Surface-Induced Energetics, Electronic Structure, and Vibrational

Subscriber access provided by University of Otago Library

Article

Surface-Induced Energetics, Electronic Structure, and Vibrational Properties of #-HMX Nanoparticles: A Computational Study Zhichao Liu, Weihua Zhu, and Heming Xiao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09795 • Publication Date (Web): 11 Nov 2016 Downloaded from http://pubs.acs.org on November 17, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Surface-Induced Energetics, Electronic Structure, and Vibrational Properties of β-HMX Nanoparticles: A Computational Study Zhichao Liu, Weihua Zhu,* Heming Xiao Institute for Computation in Molecular and Materials Science and Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, China ABSTRACT: Surface chemistry plays an prominent part in the behaviors of condensed phase materials and nanoparticles. A combinational strategy based on density functional theory (DFT) and density functional tight binding (DFTB) methods was used to study the surface-induced effect on the energetics, electronic structure, and vibrational properties of a series of β-octatetramethylene tetranitramine nanoparticles (β-HMX NPs). A comparative analysis of the NPs, isolated constituent molecule, and periodic solid-state phase of β-HMX indicates that the NPs possess quite different characteristics from either the constituent molecule or bulk crystal. The anitsotropy of surface energies, enthalpy of sublimation, and melt point for the NPs are predicted. The surface-induced surface states of the HMX NPs lead to a significant reduction of the energy gap and provide active sites at surfaces. The vibrational properties of the experimentally determined strong modes are compared and discussed among the NPs, gas phase, and solid phase of HMX. The possible role of the surface molecules for the NPs in decreasing the material stability is elucidated. Our results provide basic understandings of the high activity of nanosized energetic materials.

*

Corresponding author. E-mail: [email protected] 1

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1. INTRODUCTION The chemical events in the earliest decomposition stages of energetic materials under extreme conditions are related with their stability and sensitivity. It is known that the initiation decomposition mechanisms depend strongly on the microenvironment of their constituent molecules in the bulk materials.1-4 Both experimental and theoretical approaches can provide fundamental information about the chemistry of initiation decompositions of the energetic materials. For condensed phase energetic materials, the physicochemical phenomena in the initial decompositions under external perturbation are closely related with their surfaces and interfaces.3-9 Therefore, to uncover the role of the surfaces in the initial decomposition of the energetic materials is helpful for improving safety in storage, utilization, and transportation and for designing new high-energy low sensitivity energetic materials. Recent advances in theoretical and experimental approaches have made people obtain abundant information about the roles of the surfaces (external surfaces, interfaces, and internal surfaces such as vacancies, voids, etc.) in the decompositions of the energetic materials.3,4,10-12 For example, previous ab initio studies presented activation energy and kinetics of decomposition reactions at the surface and internal vacancies for the β- and δ-HMX crystals.3,4 These results confirmed that the surface and vacancy in the bulk altered their decomposition kinetics and mechanisms. Sharia and Kuklja3 found that the N-NO2 homolysis of the HMX molecule on the surfaces of β-HMX requires lower activation energy and progresses orders of magnitude faster reaction rate than that in the bulk crystal. They also reported that the HONO

2


Page 2 of 37

Page 3 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


elimination needs reduced activation energy due to the surface effect, but an increase of the HONO elimination reaction rate is less dramatic than that of the N-NO2 bond dissociation. Recent ReaxFF molecular dynamics simulations on the condensed phase HMX with molecular vacancies indicated that the vacancy-contained HMX presented more rapid response to the external heating as compared to the ideal bulk. This also results in lower global activation energy and faster decomposition chemistry.10 In addition, self-consistent-charge density-functional tight-binding method (SCC-DFTB) in combination with multiscale shock technique (MSST) simulations on the vacated HMX crystal initiated by shock loadings12 indicated that the decompositions of HMX primarily occurred at the molecular vacancy. But no direct evidence showed that the induced vacancies can increase the decomposition reaction rate. Recent experimental studies on the thermolysis of some nanosized energetic materials, e.g. HMX, RDX, CL-20, TATB, NTO, etc.

13-21

indicated that this

nano-structuring effects can lower the decomposition temperature and reduce apparent activation energy of the decompositions. It is known that nano energetic materials have reduced particle sizes and so lead to increased specific surface area. Therefore, the decreased particle sizes of the energetic materials are main reasons for lowering their thermal stability. It can be expected that there is a strong correlation between the surface molecules and material sensitivity to the external thermal stimulus. Many theoretical and experimental evidences indicate that the surface molecules play an important role in triggering the initial decompositions of the energetic materials. But the atomistic details of how the surface affects the stability and

3



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

sensitivity of solid energetic materials are yet to be elucidated due to their immense complexity. In this work, we used density functional tight binding method and density functional theory (DFT) to study the energetics, electronic structure, and vibrational properties of a series of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX) nanoparticles (NPs), as it being one of the most important and widely used explosives. We will explain how the surface molecules of β-HMX induce the surface states that lead to a dramatic reduction in the band gap and provide reactive sites on the surface that trigger its decomposition. Our results indicate that the nanosized phases of practical energetic materials play a vital role in lowering their thermal stability and provide insights into the comprehensive understandings of the energetic material sensitivity.

2. COMPUTATIONAL DETAILS DFT and density functional tight-binding method (DFTB) were used to do a comparative study of the NPs, isolated constituent molecule, and periodic solid-state phase of β-HMX. DFT Calculations on the HMX NPs (including isolated molecule) and periodic solid state simulations were performed using the generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) functional including dispersion correction using Grimme scheme (G06)22-23 as implemented in DMol3 code.24 The double-numerical basis set with polarization d-function for all nonhydrogen atoms (DND basis sets) were used in all DFT calculations. The basis set

4


Page 4 of 37

Page 5 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


provides reasonable accuracy for describing the model systems. DFT-predicted lattice parameters of β-HMX unit cell are as follows: a=6.56 Å, b=10.9 Å, c=8.70 Å, and β=124.9°, which are in good agreement with the experimental values of a=6.54 Å, b=11.05 Å, c=8.70 Å, and β=124.3°.25 The deviation of the lattice parameters is less than 1.4 %. The maximum deviation of the bond length is about 2.8 %. The SCF tolerance was 1.0×10-5 and Brillouin zone sampling was performed using the Monkhorst-Pack scheme with k-point grids of 2×1×2 for bulk crystal and 1×1×1 for the HMX NPs. Comparative DFTB calculations of both the HMX NPs and ideal bulk crystal were performed with self-consistent-charge density functional tight binding method with Universal

Force

Field

(UFF)-based

Lennard-Jones

dispersion

corrections

(SCC-DFTB-D, DFTB for short in this work) as implemented in the DFTB+ code.26-29 This method is based on a second-order expansion of the Kohn-Sham total energy in density functional theory (DFT) with respect to charge density fluctuations. The pbc Slater-Koster parameter set was employed to describe the atomic interactions of the organic molecular system. The SCC tolerance is 1.0×10-8 a.u. (maximum difference in charge between two SCC cycles). The Monkhorst-Pack k-point meshes of 5×2×3 was used for the deal bulk and 1×1×1 for the NPs. The optimized unit cell parameters by DFTB are a=6.43 Å, b=11.08 Å, c=8.68 Å, and β=123.6°, agreeable with the experiment results.25 The deviation of the lattice parameters is less than 1.8 %. The maximum deviation of the bond length is 3.6 %. The DFTB method has been proved to produce considerable accuracy and efficiency for many other organic materials and

5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

comparable results with DFT ones.30-32 For comparison, we performed slab model calculations for the crystal facets exposed on the β-HMX NPs by using both DFT and DFTB as mentioned above. Each slab model consists of four molecular layers with a vacuum of 20 Å during DFTB calculations and of 10 Å in DFT calculations on top. The phonon frequencies of the isolated HMX molecule, NPs, and ideal bulk crystal were calculated from the response to small atomic displacements. For different HMX NPs, the surface molecules are used to generate partial Hessian matrix for calculating the vibrational frequencies of the models.

