Sensitivity of Energetic Materials: Theoretical Relationships to

Article pubs.acs.org/IECR

Sensitivity of Energetic Materials: Theoretical Relationships to Detonation Performance and Molecular Structure Didier Mathieu* CEA, DAM, Le Ripault, 37260 Monts, France S Supporting Information *

ABSTRACT: It has been known for decades that high performances for explosives (as characterized by detonation velocity D, detonation pressure P, or Gurney energy EG) are connected with high impact sensitivities, i.e., low values of the drop weight impact height h50. This trade-off is theoretically substantiated for the first time. It stems from the primary role of the amount of chemical energy evolved per atom for both performance and sensitivity. Under realistic assumptions, log(h50) increases linearly with D−4 or equivalently with P−2 or E−1 G . This prediction proves consistent with experimental data for nonaromatic nitro compounds. The occurrence of different explosophores on the same molecule is suggested as a factor influencing the performance-sensitivity trade-off. Finally, it is shown that a large body of data may be explained by the present approach, which naturally integrates thermodynamic (energy content) as well as kinetic (activation energies) aspects. This model should help in designing powerful high energy compounds with acceptable sensitivity. variability observed for nitramines.32 On the other hand, drop weight impact test data are increasingly reported as drop energies Edr ∝ mH h50, therefore assuming that this quantity does not depend on the weight selected for the hammer. In practice, the validity of this assumption remains unclear, as illustrated by the data in Figure 1. Indeed, for the same value of drop energy, a lighter hammer strikes the sample with an increased velocity. This might affect the subsequent dynamics within the material. Finally, it must be noted that initiation is due to the presence of defects, as demonstrated by the fact that single crystals are extremely insensitive. In this context, the different h50 values observed for various crystal polymorphs of the same compound are not trivial to explain.33,34 In fact, it is not even clear whether predicting sensitivity is a reachable goal since the exact nature and number of defects in crystalline materials remains mostly elusive. Our own attempt at predicting h50 relies on the assumption that explosive initiation is thermal in origin,36 combined with the observation that h50 depends on the energy content of the material,37 which suggests that the determining step in the ignition process takes place after some molecules have already decomposed. Despite crude approximations regarding reaction mechanisms and corresponding activation energies, the first implementation of this approach yields remarkably good results, as demonstrated by values close to 0.8 obtained for the determination coefficient R2 between predicted and observed log(h50) data, using only three fitting parameters for 93 nitroaliphatic compounds38 or four fitting parameters for a

1. INTRODUCTION There is currently much interest in the design of new energetic materials providing high performance, good stability, and safety levels, while being environmentally friendly.1−12 Because of the risks inherent to these compounds, it is desirable to minimize the amount of experimental research required to develop a new explosive or propellant. Therefore, theoretical and computational approaches play an ever-increasing role.11,12 Nevertheless, predicting the overall properties and behavior of new energetic materials remains very challenging, although much progress is made possible by the invaluable insight gained from large-scale molecular simulations.13,14 Consequently, new synthetic targets are primarily selected on the basis of high values of calculated detonation velocities and presssures, as these properties can be reasonably predicted from estimated densities and formation enthalpies using standard thermochemical codes or analytical models.15−19 Despite their practical significance, other more complex properties are either ignored or estimated using purely empirical methods prone to large uncertainties. This is particularly the case for impact sensitivity, which is most often characterized through the height h50 that a given weight mH must be dropped onto the sample to trigger an observable decomposition with a 50% probability in the so-called drop weight impact test.20 The current lack of undertanding of h50 stems partly from the fact that it may potentially depend on a large number of factors, including molecular and crystal-packing features, crystal morphology and defects, and details of the equipment used and experimental conditions. To date, theoretical studies have considered a large number of factors, including hot spot formation,21−23 uppumping mechanisms by which the impact energy is transferred to intramolecular vibrations,24−26 or energetic barriers required to break chemical bonds.27−31 However, even some wellestablished observations remain to be clarified, such as the h50 © 2017 American Chemical Society

Received: Revised: Accepted: Published: 8191

May 16, 2017 June 19, 2017 June 30, 2017 June 30, 2017 DOI: 10.1021/acs.iecr.7b02021 Ind. Eng. Chem. Res. 2017, 56, 8191−8201

Article

Industrial & Engineering Chemistry Research

whole set of data presently considered. Therefore, unless mentioned otherwise, h50 values used in this work are experimental, whereas the model is primarily used here for qualitative analyses or to demonstrate its ability to account for specific observations. The full list of compounds in the database is provided as Supporting Information along with structural formulas, names, and/or acronyms. In particular, the reader is referred to this material for the meaning of trivial names and acronyms used in this paper. These compounds span a wide range of functional groups, including so-called explosophores, i.e., unstable groups that may initiate a self-sustained decomposition process. The sensitivity of a material primarily depends upon the nature of the most sensitive explosophores. The sensitivity of known explosophores tends to increase as follows: aromatic C−NO2 ≃ furazans and furoxans < C−NO2 < N−NO2 < O−NO2 < other explosophores.20 On this basis, the compounds studied in this work are split into six categories according to the following sixstep procedure: 1. A generic category, hereafter referred to as “Unst.”, encompasses all compounds with unstable explosophores deprived of the NO2 moiety, including azides, difluoroamines, diazo phenols, tetrazoles, and triazole compounds that may easily release a dinitrogen molecule, as detailed in ref 40. Furazans and furoxans are not included in this category as they are relatively stable. 2. Compounds with O−NO2 groups are assigned to the O−NO2 category (nitric esters). 3. Compounds with N−NO2 groups are assigned to the N−NO2 category (nitramines). 4. Compounds with aliphatic C−NO2 groups are assigned to the C−NO2 category (nitroalkanes). 5. Compounds with five-membered aromaric rings not included in the Unst. category; i.e., nitro-substituted azole-based compounds, furazans, and furoxans are assigned to the 5mAr category. 6. Finally, all remaining compounds only include a single kind of explosophore, namely, nitro groups bonded to carbon atoms in aromatic 6-membered rings. These nitroaromatic compounds are thus assigned to the NAC category. According to this simplified classification scheme, a compound assigned to a given category owing to the presence of a specific explosophore may also contain other types of (presumably more stable) explosophores. For instance, the nitroaromatic explosive commonly referred to as tetryl is included in the N−NO2 category because of the −N(CH3)− NO2 substituent on the benzene ring.

