A study of the solvent effect on the crystal morphology of hexogen by means of molecular dynamics simulations

Abstract

In this work, molecular dynamics simulations have been performed to study the solvent effect on the crystal morphology of hexogen. The hexogen growth habits in a vacuum predicted by the AE model are dominated by the (111), (020), (200), (002), and (210) faces. Hexogen surfaces–acetone solvent micro interface models are constructed to study the adsorption behavior of acetone on these habit planes. The modified attachment energy model considering both the solvent–surface adsorption interactions and surface structures is proposed to predict the crystal morphology of hexogen in the acetone solvent. The calculations of the modified attachment energies suggest that via the effect of acetone solvent, the (210) face has the largest morphology importance and the morphological importance of the (111), (002) and (200) faces reduces, whereas the (020) face disappears. The predicted result is in reasonable agreement with the observed experiment shape. Furthermore, the diffusion coefficients of acetone solvent toward the different RDX surfaces suggests that the (210) and (111) faces are the dominate growth faces on the final RDX crystal habits, whereas the (020) face probably disappears, which validates the reliability of the modified attachment energy model.

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1. Introduction

Hexogen (RDX, C₃H₆N₆O₆), as a famous high energetic single-compound explosive, has been widely used in the preparation of solid propellants and plastic bonded explosives since it was synthesized.^1,2 It has been reported^3–6 that an RDX crystal grown from solvents has defects, impurities and irregular crystal shapes, which results in high sensitivity and low load density. The high sensitivity can cause unintended explosion and the low packing density results in a poor detonation property, thus it seriously impacts on the product performance of RDX and cannot meet the demand of modern weapon development. The sensitivity and detonation properties of explosives are largely influenced by the diverse crystal morphologies.¹ Research has shown that the spherical RDX compared with other crystal shapes such as needle and plates, can improve the loading density and impact sensitivity of RDX to a greater extent.^7–9 Therefore, to reduce sensitivity and improve performance, research on the crystal morphology of RDX has an important practical significance.

The crystal morphology results from the relative growth rates of each crystal face in different directions, and the faster a face grows, the faster it disappears.¹⁰ The crystal morphologies are governed by the crystal internal structures and external conditions such as crystallization technologies,^4,11 solvents^12–14 and additives.^15,16 Among them, it is widely considered that solvents play an important role on that. Compared to the traditional time consuming experiments, molecular simulation has been a promising and important tool to study the crystallization process at the atomistic/molecular length scales. So far, many scholars have adopted computer simulation to study the solvent effect on the crystal morphology of explosives. Duan¹⁷ investigated the crystal habits of HMX in the solvent by molecular dynamics simulation. They modified the attachment energy model by incorporating the additional term of solvent effect, and successfully predicted the crystal morphology of HMX in acetone. Lee¹⁸ made an attempt to interpret the cosolvent effect on the shape evolution of ADNBF crystal by molecular modeling techniques. The morphology of ADNBF recrystallized from cosolvents was predicted by the modified attachment energy model taken into account the binding site densities of surfaces. Zhang¹⁹ proposed a new occupancy model for predicting the crystal morphologies of energetic materials influenced by the solvent and temperature. The model was help to understand the relationship between the adsorption interactions of solvents with habit faces and crystal growth. Shi²⁰ explored the influence of trifluoroacetic acid on the growth habit of ANPyO crystal. They found the crystal morphology was also affected by the diffusion capacity of solvent molecules. To date, the research on the growth morphology of hexogen has made some progress at the molecular level.^21–24 In these work, they focused on the morphology investigation of RDX in solvents via Monte Carlo or molecular dynamics simulations. The effect of solvents on the RDX crystal habits might be evaluated by the calculation of the adsorption energies between solvents and specific crystal faces. In addition, Shim²⁵ developed the Burton–Cabrera–Frank (BCF) model for the morphology prediction of RDX crystal. The advanced BCF model was shown the reliable results and the understanding of the growth habit of RDX grown from solvents. However, the relationship between solvent effect and RDX crystal habit is still unclear and required further clarification.

