Relationship between Energetic Performance and Clustering Effects

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Relationship between Energetic Performance and Clustering Effect on Incremental Nitramine Group: A Theoretical Perspective Huajie Xu, Lijuan Peng, Jingbo Wang, Haisheng Ren, Quan Zhu, and Xiang-Yuan Li J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b10647 • Publication Date (Web): 07 Jan 2019 Downloaded from http://pubs.acs.org on January 12, 2019

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The Journal of Physical Chemistry

Relationship between Energetic Performance and Clustering Effect on Incremental Nitramine Group: A Theoretical Perspective. Huajie Xu, Lijuan Peng, Jingbo Wang, Haisheng Ren,* Quan Zhu* and Xiangyuan Li School of Chemical Engineering, Sichuan University, Chengdu 610065, P. R. China

*Tel/ Fax: +86 2885402951. E-mail: [email protected], [email protected]

ACS Paragon Plus Environment

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Abstract: Nitramine compounds are typical high-energy density materials (HEDMs) and are widely used as explosives because of their superior explosive performance over conventional energetic materials. In this work, the thermal properties of 1-nitropiperidine

(NPIP),

1,4-dinitropiperazine

(DNP)

and

1,3,5-trinitro-1,3,5-triazinane (RDX) are investigated from quantum mechanics (QM) and reactive force field (ReaxFF) molecular dynamics simulations. We found the bond dissociation energy of N-NO2 bond, heat of formation, released energy, produced fragments and oxygen balance are closely related to the incremental nitramine group. Nitramine group has a significant effect on the energetic performance for these nitramine compounds. In addition, the increase of nitramine group will improve thermal decomposition activity, promote the generation of small molecules and restrain the formation of carbon clusters. We hope this work can shed new light on the design for energetic materials.


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1. Introduction High energy density materials (HEDMs) are a kind of special materials that store large quantities of energy which are used in numerous military and civilian fields. Nitrogen-rich heterocyclic compounds have been investigated extensively to screen promising candidates for HEDMs1-6 owing to their rather high positive heat of formation (HOF), high densities and good thermal stability. Nitrogen-containing heterocyclic compounds have drawn considerable attention because the ring moiety presented in these compounds contains N–N and C–N bonds,7 which make the compounds rich in energy content. Nitramine group is the most commonly used among these high-energy groups, as it makes the molecule capable for sustained combustion.8,

9

Some heterocyclic compounds like hexogen and octagon which

contain one or more nitramine groups are traditional HEDMs.

Figure 1. Molecular structures of NPIP, DNP and RDX. As

typical

energetic

nitramine

compounds,

1-nitropiperidine

(NPIP),

1,4-dinitropiperazine (DNP) and 1,3,5-trinitro-1,3,5-triazinane (RDX) as shown in Figure 1, which have similar and symmetric structure but different numbers of nitramine groups, have attracted attention from plenty of researchers10-13 for their structure stability under normal conditions. But to date, the influence of incremental nitramine group, especially the generation of carbon clusters from the perspective of energy release, has rarely been reported.



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Clusters made of major component of C will be produced during the detonation of some carbon-rich explosives. Shaw et al.14 showed that carbon-rich clusters take 1000 times as long to release remaining 90% of the inward energy. Manaa et al.15 reported

that

the

retardation

of

chemical

reactivity

of

1,3,5-triamino-2,4,6-trinitrobenzene (TATB) plays an important role in insensitive explosives. Wen et al.16 employed reactive force field (ReaxFF) to study the thermolysis

of

TATB,

1,3,5,7-tetranitro-1,3,5,7-tetrazocane

(HMX),

pentaerythritoltetranitrate (PETN). They found the formation of clusters decreases as the oxygen balance (OB) becomes less negative. In addition, the cluster size and amount are deeply influenced by chemical composition and reaction temperature. More recently, the study of TATB under various heating conditions revealed that the competition of intermolecular collision and molecular dissociation may balance for the generation of clusters.17 Although a lot of efforts have been devoted on clusters, the relationships between clusters and their energetic properties remain unclear.18 A systematic study combining quantum mechanics (QM) and ReaxFF molecular dynamics (MD) methods is needed. In this work, we study bond dissociation energy (BDE) of nitramine groups and gas-phase heats of formation (HOFs) by using QM method. In addition, the simulations are carried out at range of 1500-3000 K to study clustering effect during the thermal decomposition of title compounds using ReaxFF MD methodology. It is expected that our results can provide useful formation for the molecular design of the novel HEDMs. 2. Computational Methods 2.1 Quantum Mechanical Calculations


