Standard Enthalpy of Formation, Thermal Behavior, and Specific Heat

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Standard Enthalpy of Formation, Thermal Behavior, and Specific Heat Capacity of 2HNIW·HMX Co-crystals Shijie Zhang,† Jiaoqiang Zhang,*,† Kaichang Kou,† Qian Jia,† Yunlong Xu,† Ning Liu,‡ and Rongzu Hu‡ †

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Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education, Department of Applied Chemistry, School of Science, Northwestern Polytechnical University, Xi’an 710072, China ‡ Xi’an Modern Chemistry Institute, Xi’an 710065, China ABSTRACT: 2HNIW·HMX co-crystals are crystals composed of HNIW (2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexazisowurtzitane) and HMX (1,3,5,7tetranitro-1,3,5,7-tetrazocane), and the HNIW molecule and HMX molecule are combined with noncovalent bonds in a lattice at a 2:1 ratio. The 2HNIW· HMX co-crystals are successfully synthesized by Bolton’s method and characterized by powder X-ray diffraction, laser Raman spectrometer, differential scanning calorimeter (DSC), and high performance liquid chromatograph. The standard enthalpy of formation of 2HNIW·HMX cocrystals is obtained as 861.9 ± 18.6 kJ·mol−1 under the direction of a designed thermochemical cycle with a Calvet microcalorimeter. The thermal decomposition behavior of 2HNIW·HMX co-crystals was studied under the non-isothermal condition with DSC. The apparent activation energy (E) of the decomposition is 332.23 kJ·mol−1 by Kissinger method, 324.10 kJ·mol−1 by Ozawa method, 314.06 ± 4.26 kJ·mol−1 by Friedman−Reich−Levi method, and 306.81 ± 3.12 kJ·mol−1 by NL-INT-SY3 method, respectively. The pre-exponential factor (logA/s−1) is 29.33 ± 0.33 via compensation effect. A continuous Cp mode of MicroDSC III was used to determine the specific heat capacity (Cp,m) of the target co-crystals from 283.15 to 333.15 K, and the Cp,m is 1114.04 ± 10.92 J·mol−1·K−1 at 298.15 K. These results could provide valuable information on 2HNIW·HMX co-crystals for both theory and application.

1. INTRODUCTION Energetic materials (EMs) are important compounds which contain large amounts of stored chemical heat within their molecular structures and can release energy at a high rate to produce massive hot gaseous products under some stimulations such as impact, shock, or thermal effects.1,2 The highenergy-density materials (HEDMs) have potential applications in various propellants, pyrotechnics, explosives, and gas generators, in areas such as mining, armaments, space exploration, and fireworks.3 Explosive power and safety are the most important properties of EMs applied in military and civil fields. Conflict between the increase of chemical energy and decreasing the sensitivity has become more and more severe. Therefore, the research and development of highenergy and low-sensitivity compounds have been a priority in the domain of EMs.2,4−6 A significant amount of effort has been made to improve the detonation performance and insensitivity of EMs simultaneously, such as synthesis of new EMs,7,8 optimization of the existing EMs, and preparation of composites of two or more EMs.9,10 Co-crystals are a form of multiple crystal consisting of two or more components bonded by hydrogen bonding, π-stacking, and van der Waals forces, widely adopted in pharmaceutial chemistry.11−13 It is generally known that the physical properties (explosive power, thermal stability, and physical sensitivity) of EMs are critically reliant on materials properties such as density and melting point. Co© XXXX American Chemical Society

crystallization can change the internal composition and crystal type of EMs without destroying the chemical structure of the original materials, and it has been the focus of effort to modify their performances efficiently. These properties of explosives such as higher density, better explosive performance, lower sensitivity, and better stability could be acquired through cocrystals with other EMs.14,15 2,4,6,8,10,12-Hexanitro-2,4,6,8,10,12-hexazisowurtzitane (HNIW), well-known as CL-20, is an attractive explosive with cage structure, high density (>2.0 g·cm−3), high detonation velocity (9400 m·s−1), and good oxygen balance (−10.94%).16 It is regarded as one of the most powerful explosives nowadays, and the next generation high energetic material, while the application of HNIW is currently restricted due to its high sensitivity. HNIW has been co-crystallized with other EMs to improve its insensitivity, such as 2,4,6-trinitrotoluene (TNT), caprolactam (CPL), benzotrifuroxan (BTF), and 1,3,5triamino-2,4,6-trinitrobenzene (TATB).17−20 These co-crystals can effectively enhance the insensitivity of HNIW, while the explosive power of HNIW might be decreased due to the addition of other EMs. 1,3,5,7-Tetranitro-1,3,5,7-tetrazocane (HMX) is an universal damage explosive in the modern Received: June 1, 2018 Accepted: December 4, 2018

A

DOI: 10.1021/acs.jced.8b00454 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