3. RESULTS AND DISCUSSION 3.1 Model Systems. HMX has four polymorphs that exhibit markedly different chemical reactivity.33-34 It is deemed that the observed differences in the sensitivity of the four HMX phases are caused by the following reasons: crystal density (1.90 g·cm-3 for β-HMX25 and 1.78 g·cm-3 for δ-HMX35), cracks and hot spots during the β-δ phase transition, conformational change, and surface polarization.4 Hence, the main causes that determine the sensitivity of the HMX might still be obscured due to the complex interplay of many factors. To understand the size-induced influence on the chemical stability, the β-HMX, the thermodynamically stable form under ambient conditions, is suitable for selecting as an ideal model to explain the effects of those many factors.33-34 The initial configurations of the β-HMX NPs were cut spherically with specified average diameters in range 1.4-3.4 nm from the experimentally 6


Page 6 of 37

Page 7 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


obtained HMX crystal. We show several representatives of the HMX NPs in Figure 1a and other different sizes of NPs are provided in Table S1. The DFT method was used to calculate the HMX NPs with sizes up to 1.8 nm due to computational efficiency. For larger NPs with sizes up to 3.4 nm, the DFTB method was utilized. In all calculations, the geometries of the NPs (including isolated molecule) were fully relaxed in a box of 50×50×50 Å at the DFTB level and of less than 35×35×35 Å at the DFT level. The sizes of the boxes can avoid the interactions between translational cells. The relaxed configurations of the HMX NPs have an average diameter of 3.4 nm, as illustrated in Figure 1. It is found that the most abundant surface planes in the HMX NPs are marked as (120), ( 102 ), (100), (010) etc., respectively. 3.2 Energetics of HMX NPs. 3.2.1 Excess Energy in the HMX NPs. The quantum size effect on the energy of the HMX NPs can be evaluated by the excess energy than the bulk crystal as follows:

ε = (Etotal − nHMX EHMX ) / nHMX

(1.1)

where Etotal is the total energy of system, nHMX is the number of the HMX molecules in system, and EHMX is the normalized energy of the bulk HMX per molecule. It is seen in Figure 1b that DFT-predicted ε values are relatively larger than DFTB-predicated ones with the differences in the range 12.9-14.7 kJ·mol-1. However, both the two methods have yielded consistent decreasing trend of the ε values as the particle size increases. The 3.4 nm HMX NPs has more than the excess energy of 56 kJ·mol-1stored in system compared to the bulk crystal by DFTB. It can be expected 7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 37

that the surface molecules of the HMX NPs have higher energy storage. We also note that the experimentally obtained global activation energies of thermal decompositions of different HMX phases have large differences.36 This suggests that the excess energy in the HMX NPs might play as an accelerator in activating the system from the ground state to the excited vibrational or/and electronic states and further in triggering chemical decomposition. 3.2.2 Surface Energy. Most of the molecules in the HMX NPs are similar with surface molecules rather than interior molecules with bulk properties. As a consequence, the relaxation of particular exposed crystal facets often results in different surface energies. The surface energy γ can be obtained by

γ = (Etotal − nHMX EHMX ) / A

(2)

where A is estimated by the surface area of sphere with the average diameter of one HMX NP. To evaluate the accuracy of our calculated surface area, the molecular surface area for the HMX NPs was also calculated using Michael Connolly's program as implemented in Materials Studio 7.0.37 The obtained results indicate that there is a linear relationship between the two methods with R2=0.985 (see Figure S1 in Supporting Information). This confirms the reliability of the variation trend of the surface area. As seen in Figure 1c, the surface energies of the spherical HMX NPs exhibit remarkable variance as the size of the particle increases. The biggest difference of surface energies is 72 mJ·m-2 between NP1.6 (258.8 mJ·m-2) and NP2.2 (186.8 mJ·m-2). The seemingly random data in Figure 1c are originated from the particular surface morphology of the HMX NPs whose outermost molecules were

8


Page 9 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


arranged along different specific crystal facets. Then we try to understand why such a large variation in surface energies is observed by focusing on the molecules in the exterior. We used slab models to calculate the surface energies of all the crystal facets appearing on the surface of the studied HMX NPs (see Figure 1a and Table 1). The computational details of the slab models are provided in Table S2 of the Supplementary Information. The chosen slabs can reflect great differences of the surface molecules on the NPs. The surfaces of the NPs and slab models are terminated by the NO2 and/or CH2 groups. Table 1 reports the calculated γ values of different HMX crystal planes appearing on the surfaces of the studied HMX NPs using slab models. It can be seen that there exist pronounced differences between the γ values of different crystal planes. The (100) plane has the largest surface energy of 243.8 mJ·m-2, while the (011) plane has the lowest value of 131.5 mJ·m-2, leading to a great anisotropy of surface chemistry for the HMX NPs. Hence the origin of this γ distribution can be rationalized by the large difference of surface tension at different surfaces of the solid HMX. There is a general correlation between surface energy and exposed crystal plane. Thus, it can be expected that the HMX NPs with low surface energies can be associated with large surface area of high-energy exposed facet and/or small surface area of low-energy one. For example, the situation for small HMX NPs (in size range of 1.4-2.2 nm) in Figure 1a indicates that the surface energy of NP1.6 is dominated by the high-tension surfaces such as ( 100 ), ( 010 ), and ( 102 ) facets. Another example in Figure 1b that the low-tension ( 001 ) facet in NP2.2 presents greatly low surface energy among the

9



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 37

surfaces. For larger NPs, the surface energy varies within a much narrower distribution (200-220 mJ·m-2). This can be regarded as a balance between various exposed crystal facets. It is expected that the great anisotropy of the energy distribution at the surfaces of the HMX NPs will have significant influence on the electronic properties. More evidences can be seen in Section 3.3.

