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Computational Study of the Rate Coefficients for the Reactions of NO2 with CH3NHNH, CH3NNH2, and CH2NHNH2 Nozomu Kanno,*,†,⊥ Hiroumi Tani,‡ Yu Daimon,‡ Hiroshi Terashima,§ Norihiko Yoshikawa,† and Mitsuo Koshi∥ †

Department of Micro-Nano Systems Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan Japan Aerospace Exploration Agency, Ibaraki 305-8050, Japan § Department of Aeronautics and Astronautics, The University of Tokyo, Tokyo 113-8656, Japan ∥ Graduate School of Environment and Information Sciences, Yokohama National University, Kanagawa 240-8501, Japan ‡

S Supporting Information *

ABSTRACT: The reactions of NO2 with cis-/trans-CH3NHNH, CH3NNH2 and CH2NHNH2 have been studied theoretically by quantum chemical calculations and steady-state unimolecular master equation analysis based on RRKM theory. The barrier heights for the roaming transition states between nitro (RNO2) and nitrite (RONO) isomerization reactions and those for the concerted HONO and HNO2 elimination reactions from RNO2 and RONO, affect the pressure dependences of the product-specific rate coefficients. At ambient temperature and pressure, the dominant product of the reactions of NO2 with cis-/trans-CH3NHNH and CH2NHNH2 would be expected to be HONO with trans-CH3NNH and CH2NNH2, respectively, whereas it is CH3N(NH2)NO2 for CH3NNH2 + NO2. The product-specific rate coefficients for the titled and related reactions on the same potential energy surfaces were proposed for kinetics modeling.

I. INTRODUCTION Hypergolic bipropellants, which are fuel-oxidizer combinations that spontaneously ignite when they come into contact with each other even at low temperatures and pressures, are widely used for spacecraft propulsion applications requiring active thrust control. The most common combination is CH3NHNH2/(NO2)2, which is also referred to as monomethylhydrazine/dinitrogen tetroxide or MMH/NTO. For applications in which the freezing point of NTO is too high, red fuming nitric acid (RFNA) is used as an alternative oxidizer. RFNA is a mixture of nitric acid (HNO3, ∼85 wt %) and NO2 (8−15 wt %). Although the hypergolic nature of these bipropellants allows designing a simple and reliable thruster system, their combustion characteristics such as ignition or flammability conditions are still important for ensuring optimal and reliable thruster controls. Thus, the detailed chemical kinetics models for the accurate prediction of ignition phenomena have been developed for hydrazine/NTO,1 MMH/NTO,2 and MMH/RFNA3 propellants. For instance, the detailed chemical kinetics of hydrazine/NTO significantly acts on the predictions of ignition timing and locations, and flame structures in the coupling with fluid dynamics.4 At ambient temperature, the equilibrium between NTO and NO2 is readily achieved; thus the reactions between NO2 with MMH and its dehydrogenation products play an important role © 2015 American Chemical Society

at the initial steps of hypergolic ignition. For the reaction MMH + NO2, McQuaid and Ishikawa5 investigated the potential energy diagram at the CCSD(T)/6-311++G(3df,2p)//MPWB1K/6-31+G(d,p) level of theory. Liu et al. reported experimental and quantum mechanics investigation of the early reaction of MMH/NTO.6 Recently, we reported product specific rate constants of MMH + NO2 calculated from multiple-well master equation analysis based on the Rice− Ramspergar−Kassel−Marcus (RRKM) theory.7 The master equation analysis suggested that the cis-CH3NHNH + HONO formation path was dominant around ambient temperature. All of the theoretical studies suggested that the minimum activation energy of the H atom abstraction reactions for MMH + NO2 would be larger than the activation energy of MMH + NO2 → CH3NNH2 + HONO included in the kinetics models proposed in the previous studies.2,3 Moreover, the CH3NHNH + HONO formation path, which was the most energetically favorable path suggested by McQuaid and Special Issue: 100 Years of Combustion Kinetics at Argonne: A Festschrift for Lawrence B. Harding, Joe V. Michael, and Albert F. Wagner Received: January 30, 2015 Revised: May 10, 2015 Published: May 13, 2015 7659

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The Journal of Physical Chemistry A Ishikawa5 and in our previous study,7 was not taken into account in the current models. For the validation of the initial steps of the MMH/NTO ignition process and updates to their kinetics models, the evaluation of the subsequent reactions missing in the current models is highly demanded. Ishikawa and McQuaid investigated the reaction of NO2 with CH3NHNH and CH3NNH2 via direct molecular dynamic simulations and calculated the reaction barriers on the basis of QCISD(T)/6-311+G(d,p)// MPWB1K/6-31+G(d,p) level of theory.8 They suggested that the H atom abstraction reaction can proceed even at 1−2 kcal mol−1 of kinetic energy, and the recombination reactions were also observed. Liu et al. also reported the reaction barriers for HONO formation paths.6 There is no information for the thermal reaction rates and product distribution for these reactions. In the present study, we have investigated the reaction systems of NO2 with CH3NHNH, CH3NNH2, and CH2NHNH2 and evaluated the temperature- and pressuredependent, product-specific rate coefficients using multiple-well master equation analysis based on the RRKM theory.