Figure 1. Comparison of h50 values measured using 2.5- and 5-kg hammers (data from ref 35, where several values were usually reported for the lighter hammer). The implicit assumption when reporting sensitivity as a drop energy is that the former are twice larger than the latter, i.e., that the points align along the y = 2x line shown on the plot.

larger data set of 156 compounds obtained as nitroaromatics (NACs) are included as well.39 The excellent correlation obtained for nitramines with the help of only three fitting parameters is especially encouraging38 since the corresponding data were previously left unexplained.32 In light of the present model, they arise as a consequence of the interplay between N−NO2 bond dissociation energies on one hand and the molecular chemical energy per atom in the molecules on the other hand. This will be clear from the sequel. Finally, large uncertainties regarding h50 predictions made using our model are only observed as a comprehensive data set is considered, including severely under-oxygenated compounds (trinitromesitylene, trinitrostyrene) and non-nitro explosophores, such as furazan, furoxans, or triazoles with may exhibit a variety of complex decomposition mechanisms.40 Taking advantage of this extensive database and of the abovementioned model, the goals of this paper are (1) to carry out a theoretical analysis of the interplay between detonation performance and sensitivity and (2) to provide a better understanding of the possible factors explaining the sensitivity values observed for distinct chemical compounds. The content of the database is detailed in Section 2. The models used to estimate detonation performance and sensitivity are described in Section 3. On this basis, Section 4 provides a detailed analysis of the performance-sensitivity relationships, supported by experimental data. Finally, Section 5 is devoted to a discussion of the relative significance of various molecular/ crystalline features that may account for observed h50 values. In particular, it is shown that the present model for h50 explains a large body of data in terms of only two major determining factors, shedding light on previously unexplained results and providing new explanations to many earlier observations.

3. MODELS 3.1. Performances. Following a common approach,41 presently used detonation performances are evaluated using the Kamlet−Jacobs relationships.15 According to this procedure, detonation parameters are derived from a quantity ϕ defined as follows: ϕ = NM1/2Q1/2

2. IMPACT SENSITIVITY DATABASE For consistency, our database contains only h50 data measured according to the ERL Type 12 procedure using a 2.5 kg impact hammer.40 Although our model is fairly reliable for most compounds, its applicability domain does not encompass the

(1)

where N is the number of moles of gaseous species evolved from one gram of the explosive, Q is the energy released by the decomposition reaction as obtained using the H2O−CO2 arbitrary and reported on a per gram basis, and M is the 8192

DOI: 10.1021/acs.iecr.7b02021 Ind. Eng. Chem. Res. 2017, 56, 8191−8201

Article


their relative sensitivity with respect to compounds which do not exhibit such new pathways. This could explain why the ranking of sensitivities is affected by the weight of the impact hammer, as illustrated in Figure 1 and, more generally, the lack of unambiguous relationships linking h50 data measured under different conditions. 3.3. Density. The calculated performances of an explosive depend on the loading density ρ0. In this work, ρ0 is taken to be the crystal density evaluated using a physically motivated additivity model which predicts the densities of 42,880 crystals with an average relative error of 2%, using only 30 parameters for all C−H−N−O−F−Cl compounds.44 3.4. Heat of Explosion. The explosive performances also depend on the heat of explosion Q, as shown by the above equations. It is obtained as Ec/Mw, where Mw is the molecular weight of the explosive molecule, while Ec is obtained as the difference between the formation enthalpy of the material (ΔfH0sol) and the total formation enthalpy of the products

average molecular weight of the gaseous prodets. The detonation pressure is then obtained as P = Kρ02 ϕ

(2)

Another equation yields the detonation velocity D = Aϕ1/2(1 + Bρ0 )

(3)

In these equations, ρ0 is the density of the material, A, B, and K are empirical constants whose values are taken from Kamlet and Jacobs.15 Although initially obtained empirically, eq 2 may be derived analytically from a Becker−Kistiakowsky−Wilson (BKW) equation of state.42 Finally, the Gurney energy EG reported on a per-gram basis is obtained using the Cγ model,17 which consists of a simple analytic expression derived under the assumption of a constant polytropic index γ ⎡ ⎛ 1/ρ0 ⎞γ − 1⎛ γ ⎞γ ⎤ ⎢ EG = 1 − 2⎜ ⎟ ⎜ ⎟ ⎥Q ⎢⎣ ⎝ NV ⎠ ⎝ γ + 1 ⎠ ⎥⎦

(4)

0 Ec = Δf Hsol −

where γ and V are empirical constants. In view of these simple equations, some correlations are clearly to be expected between P, D, and EG. 3.2. Impact Sensitivity. The present model for sensitivity is described in detail elsewhere.39,40 Briefly, it assumes that h50 is determined by the rate constant kpr for the propagation stage of the decomposition process in the material. More specifically, h50 and kpr are related through the following empirical power law: ω

h50 = (kc/k pr)

1 NA

In this expression, the sum runs over every possible prodet k, nk is the number of moles of this specific prodet per mole of explosive, and ΔfH0(k) is the corresponding formation enthalpy. The solid-state formation enthalpy of the explosive material is obtained as the difference between the gas-phase value ΔfH0gas and the standard sublimation enthalpy ΔsubH0: 0 0 Δf Hsol = Δf Hgas − ΔsubH °

(5)

Ei† ⎞ ⎟⎟ ⎝ kBTe ⎠

i

4. PERFORMANCE-SENSITIVITY RELATIONSHIPS 4.1. Overview of Experimental Data. All presently considered properties are compiled in the database provided as Supporting Information, including measured and calculated values for the ERL Type 12 drop weight impact height h50 and calculated performance indicators D, P, and EG. In addition, alternative indicators are considered as well, namely, oxygen balance (OB) for sensitivity,47 heat of explosion (Q), and Gurney energy per unit volume (ρ0 EG) for performance.20 OB is straightforwardly defined in term of the proportion of oxygen atoms with respect to fuel elements.15 Table 1 reports the correlation matrix between these properties, sensitivity being characterized by log(h50). Not surprisingly, significant correlations are observed between all performance indicators, in line with the fact that they are

(6)

E i†

with kinetic parameters (activation energy) and Z i (corresponding prefactor). Here, NA and kB are, respectively, the number of atoms in the molecule and the Boltzmann constant. The local temperature Te arises from the decomposition of neighboring molecules: kBTe = η

Ec 3NA /2

(9)

In this work, ΔsubH0 is calculated using a simple model described previously,45 as subsequently implemented in the MATEO software package.46 Finally, ΔfH0gas is computed on the basis of density functional theory, according to a procedure described in the Supporting Information.

⎛

∑ Zi exp⎜⎜−

(8)

k

where ω = 4 and kc are fitting parameters. The rate constant is obtained classically as a sum of contributions arising from thermally activated decomposition pathways i k pr =

∑ nk Δf H °(k)

(7)

where η is related to the fraction of chemical energy effectively contributing to raise the local temperature, and Ec is the amount of energy release by a molecule upon decomposition. As emphasized previously,43 Te is more rigorously referred to as a quasi-temperature, as it is a local (rather than macroscopic) quantity. It is defined as the value of the temperature that best describes how the molecules heated by early decomposition processes are distributed on their energy levels. On the other hand, Ec is obtained using the H2O−CO2 arbitrary, as done for the heat of explosion Q involved in eq 1. Full details and numerical parameters of this model are provided in ref 40. It is important to observe that since η depends, in principle, on the exact nature and strength of the mechanical solicitation applied to the material, sensitivities obtained using distinct solicitation regimes do not necessarily correlate. Indeed, any increase in the intensity of the impact is likely to trigger new decomposition pathways in some materials, thus increasing

Table 1. Correlations between Studied Properties As Characterized Using Determination Coefficient R2