3.2.3 Sublimation Enthalpy. The sublimation enthalpy38 ( ∆ sub H ) was evaluated by the lattice energy ( Elatt ) corrected by the differences between the gas and solid phase enthalpies as follows ' Elatt = Etotal − nHMX EHMX

(3)

∆ sub H = − Elatt − 2 RT

(4)

' is the energy of an isolated HMX molecule. Figure 1d displays the where EHMX

enthalpy of sublimation of the HMX NPs calculated at 300 K along with bulk crystal and other available theoretical and experimental data. Both the DFT and DFTB predicted sublimation enthalpies for the β-HMX crystal are in reasonable agreement with experiments of 199.2 kJ·mol-1 (47.6 kcal·mol-1)39 and 175.3 kJ·mol-1 (41.89 kcal·mol-1)40 as well as other molecular dynamics simulations.41 We note that the variation trend of the enthalpy of sublimation from the DFT calculations seems to be similar with that from molecular dynamics simulations41, while the DFTB method predicts a much slower downtrend of ∆ sub H as the particle size decreases. The predicted low ∆ sub H values indicate that the HMX nanophases are more vulnerable to external heating.

3.2.4 Melt Point. With the obtained sublimation enthalpies for different HMX NPs,

10


Page 11 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


we will evaluate the size effect on their thermodynamic properties. As we know, the increased surface area will elevate the chemical potential of the system, which will induce the changed melting behavior. The differential form of the chemical potential of a particular NP can be expressed as: dµ (T , p, r ) = dµ bulk (T , p ) + γdA = dµ bulk (T , p, r ) +

2γ dV r

(5)

where µ bulk (T , p ) is the chemical potential of the bulk system, V is the molar volume of the NP which is estimated by the molar volume of the bulk crystal, and r is the average radius of the NP. Then we carried out a reversible cycle of melting process to link

the

nanophase,

liquid

state, and bulk

state

under

isothermal

and

isobaric conditions. A schematic plot of the reversible thermodynamic process is illustrated in Scheme 1. In Scheme 1, S s is the molar entropy of the solid state, S l is the molar entropy of the liquid state, ∆ fus H is the fusion enthalpy of the HMX NP, Tbulk is the normal melt point, and T is the melt point of the HMX NP. To our knowledge, there are no direct measurements of thermodynamic properties of liquid HMX since the liquid phase is very unstable. The ∆ fus H of the HMX NP was estimated by the difference between the enthalpy of sublimation ( ∆ sub H ) and vaporization ( ∆ fus H ), which was taken as 153.1 kJ·mol-1 (36.3 kcal·mol-1) from ref. 41. Throughout the entire reversible cycle the Gibbs free energy change is zero. For simplicity, ∆ fus H is assumed as a constant for different HMX NPs. The term of molar melting entropy can be obtained as

∑ ∆G

i

= -∫

Tbulk

T

(S

l

)

− S s dT +

2γVm =0 r

11


(6)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Sl − Ss =

∆ fus H T

Page 12 of 37

(7)

Combined with eqs 6 and 7, the melt point of different HMX NPs can be expressed as

 2γVm T = Tbulk exp−  ∆ fus H

1  r

(8)

The predicted melt points in Figure 1e indicate that both the DFT and DFTB results coincide with each other. Our results suggest that the HMX NPs with sizes less than 2.2 nm cannot exist in solid form at room temperature. While larger NPs with sizes up to 3.4 nm are stable at room temperature, of which the melt point is still less than 400 K, far below the normal melt point (ca. 550 K) of HMX.42 This indicates that the nano-structuring effect decreases the stability of the HMX crystal.

3.3 Electronic Properties. In this section we explore the electronic structures of several selected HMX NP systems to understand how the quantum size induces the modification in the chemical reactivity and material sensitivity of the HMX crystal. The calculated band gap of the HMX bulk is 4.812 eV from DFTB and 3.462 eV from DFT. Both the two theoretical approaches underestimate the experimentally measured band gap (ca. 5.40 eV43) of the solid HMX. But the DFTB result is more close to the experimental value. Hence, we will perform further band structure calculations using the DFTB method. Figure 2 displays the band structure and total density of states (DOS) of the 3.4 nm HMX NP along with an isolated HMX molecule and ideal bulk. In general, the energy levels of single HMX molecule and ideal bulk crystal almost coincide. However, the energy level splitting and broadening in both valence band and 12


Page 13 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


conduction band for the 3.4 nm HMX NP are more pronounced than the former two ones due to quantum size confinement. It is clearly seen that the unoccupied states of the 3.4 nm HMX NP shift towards lower energies, leading to a narrower band gap than that of the bulk HMX. Also, note that the induced energy levels in the forbidden band originate from the surface molecule states, which are denoted as surface states as shown in right of Figure 2. Similar energy level splitting and broadening are also found in the occupied states. We chose ideal spherical model of the 3.0 nm HMX NP exposing (100 ), ( 010 ), ( 001 ), ( 101 ), ( 011 ), ( 102 ), and ( 111 ) facets (Figure 3a and b) as a representative to calculate the density of states that were assigned to different constituent atoms. Figure 3c presents the atom-resolved projected density of states (PDOS) on the composing atoms with reference to the Fermi energy of the 3.0 nm HMX NP. It was reported that both the top of valence band and bottom of conduction band of the HMX crystal were predominately from the 2p states.44 But in this study the s states and p states in the

frontier energy levels were not distinguished for simplicity. It is seen in Figure 3c that the top valence band of DOS presents some main peaks, which are predominately from the 2p states of O atoms and partially from the 2p states of N atoms in ring. The surface states on the valence band side are associated with the (100 ) facet that are covered by the axial NO2 groups (see Figure 3a). The surface states are dominantly localized on the O atoms with distributions perpendicular to the N-O bond vectors, which can be attributed to the lone pair electrons of the O atoms.45 On the conduction band side, as seen in Figure 3b, the surface states are formed from the π antibonding

13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

orbitals of N-NO2 fragments on ( 102 ) facets. Similar results on the spatial distributions of the surface states are also found in other HMX NPs studied here, as shown in Figure S2 of the Supporting Information. Next we analyze why the particular localization of the surface states on the side of the valence band and conduction band is observed in different HMX NPs. As mentioned in Section 3.2, the (100 ) facet has the highest surface energy among the facets. We explored the electronic structure of the most abundant crystal facets (100) that are exposed on the HMX NPs. It is found that the exposed facets with high surface energy have a strong correlation with the induced surface states on the valence band maximum (VBM). Previous first-principle studies3 on the surface chemistry of solid HMX found that the molecules placed on (100 ) and ( 010 ) surfaces were characterized with reduced activation barriers and fast kinetics of the N-NO2 homolysis and HONO elimination reactions than the HMX molecules being isolated and in the interior of bulk crystal. They also found that both the N-NO2 homolysis and HONO elimination on (100) surface required lower activation barriers than on ( 010 ) surface. This supports our conclusions that the (100) facets are more energetic in triggering the chemical reactions than other facets. Therefore, the (100 ) facet with the highest energy strorage among the studied facets plays a vital role in lowering the band gap of the nanosized HMX and acts as the most reactive sites in triggering the chemical decompositions. Figure 4 displays the alignment of the frontier energy levels and energy gaps of the HMX NPs togethetr with an isolated molecule and ideal bulk crystal. VBM and CBM