excluding loose intermolecular modes. The optimized geometries, rotational constants, and harmonic frequencies of the most stable isomers for the reactants, products, and the transition states are listed in Tables S1 and S2 in the Supporting Information. Corresponding thermodynamic functions (standard enthalpies of formation, entropies, and heat capacities) of the reactants and products are also listed in Table S3 in the Supporting Information. RRKM/master equation calculations were carried out to evaluate the rate coefficients and to analyze the product channels. The internal rotations around the CH3 rotor for all species and the CH2 rotor for CH2NHNH2 were treated as hindered rotors by using the Pitzer−Gwinn approximations. 19−21 The other internal rotations, such as NH 2 inversion/rotational isomers, were included in the total partition functions via the rotational-conformer distribution functions,22 whereas cis-/trans-CH3NHNH, whose isomerization activation energies were calculated to be 79.5 kJ mol−1, were treated as different species. In the present study, cis and trans notations for CH3NHNH correspond to a H− N(CH3)−N−H dihedral angle. The energy differences of the rotational-conformer used in the calculation of the rotationalconformer distribution functions are listed in Table S2 in the Supporting Information. One-dimensional semiclassical tunneling corrections were included in the RRKM calculation by assuming the asymmetric Eckart potential.23,24 The imaginary vibrational frequencies used in the tunneling for the ωB97X-D/ 6-311++G(d,p) optimized transition states were adjusted by the RHF-UCCSD(T)-F12/VDZ-F12 energies by assuming that the force constants proportionally depend on the barrier energies. For the barrierless dissociation channels, the rate coefficients were calculated on the basis of microcanonical variational transition-state theory (μVTST). The minimum energy paths for the μVTST calculation were followed by partial geometry optimization and single-point energy calculation described above with fixing the N−N or O−N internuclear distances at every 0.1 Å intervals. The thermal rate coefficients were evaluated by solving the steady-state multiple-well unimolecular master equation using SSUMES program.25 The density of states and microscopic rate coefficients were calculated by using a modified version of UNIMOL program26 and GPOP program suite27 using the energy grain size of 10 cm−1. The collisional energy transfer probability was estimated by the exponential down model with the average downward energy transferred per collision of ⟨ΔEdown⟩ = 400(T/1000)0.7 cm−1. The collision frequency was estimated by assuming the Lennard-Jones (LJ) potential. The LJ parameters for all intermediates were assumed to be the same as those of ethyl acetate, σ = 5.2 Å and ε/kB = 520 K.28 The buffer gas was assumed to be N2 (σ = 3.798 Å and ε/kB = 71.4 K28).

II. COMPUTATIONAL METHODS The theoretical methods for the investigation of the potential energy diagrams of the titled reaction systems were essentially the same as those in our previous study for MMH + NO2,7 except for the diradical transition states. The geometry optimizations were carried out by density functional theory with the ωB97X-D hybrid functional9,10 and the 6-311+ +G(d,p) basis set by using the Gaussian 09 program package.11 The single-point energies at the optimized structures were refined by the explicitly correlated RHF-UCCSD(T)-F12 method12 with the VDZ-F12 basis sets.13 The spin−orbital splitting of 1.43 kJ mol−1 for NO (2Π3/2 ← 2Π1/2) was taken into account for the calculation of the 2Π1/2 ground-state energy and the electronic partition function of NO (2Π). Due to the highly diradical nature of the barrierless dissociation channels for RNO2 → R + NO2 and RONO → RO + NO (R = CH3NHNH, CH3NNH2, and CH2NHNH2) and of the roaming transition states between RNO2 and RONO, multireference treatments were required. For the geometry optimizations of the RNO2 → R + NO2 channels and the roaming transition states, the CASPT214 calculations employing the cc-pVDZ basis set using (10e, 7o) active space consisting the SOMO of R and the π space of NO2 were used. The extended multistate CASPT215 calculations with the ccpVDZ basis set using (8e, 6o) active spaces consisting of the π space of RO and NO were carried out for the geometry optimization of the RONO → RO + NO dissociation paths. The new internally contracted multireference configuration interaction method with the Davidson correction,16 i.e., MRCI +Q, with the aug-cc-pVTZ basis set and the same active space as the optimization methods was used for the single-point energy calculations. The CCSD(T)-F12 and multireference calculations were performed by using the Molpro 2012.1 program package.17 The vibrational frequencies used in the zero-point correction and partition function evaluations were obtained from the same level of theory as the geometry optimization. The scale factors for the zero-point correction and partition function evaluations for the ωB97X-D/6-311++G(d,p) calculations were 0.975 and 0.950, respectively.18 Those for the CASPT2/cc-pVDZ calculations were estimated from the above values and the harmonic frequencies calculated at 50.0 Å separated geometry,