Q D P EG ρ0 EG log(h50) 8193

OB

Q

D

P

EG

ρ0 EG

0.19 0.80 0.72 0.58 0.61 0.45

− 0.46 0.42 0.67 0.64 0.33

− − 0.97 0.82 0.94 0.45

− − − 0.71 0.91 0.43

− − − − 0.92 0.38

− − − − − 0.41


Article


picrylbenzotriazole, 1-picryl-1,2,3-triazole, and diazophenols. A notable exception is the difluoroamine HNFX, which proves highly sensitive but at the same time exhibits very high performance. 4.2. Theoretical Performance-Sensitivity Relationships. The performance-sensitivity trade-off can be simply rationalized assuming that performances are mainly determined by the amount of energy released upon decomposition and sensitivities by the energetic barriers to be overcome in order to trigger the decomposition (which implies that the compounds under study do not differ too much with regard to stoichiometry and density). In this case, the performancesensitivity trade-off can be directly derived from the textbook rule stating that the more exothermic a reaction is, the smaller the corresponding activation energy is.52 Using the models described in Sections 3.1 and 3.2, deeper insight can be obtained, including explicit analytical relationships between log(h50) and performance criteria. Indeed, putting eq 7 into eq 6 and substituting Q with (NA/Mw)(Ec/ NA) in eqs 1−4, it is clear that all properties of practical interest can be expressed in term of Ec/NA as only thermochemical energetic quantity. In particular, D, P, and EG may all be expressed as

derived from simple mathematical relationships based on the same fundamental properties. Although Q appears as a fundamental determinant of D, P, and EG, it does not exhibit any strong correlation with any of these properties. This is consistent with the fact that the latter depend also significantly on other factors: loading density ρ0, number of moles of gaseous species evolved from one gram of the explosive N, and average molecular weight of the gaseous prodets M. This is obvious from eqs 1−4 and was recently emphasized by Politzer and Murray,48 who stress the predominant role of ρ0. The significant correlation observed between D and EG (R2 = 0.82) supports the common practice consisting of approximating the Gurney velocity uG = (2EG)1/2 simply as D/3.17 However, it is especially interesting to observe that D exhibits very strong correlations with P (R2 = 0.97) and ρ0 EG (R2 = 0.94). Therefore, in what follows, we focus on D as the fundamental indicator of explosive performance. To get a broad overview of the relationship between performance, sensitivity, and molecular structure, the interplay of D and h50 is shown in Figure 2, using different colors for the

X = α(Ec/NA )1/ ν

(10)

where X = D, P, and EG. For these three properties, the integer ν takes the respective values 4, 2, and 1, and the corresponding values of the coefficient α are easily obtained from eqs 1−4. On the other hand, using eq 10, the ratio Ec/NA may be substituted by any performance criterion in eq 6, thus leading to analytic relationships between h50 and explosive performances. Focusing on compounds for which detonation is initiated essentially through a single explosophore group with activation energy E†0 and prefactor Z0, an especially simple equation is obtained ⎛k N ⎞ 3ω † log(h50) = ω log⎜ c A ⎟ + E0 (α /X )ν 2 η ⎝ Z0 N0 ⎠

(11)

where N0 is the number of such explosophore groups for one molecule (NA atoms). This equation makes it clear that simple relationships exist between sensitivity and performances. Assuming again that the compounds under consideration share similar values for the lowest activation energy E†0 and prefactor Z0, the density ρ0, the number of moles of gas produced by gram of explosive N, and the concentration N0/NA of explosophores, simple power laws are to be expected. For instance, log(h50) should increase linearly with D−4 (keeping in mind that ν = 4 for X = D). In fact, these assumptions are unlikely to be true for NACs, as these compounds are likely to exhibit widely different values of E†0 in view of the diversity of plausible initiation mechanisms.40 In contrast, these assumptions are more likely to hold for the aliphatic compounds from the C−NO2, N−NO2, and O−NO2 categories. A plot of log(h50) against D−4 is reported in Figure 3 for these three families of compounds. The general trend observed in this figure is clearly consistent with eq 11. With D expressed in km/s, a regression against all 156 data points yields a significant correlation (R2 = 0.73)

Figure 2. Interplay of detonation velocity D and log(h50) for the various families of compounds studied.

six families of compounds described in Section 2. The solid line corresponds to eq 12 discussed further below. This figure clearly illustrates well-known tendencies, including the relative sensitivity of nitric esters, the very high performance of some nitramines (HMX, HNIW, or HK-55), or the remarkable insensitivity of some NACs, especially those with −NH2 substituents like TATB or DATB. Moreover, the excellent trade-off offered by 5-membered aromatic heterocycles (5mAr category) is made especially clear. This supports the extensive effort currently put into the development of such molecules, which include, for instance, azole-based nitro compounds.49,50 A compound identified as especially interesting from this figure is NTO, a molecule that currently receives attention from both defense and civilian sectors as a potential new-generation high energy material.51 On the other hand, compounds with the most sensitive explosophores, i.e., those in the unstable category (Unst.), usually lead to poor trade-offs. This is especially obvious for 1-

log(h50) = (0.174 ± 0.065) + (5200 ± 255)D−4 8194

(12)


Article


exhibit only one type of explosophore and another one for compounds with at least two distinct explosophores. For both subsets, detonation velocities are plotted against sensitivity in Figure 4. The solid curve corresponds to eq 12 and is presently

Figure 3. Expected linear relationship between log(h50) and D−4.

This equation is shown as a straight line in Figure 3. Applying eq 10 to P and EG, similar equations linking these properties to log(h50) are obtained. 4.3. Negative Impact of Diversity of Explosophores. In principle, the search for insensitive compounds should focus on molecules with activation energies E†i as high as possible. However, high values of E†i are detrimental to the performances because they imply strong BDEs, which negatively contribute to the energy content. However, it is interesting to ask what should be an optimal set of activation energies for a promising energetic compound, given a fixed stoichiometry and keeping the other key determinant Ec/NA constant. Within the approximate picture where covalent bonds are associated with transferable additive contributions to the total energy of a chemical system,53 it is clear from present considerations that a minimum in sensitivity (maximum in h50) is obtained when all weak BDEs in the molecule exhibit equal values. Indeed, starting from a hypothetical molecule in which all explosophores are equivalent and associated with kinetic parameters Z0 and E†0, alternative sets of activation energies E†i may be reached by increasing one of them by an energetic increment δ, while decreasing another one by the same increment in order to ensure that the change is made while keeping Ec constant. Therefore, according to eq 6, the contribution of these two explosophores to kpr is modified as follows ⎛ E† ⎞ ⎛ E† ⎞ ⎛ δ ⎞ 2Z0 exp⎜⎜ − 0 ⎟⎟ → 2Z0 exp⎜⎜ − 0 ⎟⎟cosh⎜ ⎟ ⎝ kBTe ⎠ ⎝ kBTe ⎠ ⎝ kBTe ⎠

Figure 4. Interplay of detonation velocity D and log(h50) for compounds with only one type of explosophore (yellow) compared to other ones (orange).