14


Page 14 of 37

Page 15 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


represent the valence band maximum and conduction band minimum for the HMX bulk, respectively. The LUMO energies of the HMX NPs reduce in the range 0.7-1.0 eV with respect to that of the single HMX molecule, depending on the particular configuration of the nano particle. The HOMO energies exhibit an increasing variation trend between those of the isolated HMX molecule and bulk crystal. Note that the fermi level is more close to the valence band side for the isolated HMX molecule and NPs, but it is adjacent to the conduction band side in bulk HMX crystal. The disparity of HOMO and LUMO energy levels lead to decreasing the energy band gaps of the HMX NPs in the range of 0.8-1.5 eV. The first-principles band gap criterion of impact sensitivity46,47 points out that for energetic crystals with similar structure or with similar thermal decomposition mechanism, the smaller the band gap is the easier the electron transfers from the valence band to the conduction band and the more they becomes decomposed and exploded. Thus, the thermal stability of the HMX NPs may be expected to be decresed by the surface-induced energy gap reduction. Next we analyze the charge distribution on the NO2 groups of the HMX molecules in different NPs. As illustrated in Figure 5a, the charge distribution on the NO2 group in the HMX NPs has the character of the gas phase molecule and solid phase molecule at the same time, but in different regions. For example, at the surface region of NP3.4, there exists a transitional area with thickness of ca. 5Å in which the charge varies from the particle interior with bulk properties to the surface with gaseous properties. The transitional area can also be found in smaller NP1.4. It is seen in Figure 5b and c

15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

that the electrons flow from O to N atoms in the NO2 groups as the molecules are moved to the surface. This indicates that the surface molecules of the HMX NPs are polarized due to the quantum confinement, which differs from either gas phase or solid phase molecules.

3.4 Vibrational Properties. Previous molecular dynamics simulations48 reported that the vibrational properties of the crystalline HMX are dependent on the lattice parameters as well as the oscillation amplitude of the N-N bond. Here we focus on the effects of the size induced lattice distortion and configure changes on the internal motions that are related to the N-NO2 fragments, which are vital for triggering chemical decompositions. The internal vibrational and lattice modes of the HMX molecules and its bulk crystal calculated by the DFTB and DFT methods are compared with previous DFT calculations49 and experiments49,50 in Table 2 and in Figure 6, respectively. Both the vibrational modes and frequency magnitudes show the correspondence between DFTB- and DFT-predicted frequencies in this study and available theoretical and experimental results. It is seen in Table 2 that most of the calculated vibrational modes of both gas phase and solid phase HMX by the DFT methods are in good agreement with the experimental frequencies49,50 and are comparable to previous B3LYP/6-31G* calculations49. Although the DFTB results seem to overestimate the vibrational frequencies in whole frequency range, they present consistent variation trends with the DFT ones. In general, the frequencies of the internal modes for the HMX NPs present the wide distribution between those for gas phase molecule and bulk crystal, thus leading to the broadening of the IR and

16


Page 16 of 37

Page 17 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Raman bands. Figure 6 displays the frequency shifts of some strong vibrational modes of the HMX NPs in the region of 900-1200 cm-1. The modes related to the N-N bonds include the stretch of N-N bonds (ν(NN)), asymmetric stretch of C-N-N (νas(CNN)) and N-N-C2 (νas(NNC2)) bonds, and rocking of CH2 (ρ(CH2)). These stretching and rocking modes play an very important role in triggering the possible decomposition reactions of HMX by the N-NO2 homolysis and HONO elimination.3,51 Hence the strongly cooperative effects of the N-N bond stretching and CH2 rocking serve as the potential vibrational channels for energy transferring into the internal modes that trigger the decomposition.52 It is seen in Figure 6a and b that both the theoretical and experimental results display the increasing trend of the vibrational frequencies (so-called mode hardening) as the system size increases, i.e. from the isolated HMX molecule, NP, to bulk crystal. It is sent in Figure 6c and d that the experimentally determined strong vibrational modes are related to the symmetric stretch (νs(NO2), in the region of 1245-1330 cm-1) and asymmetric stretch (νas(NO2), in the region of 1250-1720 cm-1) of the O-N-O bonds.49 In the region of 1245-1330 cm-1, both the DFTB and DFT calculations in this work predict similar vibrational frequency of each mode. However, there are large discrepancies in the gas phase results between our work and previous DFT calculations.49 This may be since they used different computational methods. As the complexity of the system increases, the modes of νs(NO2) and νas(NO2) exhibit the opposite variation trend. The symmetric stretching of the NO2 groups is enhanced in

17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

bulk crystal, while the asymmetric stretching is restrained in bulk crystal. The vibrational frequencies of the HMX NPs are between those of the gas phase molecules and bulk crystal. Therefore, this increases the absorption channels for the energy transferring into the molecule from its surroundings which are responsible for triggering the initial chemical decomposition of HMX.

4. CONCLUSIONS In this study, we examined the energetics, electronic structure, and vibrational properties of a series of spherical β-HMX NPs with the size range 1.4-3.4 nm using a combination of dispersion corrected DFT and DFTB methods. It is found that the HMX NPs with 3.4 nm has higher energy storage in the surface molecules, higher surface tension with great anisotropy, significantly lower enthalpy of sublimation, and lower melt point than the HMX bulk crystal. The melt points of the HMX NPs are less than 400 K; moreover, the NPs with the sizes less than 2.2 nm cannot exist in solid form at room temperature. The electronic structure indicates that the surface molecules of the HMX NPs are polarized due to the quantum confinement, which differs from either gas phase or solid phase molecules. The induced surface states remarkably reduce the band gap of the HMX NPs by 0.8-1.5 eV, which can lower the material stability. The surface states on valence band side originate dominantly from the (100 ) facets that possesses the highest surface energy among the exposed facets on the NPs. The (100 ) facets covered by axial NO2 groups has very high activity in triggering the chemical decomposition of the NPs. This is also found in the experiments on dendely packed 18


Page 18 of 37

Page 19 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


HMX with cracks, voids, and dislocations. The charge distribution on the NO2 group in the HMX NPs has the character of the gas and solid phase molecules at the same time, but in different regions. The transitional area is found in different HMX NPs with a thickness of ca. 5Å in which the charge varies from the particle interior with bulk properties to the surface with gas properties. In general, the frequencies of the internal modes for the HMX NPs present the wide distribution between those for gas phase molecule and bulk crystal, thus leading to the broadening of the IR and Raman bands. This increases the absorption channels for the energy transferring into the molecule from its surroundings which are responsible for triggering the initial chemical decomposition of HMX. The surface molecules that build up the most part of the studied HMX NPs play a vital role in promoting the chemical initiation and so result in the thermal material instability. Our results provide basic understandings of the high activity of nanosized energetic materials

Supporting Information The total energies of the HMX NPs, the total energies, structures and lattice parameters of the slab models of β-HMX crystal, the surface states in the HMX NPs with different sizes. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgments

19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

This work was supported by the National Natural Science Foundation of China (Grant No. 21273115), the NSAF Foundation of National Natural Science Foundation of China and China Academy of Engineering Physics (Grant No. U1530104), and the Science Challenging Program.

