Kinetics Study of a Complex Reaction: Nitration of Caged 2,6,8,12

Article pubs.acs.org/OPRD

Kinetics Study of a Complex Reaction: Nitration of Caged 2,6,8,12Tetraacetyl-4,10-dinitro-2,4,6,8,10,12-hexaazaisowurtzitane Yiying Zhang,† Dongxiang Zhang,‡ Kai Dong,† Penghao Lv,† Siping Pang,† and Chenghui Sun*,† †

School of Materials Science & Engineering, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, P. R. China ‡ School of Chemical Engineering and Environment, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, P. R. China S Supporting Information *

ABSTRACT: The kinetics of the nitration reaction of 2,6,8,12-tetraacetyl-4,10-dinitro-2,4,6,8,10,12-hexaazaisowurtzitane (TADN) in HNO3−H2SO4 nitrating agent has been studied. The reaction network of the nitration reaction is constructed according to analysis of the experimental results. A kinetics model is introduced and the kinetics parameters are estimated by data fitting. Statistical analysis verifies that the kinetics model is in good agreement with the experimental data. Therefore, the reaction kinetics model can be applied to process analysis and scale-up of nitration of TADN to 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12hexaazaisowurtzitane (HNIW). KEYWORDS: CL-20, TADN, nitration, complex reaction, kinetics model groups have higher reactivity and are nitrated first because of their weaker alkalinity and less steric hindrance. The nitrolysis of the four remaining acetyl groups is more difficult, and a higher reaction temperature and a longer reaction time are necessary. As a consequence, establishing a definite and integrated reaction network based on qualitative and quantitative experiment studies continues to be a challenging task. Reaction kinetics studies reveal the reaction rate dependence on various reaction factors, such as the temperature, pressure, concentration, medium, and catalyst. A suitable kinetics model can provide an accurate description of the reaction progress and predict process dynamics under different reaction conditions or at different operation scales, avoiding the need for lots of tedious and repeated experiments. Therefore, reaction kinetics studies play an important and essential role in process simulation and scale-up, especially for hazardous reactions such as nitration reactions carried out in strong acid conditions at high temperatures. To the best of our knowledge, no relevant kinetics study of the nitration reaction to HNIW has been reported. As previously mentioned, TAIW is first nitrated to TADN in HNO3−H2SO4 nitrating agent. According to our research, this reaction is so fast and violent that it is difficult to track its process. Therefore, the whole reaction rate from TAIW to HNIW is determined by subsequent nitration of the four acetyl groups. In the meantime, this nitration process is accompanied by a high exothermicity (ΔHrxn is determined to be 202 kJ/mol for nitration of TAIW to TADN measured by a Mettler-Toledo RC1e reaction calorimeter), so TAIW must be added in batches into the nitrating agent and thus an extended feeding time is needed, which inevitably increases the uncertain factors such as

1. INTRODUCTION 2,4,6,8,10,12-Hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (HNIW, also known as CL-20) is considered to be the most powerful explosive.1−4 A considerable amount of work has been published on the synthesis of HNIW5−10 since Nielsen and coworkers first prepared HNIW.11 Most synthesis methods of HNIW are based on the starting material 2,4,6,8,10,12hexabenzyl-2,4,6,8,10,12-hexaazaisowurtzitane, 12,13 which needs to be transformed to nitrolysable precursors by a series of debenzylation reactions. The nitrolysable precursors, such as 2,6,8,12-tetraacetyl-4,10-diformyl-2,4,6,8,10,12-hexaazaisowurtzitane (TADF),14,15 2,4,6,8,10,12-hexaacetyl-2,4,6,8,10,12-hexaazaisowurtzitane (HAIW), 16 and 2,6,8,12-tetraacetyl2,4,6,8,10,12-hexaazaisowurtzitane (TAIW),17 can be easily nitrated with proper nitrating systems to obtain HNIW (Scheme 1). In particular, the synthesis route from TAIW to HNIW is considered to be a favorable method because it has some distinct advantages, such as technology simplification, high product purity, and process economy.18−20 The nitration of TAIW is usually conducted in HNO3− H2SO4 mixed acid, a type of nitrating agent widely used in industry because of its relatively strong nitration ability. The overall reaction scheme for nitration of TAIW to HNIW in HNO3−H2SO4 nitrating agent is shown in Scheme 2. The nitration of TAIW to HNIW requires introduction of six nitro groups to one cage molecule, which can proceed by various reaction paths. Hamilton21 proposed a mechanism where nitrolysis of acetyl groups occurs first, followed by nitration of free secondary amino groups, but he did not give supporting experimental evidence. Subsequently, Sun22 proposed a stepwise nitration mechanism based on a series of experimental studies. They found that TAIW was first nitrated to 2,6,8,12tetraacetyl-4,10-dinitro-2,4,6,8,10,12-hexaazaisowurtzitane (TADN) with a fast reaction rate and high yield (90.6%) at 20 °C, so it was speculated that the two free secondary amino © 2016 American Chemical Society