used to set the boundary between “good” and “poor” performance-sensitivity trade-offs. In line with theoretical expectations, only 34% of the compounds with two or more distinct explosophores exhibit a good trade-off, against 54% of the compounds with only one kind of explosophores. Furthermore, Figure 4 clearly shows that optimal trade-offs are mostly obtained for compounds with only one type of explosophore, usually aromatic C−NO2 (for the less sensitive) or N−NO2 (for the most performant) groups. Nevertheless, major exceptions to this rule are observed. A few compounds with only one type of explosophore lead to a poor trade-off. They are molecules with very negative oxygen balance, such as trinitromesitylene, trinitroxylene, or 2,4,6trinitrostyrene, or compounds with extremely unstable explosophores such as diazophenols. More interestingly, a small number of molecules lead to excellent trade-offs in spite of distinct explosophores. The most prominent example is ANTA-NQ, which was recently synthesized and put forward as a high-performing material with low sensitivity by Chavez et al.54 This compound exhibits a good combination of performance and sensitivity despite the presence of both N−NO2 and C−NO2 bonds. The reason for this remarkable stability is unclear. It might stem from the fact that the N−NO2 group is involved in a 6-membered intramolecular hydrogen-bonded ring, leading to a bonding pattern similar to those found in NACs with NO2 and NH2 substituents in ortho positions. However, according to calculations using the procedure described in ref 43, although the latter hydrogen-bonding interaction increases the C−NO2 bond dissociation energy from 221 to 235−245 kJ/mol, a BDE of only 119 kJ/mol is obtained for the N−NO2 bond in ANTA-NQ, about twice lower than BDE for the C−NO2 bond in this molecule (211 kJ/mol).

(13)

This clearly corresponds to an increase in the propagation rate kpr and thus to an enhanced sensitivity of the material. As a result, all other factors being kept constant, all explosophores in the molecule should ideally exhibit similar activation energies. This is obviously difficult to achieve in practice, and this conclusion may be blurred by the fact that substituting an explosophore by another one affects all properties of the compound. To get insight into this aspect, we consider the occurrences of the explosophores encountered in the present data set (see Section 2) in each compound studied. The data set is then split into two subsets: one for compounds that 8195


Article


nonzero, hence reflecting a trend of h50 to decrease as the energy content increases. Focusing on CHNO compounds with similar proportions of H atoms, similar trends are to be expected if the energy content is reported on a per mass (i.e., as the energy Q involved in eq 1) rather than on a per atom basis. They were actually observed by various authors.3,56 A third possibility is to consider the energy content per unit volume ρ0 Q, as done by Pepekin et al.57 and Politzer et al.32 Again, for small sets of compounds of various chemical types, h50 was found to decrease as the energy content increases. In light of the present model, increasing Ec/NA (or equivalently Q or ρ0 Q) leads to a faster propagation of the decomposition process (eq 7). This explains the observed concomitant decrease in h50 (eq 6). On the other hand, it is clear that the kinetic factor must be considered in order to obtain more quantitative correlations. 5.3. Molecular Electrostatic Potential. Other properties commonly used to develop predictive models for h50 are descriptors derived from the molecular electrostatic potential (MEP) computed from theoretical electron densities according to procedures developed for over 30 years.58−60 A couple of numbers derived only from the potential outside a molecule is probably not sufficient to obtain quantitative correlations with h50, unless they reflect primary factors, especially bond strengths. Nevertheless, a recent discussion of this topic provides some good reasons why strongly positive regions on the MEP might be linked to sensitivity.32 This approach appears to be especially interesting for NACs as a substitute for the detailed mechanistic studies that would be required in order to rigorously evaluate the E†i data used as input to physically grounded approaches. To illustrate the interest of the MEP approach,32 Politzer and Murray emphasize its consistency with the observation that the sensitivity of a TNT:HNIW cocrystal falls between the values of the pure components.61 In fact, these results and many similar ones obtained for cocrystals may be easily rationalized on the basis of the present approach, as detailed in Section 5.4. In fact, like many others, correlations reported to date between sensitivity and MEP are rather limited in scope. Politzer and Murray indicate that the role of positive regions of the MEP is especially clear from the results reported by Rice and Hare.56 The latter do point to the fact that global MEP descriptors are not sufficient to describe sensitivity, presumably because they do not depict localized charge imbalances that are more likely to be related to sensitivity, as explained by the authors. However, these results do not provide any evidence for quantitative correlations between sensitivity and MEP parameters, either global or local. To obtain such a relationship, the authors had to resort to a so-called hybrid model, wherein the heat of detonation Q is introduced as an additional descriptor, along with a global MEP parameter.56 Alternatively, quite good correlations may be obtained provided several global properties of the potential are considered simultaneously.60 These findings are fully consistent with the present approach where h50 depends primarily on thermodynamic (Q) as well as kinetic aspects. In this perspective, MEP would reflect kinetic factors to the sensitivity, as evident from its relationship with X−NO2 bond dissociation energies demonstrated in specific cases.62 5.4. Hydrogen Bonding and Crystal Packing. Extensive hydrogen bonding is another factor frequently invoked to rationalize h50 data.12,63 The role of intramolecular hydrogen bonds is especially clear as they can stabilize trigger bonds. For

Other exceptions are systematically observed for compounds with furazan or furoxan groups, including ANBF, DNTF, DNBF, and derivatives. It appears that such explosophores lead to improved performance-sensitivity trade-offs compared to nitro groups. In practice, the equivalence of explosophores on the molecule does not appear to be very useful as a guiding principle for molecular designers. The nature of the explosophores is clearly much more significant.

5. DETERMINANTS OF IMPACT SENSITIVITY A distinctive feature of the present approach to sensitivity is the fact that it satisfactorily accounts for an extensive body of experimental h50 values on the basis of only two kinds of molecular factors: a thermodynamic one, namely, the energy content per atom Ec/NA, and a kinetic one, namely, the activation energies E†i . By reducing the kinetic aspects to the lowest activation energy E†0, the thermodynamic and kinetic determinants of sensitivity can be combined into a single scalar sensitivity index.43,55 Such findings might be unexpected in view of the large number of factors known to affect sensitivity.32 They suggest that the two factors at the basis of this model are predominant, with other ones playing a secondary role. In fact, as discussed in what follows, the present model provides simple explanations for the successes and limitations of previous empirical correlations based on a variety of descriptors. 5.1. Oxygen Balance. The first and simplest molecular property introduced as a practical sensitivity indicator for explosives is the oxygen balance (OB), which is simply derived from the stoichiometry of the material.15 This single parameter or similar stoichiometry-derived quantities successfully correlate a large number of h50 values within restricted chemical families.47 Such findings are to be expected in the light of the present model. Indeed, the energy content per atom Ec/NA of many organic explosives primarily depends on the ability of oxygen-containing groups to oxide fuel hydrocarbon groups into H2O and CO2/CO. Therefore, it should correlates to some extent with OB. Considering the present database as a whole, only a general qualitative trend of log(h50) to decrease with OB is observed, as reflected by the determination coefficient R2 = 0.45 observed between both quantities (Table 1). On the other hand, the fact that correlations between h50 and stoichiometry are significant only within restricted families reflects the role of the kinetic determinant to h50 (typically X− NO2 bond dissociation energies), whose values are roughly constant within a set of molecules sharing a common kind of explosophore but may vary significantly between distinct explosophores. 5.2. Energy Content. Since OB is related to the energy content of the material, it is tempting to consider Ec/NA as an alternative sensitivity indicator, possibly better than OB in view of the fact it is a genuine physical quantity explicitly used as input to estimate h50 in the present model. In practice, however, for the whole database, OB happens to correlate better with log(h50) compared to Ec/NA, as reflected by a decrease in corresponding R2 values from 0.45 to 0.32. A similar trend is observed within individual chemical families. For instance, R2 decreases from 0.63 to 0.38 for nitroalkanes, from 0.68 to 0.45 for nitramines, and from 0.70 to 0.41 for nitric esters, although it increases from 0.37 to 0.45 for NACs. Thus, except for NACs, R2 tends to be lower when Ec/NA is considered instead of OB. Nevertheless, it remains significantly 8196


Article


Figure 5. Role of intermolecular hydrogen bonds on the sensitivity studied on series of similar compounds. Top: C7H5N3O4 isomers (OB = −62.5%). Bottom: C8H7N3O4 isomers (OB = −78%). Compounds deprived of hydrogen bonds are shown on the left.

