynamics (MD) simulation has proven itself to be effective in predicting the crystal habit of explosive crystals influenced by solvent based on the attachment energy model (AE) and its modifications5-7,14-19. Shi et al. researched the effect of ethanol solvent on the growth habit of 1,3,3-trinitroazetidine5and trifluoroacetic acid solvent on the growth habit of 2,6-diamino-3,5-dinitropyridine-1-oxide15using modified attachment energy (MAE) model. Chen et al.14,17discussed the crystal habits of hexogen in acetone and cyclohexanone via dynamic simulations. They successfully predicted the crystal morphologies of energetic materials. β-HMX is practically insoluble in water and highly soluble in organic solvents such as acetone (AC), dimethyl sulfoxide (DMSO), dimethylformamide (DMF), γ-butyrolactone (BL), cyclohexanone (CH) and so on. HMX can be crystallized from γ-butyrolactone in the desired β-modification without any detectable amount of α-HMX20. Antoine et al.10found that the presence of acetone in γ-butyrolactone prevents the complex formation between HMX and γ-butyrolactone. The crystal habits of β-HMX in acetonitrile7and acetone19solution were successfully predicted by using the MAE model. However, to the best of our knowledge, the binary solvent mixtures effects on the crystal morphology of HMX have not been explored from molecular level.

In this study, the crystal morphologies of β-HMX in acetone/γ-butyrolactone and DMF/H2O solvents, with volume ratios of 1 : 3 to 3 : 1 are predicted by the modified attachment energy (MAE) model with molecular dynamics (MD) simulations. The purpose of the work is to provide some theoretical supports for HMX crystal morphology control technology. In this paper, the HMX surface-binary solvent mixtures interfacial models were constructed and the molecular dynamics (MD) simulations were performed on these models, the interactions between HMX surfaces and binary solvent mixtures were analyzed and compared by the binding energy of each crystalline face, finally the modified attachment energies and relative growth rate of β-HMX habit faces were calculated, also the β-HMX growth morphology in the presence of binary solvent mixtures were predicted by the MAE model.

2 Computational theory and details

2.1 Computational theory

The growth morphology algorithm which proposed by Hartman and Bennema21is based on the attachment energy (AE) method. The attachment energy, Eatt, is defined as the energy released on attachment of a growth slice of thickness dhklto a growing crystal surface (hkl). Eattis computed as22:

where Elattis the lattice energy of the crystal, Esliceis the energy of a growth slice of thickness dhkl.

The relative growth rate in vacuum of the crystal surface, Rhkl, is assumed to be proportional to the absolute value of attachment energy:

R'hklrepresents the growth rate in a particular direction after the solvent effect, which is directly proportional to the modified attachment energy (MAE),. The detailed calculation method of MAE is referred to Shi et al.5-7,14,15,19.

where Aaccis the area of accessible solvent surface of an (hkl) slice in the unit cell, Aboxis the surface area of the simulated model along the (hkl) direction; Eintis the interaction energy between the solvent layer and the specific crystal face, Etotis the total energy of the surface and the solvent layer, Esurfis the energy of the surface without the solvent layer, and Esolvis the energy of the solvent layer without the surface.