(1.48 mg, 5.0 μmol) and 2-propanol (about 2 mL) were mixed in a flask with mild heating and stirring. After the solids were dissolved completely, the solution was filtrated with a 0.45 μm poly(tetrafluoroethylene) (PTFE) filter. Then the solvent slowly volatilized over several days at 298.15 K and the colorless sample (sample 1) could be obtained. To obtain the pure phase co-crystals, the following steps were also needed. HNIW (44.84 mg, 102.4 μmol), HMX (15.16 mg, 51.2 μmol), and acetone (about 800 μL) were dissolved in a flask; the solution was dried quickly with nitrogen gas at 353.15 K. Then a single seed crystal of 1 was added to the above flask with 2propanol (about 1 mL), which also was filtrated with a 0.45 μm PTFE filter. The slurry was oscillated on a shaker (SHA-C, Jintan JINDA Instrument Manufacturing Co., Ltd., China) for 1 week, after which the 2HNIW·HMX co-crystals can be acquired. They were kept in a vacuum desiccator before use. Powder X-ray diffraction patterns were recorded with a mini flex 300/600 X-ray diffractometer (D2 Phaser, Bruker AXS Gmbh, Germany) in the reflection mode with Cu Kα radiation (40 kV, 15 mA). Laser Raman spectra were analyzed by a micro-Raman spectrometer (in Via, Renishaw, England) from 200 to 3200 cm−1. Thermal analyses of raw materials and cocrystals were conducted with a differential scanning calorimeter (Q2000, TA Instrument, USA) with the heating rate of 10 K·min−1. The content ratio of the co-crystal was investigated by high-performance liquid chromatography (LC-20AD, Shimadzu Corp., Japan) with a welchrom HPLC column (150 mm × 4.6 mm i.d.). Each experiment was repeated three times. 2.2. Microcalorimeter Experiment. The thermochemical cycle (as shown in Figure 1) is designed to determine the standard molar enthalpy of 2HNIW·HMX co-crystals. The molar enthalpy of dissolution of HNIW, HMX, and 2HNIW· HMX co-crystals in corresponding solvents were measured by a Calvet microcalorimeter (DC08-1, Mianyang Phanaly Technology LLC, China), respectively. The sensitivity of the microcalorimeter is 62.05 ± 0.04 μV·mW−1, and the control and experimental precisions of temperature of the microcalorimeter can reach ±1 × 10−3 K and ±1 × 10−4 K, respectively. In order to ensure the reliability of this system, the enthalpy of dissolution (ΔdissH) of KCl (mass fraction ≥ 99.99%) was measured with distilled water at 298.15 K and its ΔdissH is 17.498 ± 0.021 kJ·mol−1, which is well-consistent with the value 17.536 ± 0.034 kJ·mol−1 reported in the literature.29 It shows that the device in this work is very reliable. Each experiment was repeated four times to ensure the precision of the data. In all of the determinations, the

weapon system with good thermal stability, and it possesses greater explosive power than most EMs.21 Bolton et al. prepared the HNIW·HMX (in a 2:1 molar ratio) co-crystals in 2012; the co-crystals were predicted to exhibit a high explosive power and were moderately resistant to detonation.22 The standard enthalpy of formation, thermal decomposition behavior, and specific heat capacity of EMs play a vital role in theoretical studies, application development, and commercial processing of materials. In the past few years, 2HNIW·HMX co-crystals have attracted increasing attention due to their high explosive energy and moderate sensitivity.22−28 However, as far as we know, there are few thermochemical studies of 2HNIW· HMX co-crystals, making it necessary to investigate their relevant properties. In this work, the 2HNIW·HMX co-crystals were prepared and characterized by powder X-ray diffraction (PXRD), laser Raman spectroscopy, differential scanning calorimetry (DSC), and high-performance liquid chromatography (HPLC). The standard molar enthalpy of formation was determined by a Calvet microcalorimeter under the direction of a programed thermochemical cycle. The thermal behaviors of 2HNIW·HMX co-crystals were studied by DSC, and the decomposition kinetic parameters and some thermodynamic parameters of 2HNIW·HMX co-crystals were acquired. Moreover, the specific heat capacity of the compound was determined using a continuous Cp mode of microcalorimeter (Micro-DSC III) from 283.15 to 333.15 K.