Figure 6. Role of hydrogen bonds on h50 for highly sensitive compounds with OB = −3%.

instance, on the basis of density functional theory (DFT) calculations, it was observed that C−NO2 bond dissociation energies in NACs steadily increase from 221 to 235 (respectively, 245) kJ/mol as one (respectively, two) NH2 groups are substitued in ortho positions.40 On the other hand, there is presently fewer evidence for a prominent role of intermolecular hydrogen bonding, which is usually discussed in relation to crystal-packing effects. In a very recent study,64 Ma et al. conclude that crystal packing is an important factor because DAAzF and DAAF are much less sensitive than HMX, in spite of similar BDEs. However, this comes as no surprise since those two molecules exhibit a very negative oxygen balance (−65% for DAAzF and −53% for DAAF) compared to HMX (−22%). Crystal-packing considerations are similarly invoked to explain the fact that hexanitrobenzene (HNB) is a very sensitive explosive in spite of rather high BDEs.65 Again, keeping in mind the role of the previously mentioned thermodynamic factor characterized by the energy content or oxygen balance, this result is to be expected as OB is exactly zero for this compound. In other words, the significant sensitivity differences reported in these earlier studies should clearly not be attributed only to crystalpacking effects. In order for the role of intermolecular hydrogen bonding not to be spoiled by stoichiometry differences, one may consider sets of isomers with similar BDE values. Those extracted from the present database do not support the idea that intermolecular hydrogen bonds would significantly contribute to decrease the sensitivity. On the contrary, as shown in Figure 5, hydrogen-bonded compounds are usually much more

sensitive than their isomers deprived of labile protons. For the compounds in this figure, h50 usually decreases from ca. 190 to 52−77 cm as hydrogen bonding is allowed, except in one case where it remains essentially unchanged (192 to 191 cm). Those examples are all for relatively insensitive NACs. In the lack of such isomeric series, sets of molecules sharing similar values of the oxygen balance OB may be considered. This leaves the above conclusions unchanged regarding the difficulty in evaluating the role of intermolecular hydrogen bonds. For instance, both molecules shown in Figure 6 exhibit a near-tooptimal value of OB = −3%. Since they also exhibit similar trigger bonds, the rightmost compound might be expected to be less sensitive in view of its ability to develop extended hydrogen-bonding networks in the crystal. In fact, both compounds exhibit very similar sensitivities. Obviously, assessing the role of hydrogen bonds and crystalpacking effects on sensitivity from comparisons between various compounds is extremely difficult because purely molecular factors are involved as well. In this context, experimental studies of energetic cocrystals are invaluable, as mentioned by Landenberger et al.66 In addition to the potential practical interest of such compounds, a comparison of the sensitivity of a cocrystal A:B with the values measured for the pure components A and B may reflect pure crystal effects. Indeed, in the lack of such effects, the sensitivity of A:B should usually fall between the values observed for A and B. This is illustrated in Figure 7 using theoretical h50 data presently obtained for a set of experimentally studied cocrystals.66−71 Our model simply explains this finding from the fact that the energy content per atom of these cocrystals 8197


Article


the well-known observation that explosives with lower loading densities (and thus larger porosities) are more sensitive.72 Like voids, free space within crystalline regions might provide an activation volume contributing to the thermal decomposition. However, the idea that is might also promote sensitivity is less obvious, considering the fact that initiation occurs within hot spots rather than in the bulk of perfect crystal lattices.36 Nevertheless, a possible role of crystal features is understandable in the light of the present model, keeping in mind the assumption that h50 is determined by the propagation of the decomposition process, rather than by the initiation itself.39 In detailed investigations of this aspect, Politzer and coworkers focus on the free space ΔV per molecule in the crystal. They point to a tendency of h50 to decrease as ΔV increases.73,74,75 However, it should be stressed that ΔV is primarily a measure of the molecular size. This is clear from the data reported in ref 75 for the 25 explosives studied: ΔV strongly correlates with the effective volume Veff per molecule in the crystal, as reflected by R2 = 0.92. Therefore, the general trend observed by these authors suggests that larger molecules tend to be more sensitive, as more explicitly pointed out in a subsequent paper.76 This might be the case because as a decomposition process is initiated within the material, for instance, through the rupture of a trigger linkage, this is likely to destabilize the whole molecule (typically a radical). The energy released by the complete decomposition of this molecule is likely to be higher for larger molecules. Although such a role of the molecular size is plausible and might be actually reflected by the general trend of h50 to decrease with ΔV, it does not appear to be significant. Indeed, although it does not incorporate such a mechanism, the present model for h50 satisfactorily describes the sensitivity of compounds spanning a wide range of molecular sizes.38,39 In line with the above-mentioned report by Landenberger et al. of a very dense packing for the surprisingly insensitive DADP:TITNB cocrystal,66 we believe that the possible role of free space in promoting sensitivity of a crystal might be better reflected by the packing coefficient κ, rather than by ΔV. Taking advantage of the data reported in ref 75, κ may be simply defined as κ = V(0.003)/Veff, where V(0.003) is the volume enclosed in the isodensity surface corresponding to 0.003 electrons/bohr3. The values of κ thus obtained for RDX and HMX, respectively, 0.78 and 0.81, indicate that the latter could be slightly more insensitive, in line with experimental results. For further insight into the possible role of κ on sensitivity, h50 is presently estimated for the 25 explosives considered in a recent study of the role of ΔV.75 As shown in Figure 8, good agreement with the experiment is obtained, except for LLM105. This failure is to be expected as no provision is made in the present model for the destabilizing effect of N+−O− for such compounds.77 Furthermore, it should be noted that calculations for FOX-7 and DNPP rely on newly obtained activation energies. This is because the chemical surroundings of nitro groups in these molecules do not match the standard environments for which standard values were tabulated in our previous studies.39,40 The detailed calculations involved are described in the Supporting Information. As mentioned above, the failure of the present scheme to account for the unexpected insensitivity of the DADP:TITNB cocrystal strongly suggests that some crystal-packing effects are missing. However, the very good agreement with the

Figure 7. Calculated sensitivities of energetic cocrystals compared to the values calculated for the pure components. Orange and green bars are, respectively, for the most sensitive and less sensitive components. Data for cocrystals are shown as yellow bars, indicating that the corresponding sensitivity value lying between that of the pure components is in qualitative agreement with the experiment. DADP:TITNB has a sensitivity value represented as a red bar, emphasizing the qualitative discrepancy between theoretical and experimental sensitivities.