References (1) Field, J. E. Hot Spot Ignition Mechanisms for Explosives. Acc. Chem. Res. 1992, 25, 489-496. (2) Badgujar, D. M.; Talawar, M. B.; Asthana, S. N.; Mahulikar, P. P. Advances in Science and Technology of Modern Energetic Materials: An Overview. J. Hazard. Mater. 2008, 151, 289-305. (3) Sharia, O.; Kuklja, M. M. Rapid Materials Degradation Induced by Surfaces and Voids: Ab Initio Modeling of β-Octatetramethylene Tetranitramine. J. Am. Chem. Soc. 2012, 134, 11815-11820. (4) Kuklja, M. M.; Tsyshevsky, R. V.; Sharia O. Effect of Polar Surfaces on Decomposition of Molecular Materials. J. Am. Chem. Soc. 2014, 136, 13289-13302. (5) Cawkwell, M. J.; Ramos, K. J.; Hooks, D. E.; Sewell, T. D. Homogeneous Dislocation Nucleation in Cyclotrimethylene Trinitramine under Shock Loading. J. Appl. Phys. 2010, 107, 063512:1-11. (6) Armstrong, R. W. Dislocation Mechanics Aspects of Energetic Material Composites. Rev. Adv. Mater. Sci. 2009, 19, 13-40. (7) Xue X.; Wen Y.; Long X.; Li J.; Zhang C. Influence of Dislocations on the Shock Sensitivity of RDX: Molecular Dynamics Simulations by Reactive Force Field. J. Phys. Chem. C 2015, 119, 13735-13742. (8) Kuklja, M.; Rashkeev, S. Shear-Strain-Induced Structural and Electronic Modifications of the Molecular Crystal 1,1-Diamino-2,2-dinitroethylene: Slip-Plane Flow and Band Gap Relaxation. Phys. Rev. B 2007, 75, 104111:1-10. (9) Kuklja, M. M.; Rashkeev, S. N. Self-Accelerated Mechanochemistry in Nitroarenes. J. Phys. Chem. Lett. 2010, 1, 363-367. (10) Zhou, T.; Huang, F. Effects of Defects on Thermal Decomposition of HMX via ReaxFF Molecular Dynamics Simulations. J. Phys. Chem. B 2011, 115, 278-287. (11) Liu, Z.; Wu, Q.; Zhu, W.; Xiao, H. Vacancy-Induced Initial Decomposition of Condensed Phase NTO via Bimolecular Hydrogen Transfer Mechanisms at High Pressure: A DFT-D Study. Phys. Chem. Chem. Phys. 2015, 17, 10568-10578. (12) He, Z.; Chen, J.; Ji, G.; Liu, L.; Zhu, W.; Wu, Q. Dynamic Responses and Initial Decomposition under Shock Loading: A DFTB Calculation Combined with MSST Method for β-HMX with Molecular Vacancy. J. Phys. Chem. B 2015, 119, 10673-10681. (13) Armstrong, R. W.; Coffey, C. S.; DeVost, V. F.; Elban, W. L. Crystal Size Dependence for Impact Initiation for Cyclotrimethylenetrinitramine Explosive. J. 20


Page 20 of 37

Page 21 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Appl. Phys. 1990, 68, 979-984. (14) Tarver, C.; Chidester, S.; Nichols, A. Critical Conditions for Impact- and Shock-Induced Hot-Spots in Solid Explosives. J. Phys. Chem. 1996, 100, 5794-5799. (15) Kumar, R.; Siril, P. F.; Soni, P. Preparation of Nano-RDX by Evaporation Assisted Solvent_Antisolvent Interaction. Propellants, Explos., Pyrotech. 2014, 39, 383-389. (16) Risse, B.; Schnell, F.; Spitzer, D. Synthesis and Desensitization of Nano-β-HMX. Propellants, Explos., Pyrotech. 2014, 39, 397-401. (17) Song, X.; Wang, Y.; An, C.; Guo, X.; Li, F. Dependence of Particle Morphology and Size on the Mechanical Sensitivity and Thermal Stability of Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine. J. Hazard. Mater. 2008, 159, 222-229. (18) Fathollahi, M.; Pourmortazavi, S. M.; Hosseini, S. G. Particle Size Effects on Thermal Decomposition of Energetic Material. J. Ener. Mater. 2008, 26, 52-69. (19) Yang, G.; Nie, F.; Huang, H.; Zhao, L.; Pang, W. Preparation and Characterization of Nano-TATB Explosive. Propellants, Explos., Pyrotech. 2006, 31, 390-394. (20) Pivkina, A.; Ulyanova, P.; Frolov, Y.; Zavyalov, S.; Schoonman, J. Nanomaterials for Heterogeneous Combustion. Propellants, Explos., Pyrotech. 2004, 29, 39-48. (21) Spitzer, D.; Comet, M.; Baras, C.; Pichot, V.; Piazzon, N. Energetic Nano-Materials: Opportunities for Enhanced Performances. J. Phys. Chem. Solids 2010, 71, 100-108. (22) Tkatchenko, A.; Scheffler, M. Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data. Phys. Rev. Lett. 2009, 102, 073005-4. (23) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787-1799. (24) Delley, B. An All-Electron Numerical Method for Solving the Local Density Functional for Polyatomic Molecules. J. Chem. Phys. 1990, 92, 508-517. (25) Choi, C. S.; Boutin, H. P. A Study of the Crystal Structure of β-Cyclotetramethylene Tetranitramine by Neutron Diffraction. Acta Crystallogr. B 1970, 26, 1235-1240. (26) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai S.; Seifert, G. Self-Consistent-Charge Density-Functional Tight-Binding Method for Simulations of Complex Materials Properties. Phys. Rev. B 1998, 58, 7260. (27) Seifert, G. Tight-Binding Density Functional Theory: an Approximate Kohn-Sham DFT Scheme. J. Phys. Chem. A 2007, 111, 5609-5613. (28) Aradi, B.; Hourahine, B.; Frauenheim, T. DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method. J. Phys. Chem. A 2007, 111, 5678-5684. (29) Ge, N. N.; Wei, Y. K.; Ji, G. F.; Chen, X. R.; Zhao, F.; Wei, D. Q. Initial Decomposition of the Condensed-Phase β-HMX under Shock Waves: Molecular Dynamics Simulations. J. Phys. Chem. B 2012, 116, 13696-13704. 21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(30) Manaa, M. R.; Reed, E. J.; Fried, L. E.; Goldman, N. Nitrogen-Rich Heterocycles as Reactivity Retardants in Shocked Insensitive Explosives. J. Am. Chem. Soc. 2009, 131, 5483-5487. (31) Margetis, D.; Kaxiras, E.; Elstner, M.; Frauenheim, Th.; Manaa, M. R. Electronic Structure of Solid Nitromethane: Effects of High Pressure and Molecular Vacancies. J. Chem. Phys. 2002, 117, 788-799. (32) Liu, Z.; Wu, Q.; Zhu, W.; Xiao, H. Formation and Growth Mechanisms of Natural Metastable Twin Boundary in Crystalline β-Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine: A Computational Study. RSC Adv. 2015, 5, 86041 (33) Herrmann, M.; Engel, W.; Eisenreich, N. Thermal Expansion, Transitions, Sensitivities and Burning Rates of HMX. Propellants, Explos., Pyrotech. 1992, 17, 190-195. (34) Asay, B. W.; Henson, B. F.; Smilowitz, L. B.; Dickson, P. M. On the Difference in Impact Sensitivity of Beta and Delta HMX. J. Energ. Mater. 2003, 21, 223-235. (35) Cobbledick, R. E.; Small, R. W. H. The Crystal Structure of the δ-form of 1,3,5,7-Tetranitro-1,3,5,7-Tetraazacyclooctane (δ-HMX): Erratum. Acta Crystallogr. B 1974, 30, 1918-1922. (36) Brill, T. B.; Gongwer, P. E.; Williams, G. K. Thermal Decomposition of Energetic Materials. 66. Kinetic Compensation Effects in HMX, RDX, and NTO. J. Phys. Chem. 1994, 98, 12242-12247. (37) Connolly, M. L. The Molecular Surface Package. J. Mol. Graphics 1993, 11, 139-141. (38) Bisker-Leib, V.; Doherty, M. F. Modeling the Crystal Shape of Polar Organic Materials: Prediction of Urea Crystals Grown from Polar and Nonpolar Solvents. Cryst. Growth Des. 2001, 1, 455-461. (39) Lyman, J. L.; Liau, Y. Thermochemical Functions for Gas-Phase, 1,3,5,7-Tetranitro-1,3,5,7-tetraazacyclooctane (HMX), Its Condensed Phases, and Its Larger Reaction Products. Combust. Flame 2002, 130, 185-203. (40) Rosen, J. M.; Dickinson, C. Vapor Pressures and Heats of Sublimation of Some High-Melting Organic Explosives. J. Chem. Eng. Data 1975, 14, 120-124. (41) Akkbarzade, H.; Parsafar, G.A.; Bayat, Y. Structural Stability of Nano-Sized Crystals of HMX: A Molecular Dynamics Simulation Study. Appl. Surf. Sci. 2012, 258, 2226-2230. (42) Bedrov, D.; Smith, G. D.; Sewell, T. D. Chapter 10-Thermodynamic and Mechanical Properties of HMX from Atomistic Simulations. Theor. & Comput. Chem. 2003, 12, 279-326. (43) Cooper, J. K.; Grant, C. D.; Zhang, J. Z. Experimental and TD-DFT Study of Optical Absorption of Six Explosive Molecules: RDX, HMX, PETN, TNT, TATP, and HMTD. J. Phys. Chem. A 2013, 117, 6043-51. (44) Zhu, W.; Xiao, J.; Ji, G.; Zhao, F.; Xiao, H. First-Principles Study of the Four Polymorphs of Crystalline Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine. J. Phys. Chem. B 2007, 111, 12715-12722. (45) Zhurova, E. A.; Zhurov, V. V.; Pinkerton, A. A. Structure and Bonding in 22