III. RESULTS AND DISCUSSION Energy Diagrams for CH3NHNH/CH3NNH2/CH2NHNH2 + NO2. The overall energy diagrams for the singlet groundstate reactions of NO2 with CH3NHNH, CH3NNH2, and CH2NHNH2 calculated in the present study are shown in Figure 1. In all of the cases, R and NO2 initially form vibrationally excited nitro species, i.e., RNO2*. Similarly to CH3NO229−31 and H2NNO2,32 the roaming transition state between RNO2 and nitrite isomers, i.e., RONO, was found with the activation energies comparable to those of R + NO2. The intrinsic reaction coordinate (IRC) calculations confirmed that 7660

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geometry optimization calculations, the calculated paths fell to the RNO2* formation channels within the moderate interfragment distances required for the μVTST calculations. The RNO2 and RONO would be dissociated via the concerted elimination paths of trans-HONO and HNO2 formation, respectively. Most of the activation energies for isomerization reactions found in the present study were lower than the reactant energy, which were consistent with the molecular dynamic simulations reported by Ishikawa and McQuaid.8 The following reaction pathways could possibly compete with each other. R + NO2 ↔ RNO2 *

(1)

RNO2 * → R′ + trans‐HONO

(2)

RNO2 * + M → RNO2 + M

(3)

RNO2 * ↔ RONO*

(4)

RONO* → R′ + HNO2

(5)

RONO* → RO + NO

(6)

RONO* + M → RONO + M

(7)

Tables 1−3 summarize the calculated energies for the reactants, products, and the transition states of the reaction of Table 1. Zero-Point-Corrected Energies (kJ mol−1) of the Reactants, Products, and Transition States for the CH3NHNH + NO2 Reaction System speciesa

this workb

c-CH3NHNH + NO2 t-CH3NHNH + NO2 CH3NHNHNO2 CH3NHNHONO c-CH3NNH + t-HONO t-CH3NNH + t-HONO c-CH3NNH + HNO2 t-CH3NNH + HNO2 CH3NHNHO + NO TS2c TS2t TS4 TS5c TS5t

0.00 0.86 −141.47 −75.18 −140.02 −155.63 −102.27 −117.88 −17.42e −37.06 −54.91 −7.93f −34.87 −40.73

Ishikawa and McQuaidc 0 1.26 −96.65 −57.32 −130.54 −150.21 −89.12 −108.78

Liu et al.d 0 0.84

−143.5 −156.9

a

Figure 1. Potential energy diagrams for the reaction of NO2 with (a) CH3NHNH, (b) CH3NNH2, and (c) CH2NHNH2 calculated at RHFUCCSD(T)-F12//ωB97X-D/6-311++G(d,p) level of theory. The energies for the roaming transition state between RNO2 and RONO were calculated at the MRCI+Q/aug-cc-pVTZ//CASPT2/cc-pVDZ level of theory.

Indexes for TSs are referred to the reaction number in the text. Suffixes c and t indicate c-CH3NNH and t-CH3NNH formation paths, respectively. bCalculated at RHF-UCCSD(T)-F12/VDZ-F12// ωB97X-D/6-311++G(d,p) level of theory. cCalculated at QCISD(T)/6-311++G(d,p)//MPWB1K/6-31+G(d,p) level of theory from Ishikawa and McQuaid.8 dReaction enthalpies at 298.15 K calculated at UCCSD(T)/6-31G**/M06-2X/6-311++G** level of theory.6 eThe energy for NO (2Π1/2) assuming the spin−orbital splitting of 1.43 kJ mol−1 for 2Π3/2 ← 2Π1/2. fCalculated at MRCI+Q/aug-cc-pVTZ// CASPT2/cc-pVDZ relative to cis-CH3NHNH + NO2 at 50 Å separation.

these reaction channels have very broad IRC profiles, as shown in Figure S1 in the Supporting Information. Klippenstein et al.32 suggested that the R + NO2 → RONO* entrance channel is also possible for the case of R = NH2. Although we tried to search the minimum energy paths for those channels for R = CH3NHNH, CH3NNH2, and CH2NHNH2 by the partial

NO 2 with CH 3 NHNH, CH 3 NNH 2 , and CH 2 NHNH 2 , respectively. The indexes for TSs are referred to the reaction number described above. In the case of TS2 and TS5, the suffixes c, t, and f indicate cis-/trans-CH3NNH and formaldehyde hydrazone, i.e., CH2NNH2, formation channels, respectively. The energies calculated in the present study 7661