2. EXPERIMENTAL SECTION 2.1. Materials, Preparation, and Characterization. All chemicals involved in the study are obtained from commercial sources, and the chemical structures of the main raw materials are shown in Scheme 1.The detailed information is listed in Table 1. Scheme 1. A, Chemical Structure of HNIW; B, Chemical Structure of HMX

2HNIW·HMX co-crystals were prepared and purified according to the literature method,22 which was briefly described as follow: HNIW (4.38 mg, 10.0 μmol), HMX

Table 1. Source and Mass Fraction Purity of Chemicals Used in This Study compd

source of supply

state

CAS Reg. No.

mass fraction purity/%

ε-HNIW β-HMX indium tin KCl acetonitrile α-Al2O3 2-propanol acetone distilled watera

Liaoning Qingyang Special Chemical Co., Ltd., China Liaoning Qingyang Special Chemical Co., Ltd., China TA Instrument, USA TA Instrument, USA Alfa Aesar, China Alfa Aesar, China Aladdin Industrial Corp., China Guangdong Guanghua Sci-Tech Co., Ltd., China Guangdong Guanghua Sci-Tech Co., Ltd., China A.S. Watson Group (Hong Kong) Ltd., China

powder powder powder powder powder liquid powder liquid liquid liquid

135285-90-4 2691-41-0 231-180-0 7440-31-5 7447-40-7 75-05-8 1344-28-1 67-63-0 67-64-1 7732-18-5

99.3 99.2 ≥99.99 ≥99.99 ≥99.99 ≥99.8 ≥99.9 ≥99.8 ≥99.8

The electrical conductivity of the distilled water is 0.3 μS·cm−1 at 298.15 K.

a

B



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the co-crystals are shown in Figure 2. The diffraction peaks of pure raw materials indicate that they are ε-HNIW and β-

Figure 1. Schematic diagram of the designed thermochemical cycle: 1, reaction of ε-HNIW dissolving in acetonitrile; 2, reaction of β-HMX dissolving in the solution formed by step 1; 3, reaction of equivalent co-crystals dissolving in equivalent acetonitrile; 4, reaction of cocrystals formed by β-HMX and ε-HNIW.

stoichiometries in each step of the reaction were controlled strictly, and the dissolutions of the co-crystals were the same composition as that of the raw materials. In addition, an UV− vis spectrophotometer (UV-3600 plus, Shimadzu. Ltd., Japan) was used to ensure the reliability of the designed thermochemical cycle (Figure 1). The maximum time of each test was about 20 min, and no solid residues could be observed after each experiment. 2.3. Thermal Decomposition Behavior. The thermal decomposition behavior of 2HNIW·HMX co-crystals was performed by DSC (Q2000, TA Instrument, USA) under 0.1 MPa at different heating rates (2, 5, 7.5, 10, and 15 K·min−1) from 323.15 to 673.15 K in N2 atmosphere at a flow rate of 60 mL·min−1, and each experiment was repeated three times. In order to ensure the accuracy of the measurement, the DSC was calibrated using the pure In and Sn particles by onset temperatures under nitrogen atmosphere at the same condition. The measured melting points (onset temperatures) of In and Sn are 429.80 ± 0.25 K and 505.12 ± 0.4 K, respectively, which are in accordance with the literature values (In of 429.76 K and Sn of 505.04 K).30 Meanwhile, the melting enthalpies of In and Sn are 28.5 ± 0.2 J·g−1 and 60.5 ± 0.4 J· g−1, respectively, which coincide with the literature values (In of 28.4 J·g−1 and Sn of 60.6 J·g−1).30 In general, this shows the accuracy of the tests is satisfactory. 2.4. Determination of the Specific Heat Capacity. A Micro-DSCIII apparatus (Seteram Instrumentation, France) on a continuous Cp mode was used to determine the specific heat capacity of 2HNIW·HMX co-crystals at a heating rate of 0.15 K·min−1 from 283.15 to 333.15 K with the sample mass of 250 mg, in which the precisions of temperature and heat flow were 10−4 K and 0.2 μW, respectively. To maintain the accuracy of the Micro-DSCIII apparatus, it was calibrated with α-Al2O3 (calcined). Its mathematical expression was Cp/(J·g−1· K−1) = 0.1839 + 1.9966 × 10−3T from 283.15 to 333.15 K, and the standard molar heat capacity Cθp,m(α-Al2O3) at 298.15 K was determined as 79.44 J·mol−1·K−1, which is in excellent agreement with the value reported previously (79.02 J·mol−1· K−1).31

Figure 2. XRD patterns of the raw materials and the co-crystals.