Received: June 26, 2016 Published: October 3, 2016 1911

DOI: 10.1021/acs.oprd.6b00221 Org. Process Res. Dev. 2016, 20, 1911−1916

Organic Process Research & Development

Article

Scheme 1. Practicable Synthetic Routes of HNIW

Table 1. Concentration Variances of the Reaction Components versus Time

Scheme 2. Nitration of TAIW to HNIW

concentration (× 10−2 mol/L)

concentration of nitration intermediates and then affects the reliability of the experiments. Hence, TADN is chosen as the starting material in kinetics study. TADN has a good solubility in HNO 3 −H 2 SO 4 nitrating agent, and no significant exothermicity exists in the feeding course. The aim of this work is to model the TADN nitration reaction in HNO3− H2SO4 nitrating agent. A kinetics model is proposed according to the constructed reaction network, and the kinetics parameters involved are estimated by a numerical method.

2. RESULTS AND DISCUSSION 2.1. Reaction Network Construction. To determine the possible reaction paths, the nitration of TADN in HNO3− H2SO4 nitrating agent was performed under the following conditions: a volume ratio of HNO3:H2SO4 = 2:1, an initial concentration of TADN = 0.26 mol/L, a reaction temperature of 50 °C, and a reaction time of 180 min. Samples were regularly withdrawn from the reaction mixture during the reaction process and qualitatively and quantitatively analyzed by high-performance liquid chromatography (HPLC)−mass spectroscopy (MS). From the MS spectra, the following components were confirmed in the reaction system: TADN, 6,8,12-triacetyl-2,4,10-trinitro-2,4,6,8,10,12-hexaazaisowurtzitane (TATN), 6,8-diacetyl-2,4,10,12-tetranitro-2,4,6,8,10,12hexaazaisowurtzitane (DATN1), 6,12-diacetyl-2,4,8,10-tetranitro-2,4,6,8,10,12-hexaazaisowurtzitane (DATN2), 8,12-diacetyl2,4,6,10-tetranitro-2,4,6,8,10,12-hexaazaisowurtzitane (DATN3), 8-monoacetyl-2,4,6,10,12-pentnitro-2,4,6,8,10,12hexaazaisowurtzitane (MPIW), and HNIW. The variation of the concentrations of these components with the reaction time was also tracked, and the results are shown in Table 1 and Figure 1. These results provide useful information to understand the integrated reaction network. From Table 1 and Figure 1, the following trends can be determined: 1. TADN concentration is very high at the start, and then it monotonically decreases to zero in the nitration process.

time (min)

TADN

TATN

DATN1

DATN2

DATN3

MPIW

HNIW

0 5 10 20 30 45 60 90 120 180

19.31 13.83 8.72 3.04 1.32 0.47 0.13 0 0 0

5.34 6.96 8.10 5.57 3.38 1.56 0.54 0.05 0 0

0.16 0.76 1.07 1.46 1.21 0.73 0.33 0.05 0.03 0

0.13 0.66 0.90 1.27 1.10 0.68 0.32 0.05 0 0

0.41 2.29 3.31 5.76 5.95 4.72 3.12 1.04 0.31 0.07

0.05 0.65 2.62 5.77 7.77 8.71 8.10 4.78 2.53 1.27

0 0.06 0.18 1.61 3.96 7.41 11.97 19.14 21.33 22.76

Figure 1. Concentration of the components versus reaction time.