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The Journal of Physical Chemistry A Table 2. Zero-Point-Corrected Energies (kJ mol−1) of the Reactants, Products, and Transition States for the CH3NNH2 + NO2 Reaction System speciesa

this workb

CH3NNH2 + NO2 CH3N(NH2)NO2 CH3N(NH2)ONO c-CH3NNH + t-HONO t-CH3NNH + t-HONO CH2NNH2 + t-HONO c-CH3NNH + HNO2 t-CH3NNH + HNO2 CH2NNH2 + HNO2 CH3N(NH2)O + NO TS2c TS2t TS2f TS4 TS5c TS5t TS5f

0.00 −138.56 −79.51 −130.82 −146.43 −152.13 −93.07 −108.68 −114.38 −29.80e −26.75 −32.48 4.23 −9.11f −18.09 −28.00 2.06

Ishikawa and McQuaidc

Liu et al.d

0

0

−121.34 −141.42 −139.75 −79.91 −99.58

−133.05 −146.44

concerted elimination of trans-HONO and HNO2 from RNO2 and RONO, i.e., TS2 and TS5, relative to the reactants were the lowest in the CH2NHNH2 system followed by CH3NHNH and CH3NNH2; hence, the contribution of the stabilization and NO formation paths, i.e., reactions 3, 6, and 7 described above, would be increased in the same order. In the case of CH3NNH2 + NO2, the barrier heights for the CH2NNH2 formation paths, i.e., TS2f and TS5f given in Table 2, were found to be slightly higher than the reactant energy. Although the accuracy of the rate coefficient calculations largely depends on those of the activation energy, there were no comparable data for the transition-state energies in the previous works. For the evaluation of the uncertainty, we have calculated the energy difference between CH3NHNHNO2 and TS2t to be 87.71 kJ mol−1 at the RHF-UCCSD(T)-F12/TZV-F12 level of theory. The energy difference between DZV-F12 and TZV-F12 basis sets was found to be 1.2 kJ mol−1, which corresponds to the rate coefficient uncertainty within a factor of 2 at 300 K. Rate Coefficients for CH3NHNH/CH3NNH2/CH2NHNH2 + NO2. The product-specific reaction rate coefficients for the titled reaction were evaluated by RRKM/master equation calculations at 300−2000 K and 0.1−100 atm in N2. Due to the high barriers for TS2 and TS5 relative to the dissociation products, the product complexes, such as CH3NNH−HONO, were safely ignored in the master equation calculations. Figure 2 summarizes the temperature dependence of the rate coefficient for reaction of NO2 with cis-CH3NHNH at various pressures. Those for trans-CH 3 NHNH/CH 3 NNH 2 / CH2NHNH2 + NO2 reactions are shown in Figures S2−S4 in the Supporting Information. The modified Arrhenius parameters at 1 atm in N2 are listed in Table 4, and those at the other pressures are in Table S4 in the Supporting

a

Indexes for TSs are referred to the reaction number in the text. Suffixes c, t, and f indicate c-CH3NNH, t-CH3NNH, and CH2NNH2 formation paths, respectively. bCalculated at RHF-UCCSD(T)-F12/ VDZ-F12//ωB97X-D/6-311++G(d,p) level of theory. cCalculated at QCISD(T)/6-311++G(d,p)//MPWB1K/6-31+G(d,p) level of theory from Ishikawa and McQuaid.8 dReaction enthalpies at 298.15 K calculated at UCCSD(T)/6-31G**/M06-2X/6-311++G** level of theory.6 eThe energy for NO (2Π1/2) assuming the spin−orbital splitting of 1.43 kJ mol−1 for 2Π3/2 ← 2Π1/2. fCalculated at MRCI+Q/ aug-cc-pVTZ//CASPT2/cc-pVDZ relative to CH3NNH2 + NO2 at 50 Å separation.

Table 3. Zero-Point-Corrected Energies (kJ mol−1) of the Reactants, Products, and Transition States for CH2NHNH2 + NO2 Reaction System speciesa

this workb

CH2NHNH2 + NO2 NH2NHCH2NO2 NH2NHCH2ONO CH2NNH2 + t-HONO CH2NNH2 + HNO2 NH2NHCH2O + NO TS2f TS4 TS5f

0.00 −245.56 −230.63 −210.27 −172.52 −64.92c −127.40 −6.78d −98.64

a

Indexes for TSs are referred to the reaction number in the text. Suffix f indicates the CH2NNH2 formation path. bCalculated at the RHFUCCSD(T)-F12/VDZ-F12//ωB97X-D/6-311++G(d,p) level of theory. cThe energy for NO (2Π1/2) assuming the spin−orbital splitting of 1.43 kJ mol−1 for 2Π3/2 ← 2Π1/2. dCalculated at MRCI+Q/ aug-cc-pVTZ//CASPT2/cc-pVDZ relative to CH2NHNH2 + NO2 at 50 Å separation.