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The density functional theory (DFT) has been proved as a powerful tool for giving proper energies, structures and other properties for nitramine compounds.19 The fully optimized molecular geometries for NPIP, DNP and RDX are calculated at the B3LYP levels of theory,20 in combination with the basis set 6-311++G** by using the GAUSSIAN 09 package.21 Generally, N-NO2 bond which leads to the detonation of the materials is the weakest one in nitramine energetic molecules.22, 23 To evaluate the strength of bonds and the relative stabilities of the title compounds, the dissociation energies for N-NO2 bond are calculated:

RN-NO 2 (g)  RN  (g)+NO 2  (g)

(1)

where RN-NO2 means the neutral reactant molecules, RN• and NO2• are product radicals after the bond dissociation. The formula for calculating BDE with zero-point energy (ZPE) correction is listed as follow:

BDE(RN-NO 2 )=E (RN)+E (NO 2 )  E (RN-NO 2 )+EZPE

(2)

here BDE(RN-NO2) stands for the bond of RN-NO2. E(RN-NO2), E(RN•) and E(NO2•) are the total energies of the reactant compound and the product radicals, respectively. ΔEZPE is the difference of the corrected ZPE between reactant and products. The standard heat of formation (HOF) of an energetic compound is a very important parameter to evaluate the explosion pressure and velocity.19 The gas-phase HOF of compound CaHbNcOd was calculated by the atomization reaction:

Ca H b N cOd  aC(g)  bH(g)  cN(g)  dO(g)

(3)

where a, b, c and d are stoichiometric coefficients for the elements of carbon, hydrogen, nitrogen and oxygen, respectively. Theoretical calculation of HOF usually needs two steps.24 The first step is calculation of HOF for the molecule at 0 K:



 f H o (M, 0K) 

 x H

o

f

atoms

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  (X, 0K)    xE (X) E0 (M)  EZPE (M)   atoms 

(4)

where M represents the molecule, X detonates each element, and x is the number of atoms of X in M, ΔfH˚(X,0K) is the heat of formation of the atoms at 0 K, E(X) is the energy of each element, E0(M) is the total energy of the molecule, EZPE(M) is its zero-point energy. Then HOF at 298.15 K can be calculated by:  f H o (M, 298.15K)   f H o (M, 0K)   H Mo (298.15K)  H Mo (0K)  

 xH

atoms

here the second term of

o X

(298.15K)  H Xo (0K) 

H Mo (298.15K)  H Mo (0K)

(5)

and the third term of

H Xo (298.15K)  H Xo (0K) on the right side correspond to the enthalpy correction of the molecule and atomic elements, respectively. To obtain the accurate values of HOF for NPIP, DNP and RDX, the Gaussian-4 (G4)25,

26

method which has been verified

applicable to predict the HOFs accurately, is carried out. 2.2 ReaxFF Molecular Dynamics Simulations To investigate the performance of thermal decomposition for NPIP, DNP and RDX, molecular dynamics (MD) simulations with ReaxFF-lg reactive force field27 were carried out by using LAMMPS packages.28 The initial crystal structures for RDX (ρ=1.868 g/cm3)29 and DNP (ρ=1.635 g/cm3)30 are taken from the Cambridge Crystallographic Data Centre (CCDC). NPIP is a liquid with a density of 1.160 g/cm3 at room temperature. To obtain a unit cell of NPIP, an amorphous cell was built and optimized using the generalized gradient approximation (GGA) with the functional of Perdew, Burke and Ernzerhof (PBE)31 for the exchange-correlation potential, as implemented through the Cambridge Serial Total Energy Package (CASTEP) code.32 Finally, a unit cell of NPIP with a density of 1.197 g/cm3 was obtained.