HMX,17,21 respectively. Comparisons show that some new peaks (such as 2θ = 13.41°, 18.59°, and 29.79°, etc.) appear in the co-crystal pattern, while several inherent peaks of pure εHNIW (such as 2θ = 12.82°, 30.58°, and so on) and pure βHMX (such as 2θ = 14.67°, 20.39°, and 31.89°, etc.) vanish or shift in their XRD pattern. The diffraction peaks of the cocrystals on pattern correspond well with the previous literature;22 these indicate that the co-crystals are prepared successfully. As shown in Figure 3A, the laser Raman spectroscopy of the co-crystals changes by comparison that of the pure ε-HNIW and β-HMX, especially the -NO2 asymmetric stretching vibrational peaks of ε-HNIW at 1595.1 and 1577.2 cm−1 and the -CH2- asymmetric stretching vibrational peaks of β-HMX at 3028.3 cm−1 are disappearing in the spectrum of the cocrystals. In addition, the -CH2- symmetric stretching vibrational peak of β-HMX shifts from 2992.1 cm−1 (individual component) to 3006.7 cm−1 (co-crystals). These could be attributed to the intermolecular hydrogen bond interactions between the -NO2 of HNIW and the -CH2- of HMX in the cocrystals. The Raman result is highly in accord with the literature.22 The DSC curve of the co-crystals (Figure 3B) displays only one exothermic decomposition peak, while that of the physics mixture shows two, and it is in agreement with the literature.24 Moreover, the decomposition peak of 2HNIW· HMX co-crystals was narrower than that of pure HNIW and near that of pure HMX, manifesting that the co-crystals possess higher energy release efficiency. The HPLC results indicate that the contents of the corresponding components are w(HNIW) = 0.747 and w(HMX) = 0.253, respectively, demonstrating that the molar ratio of HNIW and HMX in the co-crystals is 2:1. By comparison with the reported literature, these results indicate that the 2HNIW·HMX cocrystals were prepared successfully. In addition, the result of each parallel experiment was identical, illustrating that the synthesized co-crystals were homogeneous. 3.2. Confirmation of Same Final States of the Designed Thermochemical Cycle. The UV spectrum (Figure 4) was used to verify whether the solutions obtained from the dissolution of the raw materials and co-crystals in

3. RESULTS AND DISCUSSION 3.1. Characterization of 2HNIW·HMX Co-crystals. In order to indicate the successful preparation of the 2HNIW· HMX co-crystals, several methods are applied to characterize this material and the results are compared with the reported literature. The XRD patterns of pure HNIW, pure HMX, and C



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Figure 3. A, Raman spectroscopy of the raw materials and co-crystals; B, DSC curves of pure raw materials, 2HNIW/HMX mixture, and the cocrystals.

Table 2. Molar Enthalpy of ε-HNIW in Acetonitrile (1.17 g) at Temperature T = 298.15 K and Pressure p = 0.1 MPaa (Mass of Sample, m; Heat Effect in the Dissolution, Q; Molar Enthalpy of Dissolution, ΔsolHm) no.

m/mg

Q/mJ

ΔsolHm/(kJ·mol−1)

1 2 3 4 mean

12.69 12.72 12.70 12.68

213.61 212.55 213.46 210.66

7.38 7.32 7.37 7.28 7.34 ± 0.04b

a

Standard uncertainties u are u(T) = 0.001 K, u(p) = 2 KPa, and u(m) = 0.01 mg. bExpanded uncertainty U, which was estimated as twice the standard deviation of the mean with 0.95 level of confidence.

Table 3. Molar Enthalpy of β-HMX in the Mixture of εHNIW (12.7 mg) and Acetonitrile (1.17 g) at Temperature T = 298.15 K and Pressure p = 0.1 MPaa (Mass of Sample, m; Heat Effect in the Dissolution, Q; Molar Enthalpy of Solution, ΔsolHm)

Figure 4. UV spectra of the dissolution of the raw materials and cocrystals: ○, co-crystals; ■, raw materials.

reaction 4 were the same. As seen in Figure 4, the UV spectra of the corresponding dissolution obtained from reactions 2 and 3are consistent. This result shows that both the final states of the co-crystals and the raw materials in solvents are the same, which indicates that the designed thermochemical cycle is credible and reliable. The standard molar enthalpy of formation of 2HNIW·HMX co-crystals can be deduced according to the designed thermochemical cycle. 3.3. Standard Enthalpy of Formation of 2HNIW·HMX Co-crystals. From Figure 1, the standard molar enthalpy of formation of 2HNIW·HMX co-crystals could be acquired by the standard molar enthalpy of formation of HNIW(s) and HMX(s) and ΔrHθm(4). Applying Hess’s law, the value of ΔrHθm(4) can be calculated by the following formula: Δr Hmθ (4) = 2Δsol Hmθ (1) + Δsol Hmθ (2) − Δsol Hmθ (3)

no.

m/mg

Q/mJ


1 2 3 4 mean

4.29 4.31 4.32 4.30

231.61 231.44 232.89 233.40

15.99 15.91 15.97 16.08 15.99 ± 0.07b

a Standard uncertainties u are u(T) = 0.001 K, u(p) = 2 KPa, and u(m) = 0.01 mg. bExpanded uncertainty U, which was estimated as twice the standard deviation of the mean with 0.95 level of confidence.

solution of the co-crystals (about 17.0 mg) in acetonitrile (1.17 g) at 298.15 K is shown in Table 4. In these tables, the uncertainty is calculated as twice the standard deviation of the

(1)