were in good agreement with those from Ishikawa and McQuaid8 and Liu et al.6 The energy differences between RNO2 and RONO for hydrazyl radicals, i.e., CH3NHNH and CH3NNH2, were calculated to be 66.3 and 59.1 kJ mol−1, similar to 78.7 kJ mol−1 for the NH2 + NO2 system reported by Klippenstein et al.32 On the contrary, for CH2NHNH2 it was only 14.9 kJ mol−1, close to 6.7−10.5 kJ mol−1 for CH3 + NO2.29−31 The barrier heights for the transition states for the

Figure 2. Arrhenius plots of c-CH3NHNH + NO2 reaction rate coefficients at (a) 100, (b) 10, (c) 1, and (d) 0.1 atm in N2. 7662

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Table 4. Modified Arrhenius Parameter, k = ATn exp(−Ea/RT) cm3 molecule−1 s−1, for the CH3NHNH/CH3NNH2/CH2NHNH2 + NO2 Reactions at 1 atm in N2 reactant

product

c-CH3NHNH + NO2

t-CH3NHNH + NO2 t-CH3NNH + HONO c-CH3NNH + HONO CH3NHNHNO2 t-CH3NNH + HNO2 c-CH3NNH + HNO2 CH3NHNHO + NO CH3NHNHONO c-CH3NHNH + NO2 t-CH3NNH + HONO c-CH3NNH + HONO CH3NHNHNO2 t-CH3NNH + HNO2 c-CH3NNH + HNO2 CH3NHNHO + NO CH3NHNHONO t-CH3NNH + HONO c-CH3NNH + HONO CH2NNH2 + HONO CH3N(NH2)NO2 t-CH3NNH + HNO2 c-CH3NNH + HNO2 CH2NNH2 + HNO2 CH3N(NH2)O + NO CH3N(NH2)ONO CH2NNH2 + HONO NH2NHCH2NO2 CH2NNH2 + HNO2 NH2NHCH2O + NO NH2NHCH2ONO

t-CH3NHNH + NO2

CH3NNH2 + NO2

CH2NHNH2 + NO2

A 1.23 5.92 8.94 1.56 4.70 3.65 1.46 6.42 1.85 1.67 4.64 1.51 4.40 3.65 1.97 1.81 2.06 1.29 4.86 5.27 1.91 4.62 1.62 1.15 5.40 5.09 2.07 8.45 3.52 2.49

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10−14 10−9 10−14 1061 10−13 10−14 10−14 1030 10−14 10−8 10−13 1061 10−12 10−13 10−13 1030 10−11 10−12 10−23 1072 10−12 10−15 10−21 10−7 1043 10−18 1060 10−31 10−30 1067

n

Ea/R (K)

0.45 −1.45 −0.11 −25.04 −0.10 0.07 0.35 −17.38 0.40 −1.54 −0.28 −25.03 −0.35 −0.19 0.0 −17.21 −0.77 −0.41 2.59 −27.83 −0.33 0.42 2.20 −1.56 −20.70 1.57 −25.40 5.14 5.11 −26.47

1063.8 98.9 −81.8 8570.2 1395.0 1376.0 1605.6 5759.4 966.8 202.0 58.1 8570.0 1544.9 1528.5 1776.2 5635.4 589.0 576.3 828.8 11511.1 1482.9 1434.6 1560.1 1800.0 8361.9 −815.3 9234.7 1510.1 1856.6 14672.1

various pressures is shown in Figure 3. Those for the reactions of NO with CH3N(NH2)O and NH2NH2O are shown in Figure S5 and S6 in the Supporting Information. The modified Arrhenius parameters for those at 1 atm in N2 are summarized in Table 5, and those at the other pressures are in Table S4 in the Supporting Information. In the case of NH2NHCH2O + NO, the activation energy for the roaming transition state (TS4) lies sufficiently high relative to the reactant. This makes it possible to simplify the reaction mechanism, such that the stabilization to NH2NHCH2ONO and the dissociation to CH2NNH2 + HNO2 were the only significant paths, as shown in Figure S6 (Supporting Information). On the contrary, the reactions of NO with CH3NHNHO and CH3N(NH2)O showed complicated product distributions depending on both temperatures and pressures. In the case of CH3NHNHO shown in Figure 3, the barrier height for the dissociation channel for trans-CH3NNH + HNO2 (TS5t) was significantly lower than that for the reactant, resulting in negligible contributions of the stabilization process at pressures below 1 atm. In contrast to that, the CH3N(NH2)ONO would be the dominant products for the CH3N(NH2)O + NO reaction (Figure S5, Supporting Information) at the low temperature conditions. Rate Coefficients for the Thermal Dissociations of RNO 2 and RONO. Finally, thermal dissociation rate coefficients of RNO2 and RONO were also calculated at 300−2000 K and 0.1−100 atm in N2. Figures 4 and 5 and Figures S7−S10 in the Supporting Information show the