The subject of our work is to understand the solvent effect on the crystal growth of RDX at the molecular level, and offer a reliable morphology prediction for the RDX crystal in the solvent-medium. In this paper, acetone is selected as the objective solvent, which is usually used as the recrystallization solvent to improve growth habits of RDX, due to the solubility of RDX in acetone being higher than other common organic solvents.²⁶ The RDX surfaces – acetone solvent adsorption interface models with molecular dynamics (MD) simulations are employed to study the adsorption behavior of acetone molecules on RDX habit planes. A modified attachment energy model considering the adsorption interactions and interface structure is used to predict the crystal morphology of RDX in acetone solvent. Furthermore, the moiety of acetone molecules on RDX surfaces is discussed by the calculation of diffusion coefficients. This paper is to establish a reliable method to study the solvent effect on the RDX crystal habits, and hope this work can provide some theoretical supports for RDX morphology control technology.

2. Method and model

2.1 Method

The crystal growth in solution is determined by not only the internal crystal structures but also the external growth conditions, such as the supersaturation and solvent etc. These factors have great influence on the crystal morphology. The classic attachment energy (AE) model taking into account the crystal anisotropic energies¹⁰ is usually applied to predict the crystal morphology in the vapor phase.^27,28 However, it is failure to predict crystals habits grown from solution, which may be attributed to disregarding the external crystallization conditions. Obviously, it cannot be determined only by the attachment energy. For the better prediction of crystal habits in solution, therefore, AE model should be modified by considering the growth environment.

The crystal growth is regarded as the epitaxial process of growth interface. The growth interface determines the crystal growth mechanisms. Through the analysis of PBC theory, Shim²⁵ pointed out that the RDX morphologically important growth faces are corresponded to the flat surface. Here, we make a hypothesis that there are no dislocations (step/kink) at the interface in the beginning of crystal growth. For the growth of flat surface without dislocations, it can be described by the two-dimensional nucleation theory.²⁹ Furthermore, the actual RDX industrial crystallization operates at the moderate supersaturation. In general, it corresponds to the two-dimensional nucleation theory according to the relation between the supersaturation and crystal growth mechanism. Therefore, in this paper we employ such theory to investigate the RDX growth process in solution.

The crystal growth in solution is effected by the kinetic and thermodynamics factors. For two-dimensional nucleation mechanism, the growth rate of crystal face is mostly controlled by the nucleation rate of the surface (J). Then, the normal growth rate of crystal face (R_hkl) can be expressed as

R_hkl = hSJ (1)

where h is the height of the step formed by nucleation, generally thought as the interplanar space,¹¹ S is the area of the surface swept by the two dimensional critical nucleus. The nucleation rate of the crystal surface is expressed by the following equationwhere v₀ is the collision frequency of atoms or molecules in the growth surface, ΔG_c is the system free energy change when the formation of a stable critical size of crystal nucleus in the growth surface, calculated by the following equation^10,30where γ is the surface free energy in solution, ω is the molecular specific volume, kTσ is the driving force of solution growth.

Hartman¹⁰ gave the relation of the attachment energy of the crystal face with its surface free energy, shown below

Myerson³¹ thought that due to the adsorption interactions between solvents and crystal face, it resulted in the change of crystal surface free energy in solution, calculated by the following formula

where E^s_hkl represents the solvent adsorption interactions. So, γ in solution can be rewritten as:

Then, eqn (6) is substituted eqn (3) and yield:

Combining eqn (1), (2) and (7), we derive the following equation:

where Z, d_hkl and V_p are crystal bulk properties. For a given solution crystallization conditions like the determined T and σ, when the two-dimensional nucleation growth mechanism is obeyed, it is seen from eqn (8) that R_hkl is shown to be approximately proportional to the (E^att_hkl − E^s_hkl)

R_hkl ∝ (E^att_hkl − E^s_hkl) (9)

It indicates that the existence of the solvent plays an important role on the crystal growth, when other crystallization factors are determined. If the adsorption interactions between the crystal face and solvent are strong, the adsorbed solvent molecules can form the solvation surface layer at the crystal–liquid interface, thereby inhibits the growth of the corresponding crystal face.^12,32 If a crystal face can grow, it requires the remove of the adsorbed solvent molecules on the surface. Such desolvation process may cost energies and result in the decrease of the attachment energy compared with that in vacuum, due to the adsorption interactions of solvent molecules with the special surface. Here, we define the modified attachment energy (E^att,m_hkl) representing the (E^att_hkl − E^s_hkl), so the eqn (9) can be further expressed as:

R_hkl ∝ E^att,m_hkl (10)

Now, we have derived the quantitative relation between the modified attachment energy and the growth rate of crystal face in solution. The modified attachment energy (MAE) model with the incorporation of the solvent effect term is established. Therefore, the crystal morphology in solution can be predicted by the calculations of the modified attachment energies of the important (h k l) faces. However, it should be pointed that other growth parameters like supersaturation and temperature etc. are also key to control the crystal habit. Singh³³ have reported a computational method to investigate the crystal growth in solution by considering the solvent and external growth conditions. This paper is emphasis on the role of solvent effect played on the crystal morphology of RDX in the case of the determined growth environment.