The molar enthalpy of solution of ε-HNIW (about 12.7 mg) in acetonitrile (1.17 g) at 298.15 K is listed in Table 2. The molar enthalpy of solution of β-HMX (about 4.3 mg) in the mixture of ε-HNIW (about 12.7 mg) and acetonitrile (1.17 g) at 298.15 K is presented in Table 3. The molar enthalpy of

mean; that is, δ = 2 ∑ (xi − x)2 /n(n − 1) , where n is the experimental number (n = 4), xi is the value of each experiment, and x is the mean value of the repeated experiment. D



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Table 4. Molar Enthalpy of 2HNIW·HMX Co-crystals in Acetonitrile (1.17 mg) at Temperature T = 298.15 K and Pressure p = 0.1 MPaa (Mass of Sample, m; Heat Effect in the Dissolution, Q; Molar Enthalpy of Solution, ΔsolHm) no.

m/mg

Q/mJ


1 2 3 4 mean

17.00 16.98 16.99 17.02

376.54 376.32 378.63 379.23

25.97 25.99 26.13 26.13 26.05 ± 0.09b

a

Standard uncertainties u are u(T) = 0.001 K, u(p) = 2 KPa, and u(m) = 0.01 mg. bExpanded uncertainty U, which was estimated as twice the standard deviation of the mean with 0.95 level of confidence.

As shown in these Tables 2−4, the dissolutions of HNIW in acetonitrile, HMX in the mixture of HNIW and acetonitrile, and the co-crystals in acetonitrile are endothermic. With the experimental data, the value of ΔrHθm(4) can be obtained as 4.60 ± 0.13 kJ·mol−1. Table 5 shows the thermochemical cycle and the corresponding result for the derivation of the standard molar enthalpy of formation (2HNIW·HMX co-crystals). As shown in XRD patterns and Raman spectra, the raw materials are ε-HNIW and β-HMX. The standard enthalpies of formation of ε-HNIW and β-HMX are 377.4 ± 13.0 kJ· mol−1 and 102.5 ± 2.8 kJ·mol−1,32,33 respectively. Therefore, the standard enthalpy of formation of 2HNIW·HMX cocrystals according to eq 2 can be calculated as 861.9 ± 18.6 kJ· mol−1.

Figure 5. DSC curves at different heating rates of the 2HNIW·HMX co-crystals: □, 2 K·min−1; ○, 5 K·min−1; △, 7.5 K·min−1; ▽, 10 K· min−1; ◁,15 K·min−1.

exothermic decomposition reaction of the 2HNIW·HMX cocrystals. Kissinger method: ln(βi /Tpi 2) = ln(Ak R /Ek ) − Ek /RTpi

(3)

Ozawa method: log βi + 0.4567Eo /RTpi = C

(4)

In these equations, Ek and Eo are values of apparent activation energy according to Kissinger and Ozawa methods (kJ·mol−1), respectively. Ak is the value of the pre-exponential factor by Kissinger equation (s−1), βi is the different heating rates (K·min−1), R is the gas constant with the value of 8.314 J· mol−1·K−1, Tpi is the peak temperature in DSC curve at each heating rate (K), and C is a constant.

Δf Hmθ (2HNIW·HMXco‐crystals,s,298.15K) = 2Δf Hmθ (ε‐HNIW,s,298.15K) + Δf Hmθ (β‐HMX,s,298.15K) + Δr Hmθ (4)

(2)

It is generally known that the enthalpy of solid phase reaction (Figure 1, reaction 4) is difficult to determine directly. Herein, we design a thermochemical cycle to solve the problem successfully. With the help of dissolutions enthalpies and standard enthalpies of formation of HNIW and HMX, the standard enthalpy of formation of 2HNIW·HMX co-crystals can be deduced easily. 3.4. Thermal Behavior and Thermodynamic Parameters of 2HNIW·HMX Co-crystals. The DSC curves of different heating rates of the co-crystals are presented in Figure 5. As shown, the shape of the DSC curves is similar for each heating rate. The curves are shifted to higher temperatures as the heating rate increases. Equations 3 (Kissinger method34) and 4 (Ozawa method35) were applied to acquire the kinetic parameters of the main

T(eorp)i = Te0orp0 + bβi + cβi 2 + dβi 3 ,

i = 1, 2, ..., 5 (5)

where Tpi and Tei are the peak and onset temperatures in the DSC curves at different heating rates (K), respectively. βi is each heating rate. b, c, and d are coefficients. The original values of Tp and Te, the values (Te0 and Tp0) of Te and Tp corresponding to β → 0 acquired by eq 5, and the above-mentioned parameters (E and A) of the exothermic decomposition reaction at different heating rates are listed in Table 6. As can be seen from the experimental results, the apparent activation energy acquired by Kissinger’s equation