Information. At high pressure and low temperature conditions, all of the above four reaction products were stabilized to RNO2. In the case of CH2NHNH2 + NO2 shown in Figure S4 (Supporting Information), which shows the lowest barrier for the dissociation channel of RNO2 (TS2), the stabilization to RNO2 and the dissociation to CH2NNH2 + HONO were the only significant paths under the whole calculated temperature and pressure ranges. A comparison between Figures 2 and S2 (Supporting Information) shows that the reactivities of cis-/ trans-CH3NHNH with NO2 were found to be similar to each other. In both cases, not only the cis-/trans-CH3NNH + HONO formation paths but also the catalytic isomerization path between CH3NHNH, i.e., cis-CH3NHNH + NO2 = transCH3NHNH + NO2, would become important at high temperature conditions. For the CH3NNH2 + NO2 reaction shown in Figure S3 (Supporting Information), which has the highest barriers for TS2 and TS5, the CH3N(NH2)O + NO formation path via excited CH3N(NH2)ONO* was expected to be important at high temperature or low pressure conditions. Although the NO formation paths via RONO* were found, stabilization pathways for RONO were negligible under the calculated conditions. Rate Coefficients for CH 3 NHNHO/CH 3 N(NH 2 )O/ NH2NHCH2O + NO. The reactions of NO with RO would be one of the expected subsequent reactions. Those rate coefficients were calculated on the same potential energy surfaces at 300−2000 K and 0.1−100 atm in N2. The Arrhenius plots for the rate coefficient for CH3NHNHO + NO reaction at 7663

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Figure 3. Arrhenius plots of CH3NHNHO + NO reaction rate coefficients at (a) 100, (b) 10, (c) 1, and (d) 0.1 atm in N2.

Figure 4. Arrhenius plots of thermal decomposition rate coefficients of CH3NHNHNO2 at (a) 100, (b) 10, (c) 1, and (d) 0.1 atm in N2.

Arrhenius plots for these at various pressures. At the condition of 1 atm in N2, the modified Arrhenius parameters for these reactions are summarized in Tables 6 and 7. These parameters at different pressures are also listed in Table S4 in the Supporting Information. For CH 3 NHNHNO 2 and

NH2NHCH2NO2, the main dissociation products were confirmed to be HONO with trans-CH3NNH (Figure 4) and CH2NNH2 (Figure S8, Supporting Information), respectively, due to the sufficiently lower barrier compared with the other channels. In the case of CH3N(NH2)NO2 shown in Figure S7

Table 5. Modified Arrhenius Parameter, k = ATn exp(−Ea/RT) cm3 molecule−1 s−1, for the CH3NHNHO/CH3N(NH2)O/ NH2NHCH2O + NO Reactions at 1 atm in N2 reactant

product

CH3NHNHO + NO

c-CH3NHNH + NO2 t-CH3NHNH + NO2 t-CH3NNH + HONO c-CH3NNH + HONO CH3NHNHNO2 t-CH3NNH + HNO2 c-CH3NNH + HNO2 CH3NHNHONO CH3NNH2 + NO2 t-CH3NNH + HONO c-CH3NNH + HONO CH2NNH2 + HONO CH3N(NH2)NO2 t-CH3NNH + HNO2 c-CH3NNH + HNO2 CH2NNH2 + HNO2 CH3N(NH2)ONO CH2NHNH2 + NO2 CH2NNH2 + HONO NH2NHCH2NO2 CH2NNH2 + HNO2 NH2NHCH2ONO

CH3N(NH2)O + NO

NH2NHCH2O + NO

A 1.52 1.34 3.08 2.07 1.03 2.23 8.43 9.07 1.64 4.26 1.68 5.91 9.69 1.03 3.42 9.04 9.83 3.05 2.77 2.43 1.21 9.44 7664

× × × × × × × × × × × × × × × × × × × × × ×

10−11 10−10 10−6 10−10 1060 10−11 10−13 1046 10−6 10−6 10−7 10−20 1073 10−18 10−19 10−22 1045 10−29 10−15 1055 10−9 1065

n

Ea/R (K)

−0.68 −0.92 −2.42 −1.28 −25.03 −1.04 −0.77 −21.90 −2.13 −2.64 −2.23 1.36 −28.33 0.99 1.17 1.88 −21.18 4.83 0.78 −23.99 −1.10 −24.93