2.2 Simulation details

All computation simulations were performed in Materials Studio software. The initial structure of β-HMX unit cell derived from the Cambridge Crystallographic Data Center (a = 0.654 nm, b = 1.105 nm, c = 0.870 nm, β = 124.3º, α = γ = 90º). The molecular and crystal structures are displayed in Fig.1. The AE model was selected to determine the crystal morphology of β-HMX in vacuum, which gives a list of morphologically possible growth faces. Subsequently, β-HMX crystal was cleaved parallel to the predicted (hkl) faces with a depth of four unit cells. A crystal slice was constructed as a periodic superstructure of 3 × 3 unit cells. All the geometry optimizations and MD simulations were performed by the COMPASS force field23. The COMPASS force field is a powerful ab initio force field, which has been confirmedsuitable to theoretical simulations for HMX7,19. The three-dimensional periodic solvent box with 200 random distributed mixture solvent molecules, number of each solvent molecule can be determined by the volume ratios conversion into molecular ratios of the mixed solvent, was constructed by the Amorphous Cell tool and refined by MD techniques. The dimensions of the solvent box were consistent with the lattice parameters of the selected crystal surface. The densities of the mixtures were simply calculated by ρ = x1ρ1+ x2ρ2with no consideration of the excess volume, where ρ1and ρ2are the densities of pure liquid acetone/DMF and γ-butyrolactone/H2O at room temperature, respectively. The values of x1were set to be 1/4, 1/3, 1/2, 2/3, 3/4, respectively, and the corresponding values of x2were set to be 3/4, 2/3, 1/2, 1/3, 1/4.

The β-HMX surface-mixed solvents micro interface model was constructed to study the effect of mixed solvent on β-HMX habit faces. The schematic diagram of β-HMX-mixed solvents interface model is illustrated in Fig.2. The β-HMX surface layer constrained along a, b, and c directions, while the mixed solvent adsorption layer placed along c axis above the β-HMX surface, in which all solvent molecules were able to move freely. A thickness of 5 nm vacuum was set above the adsorption layer to eliminate the effect of additional free boundaries. Energy minimization for the interfacial model was carried out before the dynamics simulation. MD simulation was performed for 200 ps with a time step of 1 fs (T = 298 K and p = 1.01 × 105Pa) with the NVT (constant number of particles, volume and temperature) ensemble. When equilibration has been achieved, energy and temperature fluctuate around their averages, which remain constant over time. Fig.3 showed that the fluctuation curves of temperature and energy of the β-HMX (020) surface-acetone/γ-butyrolactone (volume ratio of 1 : 1) solvent interfacial model for equilibration stage of 200 ps in the MD simulation. It can be observed that the system quickly equilibrates in less than 30 ps and then continues to fluctuate around the equilibrium state. Similarly, all other β-HMX-mixed solvents interface models have been equilibrated. After the system was equilibrated at the target temperature, the interfacial configurations were sampled for 100 ps with a sampling interval of 1 ps. For potential-energy calculations, the Coulomb interactions and van der Waals forces were calculated by employing the standard Ewald and atom based method, respectively, with a calculation accuracy of 0.004 kJ·mol-1and cutoff distance was set as 1.25 nm. The solvent-accessible area of the crystal surface is calculated by the Connolly surface model. For the Connolly surface calculation, the grid interval was set to be 0.04 nm at a probe radius of 0.1 nm in this paper. At last, the modified attachment energies of β-HMX habit faces were calculated according to the Eq.(4), and the corresponding crystal morphology of β-HMX in mixed solvents was predicted by the MAE model.

Fig.1 Molecular (left) and crystal (right) structures of β-HMX

Fig.2 Schematic diagram of β-HMX-mixed solvents interface model

3 Results and discussion

3.1 β-HMX crystal morphology in vacuum

Morphology of β-HMX crystal obtained in vacuum at the crystallization temperature of 550 K has been reported to be as hexahedron with an aspect ratio of 2.06, and the major faces are (020), (011),(102),(111) and (100), the surface chemistry and topography of these habit faces were further analyzed19.We also simulated the morphology of β-HMX crystal in vacuum by the AE model and the aspect ratio is 1.59, as shown in Fig.4. The difference of aspect ratio between the calculated result and the literature19may be due to the different simulation temperature. Table 1 lists the relevant parameters of the main crystal habit faces of β-HMX. The order of relative growth rate (Rhkl) in vacuum on different crystal surface is written as follows: (100) ＞(102) ＞ (020) ≈(111) ＞ (011). In those five planes, the (100) surface is expected to grow faster than the other main surfaces since this surface has the largest attachment energy (Eatt= -119.53 kJ·mol-1). The (011) face whose total facet area was much larger than that of the other faces, was morphologically the most important.