Table 5. Designed Thermochemical Cycle and Experimental Results of Each Test for the Derivation of the Standard Molar Enthalpy of Formation (ΔfHθm, at 298.15 K and 0.1 MPaa) (2HNIW·HMX Co-crystals; Molar Enthalpy of Reaction, ΔrHθm) ΔrHθm/(kJ·mol−1)

no.

reaction

1 2 3 4

2ε-HNIW(s) + CH3CN(l) = 2HNIW(aq) + CH3CN(l) β-HMX(s) + 2HNIW(aq) + CH3CN(l) = HMX(aq) + 2HNIW(aq) + CH3CN(l) 2HNIW·HMX(s) + CH3CN(l) = HMX(aq) + 2HNIW(aq) + CH3CN(l) β-HMX(s) + 2ε-HNIW(s) = 2HNIW·HMX(s)

7.34 15.99 26.04 4.60

± ± ± ±

0.04b 0.07b 0.31b 0.13c

a Standard uncertainties u are u(T) = 0.001 K and u(p) = 2 KPa. bExpanded uncertainty U, which was estimated as twice the standard deviation of the mean with 0.95 level of confidence. cUncertainty of the combined reaction was estimated as the square root of the sum of the squares of uncertainty of each individual reaction.

E



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Table 6. Values of Kinetics of the Exothermic Decomposition Reaction of 2HNIW·HMX Co-crystals Determined by DSC Curves at Different Heating Rates (β) [Onset Temperature, Te; Peak Temperature, Tp; Onset Temperature (β → 0), Te0; Peak Temperature (β → 0), Tp0; Apparent Activation Energy by Kissinger Method, Ek; Apparent Activation Energy by Ozawa Method, Eo; Apparent Activation Energy by Friedman−Reich−Levi Method, Ef; Apparent Activation Energy by NL-INT-SY3 Method, E NL‑INT‑SY3; Pre-exponential Factor by Compensation Effect, log(A/s−1)]a βi/ (K·min−1)

Te/K

2 5 7.5 10 15

± ± ± ± ±

506.23 513.61 516.55 518.60 520.60

Tp/K b

0.21 0.26b 0.19b 0.12b 0.15b

510.29 515.84 519.24 520.98 523.01

± ± ± ± ±

Te0/K b

0.08 0.09b 0.12b 0.04b 0.11b

498.82

Tp0/K

Ek/ (kJ·mol−1)

505.03

332.23

Eo/ (kJ·mol−1)

ENL‑INT‑SY3/ (kJ·mol−1)

324.10

306.81 ± 3.12

b

Ef/(kJ·mol−1)

log(A/s−1)

314.06 ± 4.26

29.33 ± 0.33b

b

a

The values of Te0 and Tp0 were calculated with the mean values of Tei and Tpi. bExpanded uncertainty U, which was estimated as twice the standard deviation of the mean with 0.95 level of confidence.

(Ek) is in good agreement with that acquired by Ozawa’s equation (Eo); both the linear correlation coefficients of rk = 0.9974 and ro = 0.9975 are very close to 1. These indicate that the result is persuasive. Moreover, considering the limitations in Kissinger and Ozawa methods, the Friedman−Reich−Levi method (eq 6) and the NL-INT-SY3 method (eq 7) (nonlinear integration iso-conversional method) were used to analyze the decomposition of 2HNIW·HMX co-crystals.36−39 The average apparent activation energy (Ef) acquired by Friedman− Reich−Levi method is 314.06 ± 5.26 kJ·mol−1. The results of the NL-INT-SY3 method are shown in Figure 6. When α is

n

Ω1I (Eα) = min

n

∑∑ i=1 j≠i

βjI(Eα , Tα , i) βi I(Eα , Tα , j)

− n(n − 1) (7)

where the value of I(Eα,Tα) integral is acquired by taking Senum−Yang approximation calculation for approximation of the third degree: ÄÅ É 2 yzÑÑÑÑ ÅÅÅ −uij u + 10 u + 18 zzÑÑ ISY‐3(E , T ) = ÅÅÅT e jjj 3 zÑ 2 ÅÅ k u + 12u + 36u + 24 {ÑÑÑÖ ÅÇ u = E/RT in the equation. Compensation effect (eq 8) was used to evaluate the preexponential factor:43 (8)

ln A = aE + b

where a and b are the compensation parameters. With the original data of DSC and our own software, the compensation effect can be obtained as follows (eq 9), and r = 0.9996. This integral model function (G(α)) of the reaction model is [− ln(1−α)]2/3. (9)

ln A = 0.2414E − 6.528 −1

By substituting ENL‑INT‑SY3 = 306.81 ± 3.12 kJ·mol into eq 8, log(A/s−1) can be calculated as 29.33 ± 0.33. All the kinetic parameters are listed in Table 6. These kinetic parameters can aid in making reliable kinetic predictions providing information about the mechanism of the decomposition, which will be discussed in more detail in further work. The critical temperature of a thermal explosion (Tb) is a significant parameter for evaluating safety and can explicate the transition tendency from thermal decomposition to thermal explosion on a small scale. The value of Tb can be obtained as 505.75 ± 0.12 K according to eq 10.44 The greater value of Tb indicates that the heat resistance of EM is better. The Tb of cocrystals is a little lower than that of 3,4-dinitrofurazanfuroxan (DNTF) (Tb = 513.75 K), which is well-known for high energy and low sensitivity.45 This means that the heat resistance of 2HNIW·HMX co-crystals is close to that of DNTF.