For the calculation of E^att,m_hkl, we adopt the following equation that has been successfully applied in the study of explosives morphologies like HMX and ANPyO crystals, especially HMX whose molecular structure is close to RDX.^17,20

where E^s_hkl is the adsorption energy between the solvent and the specific crystal face; A_box is the surface area of the simulated model along the (h k l) direction, and A_acc is the solvent-accessible area of the crystal face in the unit cell.

2.2 Model

All computation simulations were completed in Materials Studio 4.2 software.³⁴ The initial structure of RDX unit cell derived from Choi³⁵ is displayed in Fig. 1(a), which has eight irreducible RDX molecules with lattice parameters a = 13.182 Å, b = 11.574 Å, c = 10.709 Å, α = β = γ = 90°. And RDX molecule consists of three CH₂–N–NO₂ units arranged in a six-member ring as shown in Fig. 1(b), in which two nitro groups occupy axial positions (A) and the remaining nitro group is in the pseudo-equatorial positions (E). The AE model was selected to determine the crystal morphology of RDX in vacuum, which gives a list of morphologically possible growth faces. Subsequently, RDX crystal was cleaved parallel to the predicted (h k l) faces with a depth of three unit cell. 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 field.³⁶ The COMPASS force field is a powerful ab initio force field, which has been confirmed to able to give accurate prediction of structures and properties for condensed-phase materials including the energetic compounds.^24,37–39 In spite of this, COMPASS force field still needed to be validated by the lattice energy of RDX and the liquid properties of acetone solvent such as density and solubility parameter. The former was calculated by the geometry optimization method and the latters were obtained by simulating the acetone solvent phase. The three-dimensional periodic solvent box with 100 random distributed acetone molecules 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. For the acetone density, MD simulations with NPT ensemble were carried out at 298 K and 0.1 MPa, which were controlled by the Andersen thermostat⁴⁰ and Berendsen barostat.⁴¹ In the case of solubility parameter, NVT molecular dynamics simulations were performed at the same temperature by the Andersen thermostat. Geometry optimizations were used before respective MD simulations were run with the time of 500 ps.

Fig. 1 The RDX unit cell structure (a) and molecular configuration (b).

The RDX surface – acetone solvent micro interface model was constructed to study the influence of acetone solvent on RDX habit faces. The RDX surface layer constrained along a, b, and c directions, while the acetone adsorption layer placed along c axis above the RDX surface, in which all solvent molecules were able to move freely. A thickness of 50 Å vacuum was set above the adsorption layer to eliminate the effect of additional free boundaries. First, the initial interface models were geometry optimization. After that, MD simulations with NVT ensemble were carried out at the RDX crystallization temperature of 298 K, controlled by Andersen thermostat. For the equilibration stage, a period of 200 ps with a time step 0.1 fs dynamics was run. When the system reach the equilibrium, the production stage was performed with the time of 200 ps during which data were collected every 100 time steps. For the potential energy calculation, the atom based method with a cut off distance of 12.5 Å was set to calculate the van der Waals (vdW) interaction and the Ewald summation method was applied to calculate the Coulomb interaction. The final 100 frames of dynamic trajectory (last 10 000 steps) were used to calculate the adsorption energy by the following equation

where E_tot,i is the total energy of each frame, E_sur,i and E_sol,i are the energies of isolated RDX surface layer and acetone adsorption layer of each frame, respectively. The calculation of E_ads indicates a statistical result derived from the ensemble average of MD simulations. The solvent-accessible area of the crystal surface is calculated by the Connolly surface model. The Connolly surface model provides a quantitative approach to locate the regions on the crystal surface that are accessible to solvent molecules, which is widely applied in the fields of enzymology, rational drug design, and the location of possible antigenic determinants on viruses.⁴² At last, the modified attachment energies of RDX habit faces were calculated according to the eqn (10), and the corresponding crystal morphology of RDX in acetone solvent was predicted by the MAE model.