2. The concentrations of TATN, DATN1, DATN2, DATN3, and MPIW first increase to their maxima and then gradually decrease with reaction time, revealing the typical behaviors of intermediates in a consecutive reaction. At the beginning a considerable concentration of TATN exists, indicating that an acetyl group of TADN is sequentially nitrated in the feeding course. DATN is generated in three types of isomers (DATN1, DATN2, and DATN3), because the fourth NO2+ ion might 1912



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Scheme 3. Reaction Network

In the nitration process of TADN to HNIW, the feeding concentration of fuming HNO3 was much higher than the stoichiometric ratio because it acts as both a reactant and a solvent. Therefore, although this process was accompanied by liberation of acetic acid, the concentration of the resultant acetic acid was fairly low and caused no variations of the nitrating activity of the mixture, so the variation factor of the composition of the medium was left out of consideration in establishment and solution of the kinetics model. The feeding concentration of fuming HNO3 was more than 10 times higher than its consumption for the formation of HNIW in the kinetics experiments, so its concentration in the reaction course could be regarded as a constant value. In this sense, the concentrations of fuming HNO3 along with the reaction rate constants (k1, k2, k3, k4, k5, k6, k7, and k8) can be combined to give effective rate constants (k1′, k2′, k3′, k4′, k5′, k6′, k7′, and k8′). Hence, the reaction rate expressions can be simplified as follows (equation system 2):

attack different N atoms on the TATN cage. However, an obvious disparity exists between the concentrations of the three DATN isomers: the concentrations of DATN1 and DATN2 are much less than that of DATN3, probably because the two acetyl groups on the same side of the cage have greater steric hindrance and the fourth NO2+ ion would preferentially attack another side of the TATN molecule.22 It is also worth noting that TATN, DATN, and MPIW achieve their maximum concentrations in proper sequence, indicating that the whole nitration process advances in a wave-like manner. 3. The concentration of HNIW monotonically increases from zero and finally stabilizes near the maximum value, while the concentrations of the aforementioned reaction intermediates decrease to nearly zero at the end of the reaction. From the above trends, an integrated reaction network for nitration of TADN to HNIW in HNO3−H2SO4 nitrating agent is constructed as Scheme 3: the four acetyl groups of TADN undergo nitrolysis processes one by one, and eight single reactions in consecutive and parallel structures compose a complex reaction system. 2.2. Establishment and Solution of the Reaction Kinetics Model. The reaction rate equation of every single reaction in the reaction network was expressed by a power law rate model, including a rate constant and the concentration of the involved reactants raised to certain powers. The stoichiometric equations and the corresponding rate expressions (equation system 1) applied to the reactions in a constant-volume batch reactor are listed in Table 2.

ri = ki′CIαi

stoichiometric equation TATN + HNO3 = DATN1 + CH3COOH (R2)

2 2 r2 = k2CTATN CHNO 3

α

TATN + HNO3 = DATN2 + CH3COOH (R3)

r3 =

TATN + HNO3 = DATN3 + CH3COOH (R4)

r4 =

DATN1 + HNO3 = MPIW + CH3COOH (R5)

r5 =


r6 =


r7 =

MPIW + HNO3 = HNIW + CH3COOH (R8)

r8 =

(2)

k = k 0e−E / RT

where k0 is the frequency or pre-exponential factor, which is considered to be constant in a certain temperature range, E is the activation energy of the reaction, and R is the ideal gas constant. When the effective rate constants above are expressed by Arrhenius equations, a series of equations in new forms are obtained (equation system 3):

reaction rate 1 1 r1 = k1CαTADN CβHNO 3

(i = 1, 2, 3..., 8)

where I is an intermediate, and when i = 1, I = TADN; i = 2,3,4, I = TATN; i = 5, I = DATN1; i = 6, I = DATN2; i = 7, I = DATN3; i = 8, I = MPIW. It is well-known that the Arrhenius law reveals the dependence of the reaction rate constant on the temperature:

Table 2. Kinetics Model for TADN Nitration in HNO3− H2SO4 Nitrating Agent

TADN + HNO3 = TATN + CH3COOH (R1)

β

i ki′ = kiC HNO 3

β

ri = k 0i e−Ei / RT CIαi

3 3 k3CαTATN CβHNO 3 β4 α4 k4CTATNCHNO3 α5 β5 k5CDATN1 CHNO 3 α6 β6 k6CDATN2CHNO 3 7 7 k7CαDATN3 CβHNO 3 α8 β8 k8CMPIW CHNO 3

(i = 1, 2, 3..., 8)

(3)

where i and I have the identical meanings as in equation system 2. According to the reaction network, the kinetics equations of all of the reaction species with respect to the concentration function changes over time are expressed as follows (equation system 4): 1913



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dC TADN α1 = −r1 = −k 01e−E1/ RT C TADN dt

where T is the reaction temperature and i is the number of samples withdrawn. The subscripts exp and cal represent the experimental and calculated values, respectively. By calculating the minimum of SRS, the kinetics parameters (k0i, Ei, αi, i = 1, 2, 3, ..., 8) can be estimated. 2.3. Determination of the Kinetics Parameters and Model Testing. The kinetics parameters of every reaction rate expression were calculated by the mathematical procedure described in Section 2.2, and the calculated results are shown in Table 3.