3813.2 4081.3 3084.3 2982.3 10612.5 −179.5 −212.6 5536.5 5233.8 4222.2 4176.9 4105.8 14595.6 −108.7 916.2 2936.4 5189.1 9639.7 8504.7 17255.5 2951.7 12148.6 DOI: 10.1021/acs.jpca.5b00987 J. Phys. Chem. A 2015, 119, 7659−7667

Article

The Journal of Physical Chemistry A

and CH3NNH2 + NO2 formation paths would be also increased. As shown in Tables 1−3, the lowest barriers for the dissociation reactions of RNO2 were calculated to be 86.6, 106.1, and 118.2 kJ mol−1 for CH3NHNHNO2, CH3N(NH2)NO2, and NH2NHCH2NO2, respectively. According to these energies, the temperature dependence of total dissociation rate and hence the lifetimes of RNO2 at low temperature would increase in the above order. For the thermal dissociation of RONO, the RO + NO and HNO2 formation paths were revealed to be significant. Due to the high stabilization energy of the NH2NHCH2ONO, the total dissociation rate was quite slow at 300 K as shown in Figure S10 (Supporting Information), indicating that NH2NHCH2ONO would be stable and exist at such low temperatures. Implication to Thruster Modeling. For the efficient design of the MMH/NTO thruster, the understanding of the hypergolic ignition process, especially for the initial stage at ambient temperature, is important. At 300 K and 1 atm in N2, our previous study for MMH + NO2 reactions7 suggested that the product branching ratios for cis-CH3NHNH, transCH3NHNH, and CH3NNH2 would be 0.66, 0.21, and 0.13, respectively, and that for CH2NHNH2 was negligible. For cisand trans-CH3NHNH with NO2 reactions, the branching ratio for the main products at the same condition were calculated to be (trans-CH3NNH + HONO):(cis-CH3NNH + HONO): (CH 3NHNHNO2) = 0.87:0.05:0.08 and 0.88:0.05:0.07, respectively. In the case of CH3NNH2 + NO2, that was calculated to be (CH3N(NH2)NO2):(CH3N(NH2)O + NO): (trans-CH3NNH + HONO):(cis-CH3NNH + HONO) = 0.79:0.09:0.08:0.04. CH3NNH is expected to further react with NO2 to produce CH3NN, whose dissociation reaction to CH3 + N2 is considered as the main heat source for the hypergolic ignition.2 Therefore, the stabilization paths to CH3NHNHNO2 and CH3N(NH2)NO2 would have a retarding effect on hypergolic ignition. The rate coefficients proposed in

Figure 5. Arrhenius plots of thermal decomposition rate coefficients of CH3NHNHONO at (a) 100, (b) 10, (c) 1, and (d) 0.1 atm in N2.

(Supporting Information), the barrier height for HONO with cis- and trans-CH3NNH formation paths, i.e., TS2c and TS2t, were close to each other; thus, these channels were both important at low temperature. At the high temperature conditions, the contributions of the CH3N(NH2)O + NO

Table 6. Modified Arrhenius Parameter, k = ATn exp(−Ea/RT) s−1, for the Thermal Dissociation Reactions for CH3NHNHNO2, CH3N(NH2)NO2, and NH2NHCH2NO2 at 1 atm in N2 reactant

product

A

n

Ea/R (K)

CH3NHNHNO2

c-CH3NHNH + NO2 t-CH3NHNH + NO2 t-CH3NNH + HONO c-CH3NNH + HONO CH3NHNHO + NO t-CH3NNH + HNO2 c-CH3NNH + HNO2 CH3NHNHONO CH3NNH2 + NO2 t-CH3NNH + HONO c-CH3NNH + HONO CH2NNH2 + HONO CH3N(NH2)O + NO t-CH3NNH + HNO2 c-CH3NNH + HNO2 CH2NNH2 + HNO2 CH3N(NH2)ONO CH2NHNH2 + NO2 CH2NNH2 + HONO NH2NHCH2O + NO CH2NNH2 + HNO2 NH2NHCH2ONO

9.05 × 1033 7.19 × 1033 4.51 × 1033 2.46 × 1034 9.76 × 1029 1.15 × 1032 1.59 × 1031 7.72 × 1045 4.36 × 1049 6.35 × 1042 1.96 × 1044 7.91 × 1045 5.66 × 1049 1.47 × 1048 1.85 × 1047 2.89 × 1044 4.87 × 1069 1.50 × 1036 3.47 × 1039 2.11× 1030 9.63 × 1031 6.36 × 1094

−7.33 −7.30 −6.85 −7.38 −6.38 −6.84 −6.77 −13.62 −11.51 −9.66 −10.15 −11.27 −11.45 −11.32 −11.21 −10.89 −20.22 −8.75 −8.37 −7.07 −7.63 −27.43