falls between the values calculated for the individual components. It must be stressed that this is not necessarily the case. For instance, if A and B are, respectively, under- and overoxygenated, A:B can, in principle, release more energy and prove more sensitive than the separated components. However, such a case is not observed here. In Figure 7, orange and green bars are, respectively, for the most sensitive and less sensitive components. The data for cocrystals are usually shown as yellow bars, indicating that the corresponding sensitivity value lying between that of the pure components is in qualitative agreement with the experiment. No quantitative agreement is to be expected here in view of the specific experimental procedures used to measure the sensitivities of cocrystals. Unlike other cocrystals, DADP:TITNB has a sensitivity value represented as a red bar in Figure 7. This is to emphasize the qualitative discrepancy between theoretical and experimental sensitivities. Indeed, it was observed that this cocrystal is less sensitive than its components, in contrast to the usual findings.66 This was tentatively attributed to the specificity of the halogen−peroxide interactions in this material. Interestingly, the authors also mentioned that this cocrystal is characterized by a specially large packing coefficient, which is consistent with the possible role of the crystal-free space discussed in the next section. 5.5. Voids and Free Space within Crystals. Beyond the presence of intermolecular hydrogen bonds, another feature related to the crystal-packing mode and increasingly believed to play a role in promoting sensitivity is the amount of free space ΔV per molecule in the crystal.32 This picture is reminiscent of 8198


Article


In addition, the differences between activation energies associated with available decomposition pathways is suggested as a factor having a negative impact on the performancesensitivity trade-off, although in practice this criterion cannot easily be taken into account for the design of optimized explosives. As it stands, the present model provides a valuable alternative to empirical approaches most often used to guide the design of new energetic compounds. Furthermore, it provides a framework for future work aiming to develop further improved methods. Among the various molecular or crystal descriptors presently ignored by this model, the crystal-packing coefficient appears as specially attractive. First, it is not redundant with presently included thermodynamic and kinetic determinants of sensitivity. Second, assuming that large values of this coefficient promote insensitivity would lead to a rationalization of aspects that remain to be clarified, including the occurrence of cocrystals that prove less sensitive than their components or the interplay between free crystal volume and energy content. Finally, further progress is to be expected from investigations on cocrystals that provide valuable insight into the potential role of crystal packing.

Figure 8. Predicted versus observed h50 values for the 25 explosives studied in ref 75.

■

experiment observed in Figure 8 demonstrates that such effects are mostly insignificant for the 25 explosives studied in ref 75, by comparison with the role of activation energies and total energy content. An interesting aspect of κ is the fact that, unlike many other factors introduced to rationalize available sensitivity data (including OB, energy content, MEP...), it is not redundant with the two factors (thermodynamic and kinetic) at the basis of our model. Therefore, it is worth investigating whether it could improve current h50 predictions. In particular, over(respectively, under-) estimated values of h50 might be associated with especially low (respectively, high) values of κ. While this is not the case for the calculations reported in Figure 8, such a possibility should be kept in mind in view of future studies.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b02021. Describes the procedure employed to evaluate gas-phase formation enthalpies along with the corresponding increments (Table S1) and provides worked out examples of activation energies and h50 estimation for FOX-7 and DNPP. (PDF) Table S2: Database of presently studied explosives, along with experimental sensitivities and presently computed properties. Table S3: Database of formation enthalpies of F-/Cl-containing compounds in gas phase used to derived the F and Cl atomic increments listed in Table S1. (XLSX)

■

6. CONCLUSION Notwithstanding its unprecedented performance at predicting the magnitude of impact sensitivities for a large number of energetic materials, the model put forward in this work proves extremely useful to rationalize and qualitatively explain a large body of experimental observations, including the following: 1. Relatively high sensitivity of explosives with high detonation performance 2. Dependence of sensitivity ranking of explosives on the detailed experimental protocol used 3. Fact that impact sensitivity proves predictable, in spite of the critical role of defects whose features are largely unknown 4. Fact that crystal-packing features appear to play a role (as observed for HMX or RDX), despite the fact that initiation starts in defective regions of the material 5. Few remarkable successes (like the correlation between sensitivity and bond dissociation energy reported in ref 27) and the limitations of previous empirical approaches to correlate sensitivity data with molecular features 6. Variability of sensitivity among nitramines, which was recently pointed out in ref 32 as an issue to be clarified 7. Fact that cocrystals usually exhibit a sensitivity falling between the values observed for the pure components

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +33 (0)2 47344185. Fax: +33 (0)2 47345158. ORCID

Didier Mathieu: 0000-0003-3832-2286 Notes

The author declares no competing financial interest.

■

REFERENCES

(1) Mathieu, D.; Beaucamp, S. Matériaux Energétiques Encyclopédie “Techniques de l’Ingénieur”, Traité “Sciences Fondamentales”, Fascicule AF 6710: Paris, 2004. (2) Rice, B. M.; Byrd, E. F. C. Theoretical chemical characterization of energetic materials. J. Mater. Res. 2006, 21, 2444−2452. (3) Zeman, S. In High Energy Density Materials; Klapötke, T. M., Ed.; Springer: Berlin, Heidelberg, 2007; pp 195−271. (4) Badgujar, D.; Talawar, M.; Asthana, S.; Mahulikar, P. Advances in science and technology of modern energetic materials: An overview. J. Hazard. Mater. 2008, 151, 289−305. (5) Anders, G.; Borges, J. Topological Analysis of the Molecular Charge Density and Impact Sensitivity Models of Energetic Molecules. J. Phys. Chem. A 2011, 115, 9055−9068.