(4)

dC TATN = r1 − r2 − r3 − r4 dt α1 α2 = k 01e−E1/ RT C TADN − k 02e−E2 / RT C TATN α3 α4 − k 03e−E3 / RT C TATN − k 04 e−E4 / RT C TATN

dC DATN1 = r2 − r5 dt

Table 3. Estimation of the Kinetics Parameters

α5 α2 = k 02e−E2 / RT C TATN − k 05e−E5 / RT C DATN1

1 2 3 4 5 6 7 8

α3 α6 = k 03e−E3 / RT C TATN − k 06e−E6 / RT C DATN2

dC DATN3 = r4 − r7 dt α4 α7 = k 04 e−E4 / RT C TATN − k 07e−E7 / RT C DATN3

dCMPIW = r5 + r6 + r7 − r8 dt = k 05e

−E5 / RT

+ k 07e

α5 C DATN1

−E 7 / RT

+ k 06e

α7 C DATN3

− k 08e

α6 C DATN2

−E8 / RT

× × × × × × × ×

105 105 105 105 105 105 105 104

E (J/mol)

α

× × × × × × × ×

0.49 1.49 1.23 1.85 0.92 0.59 0.78 0.41

5.78 5.55 5.49 4.96 5.67 5.71 5.93 6.14

104 104 104 104 104 104 104 104

⎛ −5.78 × 104 ⎞ 0.49 dC TADN = −r1 = −9.82 × 105 exp⎜ ⎟C TADN dt RT ⎝ ⎠

α8 CMPIW

dC TATN = r1 − r2 − r3 − r4 dt ⎛ −5.78 × 104 ⎞ 0.49 = 9.82 × 105 exp⎜ ⎟C TADN RT ⎝ ⎠

Kinetics equation system 4 is a combination of first-order ordinary differential equations. To determine the kinetics parameters involved, integration of equation system 4 and subsequent nonlinear regression are required. MATLAB software (MathsWorks Inc., Natick, MA, USA) provides the specialized function ode45 that is based on classical fourthorder Runge−Kutta algorithms to solve such complex mathematic problems.23 First, every kinetics parameter (k0i, Ei, αi, i = 1, 2, 3, ..., 8) is assigned an initial value. Every concentration function of each reaction species can then be solved in the form of a numerical solution at every sampling time point by integration in the time interval [0, t] (t = 5, 10, 20, ..., 180 min). In the following step, the calculated values and the experimental concentration data are compared, and the sum of residual squares (SRS) between them is calculated. The objective function SRS constructed for the estimation of the kinetics parameters is as follows:

⎛ −5.55 × 104 ⎞ 1.49 − 9.84 × 105 exp⎜ ⎟C TATN RT ⎝ ⎠ ⎛ −5.49 × 104 ⎞ 1.23 − 4.01 × 105 exp⎜ ⎟C TATN RT ⎝ ⎠ ⎛ −4.96 × 104 ⎞ 1.85 − 7.78 × 105 exp⎜ ⎟C TATN RT ⎝ ⎠

⎛ −5.55 × 104 ⎞ dC DATN1 = r2 − r5 = 9.84 × 105 exp⎜ ⎟ dt RT ⎠ ⎝ ⎛ −5.67 × 104 ⎞ 0.92 1.49 × C TATN − 4.73 × 105 exp⎜ ⎟C DATN1 RT ⎝ ⎠

∑ ∑ [(CTADN ‐ i‐ exp − CTADN ‐ i‐ cal)2 T

9.82 9.84 4.01 7.78 4.73 4.38 1.30 6.62

The kinetics equations were expressed as follows: −E6 / RT

dC HNIW α8 = r8 = k 08e−E8 / RT CMPIW dt

SRS =

k0

reaction

dC DATN2 = r3 − r6 dt

⎛ −5.49 × 104 ⎞ dC DATN2 = r3 − r6 = 4.01 × 105 exp⎜ ⎟ dt RT ⎠ ⎝

i

+ (C TATN ‐ i ‐ exp − C TATN ‐ i ‐ cal)2

⎛ −5.71 × 104 ⎞ 0.59 1.23 × C TATN − 4.38 × 105 exp⎜ ⎟C DATN2 RT ⎝ ⎠

+ (C DATN1 ‐ i ‐ exp − C DATN1 ‐ i ‐ cal)2 + (C DATN2 ‐ i ‐ exp − C DATN2 ‐ i ‐ cal)2