Fig.3 Plot of energies and temperature vs simulation time for β-HMX (020) surface-acetone/γ-butyrolactone (volume ratio of 1 : 1) solvent interface at 298 K

Fig.4 Crystal morphology of β-HMX in vacuum calculated by the AE model

Table 1 Habit parameters of β-HMX crystal in vacuum calculated by the AE model

3.2 β-HMX crystal morphology in mixed solvents of acetone/γ-butyrolactone

The interaction energy can accurately reflect the ability for solvents to interact with crystal faces. Due to the solvent-surface interactions, the solute molecules are hampered in depositing at crystal faces, the relative growth rates of corresponding surfaces are slowed and the growth of crystal faces are inhibited, so ultimately the crystal morphology is affected which results from the relative growth rates of its faces in different directions. To examine the morphology changes of β-HMX crystals from solutions with different acetone/ γ-butyrolactone volume ratio mixtures, according to the Eq.(5), the interaction energies of acetone/γ-butyrolactone molecules adsorbed on different β-HMX surfaces under a variety of acetone/γ-butyrolactone ratios are calculated and the results are tabulated in Table 2. From Table 2, it can be found all of the interaction energies of β-HMX face-acetone/γ-butyrolactone mixed solvents interfacial model systems are negative. A negative value of the interaction energy represents an attractive interaction, and the larger the absolute value of the interaction energy, the stronger the interaction and the growth rate becomes slower for a particular face. So the results indicate that the adsorption of acetone/γ-butyrolactone mixed solvents on β-HMX surface is exothermic and thermodynamically favorable. Binding energy is defined as the negative value of the interaction energy. As can be seen from Table 2, for the co-solvents of acetone/γ-butyrolactone with the volume ratio of 1 : 2 and 3 : 1, the order of binding energies on different β-HMX growth faces can be compared in the following sequence: (100) ＞(102)＞(111) ＞ (011) ＞ (020). For the co-solvents with the volume ratio of 2 : 1, the order of binding energies is as follows:(102)＞ (100) ＞ (011) ＞(111) ＞ (020). For the co-solvents with the volume ratios of 1 : 1 and 1 : 3, the order of binding energies is as follows:(102)＞(111) ＞(011) ＞ (100) ＞ (020). The (020) face has the smallest binding energy in all case of co-solvents which indicates that (020) face has the weakest capability to interact with acetone/ γ-butyrolactone molecules and therefore (020) face is more easily grown.

According to the Eq.(4), the modified attachment energies and the relative growth rate in co-solvents of acetone/γ-butyrolactone under different volume ratios are calculated and the detailed results are summarized in Table 2.The simulation results showed that the relative growth rate of various crystal faces is different for the different volume ratios co-solvents. For crystals grown in co-solvents with the volume ratio of 1 : 3 and 1 : 1, the relative growth rate of the different crystal faces are (020) ＞ (100) ＞(102)＞(111)＞ (011). For crystals grown in co-solvents with the volume ratio of 1 : 2, the relative growth rate of the different crystal faces are (020) ＞(111) ≈(102) ＞ (011) ＞ (100). For crystals grown in co-solvents with the volume ratio of 2 : 1, the relative growth rate of the different crystal faces are (020) ＞(111) ＞ (100) ＞(102) ＞ (011). For crystals grown in co-solvents with the volume ratio of 3 : 1, the relative growth rate of the different crystal faces are (020) ＞ (011) ＞ (111¯) ＞(102) ＞ (100). As a whole, the relative growth rate of (020) face is highest in all cases which is consistent with the results of the analysis of the binding energy. As shown in Table 2, the absolute value of attachment energy decreased for all the habit faces with the co-solvent effect taken into consideration. This decrease indicated that the solvent effect restrained the growth rate. The comparison of the relative growth rate between in vacuum and in co-solvent revealed that the order on different crystal surface has changed due to strong co-solvent interactions and the fast-growing faces will disappear during the growth process.