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For MD simulation, the supercells of 2×2×4, 2×2×4 and 2×2×2 for NPIP, DNP and RDX were constructed along with the corresponding orientations. After energy minimization, isothermal-isobaric (NPT) ensemble was employed to release internal pressure for 100 ps. The last 50 snapshots were chosen to analyze the average densities. Our results of 1.318 g/cm3 for NPIP, 1.716 g/cm3 for DNP and 1.820 g/cm3 for RDX, are in good agreement with original values. After equilibration, isothermal-isochoric (NVT) ensembles were performed at 1500 K, 2000 K, 2500 K and 3000 K to investigate the temperature effect. Each simulation run for 100 ps with a time step of 0.1 fs, and temperature was controlled by Berendsen thermostat (100 fs). The recordation interval of 0.1 ps was chosen for all simulations. For studying the density effect on clustering, we compressed the balanced systems of NPIP and DNP into the same density of RDX with 1.820 g/cm3. Thus, the condensed systems were increased 1.37 times and 1.06 times in density which are named as 1.37NPIP and 1.06DNP. The NVT molecular dynamics simulations of 100 ps were also performed for these two systems. The main data of this portion was placed in the Supporting Information (SI). 3. Results and Discussion 3.1 Quantum Mechanics Calculations for Energetic Properties 3.1.1 Bond Dissociation Energy Thermal stability and pyrolysis mechanism are essential characterizations for energetic materials. BDE is one of the most important factors that determine the stability of an energetic material.33 As a key factor, BDE is often concerned in investigating the pyrolysis mechanism. In generally, the smaller value of BDE for breaking a bond, the more easily the bond is broken. The rupture of the bond with the smallest BDE will be the initial step during thermolysis process.34 For nitramine



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compounds, the bond of N-NO2 has been proved the weakest bond by many researches. Table 1 lists the calculated BDE for the bond of N-NO2 in NPIP, DNP and RDX, along with available other theoretical values33 and experimental findings.35-39 The value of BDE for RDX using B3LYP/6-311++G** is in good agreement with that calculated by Wang et al.,33 using B3LYP with different basis sets. The experimental values of gas-phase BDE for NPIP, DNP and RDX by manometric method are 176.2 kJ/mol, 159.9 kJ/mol and 145.7 kJ/mol, respectively. These values are very close to our calculated results. Of course, the BDEs for gas phase are much lower than condense phase due to absence of intermolecular interaction and in the solid state due to absence of stabilizing effect of crystal lattice.40 Table 1. The BDEs of N-NO2 bond and gas-phase standard HOFs for NPIP, DNP and RDX. Compd.

BDE(kJ/mol) Ours a

Other work

HOFs (kJ/mol) Expt

Ours a

Expti

NPIP

168.7

176.2c

-41.9

-44.4

DNP

160.7

159.9d, 198.4e

51.9

58.2

RDX

141.1 146.1b1, 142.7b2 146.5f, 197.2g, 213.1h

173.3

191.7

aBDE

using B3LYP/6-311++G**; HOFs using G4. Ref. 33 using b1B3LYP/6-31G**; b2B3LYP/6-311G**. cFrom Ref. 35 (gas, 210-240 ˚C). dFrom Ref. 36 (gas, 200-240 ˚C). eFrom Ref. 37 (liquid, 216-250 ˚C). fFrom Ref. 36 (gas, 170-200 ˚C). gFrom Ref. 38 (liquid, 232-247 ˚C). hFrom Ref. 39 (solid, 150-197 ˚C). iFrom Ref. 42. bFrom

It can be found RDX has the smallest BDE of N-NO2 bond among these nitramine compounds, which indicates relatively thermally unstable and easily broken. That is, more nitramine groups are prone to induce reactions. But all values of BDE of N-NO2 bond are over the threshold of 83.7 kJ/mol, which is the critical value


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for high energy density materials to maintain stability.41 This nature can be utilized to design stable and relatively active HEDMs. 3.1.2 Heats of Formation HOF is a key energetic argument of energy contents of a compound that can affect the energy released on detonation. A large positive of HOF is a criterion for an effective energetic material.19 The values of HOFs at 298.15 K for the three compounds are also listed in Table 1, together with available experimental data.42 Obviously, our calculated results from G4 method coincide very well with experimental findings. In addition, the values of HOF increase in nitramine compounds of NPIP, DNP and RDX along with nitramine groups. The negative HOF of NPIP is undesirable for HEDMs, while the larger positive HOF of RDX predicts a good HEDM. Therefore, to some extent the aggrandizing nitramine groups may be feasible for molecular design of energetic explosives. 3.2 Molecular Dynamics Simulations for Clustering Effect 3.2.1 Potential Energy The time distributions of potential energy are depicted in Figure 2. It is found that the potential energy decreases rapidly along with increasing temperature at the exothermic decomposition reactions. To analyze the decreasing rate of potential energy related to exothermic reactions progress, an exponential function has been employed to fit the potential energy curve:43

U (t )  U   U exp[(t  t0 ) /  ]

(6)

where U∞ is the asymptotic energy of the products, ΔU is the change of heat for reaction, t0 is the initial energy-releasing tipping point, τ is the characteristic time (i.e. inverse reaction rate) of exothermic process.