Figure 6. Results of iso-conversional analysis of DSC: apparent activation energy by NL-INT-SY3 method, Eα; conversion, α.

in the range of 0.55−0.975, the average of ENL‑INT‑SY3 is 306.81 ± 3.12 kJ·mol−1. The average ENL‑INT‑SY3 is similar to the average Ef, indicating that the ENL‑INT‑SY3 is believable. For comparison, the apparent activation energy of decomposition for the co-crystals is greater than that of the pure HNIW (E = 205−268 kJ·mol−1, α = 0.4−0.8,40 and Ek = 156.16 kJ·mol−141) but less than that of the pure HMX (Ek = 444 kJ·mol−1).42 i dα yz zz = ln[A α f (α)] − Eα /RTα , i lnjjjβi k dT { α

Tb = (E NL‐INT‐SY3 −

E NL‐INT‐SY32 − 4E NL‐INT‐SY3RTe0 )/2R (10)

(6)

where ENL‑INT‑SY3 is the apparent activation energy obtained by NL-INT-SY3 method (kJ·mol−1). Te0 is the temperature of Te corresponding to β → 0 (K), and R is the gas constant, 8.314 J· mol−1·K−1.

where βi is the heating rate. T is the temperature. α is the extent of reaction. Eα is the apparent activation energy. R is the gas constant with the value of 8.314 J·mol−1·K−1. F



Article

The entropy of activation (ΔS⧧), enthalpy of activation (ΔH⧧), and Gibbs free energy of activation (ΔG⧧) of the exothermic decomposition stage can be obtained eqs 11−1346 corresponding to T = Tp0, log A, and E = ENL‑INT‑SY3 as 303.88 ± 6.32 J·mol−1·K−1, 302.64 ± 3.12 kJ·mol−1, and 149.17 ± 3.86 kJ·mol−1, respectively. The positive values of ΔG⧧ and ΔH⧧ indicate that the 2HNIW·HMX co-crystals exhibit good resistance to heat when the exothermic decomposition reaction occurs by heat treatment. A e−E / RT = kBT e−ΔG

⧧

/ RT

/h

Cp,m/(J·mol−1·K−1) = −4.35692 × 103 + 4.32914 × 101(T /K) − 1.13468 × 10−1(T /K)2 + 1.00000 × 10−4(T /K)3 (283.15 < T /K < 333.15)

The correlation coefficient of fitting R is 0.9932 and the specific heat capacity of 2HNIW·HMX co-crystals is 1114.04 ± 10.92 J·mol−1·K−1 at 298.15 K. Although the testing temperature is from 283.15 to 333.15 K, the equation of Cp,m is stable and continuous, which can serve as a guidance for the application of 2HNIW·HMX co-crystals in the temperature range. 3.6. Thermodynamic Functions of 2HNIW·HMX Cocrystals. Equations 15 and 1647 are used to calculate the enthalpy change, entropy change, and Gibbs free energy change of 2HNIW·HMX co-crystals within 283 and 333 K, taking 298.15 K as the benchmark temperature; Table 7 shows

(11)

ΔH ⧧ = E − RT

(12)

ΔG⧧ = ΔH ⧧ − T ΔS ⧧

(13) −23

(14) 2

−1

where kB is the Boltzmann constant, 1.3807 × 10 J·K , and h is the Planck constant, 6.626 × 10−34 J·s. These thermal parameters of 2HNIW·HMX co-crystals could provide available theoretical information for the detonation property and safety, instructing its practical application. 3.5. Specific Heat Capacity of 2HNIW·HMX Cocrystals. Specific heat results of 2HNIW·HMX co-crystals with a continuous specific heat capacity mode of the MicroDSC III apparatus and the comparison with that of 2Cp,m(εHNIW) + Cp,m(β-HMX) in literature are shown in Figure 7.33,41 It can be seen that the specific heat capacity of 2HNIW·

Table 7. Enthalpy Change, Entropy Change, and Gibbs Free Energy Change of 2HNIW·HMX Co-crystals at Different Temperature of Taking T = 298.15 K as the Benchmark and Pressure p = 0.1 MPaa (Specific Heat Capacity, Cp,m; Enthalpy Change, HT − H298.15K; Entropy Change, ST − S298.15K) T/K