⎛ −4.96 × 104 ⎞ dC DATN3 = r4 − r7 = 7.78 × 105 exp⎜ ⎟ dt RT ⎝ ⎠

+ (C DATN3 ‐ i ‐ exp − C DATN3 ‐ i ‐ cal)2 + (CMPIW ‐ i ‐ exp − CMPIW ‐ i ‐ cal)2

⎛ −5.93 × 104 ⎞ 0.78 1.85 × C TATN − 1.30 × 105 exp⎜ ⎟C DATN3 RT ⎝ ⎠

2

+(C HNIW ‐ i ‐ exp − C HNIW ‐ i ‐ cal) ] 1914



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dCMPIW = r5 + r6 + r7 − r8 dt ⎛ −5.67 × 104 ⎞ 0.92 = 4.73 × 105 exp⎜ ⎟C DTATN1 RT ⎝ ⎠

The correlation coefficient R obtained from the results of the ANOVA is 0.974, which shows that there is a strong correlation between the experimental data and the predicted values. The determination coefficient (R2) value was used to measure the “goodness of fit” of the model. The R2 value of 0.948 shows that the mathematic model fits the experimental data well and it can explain 94.8% of the variation in the reaction component concentrations. According to statistics theory, it can be deduced that the R2 value increases along with extending the sample capacity even of the new samples have weaker correlations with the consequent variables. To eliminate the influence of sample capacity, the adjusted R2 value was used to better reflect the goodness of fit and assess the accuracy of the model across different samples.26 The adjusted R2 value is 0.933, which is very close to the R2 value, indicating that the cross-validity of the model is good.

⎛ −5.71 × 104 ⎞ 0.59 + 4.38 × 105 exp⎜ ⎟C DATN2 RT ⎝ ⎠ ⎛ −5.93 × 104 ⎞ 0.78 + 1.30 × 105 exp⎜ ⎟C DATN3 RT ⎝ ⎠ ⎛ −6.14 × 104 ⎞ 0.41 − 6.62 × 104 exp⎜ ⎟CMPIW RT ⎝ ⎠

⎛ −6.14 × 104 ⎞ 0.41 dC HNIW = r8 = 6.62 × 104 exp⎜ ⎟CMPIW dt RT ⎝ ⎠

3. CONCLUSION An integrated reaction network for the nitration of TADN to HNIW in HNO3−H2SO4 nitrating agent was constructed based on qualitative and quantitative experiment research, which provided deep insight into the complex nitration reactions. Subsequently, a series of kinetics experiments were carried out at various temperatures to collect experimental data. A mathematical model that described the kinetics of the nitration reaction of TADN was proposed, and the kinetics parameters involved were estimated by a numerical method. Finally, statistical tests showed that there was a good agreement between the kinetics model and the experimental data, indicating that the model can be applied to simulate the process of nitration of TADN to HNIW.

After building the kinetics model, it was necessary to investigate its acceptability and reliability. The residual errors were the differences between the values calculated by the model and the data observed in the experiments, and an intuitive testing method was to check whether the set of residual error data obeyed a normal distribution.24 Figure 2 shows the

4. EXPERIMENTAL SECTION 4.1. General Information. Caution! Although none of the compounds described herein have exploded or detonated in the course of this research, these energetic materials should be handled with extreme care using the best safety practices (leather gloves, face shield, and ear plugs). TADN was self-prepared22 and recrystallized with glacial acetic acid and water before use. Fuming HNO3 (98%) and fuming H2SO4 (30% SO3) were supplied by Beijing Chemical Works. Analytical grade NaOH and NaHCO3 were purchased from Beijing Chemical Works. Glacial acetic acid was purchased from Aladdin Reagent Inc., and water was purchased from Watsons Group Ltd.. The standard samples of the nitration products were prepared by nitration reactions of TADN with different reaction times, followed by purification by column chromatography on a Biotage Isolera One (Flash Silica-CS 20 g column, eluting with petroleum ether and ethyl acetate solvents with appropriate ratios). 4.2. Typical Reaction Procedure. The kinetics experiments were conducted in a three-necked batch reactor (50 mL) equipped with a reflux condenser and a magnetic stirrer. The reactor was immersed in a constant-temperature oil bath to maintain the required temperature. In a typical operation, HNO3−H2SO4 nitrating agent was first prepared by adding fuming H2SO4 (3 mL) dropwise to fuming HNO3 (6 mL) in an ice−water bath, maintaining the temperature below 10 °C to avoid the potential dangers resulting from the large amount of heat generated in the acid mixing process. The nitrating agent was then heated to 50 °C, and TADN (1 g) was added in one portion with vigorously stirring (the reaction exothermicity was