8199


Article

Industrial & Engineering Chemistry Research (6) Chen, Z.-X.; Xiao, H.-M. Quantum Chemistry Derived Criteria for Impact Sensitivity. Propellants, Explos., Pyrotech. 2014, 39, 487− 495. (7) Politzer, P.; Murray, J. S. Detonation Performance and Sensitivity: A Quest for Balance. Adv. Quantum Chem. 2014, 69, 1−30. (8) Shen, C.; Wang, P.; Lu, M. Molecular Design and Property Prediction for a Series of Novel Dicyclic Cyclotrimethylene Trinitramines (RDX) Derivatized as High Energy Density Materials. J. Phys. Chem. A 2015, 119, 8250−8255. (9) Ghule, V. D.; Deswal, S.; Devi, A.; Kumar, T. R. Computer-Aided Design of Energetic Tris(tetrazolyl)amine Derivatives and Salts. Ind. Eng. Chem. Res. 2016, 55, 875−881. (10) Klapötke, T. M.; Witkowski, T. G. Covalent and Ionic Insensitive High-Explosives. Propellants, Explos., Pyrotech. 2016, 41, 470−483. (11) Gupta, S.; Basant, N.; Singh, K. P. Three-Tier Strategy for Screening High-Energy Molecules Using Structure-Property Relationship Modeling Approaches. Ind. Eng. Chem. Res. 2016, 55, 820−831. (12) Pagoria, P. A comparison of the structure, synthesis, and properties of insensitive energetic compounds. Propellants, Explos., Pyrotech. 2016, 41, 452−469. (13) Yan, Q.-L.; Zeman, S.; Sánchez Jiménez, P. E.; Zhang, T.-L.; Pérez-Maqueda, L. A.; Elbeih, A. The Mitigation Effect of Synthetic Polymers on Initiation Reactivity of CL-20: Physical Models and Chemical Pathways of Thermolysis. J. Phys. Chem. C 2014, 118, 22881−22895. (14) An, Q.; Cheng, T.; Goddard, W. A.; Zybin, S. V. Anisotropic Impact Sensitivity and Shock Induced Plasticity of TKX-50 (Dihydroxylammonium 5,5′-bis(tetrazole)-1,1′-diolate) Single Crystals: From Large-Scale Molecular Dynamics Simulations. J. Phys. Chem. C 2015, 119, 2196−2207. (15) Kamlet, M. J.; Jacobs, S. J. Chemistry of detonations. I. A simple method for calculating detonation properties of C−H−N−O explosives. J. Chem. Phys. 1968, 48, 23. (16) Kamlet, M. J.; Finger, M. An alternative method for calculating Gurney velocities. Combust. Flame 1979, 34, 213. (17) Mathieu, D. Prediction of Gurney Parameters Based on an Analytic Description of the Expanding Products. J. Energ. Mater. 2015, 33, 102−115. (18) Fried, L. E.; Howard, M. Cheetah 3.0 User’s Manual; UCRL-MA117541; Lawrence Livermore National Laboratory, 2001. (19) Sućeska, M. Evaluation of Detonation Energy from EXPLO5 Computer Code Results. Propellants, Explos., Pyrotech. 1999, 24, 280− 285. (20) Akhavan, J. The Chemistry of Explosives; The Royal Society of Chemistry: London, 1998. (21) Belmas, R.; Plotard, J.-P. Physical Origin of Hot Spots in Pressed Explosive Compositions. J. Phys. IV 1995, 5, 61−87. (22) Akiki, M.; Menon, S. A model for hot spot formation in shocked energetic materials. Combust. Flame 2015, 162, 1759−1771. (23) Zhou, T.; Lou, J.; Zhang, Y.; Song, H.; Huang, F. Hot spot formation and chemical reaction initiation in shocked HMX crystals with nanovoids: a large-scale reactive molecular dynamics study. Phys. Chem. Chem. Phys. 2016, 18, 17627−17645. (24) Dlott, D. D.; Fayer, M. D. Shocked molecular solids: vibrational up pumping, defect hot spot formation, and the onset of chemistry. J. Chem. Phys. 1990, 92, 3798−3811. (25) Ye, S.; Tonokura, K.; Koshi, M. Energy transfer rates and impact sensitivities of crystalline explosives. Combust. Flame 2003, 132, 240− 246. (26) Su-Hong, G.; Xin-Lu, C.; Li-Sha, W.; Xiang-Dong, Y. Correlation between normal mode vibrations and impact sensitivities of some secondary explosives. J. Mol. Struct.: THEOCHEM 2007, 809, 55−60. (27) Rice, B. M.; Sahu, S.; Owens, F. J. Density functional calculations of bond dissociation energies for NO2 scission in some nitroaromatic molecules. J. Mol. Struct.: THEOCHEM 2002, 583, 69− 72.

(28) Song, X.-S.; Cheng, X.-L.; Yang, X.-D.; He, B. Relationship between the Bond Dissociation Energies and Impact Sensitivities of Some Nitro-Explosives. Propellants, Explos., Pyrotech. 2006, 31, 306− 309. (29) Li, J. Relationships for the impact sensitivities of energetic CNitro compounds based on bond dissociation energy. J. Phys. Chem. B 2010, 114, 2198−2202. (30) Zhao, J.; Xu, D.-h.; Cheng, X.-l. Investigation of correlation between impact sensitivities and bond dissociation energies in some triazole energetic compounds. Struct. Chem. 2010, 21, 1235−1240. (31) Tan, B.; Long, X.; Peng, R.; Li, H.; Jin, B.; Chu, S.; Dong, H. Two important factors influencing shock sensitivity of nitro compounds: bond dissociation energy of X−NO2 (XC,N,O) and Mulliken charges of nitro group. J. Hazard. Mater. 2010, 183, 908− 912. (32) Politzer, P.; Murray, J. S. Some molecular/crystalline factors that affect the sensitivities of energetic materials: molecular surface electrostatic potentials, lattice free space and maximum heat of detonation per unit volume. J. Mol. Model. 2015, 21, 25. (33) 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. (34) Cady, H. H.; Smith, L. C. Studies on the Polymorphs of HMX; Los Alamos Naional Laboratory, 1962. (35) Dobratz, B. M.; Crawford, P. C. LLNL Explosives Handbook; Lawrence Livermore National Laboratory: Livermore, CA, 1985. (36) Field, J. E. Hot spot ignition mechanisms for explosives. Acc. Chem. Res. 1992, 25, 489−496. (37) Fried, L. E.; Manaa, M. R.; Pagoria, P. F.; Simpson, R. L. Design and synthesis of energetic materials. Annu. Rev. Mater. Res. 2001, 31, 291−321. (38) Mathieu, D. Physics-Based Modeling of Chemical Hazards in a Regulatory Framework: Comparison with Quantitative StructureProperty Relationship (QSPR) Methods for Impact Sensitivities. Ind. Eng. Chem. Res. 2016, 55, 7569−7577. (39) Mathieu, D.; Alaime, T. Predicting Impact Sensitivities of Nitro Compounds on the Basis of a Semi-empirical Rate Constant. J. Phys. Chem. A 2014, 118, 9720−9726. (40) Mathieu, D.; Alaime, T. Impact sensitivities of energetic materials: exploring the limitations of a model based only on structural formulas. J. Mol. Graphics Modell. 2015, 62, 81−86. (41) Tian, M.; Chi, W.-J.; Li, Q.-S.; Li, Z.-S. Theoretical design of highly energetic poly-nitro cage compounds. RSC Adv. 2016, 6, 47607−47615. (42) Kazandjian, L.; Danel, J.-F. A Discussion of the Kamlet-Jacobs Formula for the Detonation Pressure. Propellants, Explos., Pyrotech. 2006, 31, 20−24. (43) Mathieu, D. Toward a Physically Based Quantitative Modeling of Impact Sensitivities. J. Phys. Chem. A 2013, 117, 2253−2259. (44) Beaucamp, S.; Mathieu, D.; Agafonov, V. Optimal partitioning of molecular properties into additive contributions: the case of crystal volumes. Acta Crystallogr., Sect. B: Struct. Sci. 2007, 63, 277−284. (45) Mathieu, D. Simple Alternative to Neural Networks for Predicting Sublimation Enthalpies from Fragment Contributions. Ind. Eng. Chem. Res. 2012, 51, 2814−2819. (46) Mathieu, D. MATEO: A software package for the molecular design of energetic materials. J. Hazard. Mater. 2010, 176, 313−322. (47) Storm, C. B.; Stine, J. R.; Kramer, J. F. Sensitivity Relationships in Energetic Materials.. Chemistry and Physics of Energetic Materials1990; pp 605−309.10.1007/978-94-009-2035-4_27 (48) Politzer, P.; Murray, J. S. High Performance, Low Sensitivity: Conflicting or Compatible? Propellants, Explos., Pyrotech. 2016, 41, 414−425. (49) Yu, Z.; Bernstein, E. R. Sensitivity and Performance of AzoleBased Energetic Materials. J. Phys. Chem. A 2013, 117, 10889−10902. (50) Yuan, J.; Long, X.; Zhang, C. Influence of N-Oxide Introduction on the Stability of Nitrogen-Rich Heteroaromatic Rings: A Quantum Chemical Study. J. Phys. Chem. A 2016, 120, 9446−9457. 8200