3. Results and discussion

The validation of COMPASS force field can be evaluated by calculating the RDX lattice energy and the liquid properties of acetone such as solvent density and solubility parameter. The lattice energy (E_latt) is defined as the total internal (intermolecular plus intramolecular) energy of the molecule in the crystal minus the corresponding energy of the molecule in the gas-phase.^43,44 It also can be determined from the experimental sublimation enthalpy (ΔH_sub) by the following equation⁴⁵

E_latt = −ΔH_sub − 2RT (13)

where R and T are the gas constant and temperature, respectively; 2RT factor is commonly accepted correction to take into account the zero point energy and thermal corrections at 298 K. Therefore, the reliability of the force field is assessed via the comparison of the calculated lattice energy with the “experimental” value. The Hildebrand solubility parameter (δ) is defined as follow⁴⁶where ΔE is cohesive energy; ΔH_vap is vaporization enthalpy and V is the mole volume of the solvent.

The solvent density and solubility parameter of acetone as well as the RDX lattice energy calculated by COMPASS force field are presented in Table 1. From Table 1, it is seen that the calculation value of RDX lattice energy is close to its experiment value, indicating COMPASS force field parameters suitable to RDX crystal. Besides, the computed solvent density and solubility parameter of acetone are agreement with the corresponding experiment values, which shows that COMPASS force field is also applicable to acetone solvent. Consequently, COMPASS force field is validation for our simulation model.

Table 1 The density and solubility parameter of acetone solvent as well as the RDX lattice energy calculated by COMPASS force field

	Elatt/kcal mol^−1	ρ/g cm^−3	δ/(J cm^−3)^1/2
Exp.	−30 × 10 (ref. 47)	0.781 (ref. 48)	19.99 (ref. 49)
COMPASS	−27.90	0.761	19.09

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The crystal morphology of RDX predicted by the AE model in vacuum is shown in Fig. 2. The calculated crystal habit parameters of RDX are presented in Table 2. As seen from Fig. 2, the predicted RDX morphology in vacuum is similar to the hexahedron shape, which comprises of (111), (020), (002), (200) and (210) growth faces. It can be found from Table 2 that (111) face has the minimum attachment energy of 103.32 kcal mol⁻¹ and (210) face has the maximum value of 133.26 kcal mol⁻¹. Accordingly, the morphology importance of (111) face is the largest among the RDX habit faces, while (210) face has the lowest morphological importance.

Fig. 2 The crystal morphology of RDX in vacuum predicted by the AE model.

Table 2 The habit parameters of RDX crystal in vacuum calculated by the AE model

(h k l)	dhkl/Å	E^atthkl/kcal mol^−1
(210)	5.73	−133.26
(200)	6.59	−131.47
(002)	5.35	−108.90
(020)	5.79	−108.10
(111)	6.75	−103.32

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The equilibrium configurations of RDX surface – acetone solvent adsorption interface models are displayed in Fig. 3. From these snapshots, it can be seen that acetone molecules have close attached on RDX surfaces and formed acetone surface layers, which implies that there are strong adsorption interactions between RDX surfaces and acetone solvent. The adsorption energies of acetone solvent adsorbed on different RDX surfaces are listed in Table 3. As seen From Table 3, it is found that (210) face has the largest adsorption energy of 807.30 kcal mol⁻¹ while (020) face has the least value of 315.09 kcal mol⁻¹. Besides, it also shows that the adsorption energies of (210), (111), (200) and (002) faces are much larger than that of (020) face. The rank of adsorption energies of different RDX growth faces can be written as follow: (210) > (111) > (200) ≈ (002) > (020). The adsorption energy reflects the affinity capacity of solvents on the particular surfaces. Therefore, the adsorption ability of acetone solvent with (210) face is the strongest while the adsorption interaction between acetone molecules and (020) face is the weakest.

Fig. 3 The snapshots of equilibrium configurations of different RDX surface-acetone solvent adsorption models.

Table 3 The adsorption energies between acetone solvent and different RDX crystal surfaces^a

(h k l)	Etot	Esur	Esol	Eads
a Note: all energies are in kcal mol^−1.
(020)	−22 182.95	−20 243.63	−1624.23	−315.09
(002)	−22 968.43	−20 257.97	−2280.89	−429.57
(200)	−22 845.89	−20 134.09	−2269.00	−442.80
(111)	−28 637.86	−22 897.01	−5099.06	−641.79
(210)	−47 673.95	−40 158.11	−6708.54	−807.30

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It is well known that the solvent has an important effect on the crystal morphology.^12,50 It is believed that through the surface diffusion solvent molecules may adsorb on the surface, resulted in blocking the incorporation of solute molecules on the surface bonding sites, thus inhibit the growth of crystal surface and finally change the crystal morphology. Hence, the solvent–surface adsorption interaction represented the solvent effect to a large extent is usually considered as an important factor changing crystal habit. However, it is insufficient only from the adsorption energy to explain the solvent effect on the crystal morphology, which is unable to determine the morphology change influenced by the solvent. The solvent effect may depend on not only the adsorption interaction, but also the surface structure.