Figure 2. Residual error distribution.

residual error distribution of the reaction component concentrations calculated by the model. The residual error points are randomly distributed and symmetrically scattered on both sides of the zero coordinate. This shows that the residual errors are random without a systematic trend and the model is suitable and acceptable to predict the nitration process of TADN in the HNO3−H2SO4 nitrating agent. Analysis of the variance (ANOVA) was used to test the degree of fit between the model and the experimental data and determine whether the model was statistically significant.25 The analysis results of the ANOVA are shown in Table 4. The F-test value with regard to the kinetics model is 68.07, which is 10 times greater than the critical statistical value F0.01. This indicates that the kinetics model is highly significant at the α = 0.01 level and the prediction for the nitration reaction is valid.26 Table 4. ANOVA for Kinetics Model

regression residual total

sum of squares

freedom

variance

F

F0.01(24, 83)

1.28 0.065 1.25

24 83 107

5.33 × 10−2 7.83 × 10−4

68.07

2.11

1915



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Notes

not significant). The reaction system was subsequently maintained at this temperature for 180 min. When the feeding was completed, the time was defined as t = 0. During the reaction process, 0.2 mL samples were taken with a pipet at the following times: 0, 5, 10, 20, 30, 45, 60, 90, 120, and 180 min. The samples were immediately quenched by dropping NaOH aqueous solution and then adjusted to pH = 7 by titrating saturated NaHCO3 solution. The neutralized sample solutions became suspensions, and then acetic acid was added to dissolve the emerging precipitates. All of the samples were finally diluted to 20 mL and homogenized. Transparent liquids were obtained that could be directly analyzed by HPLC. 4.3. Product Analysis Method. To determine the compositions of the reaction mixtures in different reaction periods, the samples after treatment were quantitatively analyzed by a high-performance liquid chromatograph (Agilent 6100 series) equipped with an Agilent G1311B quaternary pump and an Agilent G1314F UV detector operated at 230 nm to detect each component in the reaction system. HPLC was conducted through an Agilent Technologies C18 column (5 μm, 4.6 mm × 250 mm) for separation, which was operated at 30 °C with a 5 μL injection volume. The mobile phase composition was a mixture of methanol and water with a volume ratio of 4:6, and the flow rate was 0.4 mL/min. The concentration of each component was determined according to standard curves obtained by the corresponding standard samples. The determination of each species involved in the reaction was performed using a quadrupole model high performance liquid chromatograph−mass spectrometer equipped with an Agilent Technologies C18 column (5 μm, 4.6 mm × 250 mm), and the mass spectra were obtained in the range of 10−600 amu. 4.4. Kinetics Experiment Conditions. In the kinetics study, a wide range of experimental conditions were used to obtain sufficient experimental data for the regression analysis of the kinetics model. The feeding concentration of fuming HNO3 was more than 10 times higher than its consumption for the formation of HNIW, and the volume ratio of HNO3 to H2SO4 was 2:1. The kinetics experiments were conducted by changing the reaction temperature (50, 60, 70, and 80 °C). TADN (1 g) was added into nitrating agent directly at the setting reaction temperature, and the times when the feeding was completed were regarded as the starting points of the reactions. Ten samples were taken and analyzed at specific time points from t = 0 to 180 min during the reaction process. All of the experiments were performed three times to check the reproducibility of the results.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the National Natural Science Foundation of China (Grant No. 21576026) and the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics (Grant No. 11176004) for financial support.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.oprd.6b00221. S1. Naming rule of hexaazaisowurtzitane derivatives; S2. HPLC-MS method for analysis of the reaction samples; S3. MS identification of nitration intermediates; S4. quantitative analysis method of reaction components; S5. calculation formula of R, R2, and adjusted R2 (PDF)

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REFERENCES

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Kinetics Study of a Complex Reaction: Nitration of Caged 2,6,8,12

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