Table 2 Calculated attachment energies for dominant crystal habit faces together with modified attachment energy and relative growth rates of faces under a variety of acetone/γ-butyrolactone ratios

Table 3 Crystal morphology for different crystal habits of β-HMX in co-solvents of acetone/γ-butyrolactone

The co-solvent effect crystal habits of β-HMX could be obtained by applying the generate habit task. Table 3 illustrates the morphology of these habits by listing the total facet percentage areas (%) and aspect ratio of their morphologically important crystal faces. It can also provide a comparison with the morphology of β-HMX in vacuum. The comparison between Table 1 and Table 3 revealed that with the effect of co-solvent the number of exhibiting faces decreased from 5 to 4 or 3, and the same variation was that the (020) face was invisible, (100) face also disappeared with the volume ratios of 1 : 3 and 1 : 1. Co-solvents with volume ratio of 1 : 3 enlargedthe total facet percentage area of (011) andwhile lowering that of (102). Co-solvents with volume ratio of 1 : 2 and 3 : 1 enlarged the total facet percentage area of (100) and (102) while lowering that ofand (011). Co-solvents with volume ratio of 1 : 1 enlarged the total facet percentage area of (011) while lowering that ofand(102). Co-solvents with volume ratio of 2 : 1 enlarged the total facet percentage area of (100),(102) and (011) while lowering that of

Fig.5 Crystal morphology of β-HMX in co-solvent of acetone/γ-butyrolactone with volume ratios of 1 : 3 to 3 : 1 predicted by the modified AE model

Fig.6 Comparison of the predicted β-HMX crystal morphology and the corresponding experiment shape grown from 1 : 1 molar acetone/γ-butyrolactone mixture (a): the experimental shape by the cooling crystallization10(Copyright (2004) American Chemical Society); (b) the predicted β-HMX crystal morphology by the MAE model with volume ratios of 1 : 1

Crystal habits of β-HMX calculated from co-solvents of acetone/γ-butyrolactone were depicted in Fig.5. The crystals morphologies grown from co-solvents were observed to have characteristic morphologies with the composition of the co-solvents. Compared to normal β-HMX, spherical β-HMX particles are less sensitive to impact force24. Aspect ratio can be used to characterize the degree of sphericity of particles. The aspect ratio for the crystal habit of β-HMX in vacuum was 1.59. The order of aspect ratio for the co-solvent effect crystal habit with different volume ratio is as follows: 3 : 1(5.28) ＞ 1 : 2(4.41) ＞ 1 : 1(2.24) ≈ 2 : 1(2.23) ＞ 1 : 3(1.93). When β-HMX grown from co-solvent (volume ratio = 3 : 1 and 1 : 2), the crystal shape was ship-like, in case of co-solvent with volume ratios of 2 : 1 and 1 : 1, morphologies were shown to be rectangular plate-like, in case of co-solvent with volume ratio of 1 : 3, morphologies were shown to be diamond-like. These results revealed that using co-solvent of acetone/γ-butyrolactone in the crystallization process might not be good for the spheroidization of β-HMX. Within the scope of our simulation, morphology of β-HMX is most close to sphere-like grown from acetone/γ-butyrolactone with volume ratio of 1 : 3. The β-HMX crystal morphology grown from acetone/γ-butyrolactone co-solvent with volume ratio of 1 : 1 predicted by the MAE model is shown in Fig.6(b), and the corresponding experimental shape obtained by the cooling crystallization grown from 1 : 1 molar acetone/ γ-butyrolactone mixture on the 2.0-L scale10is shown in Fig.6(a). It is seen that the predicted β-HMX morphology is in reasonable agreement with the experimental result.