Cp,m/ (J·mol−1·K−1)

HT − H298.15K/ (kJ·mol−1)

ST − S298.15 K/ (J·K−1·mol−1)

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

1073.84 1088.57 1101.94 1114.04 1124.94 1134.71 1143.43 1151.18 1158.02 1164.04 1169.30

−16.43 −11.02 −5.54

−56.52 −37.59 −18.74

5.60 11.25 16.95 22.68 28.46 34.26 40.10

18.62 37.11 55.45 73.62 91.63 109.46 127.11

a

Standard uncertainties u are u(T) = 0.001 K, u(p) = 1 kPa, ur(Cp,m) = 0.0098, u(HT − H298.15K) = ur(Cp,m)(Cp,m/(J·K−1·mol−1))|(T/K) − 298.15|, and u(ST − S298.15K) = ur(Cp,m)(Cp,m/(J·K−1·mol−1))| ln(T/ (298.15 K))|.

the results. As can be seen, the values of Cp,m, HT − H298.15K, and ST − S298.15K increase with the rise of temperature. Both the values of HT − H298.15K and ST − S298.15K are negative when the temperature is below 298.15 K. These results are similar to that of 3-(3,5-dimethylpyrazol-1-yl)-6-(benzylmethylene)hydrazone-s-tetrazine.48

Figure 7. Specific heat capacity experimental result of co-crystals compared with that of 2Cp,m(ε-HNIW) + Cp,m(β-HMX) in literature: ---, experimental values of 2Cp,m(ε-HNIW) + Cp,m(β-HMX) in literature; , experimental values of co-crystals.

T

HT − H298.15K =

HMX co-crystals shows a fine cubic polynomial relationship with temperature from 283.15 to 333.15 K. By contrast with the literature,33,41 the Cp (J·mol−1·K−1) of co-crystals is different from those of pure ε-HNIW and β-HMX from 283.15 to 333.15 K. Especially, the experimental values of cocrystals are significantly lower than those of 2Cp,m(ε-HNIW) + Cp,m(β-HMX) in literature, which indicate that the co-crystals are different from the mixture.. The specific heat capacity equation is described as follows (eq 14):

∫298.15K Cp,m dT

(15)

T

ST − S298.15K =

∫298.15K Cp,mT −1 dT

(16)

In these equations (eqs 15 and 16), Cp,m has been evaluated by eq 14.

4. CONCLUSIONS The 2HNIW·HMX co-crystals were synthesized and characterized by XRD, Raman spectra, DSC, and HPLC. The standard enthalpy of formation of 2HNIW·HMX co-crystals is G



Article

obtained as 861.9 ± 18.6 kJ·mol−1 through a programmed thermochemical cycle using a Calvet microcalorimeter. The thermal behavior of the co-crystals has been studied by DSC. The apparent activation energy (E) of the decomposition is 332.23 kJ·mol−1 by Kissinger method, 324.10 kJ·mol−1 by Ozawa method, 314.06 ± 4.26 kJ·mol−1 by Friedman−Reich− Levi method, and 306.81 ± 3.12 kJ·mol−1 by NL-INT-SY3 method, respectively. The pre-exponential factor (logA/s−1) is 29.33 ± 0.33 via compensation effect. The thermal decomposition parameters (Te0 = 498.82 K, Tp0 = 505.03 K, and Tb = 505.75 ± 0.12 K) of 2HNIW·HMX co-crystals are acquired. The entropy of activation (ΔS⧧), enthalpy of activation (ΔH⧧), and Gibbs free energy of activation (ΔG⧧) of the exothermic decomposition stage are obtained as 303.88 ± 6.32 J·mol−1·K−1, 302.64 ± 3.12 kJ·mol−1, and 149.17 ± 3.86 kJ·mol−1. These parameters can contribute to the understanding the thermal property of 2HNIW·HMX cocrystals. The specific heat capacity of 2HNIW·HMX co-crystals is Cp,m/(J·mol−1·K−1) = −4.35692 × 103 + 4.32914 × 101(T/ K) − 1.13468 × 10−1(T/K)2 + 1.00000 × 10−4(T/K)3 from 283.15 to 333.15 K and the Cp,m is 1114.04 ± 10.92 J·mol−1· K−1 at 298.15 K. In addition, the enthalpy change and entropy change of 2HNIW·HMX co-crystals within 283.15 and 333.15 K, taking 298.15 K as the benchmark, are also obtained. These results obtained can provide valuable information for both theory and applications of co-crystalline materials.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 02988431616. ORCID

Jiaoqiang Zhang: 0000-0002-9414-3779 Ning Liu: 0000-0002-5113-2658 Funding

We gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 21673182 and 21703168). Notes

The authors declare no competing financial interest.

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Standard Enthalpy of Formation, Thermal Behavior, and Specific Heat

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