The surface anisotropy characteristic of crystal results in the different atoms or molecules packing structures of crystal surfaces. Since the RDX molecule is the non-centrosymmetric growth unit,^18,25 RDX surfaces have diverse and complex molecular packing orientations. Thus, it makes the adsorption behaviors of solvent molecules on different RDX surfaces complicated. The molecular packing structures of RDX surfaces are displayed in Fig. 4. It shows that the molecular arrangement of (111) plane are relative flat at the molecular level, while those of (020), (002), (210) and (200) surfaces are uneven with many large voids, which may contribute to solvent molecules adsorption. To quantitatively describe the surface features, we introduce a parameter S defined as the ratio of the solvent-accessible area to the corresponding crystal face area.¹⁷ The parameter S values of RDX surfaces calculated by the Connolly surface model are listed in Table 4. From Table 4, it is seen that among all RDX habit faces, (200) face has the maximum S value of 1.52 and (111) face has the minimum S value of 1.04. The larger S indicates the rougher topography of crystal surface, which is more convenient for solute or solvent molecules incorporation.

Fig. 4 The geometry structures of different RDX planes represented by the Connolly surface The pink grid on the RDX crystal face devotes the Connolly surface.

Table 4 The parameter S values of RDX surfaces calculated by the Connolly surface model^a

(h k l)	(111)	(020)	(002)	(200)	(210)
a Notes: Aacc is the solvent-accessible area of a (h k l) face, and Ahkl is the area of the corresponding (h k l) face. Area unit is Å^2.
Aacc	279.49	167.23	187.16	188.50	360.84
Ahkl	267.75	141.15	152.55	123.93	285.19
S	1.04	1.18	1.23	1.52	1.26

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The slices of RDX habit faces represented by the Connolly surface along the ab plane are shown in Fig. 5, which can reflect the step structures of different crystal surfaces. It shows that (200), (210), (002) and (020) surfaces have more multiform and regular step structures than (111) surface. In addition, it is also observed that the polar nitro groups and nonpolar hydrogen atoms are exposed to (002) and (200) surfaces, and (111) surface appears the polar nitro groups and methylene amine groups as well as nonpolar hydrogen atoms. The slice of (210) face shows the exposure of strong polar nitroamine and non-polar methylene as well as hydrogen atoms, while only the nonpolar methylene groups are appeared on the (020) slice. From the surface chemistry, (210), (002) and (200) as well as (111) faces may be classified as the polar surfaces due to the exposed polar groups (e.g. the NO₂ groups), and (020) face is considered as the non-polar surface because of the appeared nonpolar groups (e.g. the CH₂ groups).

Fig. 5 The view of the slices of different RDX Connolly surfaces along the ab plane color codes: red, white, gray and blue ones represent the O, H, C and N atoms of RDX molecule, respectively.

The Connolly surface model provides a quantitative approach for locating the regions of the crystal surface that would be likely solvent molecules adsorb on. The larger solvent-accessible surface area means the more adsorption sites on the surface. Consequently, it is thought that the area ratio of solvent-accessible surface to the crystal surface may be approximately considered as the active sites density for solvent adsorption to some extent, which may be used to describe the solvent effect. Furthermore, it is suggested that polar solvents like acetone preferentially adsorb on polar faces especially the strong polar faces, and nonpolar solvents on nonpolar faces.^51,52 This can explain why the adsorption energies of (210), (111), (200) and (002) faces are much larger than that of (020) face. That is to say, the adsorption interactions of acetone solvent on RDX polar surfaces are much stronger than those on nonpolar (020) surface. Besides, the morphology importance of polar face increases in the polar solvent, while it weakens in the non-polar solvent.⁵³ Here, we may qualitatively predict that the morphology importance of RDX polar faces increases in the acetone solvent, while that of non-polar (020) face decreases, even probably disappears. In a word, the above discussions indicate that the solvent effect depends on both the solvent–surface adsorption interactions and surface structures.