Page 22 of 37

Page 23 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


β-HMX-Characterization of a Trans-Annular N···N Interaction. J. Am. Chem. Soc. 2007, 129, 13887-93. (46) Zhu, W.; Xiao, H. First-Principles Band Gap Criterion for Impact Sensitivity of Energetic Crystals: A Review. Struct. Chem. 2010, 21, 657-665. (47) Zhu, W.; Xiao, H. Ab Initio Study of Energetic Solids: Cupric Azide, Mercuric Azide, and Lead Azide. J. Phys. Chem. B, 2006, 110, 18196-18203. (48) Kohno, Y.; Ueda, K.; Imamura, A. Molecular Dynamics Simulation of Initial Decomposition Process on the Unique N-N Bond in Nitramines in the Crystalline State. J. Phys. Chem. 1996, 100, 4701-4712. (49) Brand, H. V.; Rabie, R. L.; Funk, D. J.; Diaz-Acosta, I.; Pulay, P.; Lippert, T. K. Theoretical and Experimental Study of the Vibrational Spectra of the α, β, and δ Phases of Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX). J. Phys. Chem. B 2002, 106, 10594-10604. (50) Goetz, F.; Brill, T. B. Laser Raman Spectra of α-, β-, γ-, and δ-Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine and Their Temperature Dependence. J. Phys. Chem. 1979, 3, 340-346. (51) Sharia, O.; Kuklja, M. M. Surface-Enhanced Decomposition Kinetics of Molecular Materials Illustrated with Cyclotetramethylene-tetranitramine. J. Phys. Chem. C 2012, 116, 11077-11081. (52) Zhu, W.; Zhang, X.; Wei, T.; Xiao, H. DFT Studies of Pressure Effects on Structural and Vibrational Properties of Crystalline Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine. Theor. Chem. Acc. 2009, 124, 179-186.

23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 1. Energetics of spherical β-HMX NPs together with bulk crystal and available theoretical and experimental data. (a) models viewed along c and b directions, (b) excess energy in the NPs (ε), (c) surface energy (γ), (d) sublimation enthalpy ( ∆ sub H ), and (e) melt point (T) of the HMX NPs. Fig. 2. Comparison of (a) band structure (left) and (b) total DOS (right) of the 3.4 nm HMX NP, isolated HMX molecule, and HMX bulk crystal. Fig. 3. Surface states in a spherical 3.0 nm HMX NP. (a) HOMO, (b) LUMO, and (c) projected density of states (PDOS). The isosurfaces are plotted with isovalue of 0.02. The Fermi level is denoted as a vertical dotted line. Fig. 4. (a) Alignment of the frontier energy levels and (b) energy gaps of the HMX NPs, isolated HMX molecule, and HMX bulk crystal. VBM and CBM are the valence band maximum and conduction bad minimum for the HMX bulk, respectively. Fig. 5. Charge distribution of atoms/groups in the 1.4 and 3.4 nm HMX NPs as a function of distance from centroid of NP. The position of the NO2 group is evaluated by the position of N atom in NO2 group. Fig. 6. Calculated IR and Raman active internal modes as a function of the system size by using DFTB and DFT methods with available theoretical and experimental data. calc.a and exp.b were taken from Ref. 48. exp.b were taken from Ref. 49.