3.3 β-HMX crystal morphology in mixed solvents of DMF/H2O

The use of different solvent mixtures in the crystallization of organic/inorganic compounds can lead to pronounced morphology changes11. In an attempt to comprehend the morphology changes of β-HMX crystals from solutions with different DMF/H2O volume ratio mixtures, the interaction energies on different β-HMX surfaces under a variety of DMF/H2O ratios are calculated and the results are summarized in Table 4. From Table 4, it can be found all of the interaction energies of β-HMX face-DMF/H2O mixed solvents interfacial model systems are still negative. Binding energy is defined as the negative value of the interaction energy. As can be seen from Table 4, for the co-solvents of DMF/H2O with the volume ratio of 1 : 3 and 1 : 2, the order of binding energies ondifferent β-HMX growth faces is written as follows:(102) ＞(100) ＞(111) ＞ (011) ＞ (020). For the co-solvents with the volume ratio of 1 : 1, the order of binding energies is as follows: (100) ＞(102) ＞ (011) ＞(111) ＞ (020). For the co-solvents with the volume ratio of 2 : 1, the order of binding energies is as follows:(102) ＞ (011) ＞(111) ＞ (100) ＞ (020). For the co-solvents with the volume ratio of 3 : 1, the order of binding energies is as follows: (100) ＞(102) ＞(111) ＞ (011) ＞(020). For the co-solvents of DMF/H2O, the (020) face still has the minimum solvent binding energy, indicating that (020) face has the weakest capability for solvent adsorption.

Table 4 Calculated attachment energies for dominant crystal habit faces together with modified attachment energy and relative growth rates of faces under a variety of DMF/H2O ratios

The modified attachment energies and the relative growth rate in co-solvents of DMF/H2O under different volume ratios are calculated and the detailed results are summarized in Table 4. The simulation results showed that the relative growth rate of various crystal faces is different for the different volume ratios co-solvents. For example, with the volume ratio of 1 : 3 the relative growth rate of the different crystal faces are (020) ＞(100) ＞(102) ＞(111) ＞ (011), with the volume ratio of 1 : 2 the relative growth rate changes in the order of (020) ＞(100) ＞(111) ＞(102) ＞ (011), with the volume ratio of 1 : 1 and 3 : 1 the relative growth rate changes in the order of (020) ＞(102) ＞(111) ＞ (011) ＞ (100), with the volume ratio of 2 : 1 the relative growth rate changes in the order of (100) ≈ (020) ＞(111) ＞(102) ＞ (011). On the whole, the relative growth rate of (020) face is higher which indicating that β-HMX crystal would grow more rapidly in the (020) direction.

Table 5 gives the morphology of these habits by listing the total facet percentage areas and aspect ratio of their morphologically important crystal faces. The comparison between Table 1 and Table 5 revealed that excluding the volume ratio of 1 : 3, with the effect of DMF/H2O co-solvent the number of exhibiting faces decreased, and the same variation was that the (020) face was invisible, (100) face also disappeared with the volume ratio of 2 : 1. Crystal habits of β-HMX calculated from co-solvents of DMF/H2O are displayed in Fig.7. The changes of β-HMX on crystal morphology depend on the DMF/H2O volume ratio. Generally, the crystal aspect ratio grows gradually with the increase in the relative volume of the organic solvent11. For instance, β-HMX crystal crystallized from co-solvents (DMF/H2O) with volume ratio of 1 : 3 exhibits a crystal aspect ratio of 1.70 were observed close to the sphere. Liu et al.25investigated the co-solvent effect on HMX in DMF/H2O by recrystallization technology. They found the HMX particle got the best spherical effect from DMF/H2O with volume ratio of 1 : 3.5. When the volume ratio is 1 : 2, the crystal aspect ratio is 1.89. A crystal aspect ratio of 2.08 is calculated for the crystallization of β-HMX with the volume ratio of 1 : 1, the crystal shape was rectangular plate-like. When the volume ratios are 2 : 1 and 3 : 1, the crystal aspect ratio are 2.76 and 2.73, respectively. The overall trend in crystal morphology is clear, the crystal aspect ratio of β-HMX crystal by and large rises linearly with the increase in the relativequantity of the organic solvents.