The modified attachment energies of RDX habit faces in acetone solvent calculated by eqn (11) are summarized in Table 5. From Table 5, it can be found that (210) face has the minimum E^att,m_hkl of 19.76 kcal mol⁻¹ and (020) face has the maximum E^att,m_hkl of 66.62 kcal mol⁻¹. The order of the modified attachment energies of RDX habit faces is (210) < (111) < (002) < (200) < (020), which is different from that in vacuum. This indicates that acetone solvent has an important effect on RDX crystal growth.

Table 5 The modified attachment energies of RDX habit faces in acetone solvent^a

(h k l)	E^atthkl	Eads	Aacc	Abox	E^att,mhkl
a Note: all energies are in kcal mol^−1, areas are in Å^2.
(111)	−103.32	−641.79	279.49	2409.73	−28.88
(020)	−108.10	−315.09	167.23	1270.30	−66.62
(002)	−108.90	−429.57	187.16	1372.97	−50.34
(200)	−131.47	−442.80	188.50	1115.31	−56.63
(210)	−133.26	−807.30	360.84	2566.71	−19.76

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Table 6 gives the relative growth rates of RDX habit faces in acetone solvent. As seen from Table 6, compared with those in vacuum, the relative growth rate of (210) face becomes the slowest and the relative growth rates of (020), (002) and (200) faces are faster, in which the growth of (020) face is fastest. It suggests that via the effect of acetone solvent, (210) face should have the largest morphology importance and the morphology importance of (111), (002) and (200) faces reduces, while (020) face disappears. The crystal morphology of RDX grown from acetone predicted by the MAE model is shown in Fig. 6(a), and the corresponding experiment result by the cooling crystallization¹⁸ is shown in Fig. 6(b). It can be seen that the MAE model prediction is in good agreement with the observed experiment shape.

Table 6 The relative growth rates of RDX habit faces in vacuum and acetone solvent, respectively

(h k l)	E^atthkl	R^vachkl	E^att,mhkl	R^solhkl
(111)	−103.32	1	−28.88	1
(020)	−108.10	1.05	−66.62	2.31
(002)	−108.90	1.05	−50.34	1.74
(200)	−131.47	1.27	−56.63	1.96
(210)	−133.26	1.29	−19.76	0.68

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Fig. 6 The comparison of the predicted RDX crystal morphology and the corresponding experiment shape grown from acetone (a): the predicted RDX crystal morphology by the MAE model; (b): the experimental shape by the cooling crystallization¹⁸ (Copyright (2013) American Chemical Society).

In addition to the discussion above, the surface diffusion of solvent molecules at the interface is contribute to comprehend the effect of solvents on the crystal morphology.^20,54 The diffusions of acetone molecules to RDX surfaces are evaluated by the diffusion coefficients. The diffusion coefficient (D) is defined as the derivative of the mean square displacement (MSD) with respect to time, calculated by the following equation⁵⁵

The calculated diffusion coefficients of acetone solvent at the different RDX planes according to eqn (15) are presented in Table 7. As seen from Table 7, the D value of acetone solvent at the (210) face is the largest of 3.3 × 10⁻⁵ cm² s⁻¹, while that at the (020) face is the lowest of 0.7 × 10⁻⁵ cm² s⁻¹. The sequence of diffusion coefficients at RDX habit faces is that (210) > (111) > (002) ≈ (200) > (020), which is just reversed the order of modified attachment energy. It indicates that the surface diffusions of acetone solvent at RDX polar faces especially (210) and (111) faces are much stronger than that non-polar (020) face. The diffusion coefficient reflects the diffusion capability of the solvent toward the surface. It is considered that the stronger diffusivity means solvent molecules adsorbed on the surface more easily to a great extent. Namely, if the diffusion coefficient is larger, the solvent interaction is stronger, that the solvent effect on the growth of crystal face is more notable. Due to the diffusion coefficient of (210) and (111) faces being about three times than that (020) face, it means that the growth rate of (020) face should be much faster than those of (210) and (111) faces in the acetone-medium. If RDX grown from acetone without stirring, (210) and (111) faces will have the largest morphology importance and (020) face is probably to disappear on the final RDX crystal, which is consistent with the prediction results of MAE model. The analysis of diffusion coefficient, on the one side, shows another visual angle to assess the solvent effect on the RDX morphology, on the other hand, validates the reliability of MAE model.