24


Page 24 of 37

Page 25 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1 Calculated surface energies (γ, mJ·m-2) of the HMX crystal from slab models at two theoretical levels at two theoretical levels. crystal facet method (100 ) ( 010 )

( 001 )

( 101 )

( 011 ) (120 ) ( 102 )

( 304 )

(111)

DFTB

243.8

174.4

154.1

225.7

131.5

215.6

183.7

216.5

198.4

DFT

263.2

192.4

191.7

249.4

160.6

245.3

214.0

228.2

218.4

γ

25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 37

Table 2 Vibrational modes of the β-form HMX molecule in isolated state, the surface of the HMX NPs, and bulk crystal. All frequencies are in cm-1. assignmenta 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

librational vibration translational vibration rotational lattice vibration librational vibration translational vibration γNN(NO2) γNN(NO2) γNN(NO2) γNN(NO2) σ(CNC) b(NNC) σ(CNC) b(NNC),b(CNC) b(NNC),b(NCN) b(NNC),b(NNO) b(NNC) ν(CN), ν(NN) ,b(NCN) ν(NN), b(CNC),b(NNC) b(NNO),b(NNC) b(NNO),b(NNC) b(CNC),b(NNC) b(CNC),b(NNO) b(NNC) b(NNO) b(NNO) b(NNO),ν(NN) b(NNO),ν(NN) b(NNO),ν(NN) b(NNO),ν(NN)

uni DFTB (DFT)

NP1.4 DFTB (DFT)

NP1.8 NP2.2 NP2.6 DFTB DFTB DFTB (DFT)

22(13)

53(100)

51

55

37(51)

54(108)

54

47(64)

70(110)

60(64)

exp.b

exp.c

IR

Raman

bulk DFTB (DFT)

calc.b

65

81(121)

15

64

75

88(132)

51

67

65

83

90(134)

60

74(119)

80

77

85

112(142)

64

68(72)

85(121)

81

85

92

117(157)

66

73(86) 75(95) 98(121) 99(127) 154(161) 190(164) 253(215) 269(220) 275(265) 293(284) 343(322)

94(138) 101(143) 104(147) 130(170) 159(171) 196(294) 247(226) 275(242) 277(277) 296(298) 344(340)

92 102 106 132 156 194 231 257 272 282 337

94 106 109 128 158 195 236 264 272 288 338

99 111 130 132 158 189 240 252 272 287 336

123(161) 126(166) 147(168) 151(169) 172 (196) 204(212) 239(233) 254(253) 277(276) 296(322) 327(355)

87 92 115 125 154 166 206 217 270 299 337

364(341)

369(353)

359

366

362

361(364)

342

384(360)

378(374)

377

375

372

367(386)

371

407(385) 418(390) 428(405)

412(407) 430(412) 434(420)

395 410 428

400 417 432

392 411 432

406(405) 416(408) 427(432)

399 402 420

419

433(405)

450(444)

439

451

441

443(435)

425

438

571(575) 595(578) 624(603) 638 (608) 660 (628) 671 (635)

572(577) 596(587) 624(606) 634(619) 665(636) 673(639)

573 593 627 638 658 672

573 594 628 635 659 674

575 596 627 640 660 671

578(586) 596(591) 625(615) 639(627) 665(641) 667(652)

594 594 622 625 644 650

600

26


230 281 312

358 412 432

597 627 638 662

Page 27 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

b(ONO),ν(CN) σ(ONO) σ(ONO) σ(ONO) σ(ONO) b(NCN) νs(NC2) νs(NC2) νs(NNC2) νs(NNC2) νas(NNC2) ν(NN),ρ(CH2) νas(CNN),ρ(CH2) νas(CNN),ρ(CH2) ν(NN),ρ(CH2) νas(NNC2) νas(CNN),ρ(CH2) νas(CNN),ρ(CH2) νas(NC2) νas(NC2) νas(NC2) νas(NC2) νs(NO2) νs(NO2) νs(NO2) γ(CH2) νs(NO2) γ(CH2) γ(CH2) γ(CH2) ω(CH2) ω(CH2) ω(CH2) ω(CH2) b(HCH) b(HCH) b(HCH) b(HCH) νas(NO2) νas(NO2) νas(NO2) νas(NO2)


691 (708) 700 (731) 716 (734) 721 (741) 731 (742) 742 (763) 821 (820) 839 (824) 877 (849) 893 (856) 945 (906) 958 (909) 971 (922) 988 (925) 1072(1035) 1089(1040) 1121(1110) 1155(1146) 1183(1192) 1202(1207) 1216(1227) 1239(1232) 1246(1251) 1271(1258) 1287(1277) 1289(1298) 1312(1302) 1317(1308) 1329(1320) 1348(1328) 1356(1362) 1361(1381) 1373(1392) 1374(1408) 1382(1424) 1385(1428) 1389(1448) 1411(1450) 1682(1598) 1691(1602) 1702(1609) 1703(1610)

691(708) 700(734) 718(738) 719(742) 734(743) 739(761) 819(814) 839(828) 870(853) 894(859) 944(902) 970(906) 976(921) 994(941) 1070(1029) 1107(1051) 1116(1123) 1150(1152) 1181(1182) 1203(1195) 1213(1221) 1246(1236) 1258(1249) 1277(1261) 1280(1272) 1299(1293) 1315(1307) 1325(1308) 1334(1330) 1347(1354) 1357(1359) 1364(1375) 1369(1396) 1370(1410) 1385(1420) 1393(1446) 1396(1447) 1442(1464) 1647(1555) 1667(1586) 1687(1592) 1707(1621)

684 694 709 718 736 743 812 831 877 900 946 975 979 999 1103 1105 1114 1154 1179 1207 1218 1251 1256 1284 1290 1308 1316 1325 1331 1341 1363 1371 1373 1376 1387 1394 1395 1449 1650 1670 1674 1691

689 695 711 720 735 742 813 836 870 897 952 975 980 997 1096 1104 1114 1147 1181 1205 1216 1250 1259 1283 1289 1307 1314 1326 1331 1344 1358 1367 1375 1376 1387 1396 1396 1439 1655 1670 1672 1686

686 694 706 718 733 744 810 833 878 903 956 979 984 1002 1100 1113 1127 1162 1193 1209 1225 1252 1261 1287 1294 1313 1317 1324 1334 1347 1359 1370 1374 1377 1388 1391 1405 1453 1647 1655 1670 1685

27


689(707) 692(736) 710(738) 714(739) 719(742) 742(762) 805(817) 823(823) 876(862) 904(870) 972(929) 982(933) 1001(951) 1001(954) 1107(1088) 1129(1091) 1135(1131) 1145(1156) 1191(1185) 1202(1194) 1240(1252) 1259(1262) 1271(1265) 1288(1276) 1304(1280) 1306(1309) 1315(1324) 1320(1326) 1333(1336) 1343(1349) 1360(1389) 1360(1396) 1365(1422) 1367(1425) 1391(1435) 1395(1441) 1416(1463) 1464(1472) 1626(1559) 1634(1561) 1642(1572) 1642(1578)

726 740 741 745 746 778 826 828 862 872 922 925 936 937 1057 1061 1137 1167 1197 1213 1236 1238 1272 1280 1294 1311 1322 1323 1347 1348 1369 1397 1404 1422 1446 1448 1461 1464 1611 1615 1624 1626

721 754 759 760 772 834 832 872 881 947 950 965 967 1088 1090 1146 1168 1190 1204 1239 1248 1268 1279 1296 1312 1325 1349 1350 1368 1385 1395 1418 1438 1433 1460 1462 1532 1534 1558 1563