Figure 2. Time evolution of potential energy (dots) and exponential function fits (black lines) at different temperatures. Table 2 lists the fitting parameters based on the exponential attenuation. The values of t0 decrease quickly with the increase of temperature as well as nitramine groups at the same temperature. In fact, the temperature will influence both thermolysis to produce small molecules and aggregation to form clusters. The two effects are competitive relationship and the latter impairs decomposition reaction to release energies. A larger value of ΔU means more energy will be released during thermal decomposition. The values of ΔU for RDX systems increase with the increase of temperature, indicating the thermal decomposition play the dominant role. For NPIP systems and DNP systems, the values increase firstly and then decrease along with the temperature increase. This phenomenon reflects that clustering effect will reduce energy release significantly. The values of τ for NPIP and DNP systems are smaller than those of RDX system at 2500 K and 3000 K. This can be illustrated by clustering effect and reaction activity. For NPIP and DNP systems, relatively stable clusters may retard energy release and lower the reaction activity of whole system, while RDX systems are influenced by more fierce intermolecular collisions and need more time to react completely. Therefore, more nitramine groups with higher temperature will contribute to the reinforcement of energy release and reaction activity.


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Table 2. Energy fitting results of exothermic process for NPIP, DNP and RDX systems. Compd. NPIP

DNP

RDX

Temp. (K) 1500 2000 2500 3000 1500 2000 2500 3000 1500 2000 2500 3000

ΔU (kJ/mol) 232.7 465.0 404.4 351.2 406.0 695.7 704.9 702.4 429.0 562.6 1112.2 1221.9

t0 (ps) 28.2 3.4 2.1 1.5 58.2 3.0 1.8 1.0 16.3 2.9 1.3 0.9

τ (ps) 208.9 50.6 15.5 7.5 109.4 35.1 12.8 7.3 87.2 44.3 33.0 10.9

3.2.2 Total Fragments The time distributions of total fragments per molecular are inspected in Figure 3. The slope of total fragments per molecule can intuitively reflect the overall reaction rate which matches the results of potential energy. Comparing to the fragments produced by NPIP system, DNP and RDX systems yield more fragments at 1500 K. Apparently, the highest reactivity is RDX system at 3000 K with the number of total fragments per molecule in RDX system is up to 7, consisting with the following results of atomic ratio of maximum cluster.

Figure 3. Time evolution of fragments per molecule at different temperatures. 3.2.3 Total Species The time evolutions of species are displayed in Figure 4. The number of species grows shortly with increasing temperature, particularly for RDX system at 3000 K,



reflecting detonation process as a typical explosive. The peak values of species for RDX system among primary stages are higher than those of NPIP and DNP systems, which can be accounted for more N and O atoms to form multiple nitrogenous and oxygenous molecules. On the other hand, the final number of species for NPIP and DNP systems at 3000 K is slightly lower than that at 2000 K and 2500 K. The ultimate number of species for NPIP system is far lower than that of RDX system. Because the aggregated effect for NPIP and DNP systems at 3000 K is more serious and plenty of small molecules concentrate together to form clusters. The species for initial thermolysis along with the increase of temperature are listed in Table S1-S3. It is found the main species is NO2 due to homolysis of one N-N bond at relatively low temperature of 1500 K. With the increase of temperature and time, more fragments are found, particularly, the specie of H2C=N-NO2 in RDX. These events are in line with the mechanism of experimental thermolysis.44

Figure 4. Time evolution of species at different temperatures. 3.2.4 Molecular Weight of Maximum Clusters To evaluate the influence of clusters, the molecular weight (Mw.) of maximum (max.) clusters at every time step is displayed in Figure 5. Obviously, the aggregation effect of clusters is strengthened and larger clusters have produced for DNP and NPIP systems at higher temperature. The situation of DNP system is slightly better than that of NPIP system. Nevertheless, there still exist larger clusters at the temperature above


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2500 K. The Mw. of maximum clusters of RDX system is far less than 1000 amu. Thus, the more nitramine groups indeed affect the formation of clusters.