Table 7 The diffusion coefficient of acetone solvent at different RDX surfaces

(h k l)	D/ × 10^−5 cm^2 s^−1
(020)	0.7
(200)	0.9
(002)	1.0
(111)	2.8
(210)	3.3

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4. Conclusion

In this work, the growth morphology of RDX crystal in acetone solvent is predicted by the modified attachment energy model incorporating the solvent effect. The micro interface adsorption model with molecular dynamics simulations is performed to study the solvent effect on the RDX morphology. In addition, the moiety of acetone molecules on the RDX growth faces is discussed via the calculation of diffusion coefficient.

The crystal morphology of RDX in vacuum predicted by AE model is dominated by the (111), (020), (200), (002), and (210) faces, in which (111) face has the largest morphology importance. From surface chemistry, (210), (002) and (200) as well as (111) faces may be classified as the polar surfaces due to the exposed polar groups (e.g. the NO₂ groups), and (020) face is considered as the non-polar surface because of the appeared nonpolar groups (e.g. the CH₂ groups). The calculation of adsorption energy indicates that the adsorption interactions between acetone solvent and RDX polar faces are much stronger than that the nonpolar (020) face. The analysis of RDX surface structures shows that compared with (111) surface, the rougher topographies of (200), (210), (002) and (020) surfaces are more convenient for acetone molecules incorporation. Therefore, the solvent effect depends on both the solvent–surface adsorption interactions and surface structures.

The modified attachment energies calculated in the acetone solvent suggest that (210) and (111) faces become the morphologically important growth face and the morphology importance of (002) and (200) faces reduces, whereas (020) face disappears. The predicted RDX morphology in the acetone is in reasonable agreement with the observed experiment shape. Furthermore, the discussion on the diffusion coefficient suggests that (210) and (111) faces will be the dominate growth faces on the final RDX crystal habits, whereas (020) face is probably to disappear. It validates the reliability of the proposed MAE model.