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

71 72 73 74 75 76 77 78

νs(CH2) νs(CH2) νs(CH2) νs(CH2) νas(CH2) νas(CH2) νas(CH2) νas(CH2) a

2803(2987) 2804(2989) 2815(3002) 2816(3002) 2916(3038) 2916(3038) 2921(3064) 2921(3064)

2805(2970) 2819(2985) 2831(3006) 2833(3011) 2912(3049) 2936(3060) 2941(3065) 2944(3093)

2806 2809 2830 2832 2915 2926 2938 2943

2808 2815 2830 2832 2911 2931 2940 2944

2800 2810 2831 2835 2906 2933 2943 2943

Page 28 of 37

2820(2982) 2820(2982) 2841(3037) 2841(3038) 2934(3044) 2935(3044) 2955(3162) 2955(3162)

2966 2967 2982 2983 3046 3046 3049 3049

2985 2992 2992 3028 3027 3037

γNN(XY2): twist of XY2 about N-N bond; σ(XY2): wag of X atom out of XY2 plane;

b(XYZ): bend of X-Y-Z angle; υs(XY2): symmetric stretch of Y-X-Y bonds; υs(XXY2): symmetric stretch of X-X-Y2 bonds; υas(XY2): asymmetric stretch of Y-X-Y bonds; υas(XXY2): asymmetric stretch of X-X-Y2 bonds; ρ(XY2): rocking in XY2 plane; γ(XY2): twist about bisector of Y-X-Y angle; ω(XY2): wag of Y atoms out of XY2

plane. b

c

Ref. 48.

Ref. 49.

28


3037

Page 29 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Scheme 1 Reversible Thermodynamic Cycle of Melting Process of HMX NPs. T

NP T, p

∆G5 = - ∫ S s dT Tbulk

∆G4 =

NP Tbulk, p

∆G1 = 0 liquid state T, p

2γVm r

bulk crystal Tbulk, p

∆G3 = 0 ∆G2 = - ∫

Tbulk

T

l

S dT

29


liquid state Tbulk, p


(b)

300 (c)

DFTB DFT

120

DFTB DFT

-2

γ (mJm )

100

-1

ε (kJmol )

270

80

240

210 60 180 0 200 (d)

20

40

60

80

0 400 (e)

DFTB DFT ref. 40

160

Melt point (K)

-1

∆Hsub (kJmol )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 37

120

20

40

60

80

DFTB DFT

320

300 K

240

160 bulk crystal DFTB DFT ref. 38 ref. 40 ∆Hsub 176.0 200.0 184.8 199.2

80 0

20

40

60

80

80 0

Number of molecules

20

40

60

80

Number of molecules

Fig. 1. Energetics of spherical β-HMX NPs together with bulk crystal and available theoretical and experimental data. (a) models viewed along c and b directions, (b) excess energy in the NPs (ε), (c) surface energy (γ), (d) sublimation enthalpy ( ∆ sub H ), and (e) melt point (T) of the HMX NPs.

30


Page 31 of 37

10

G

F

Q

Z

G

(a)

(b)

uni NP3.4 bulk

/

bulk state

5 Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


surface state

0

-5

-10 Z

G Y

A B

D E

C

10

30

50

70

DOS (states/eV cell)

Fig. 2. Comparison of (a) band structure (left) and (b) total DOS (right) of the 3.4 nm HMX NP, isolated HMX molecule, and HMX bulk crystal.

31


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

PDOS (States/eV cell)


(c)

Page 32 of 37

20

O N in NO2

15

N in ring C H

10 5 0 -20

-15

-10

-5

0 5 Energy (eV)

10

15

20

Fig. 3. Surface states in a spherical 3.0 nm HMX NP. (a) HOMO, (b) LUMO, and (c) projected density of states (PDOS). The isosurfaces are plotted with isovalue of 0.02. The Fermi level is denoted as a vertical dotted line.

32


Page 33 of 37

Energy (eV)

(a) -1.5

LUMO/CBM HOMO/VBM

-3.0

Fermi level 0.3 eV

-4.5 3.1 eV

2.3 eV

-6.0 -7.5 uni

NP1.4

NP1.8

NP2.2

NP2.6

NP3.0

NP3.4

bulk

(b) 5.0

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4.5

-0.8 eV -1.5 eV

4.0 3.5 3.0 uni

Band gap NP1.4

NP1.8

NP2.2

NP2.6

NP3.0

NP3.4

bulk

Fig. 4. (a) Alignment of the frontier energy levels and (b) energy gaps of the HMX NPs, isolated HMX molecule, and HMX bulk crystal. VBM and CBM are the valence band maximum and conduction bad minimum for the HMX bulk, respectively.

33



0.00

(a) NO2 group

uni

NP1.4

NP3.4

bulk

Charge (-e)

-0.031 (aNO2)

-0.04

-0.032 (eNO2)

-0.08

-0.095 (aNO2) -0.107 (eNO2)

-0.12 0.97 (b) Nitrogen in NO2 group

Charge (-e)

0.96

0.953 (N4)

0.95

0.946 (N1)

0.94 0.932 (N1)

0.93

0.925 (N4)

0.92

-0.44

(c) Oxygen -0.473 (O1) -0.477 (O3) -0.480 (O4) -0.490 (O2)

Charge (-e)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 37

-0.48 -0.52 -0.56

-0.505 (O1) -0.515 (O3) -0.538 (O2) -0.545 (O4)

0

5

10 15 Distance from centroid (Å)

20

Fig. 5. Charge distribution of atoms/groups in the 1.4 and 3.4 nm HMX NPs as a function of distance from centroid of NP. The position of the NO2 group is evaluated by the position of N atom in NO2 group.

34


Page 35 of 37

(a)

-1

Frequency (cm )

990

960

930 mode DFTB DFT 39 40 41 42

900 uni

NP1.4

NP1.8

ref.

ref.

NP2.2

ref.

Activity IR Raman Raman IR

NP2.6

bulk

Molecular environment (b)

-1

Frequency (cm )

1160

1120

1080 a

a

mode DFTB DFT calc. exp. 43 44 45 46

1040 uni

NP1.4

NP1.8

NP2.2

b

exp. Activity IR Raman IR Raman

NP2.6

bulk

Molecular environment 1325

-1

Frequency (cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(c)

1300

1275

1250

a

a


1225 uni

NP1.4

NP1.8

NP2.2

NP2.6

Molecular environment

35


b

exp. Activity Raman IR IR Raman

bulk


1700

-1

Frequency (cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 37

(d)

1650

1600

1550

1500

a

a


uni

b

exp. Activity Raman IR Raman IR

NP1.8 NP2.2 NP2.6 NP1.4 Molecular environment

bulk

Fig. 6. Calculated IR and Raman active internal modes as a function of the system size by using DFTB and DFT methods with available theoretical and experimental data. calc.a and exp.b were taken from Ref. 48. exp.b were taken from Ref. 49.

36


Page 37 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic

37


Surface-Induced Energetics, Electronic Structure, and Vibrational

Recommend Documents