Figure 5. Time evolution of molecular weight of maximum clusters at different temperatures. 3.2.5 Carbon Atoms of Maximum Clusters Due to the scarcity of oxygen atoms to form stable gaseous products, large clusters are always carbon-rich molecules. Usually, Oxygen balance (OB) is employed to evaluate this behavior. The OB is expressed the percentage for oxygen to entirely covert into stable molecules, such as carbon dioxide and water.45 The OB can be calculated by:

1600  (2nC  1 nH  nO ) 2 OB   100% Mw. of compouds

(7)

where n is the atom number of corresponding elements. The calculated values of OB for NPIP, DNP and RDX are -159.9%, -72.7% and -21.6%, respectively. The more negative value means more carbon-rich clusters will generate. The number of carbon atoms of maximum clusters at every time step is counted to assess the effect of carbon-rich clusters. The number of carbon atoms of maximum clusters is shown in Figure 6. Obviously, the number of carbon atoms and Mw. of maximum clusters are closely related. Carbon atoms can cluster together to form super-large-scale particles. So carbon-rich clusters directly correspond to larger clusters. To intuitively



comprehend the formation of carbon-rich clusters, it is assumed the fragments whose molecular weight exceeds 600 amu (about three times of molecular weight of parent compound) to be carbon clusters in this work.

Figure 6. Time evolution of carbon atoms of maximum clusters at different temperatures. 3.2.6 Molecular Weight Ratio of Carbon Clusters The Mw. ratio of carbon clusters which is the value of sum of molecular weight of carbon clusters at every time step divided by total molecular weight of whole system is illustrated in Figure 7. There is almost no carbon cluster existing at 1500 K and 2000 K, since the thermal decomposition is not completely. The degree of aggregating into carbon clusters for NPIP and DNP systems is very deep at higher temperature, especially at 3000 K. Besides, the Mw. ratio of carbon clusters for NPIP system at 3000 K is about 0.5, and almost half of mass of whole system begets carbon clusters. However, no carbon cluster emerges in RDX system. In summary, the increase of nitramine group will promote the generation of small molecules and restrain the formation of carbon clusters.


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Figure 7. Time evolution of molecular weight ratio of carbon clusters at different temperatures. 3.2.7 Atomic Ratio of Maximum Clusters To analyze the behavior of elemental composition of the maximum cluster, the atomic ratio of maximum clusters is defined as the ratio for the number of hydrogen, oxygen and nitrogen atoms divided by the number of carbon atoms, i.e., H/C:O/C:N/C. The original atomic ratio for NPIP, DNP and RDX systems is 2:0.4:0.4, 2:1:1 and 2:2:2, respectively, indicating the relative contents of the oxygen and nitrogen gradually increase with the increase of nitramine group. The atomic ratios of maximum cluster for NPIP, DNP and RDX systems at 3000 K are examined and displayed in Figure 8. Clearly, the atomic ratios will trend to be stable for NPIP and DNP systems, while those of RDX system show wide fluctuation. Meanwhile, the original atomic ratios are higher than those at the end of the simulation, standing for the high percentage of carbon in the maximum cluster, i.e., carbon-rich cluster.

Figure 8. Time evolution of atomic ratio of maximum clusters at 3000 K. The atomic ratio of N/C decreases quickly, indicating that N atom is prone to depart away from clusters, while the variable ratios of H/C and O/C depend on the nitramine compounds. The atomic ratio of H/C decreases to relatively small value with the increase of time. Because the combination of C and H atoms is unstable under high temperature and the effect of dehydrogenation always exists. Additionally,



the ratio of O/C effects the size of carbon cluster. Higher ratio of O/C means more O atoms combine with C atoms forming stable gaseous oxides, which destroys the aggregation of large-scale carbon clusters. 3.2.8 Final Snapshots of Maximum Clusters Figure 9 shows the final snapshots of maximum clusters for NPIP, DNP and RDX systems at 3000 K. The maximum cluster from NPIP system has the composition C222H108O48N43 with a weight of 4018 amu (~48% of the total system mass), which is made up of a few interlinked heterocyclic rings containing N and O atoms. The maximum cluster (C88H23O45N8) from DNP system is smaller than that from NPIP system which contains more oxygen atoms. For RDX system, the maximum cluster (C8H7O11N2) shows a non-loop chain segment with relatively abundant oxygen atoms. These evidences show the scales of carbon clusters are closely related to the atomic ratio of O/C. Hence, the increase of nitramine group will promote the thermal decomposition.