It should be mentioned that the crystallization of β-HMX in the presence of acetone/γ-butyrolactone (volume ratio = 3 : 1 and 1 : 2) as co-solvent, which showed a higher crystal aspect ratio, with respect to the crystallized with the same relative quantity of DMF/H2O as co-solvent. For instance, β-HMX crystallized in the presence of acetone/γ-butyrolactone (volume ratio = 3 : 1) exhibited a crystal aspect ratio of 5.28, while crystallization with DMF/H2O as a co-solvent under the same relative quantity yields crystals with an aspect ratio of 2.73. The comparison of the β-HMX crystal aspect ratios between acetone/γ-butyrolactone and DMF/H2O solvents with volume ratios of 1 : 3 to 3 : 1, which revealed that co-solvents of DMF/H2O with volume ratio of 1 : 3 could favor the spheroidization of β-HMX.

Table 5 Crystal morphology for different crystal habits of β-HMX in co-solvents of DMF/H2O

Fig.7 Crystal morphology of β-HMX in co-solvent of DMF/H2O with volume ratios of 1 : 3 to 3 : 1 predicted by the modified AE model

4 Conclusions

In this paper, we present the results of the effect of solvents on the crystal morphology of β-HMX crystal grown from mixed acetone/γ-butyrolactone solutions and DMF/H2O solutions with volume ratios of 1 : 3 to 3 : 1 by the modified AE with MD simulations. It was found that the binary solvent effects on different crystal faces varied, which changed the crystal morphology significantly. The morphology of β-HMX in mixed solvents was determined by the volume ratio of co-solvents. Excluding the volume ratio of 1 : 3 for the co-solvents of DMF/H2O, (020) face was not visible at all due to the smaller binding energy. The crystallization of β-HMX in the presence of acetone/γ-butyrolactone (volume ratio = 3 : 1 and 1 : 2) as co-solvent showed a higher crystal aspect ratio, with respect to the crystallized with the same relative quantity of DMF/H2O as co-solvent. The comparison of the β-HMX crystal aspect ratios between acetone/γ-butyrolactone and DMF/H2O solvents with volume ratios of 1 : 3 to 3 : 1, indicating that co-solvents of DMF/H2O with volume ratio of 1 : 3 could favor the spheroidization of β-HMX. This study would provide some suggestions on how to select solvents with expected morphology.

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Investigation of the Co-Solvent Effect on the Crystal Morphology of β-HMX Using Molecular Dynamics Simulations

CHEN Fang1,＊LIU Yuan-Yuan1WANG Jian-Long1SU Ning-Ning2LI Li-Jie3CHEN Hong-Chun1
(1School of Chemical Engineering and Environment, North University of China, Taiyuan 030051, P. R. China;2School of Science, North University of China, Taiyuan 030051, P. R. China;3School of Material Science and Engineering, Beijing Institute of Technology, Beijing 100081, P. R. China)

In an attempt to explain the co-solvent effect on the shape of β-HMX crystals, molecular dynamics simulations were applied to systematically investigate the interactions of β-HMX crystal faces and the co-solvents (acetone/γ-butyrolactone, dimethylformamide/H2O) by varying the volume ratio from 1 : 3 to 3 : 1. The growth habit of β-HMX in co-solvent was predicted using the modified attachment energy model. The results indicated that the (020) face of the β-HMX crystal has the weakest interaction with solvent molecule, and the binary solvent effects on different crystal faces varied such that the crystal morphology was affected significantly. The comparison of the β-HMX crystal aspect ratios grown from co-solvents with different volume ratios revealed that dimethylformamide/H2O with volume ratio of 1 : 3 favors the spheroidization of β-HMX.

β-HMX; Crystal morphology; Co-solvent; Molecular dynamics simulations; Attachment energy

November 28, 2016; Revised: February 24, 2017; Published online: February 24, 2017.

O641

10.3866/PKU.WHXB201702242

＊Corresponding author. Email: f_chen@nuc.edu.cn; Tel: +86-351-3922116.

The project was supported by the National Natural Science Foundation of China (11447219, 11547264).

国家自然科学基金(11447219, 11547264)资助项目

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