Article

Industrial & Engineering Chemistry Research (51) Agrawal, J. P. High Energy Materials; Wiley: Weinheim, Germany, 2010; Chapter 2, p 113. (52) Glassman, I.; Yetter, R. A.; Glumac, N. G. Combustion, 5th ed.; Academic Press: Waltham, MA, 2015; Chapter 2, p 44. (53) Mathieu, D. Formation Enthalpies Derived from Pairwise Interactions: A Step toward More Transferable Reactive Potentials for Organic Compounds. J. Chem. Theory Comput. 2012, 8, 1295−1303. (54) Chavez, D. E.; Parrish, D. A. Synthesis and Characterization of 1-Nitroguanyl-3-nitro-5-amino-1,2,4-triazole. Propellants, Explos., Pyrotech. 2012, 37, 536−539. (55) Mathieu, D. Theoretical Shock Sensitivity Index for Explosives. J. Phys. Chem. A 2012, 116, 1794−1800. (56) Rice, B. M.; Hare, J. J. A Quantum Mechanical Investigation of the Relation between Impact Sensitivity and the Charge Distribution in Energetic Molecules. J. Phys. Chem. A 2002, 106, 1770−1783. (57) Pepekin, V. I.; Korsunskii, B. L.; Denisaev, A. A. Initiation of solid explosives by mechanical impact. Combust., Explos. Shock Waves 2008, 44, 586−590. (58) Owens, F. J.; Jayasuriya, K.; Abrahmsen, L.; Politzer, P. Computational analysis of some properties associated with the nitro groups in polynitroaromatic molecules. Chem. Phys. Lett. 1985, 116, 434−438. (59) Murray, J. S.; Lane, P.; Politzer, P.; Bolduc, P. R. A relationship between impact sensitivity and the electrostatic potentials at the midpoints of C−NO2 bonds in nitroaromatics. Chem. Phys. Lett. 1990, 168, 135−139. (60) Politzer, P.; Murray, J. S.; Lane, P. Effects of strongly electronattracting components on molecular surface electrostatic potentials: application to predicting impact sensitivities of energetic molecules. Mol. Phys. 1998, 93, 187−194. (61) Li, H.; Shu, Y.; Gao, S.; Chen, L.; Ma, Q.; Ju, X. Easy methods to study the smart energetic TNT/CL-20 co-crystal. J. Mol. Model. 2013, 19, 4909−4917. (62) Politzer, P.; Murray, J. S. Relationships between dissociation energies and electrostatic potentials of C−NO2 bonds: applications to impact sensitivities. J. Mol. Struct. 1996, 376, 419−424. (63) Kohno, Y.; Mori, K.; Hiyoshi, R. I.; Takahashi, O.; Ueda, K. Molecular dynamics and first-principles studies of structural change in 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) in crystalline state under high pressure: Comparison of hydrogen bond systems of {TATB} versus 1,3-diamino-2,4,6-trinitrobenzene (DATB). Chem. Phys. 2016, 472, 163−172. (64) Ma, Y.; Zhang, A.; Zhang, C.; Jiang, D.; Zhu, Y.; Zhang, C. Crystal Packing of Low-Sensitivity and High-Energy Explosives. Cryst. Growth Des. 2014, 14, 4703−4713. (65) Ma, Y.; Zhang, A.; Xue, X.; Jiang, D.; Zhu, Y.; Zhang, C. Crystal Packing of Impact-Sensitive High-Energy Explosives. Cryst. Growth Des. 2014, 14, 6101−6114. (66) Landenberger, K. B.; Bolton, O.; Matzger, A. J. EnergeticEnergetic Cocrystals of Diacetone Diperoxide (DADP): Dramatic and Divergent Sensitivity Modifications via Cocrystallization. J. Am. Chem. Soc. 2015, 137, 5074−5079. (67) Yang, Z.; Zeng, Q.; Zhou, X.; Zhang, Q.; Nie, F.; Huang, H.; Li, H. Cocrystal explosive hydrate of a powerful explosive, HNIW, with enhanced safety. RSC Adv. 2014, 4, 65121−65126. (68) Shen, J. P.; Duan, X. H.; Luo, Q. P.; Zhou, Y.; Bao, Q.; Ma, Y. J.; Pei, C. H. Preparation and Characterization of a Novel Cocrystal Explosive. Cryst. Growth Des. 2011, 11, 1759−1765. (69) Bolton, O.; Simke, L. R.; Pagoria, P. F.; Matzger, A. J. High Power Explosive with Good Sensitivity: A 2:1 Cocrystal of CL20:HMX. Cryst. Growth Des. 2012, 12, 4311−4314. (70) Landenberger, K. B.; Matzger, A. J. Cocrystals of 1,3,5,7Tetranitro-1,3,5,7-tetrazacyclooctane (HMX). Cryst. Growth Des. 2012, 12, 3603−3609. (71) Bennion, J. C.; McBain, A.; Son, S. F.; Matzger, A. J. Design and Synthesis of a Series of Nitrogen-Rich Energetic Cocrystals of 5,5′Dinitro-2H,2H′-3,3′-bi-1,2,4-triazole (DNBT). Cryst. Growth Des. 2015, 15, 2545−2549.

(72) Levesque, G. A.; Vitello, P.; Nichols, A. L.; Tarver, C.; Willey, T.; Friedman, G.; Oppelstrup, T. Analyses on the effect of hot spot density on material consumption rate. J. Phys. Conf. Ser. 2014, 500, 152010. (73) Pospíšil, M.; Vávra, P.; Concha, M. C.; Murray, J. S.; Politzer, P. A possible crystal volume factor in the impact sensitivities of some energetic compounds. J. Mol. Model. 2010, 16, 895−901. (74) Pospíšil, M.; Vávra, P.; Concha, M. C.; Murray, J. S.; Politzer, P. Sensitivity and the available free space per molecule in the unit cell. J. Mol. Model. 2011, 17, 2569−2574. (75) Politzer, P.; Murray, J. S. Impact sensitivity and crystal lattice compressibility/free space. J. Mol. Model. 2014, 20, 2223. (76) Politzer, P.; Murray, J. S. Perspectives on the crystal densities and packing coefficients of explosive compounds. Struct. Chem. 2016, 27, 401−408. (77) Yuan, J.; Long, X.; Zhang, C. Influence of N-Oxide Introduction on the Stability of Nitrogen-Rich Heteroaromatic Rings: A Quantum Chemical Study. J. Phys. Chem. A 2016, 120, 9446−9457.

8201


Sensitivity of Energetic Materials: Theoretical Relationships to

Recommend Documents