Figure 9. The final snapshots of maximum clusters at 3000 K. 3.2.9 Stable Products We trace the time distributions of stable products at 3000 K as plotted in Figure 10. The number of H2O firstly increases and then decreases, and finally maintains dynamic equilibrium. This illustrates some newly produced H2O will involve in subsequent reactions. Additionally, the number of N2 and CO2 increases orderly in accordance with NPIP, NDP and RDX systems, while that of H2 declines in turn.


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Higher productions of N2 and CO2 in RDX system suggest that the stable gaseous molecules will be produced as the increase of nitramine group.

Figure 10. Time evolution of stable products at 3000 K. 3.2.10 Comparison of Compressed and Uncompressed Systems To investigate the density effect on clustering, the results for the contrasts of 1.37NPIP and NPIP as well as 1.06DNP and DNP systems are presented in Supporting Information (SI). There are no significant differences on time evolution of potential energy (Figure S1), total fragments (Figure S2) and species (Figure S3) for the compression of NPIP and DNP systems. But the compressed systems show more aggregates than those of uncompressed systems (Figure S4-S7). The order of clustering effect at the same density is: 1.37NPIP>1.06DNP>RDX. Therefore, the nitramine group, not density, will promote the thermal decomposition. 3.3 The Influence of Incremental Nitramine Group To synthetically evaluate the correlation of incremental nitramine group, we list energetic properties and the ultimate results of ReaxFF simulation of 3000K in Table 3. To simply each item, we name number of fragments per molecule as NFPM, molecular weight of maximum cluster as MWMC, number of carbon atoms of maximum cluster as NCMC and molecular weight ratio of carbon clusters as MWRCC. Apparently, each item in its column presents a tendency to increase or decrease along with the incremental nitramine group. In fact, these properties are



intrinsically relevant. MWMC, NCMC and MWRCC which are directly associated to clusters, especially carbon clusters, exhibit similarly downward trend. Table 3. Energetic properties and the final simulated results of ReaxFF simulation at 3000 K for NPIP, DNP and RDX systems. Compd. OBa BDEb HOFb NPIP -159.9 168.7 -41.9 DNP -72.7 160.7 51.9 RDX -21.6 141.1 173.3 Units: a (%); b (kJ/mol); c (amu).

ΔUb 83.9 167.8 291.9

NFPM MWMC NCMC MWRCCa 4.1 4017.5 222 48 4.8 1912.2 88 17 6.4 307.2 8 0

4. Conclusions In this work, we reported the systematic study of nitramine group effect on the thermal properties of NPIP, NDP and RDX bashed on the high level quantum mechanism calculations and ReaxFF molecular dynamics simulations. The energetic properties and characteristic of clusters for NPIP, NDP and RDX systems were investigated. From the results of energy fitting and fragments, we found clustering effect on retardation of energy release even exceeds temperature effect on promotion of energy release. More nitramine groups with higher temperature will promote energy release and reaction activity. Actually, the incremental nitramine group will facilitate the generation of small fragments and the yield of stable gaseous products. Furthermore, we note that large-scale carbon clusters comprise only a small number of oxygen atoms, while its ring structure can be destroyed by abundant oxygen atoms. From the simulation of compressed systems, we found nitramine group, not density, will promote the thermal decomposition. The calculated results are self-consistent from different perspectives, which can provide meaningful reference for the design of new HEDMs. Acknowledgement


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This work was supported by the National Natural Science Foundation of China (Grant No. 91641121 and No. 91841301). The authors thank Prof. Huaqing Yang for providing usage of Material Studio software. Supporting Information Tables: The initial species during thermolysis for NPIP, DNP and RDX systems. Figures: MD simulations data for compressed and uncompressed systems. Author information ORCID Haisheng Ren: 0000-0002-8638-7570. Quan Zhu: 0000-0002-5280-0320. Notes The authors declare no competing financial interest. References 1. 2. 3. 4.

5.

6. 7.

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Relationship between Energetic Performance and Clustering Effects

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