References

1. U. Teipel, Energetic materials: particle processing and characterization, John Wiley & Sons, 2006.
2. I. J. Lochert, R. M. Dexter and B. L. Hamshere, Evaluation of Australian RDX in PBXN-109, 2002.
3. P. Halfpenny, K. Roberts and J. Sherwood, J. Cryst. Growth, 1984, 69, 73–81.
4. T. Tillotson, L. Hrubesh, R. Simpson, R. Lee, R. Swansiger and L. Simpson, J. Non-Cryst. Solids, 1998, 225, 358–363.
5. R. M. Doherty and D. S. Watt, Propellants, Explos., Pyrotech., 2008, 33, 4–13.
6. C. W. Roberts, S. M. Hira, B. P. Mason, G. F. Strouse and C. A. Stoltz, CrystEngComm, 2011, 13, 1074–1076.
7. A. E. van der Heijden and R. H. Bouma, Cryst. Growth Des., 2004, 4, 999–1007.
8. A. E. van der Heijden, Y. L. Creyghton, E. Marino, R. H. Bouma, G. J. Scholtes, W. Duvalois and M. C. Roelands, Propellants, Explos., Pyrotech., 2008, 33, 25–32.
9. C. Spyckerelle, G. Eck, P. Sjöberg and A. M. Amnéus, Propellants, Explos., Pyrotech., 2008, 33, 14–19.
10. P. Hartman and P. Bennema, J. Cryst. Growth, 1980, 49, 145–156.
11. J.-W. Kim, D. B. Park, H.-M. Shim, H.-S. Kim and K.-K. Koo, Ind. Eng. Chem. Res., 2012, 51, 3758–3765.
12. M. Lahav and L. Leiserowitz, Chem. Eng. Sci., 2001, 56, 2245–2253.
13. M. N. Bhat and S. Dharmaprakash, J. Cryst. Growth, 2002, 242, 245–252.
14. J. Chen, J. Wang, J. Ulrich, Q. Yin and L. Xue, Cryst. Growth Des., 2008, 8, 1490–1494.
15. C. Thompson, M. C. Davies, C. J. Roberts, S. J. Tendler and M. J. Wilkinson, Int. J. Pharm., 2004, 280, 137–150.
16. M. J. Siegfried and K.-S. Choi, J. Am. Chem. Soc., 2006, 128, 10356–10357.
17. X. Duan, C. Wei, Y. Liu and C. Pei, J. Hazard. Mater., 2010, 174, 175–180.
18. H.-E. Lee, T. B. Lee, H.-S. Kim and K.-K. Koo, Cryst. Growth Des., 2009, 10, 618–625.
19. C. Zhang, C. Ji, H. Li, Y. Zhou, J. Xu, R. Xu, J. Li and Y. Luo, Cryst. Growth Des., 2012, 13, 282–290.
20. W. Shi, M. Xia, W. Lei and F. Wang, J. Mol. Graphics Modell., 2014, 50, 71–77.
21. J. Ter Horst, R. Geertman, A. Van der Heijden and G. Van Rosmalen, J. Cryst. Growth, 1999, 198, 773–779.
22. J. Ter Horst, R. Geertman and G. Van Rosmalen, J. Cryst. Growth, 2001, 230, 277–284.
23. G. Chen, M. Xia, W. Lei, F. Wang and X. D. Gong, Can. J. Chem., 2014, 92, 849–854.
24. G. Chen, M. Xia, W. Lei, F. Wang and X. Gong, J. Mol. Model., 2013, 19, 5397–5406.
25. H.-M. Shim and K.-K. Koo, Cryst. Growth Des., 2014, 14, 1802–1810.
26. D.-Y. Kim and K.-J. Kim, J. Chem. Eng. Data, 2007, 52, 1946–1949.
27. P. Hartman, J. Cryst. Growth, 1980, 49, 157–165.
28. P. Hartman, J. Cryst. Growth, 1980, 49, 166–170.
29. H. J. Leamy, G. H. Gilmer, K. A. Jackson and J. M. Blakely, Surface Physics of Materials, New York, Academic Press, 1975.
30. Y. Zhang, PhD thesis, Tianjing university, 2004.
31. M. Saska and A. S. Myerson, J. Cryst. Growth, 1983, 61, 546–555.
32. J. Chen and B. L. Trout, Cryst. Growth Des., 2010, 10, 4379–4388.
33. M. K. Singh and A. Banerjee, Cryst. Growth Des., 2013, 13, 2413–2425.
34. Materials Studio 4.0, Discover/Accelrys, San Diego, CA, 2007.
35. C. S. Choi and E. Prince, Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem., 1972, 28, 2857–2862.
36. H. Sun, J. Phys. Chem. B, 1998, 102, 7338–7364.
37. S. W. Bunte and H. Sun, J. Phys. Chem. B, 2000, 104, 2477–2489.
38. L. Qiu, H.-M. Xiao, W.-H. Zhu, J.-J. Xiao and W. Zhu, J. Phys. Chem. B, 2006, 110, 10651–10661.
39. X.-J. Xu, H.-M. Xiao, J.-J. Xiao, W. Zhu, H. Huang and J.-S. Li, The J. Phys. Chem. B, 2006, 110, 7203–7207.
40. H. C. Andersen, J. Chem. Phys., 1980, 72, 2384–2393.
41. H. J. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola and J. Haak, J. Chem. Phys., 1984, 81, 3684–3690.
42. M. L. Connolly, Science, 1983, 221, 709–713.
43. D. S. Coombes, C. R. A. Catlow, J. D. Gale, M. J. Hardy and M. R. Saunders, J. Pharmaceut. Sci., 2002, 91, 1652–1658.
44. M. Singh, J. Cryst. Growth, 2014, 396, 14–23.
45. A. Gavezzotti, Modell. Simul. Mater. Sci. Eng., 2002, 10, R1.
46. J. Hildebrand and R. Scott, The solubility of nonelectrolytes, Reinhold, New York, 1964, p. 411.
47. J. M. Rosen and C. Dickinson, J. Chem. Eng. Data, 1969, 14, 120–124.
48. A. Goyal and M. Singh, J. Indian Chem. Soc., 2007, 84, 250–255.
49. B. Liang, Polymer Physics, Chinese Textile Press, Shanghai, 2000.
50. C. Stoica, P. Verwer, H. Meekes, P. Van Hoof, F. Kaspersen and E. Vlieg, Cryst. Growth Des., 2004, 4, 765–768.
51. A. Nokhodchi, N. Bolourtchian and R. Dinarvand, Int. J. Pharm., 2003, 250, 85–97.
52. V. Bisker-Leib and M. F. Doherty, Cryst. Growth Des., 2003, 3, 221–237.
53. Z. Berkovitch-Yellin, J. Am. Chem. Soc., 1985, 107, 8239–8253.
54. J. Z. Yang, Q. L. Liu and H. T. Wang, J. Membr. Sci., 2007, 291, 1–9.
55. A. Einstein, Investigations on the Theory of the Brownian Movement, Courier Dover Publications, 1956.

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Footnote

† These authors contributed equally to this work.

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