17417.5 17531.4 12794.1 14487.3 17281.5 17265.6 17258.7 17935.3 20368.3 16823.3 17583.3 20609.9 20018.2 20094.3 20250.5 20813.9 21711.9 30822.1 18219.3 31062.2 31144.0 40031.8

CH3N(NH2)NO2

NH2NHCH2NO2

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DOI: 10.1021/acs.jpca.5b00987 J. Phys. Chem. A 2015, 119, 7659−7667

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The Journal of Physical Chemistry A Table 7. Modified Arrhenius Parameter, k = ATn exp(−Ea/RT) s−1, for the Thermal Dissociation Reactions for CH3NHNHONO, CH3N(NH2)ONO, and NH2NHCH2ONO at 1 atm in N2 reactant

product

CH3NHNHONO

c-CH3NHNH + NO2 t-CH3NHNH + NO2 t-CH3NNH + HONO c-CH3NNH + HONO CH3NHNHNO2 CH3NHNHO + NO t-CH3NNH + HNO2 c-CH3NNH + HNO2 CH3NNH2 + NO2 t-CH3NNH + HONO c-CH3NNH + HONO CH2NNH2 + HONO CH3N(NH2)NO2 CH3N(NH2)O + NO t-CH3NNH + HNO2 c-CH3NNH + HNO2 CH2NNH2 + HNO2 CH2NHNH2 + NO2 CH2NNH2 + HONO NH2NHCH2NO2 NH2NHCH2O + NO CH2NNH2 + HNO2

CH3N(NH2)ONO

NH2NHCH2ONO

A 5.34 1.14 9.04 3.74 1.73 3.09 4.92 3.89 3.58 2.31 4.99 2.32 3.15 1.13 2.24 3.42 2.79 7.08 7.07 8.27 8.52 2.98

n

Ea/R (K)

4.93 5.14 2.78 3.49 −13.06 0.06 −1.51 −1.40 0.93 0.57 0.70 1.32 −14.83 −2.46 −1.53 −0.04 2.48 −10.27 −11.36 −28.03 −8.59 −5.78

6313.4 6293.8 5915.7 5796.6 11957.1 4784.2 3296.1 3344.1 9203.8 8032.3 8094.6 9365.5 13805.9 4631.0 4544.7 4986.8 7517.4 33829.8 31912.9 37687.0 23593.4 18594.6

The authors declare no competing financial interest.

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IV. CONCLUSIONS The potential energy diagrams and the rate coefficients for the reactions of NO2 with CH3NHNH/CH3NNH2/CH2NHNH2 have been investigated by quantum chemical calculations and RRKM/master equation calculations. The results indicated that the reactivity of the above radicals with NO2 highly depends on the barrier height of the roaming transition states between RNO2 and RONO and those for dissociation paths. At ambient temperature and pressure, the reactions cis-/trans-CH3NHNH + NO2 and CH2NHNH2 + NO2 predominantly produce transCH3NNH + HONO and CH2NNH2 + HONO, respectively. On the contrary, CH3NNH2 + NO2 will recombine to thermally stable CH3N(NH2)NO2. The product-specific rate coefficients on the calculated potential energy surfaces were proposed for the detailed chemical kinetic models of the MMH/NTO bipropellant.

ACKNOWLEDGMENTS The authors thank A. Miyoshi (University of Tokyo) for helpful discussions. This study was supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (C) Grant Number 26420164.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Figures S1 of the IRC profile and Figures S2−10 of Arrhenius plots. Tables S1−4 of optimized geometries (S1), rotational constants and harmonic frequencies (S2), thermodynamic functions (S3) of the most stable isomers, and modified Arrhenius parameters for the investigated reactions (S4). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b00987.

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10−10 10−10 10−2 10−5 1046 108 1014 1013 105 106 105 101 1054 1018 1013 107 10−3 1042 1048 1094 1040 1030

Notes

the present study are useful for the accurate prediction of the hypergolic ignition phenomena for MMH/NTO bipropellant.

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× × × × × × × × × × × × × × × × × × × × × ×

AUTHOR INFORMATION

Corresponding Author

*N. Kanno. E-mail: [email protected]. Present Address ⊥

Department of Vehicle and Mechanical Engineering, Meijo University, Tempaku-ku, Nagoya 468-8502, Japan. 7666

DOI: 10.1021/acs.jpca.5b00987 J. Phys. Chem. A 2015, 119, 7659−7667

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NOTE ADDED AFTER ASAP PUBLICATION This article was published ASAP on May 22, 2015, with minor text errors. The corrected article was published ASAP on May 26, 2015.

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DOI: 10.1021/acs.jpca.5b00987 J. Phys. Chem. A 2015, 119, 7659−7667