Article pubs.acs.org/JPCA
Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX
Theoretical Investigation of the Reactivity of Sodium Dicyanamide with Nitric Acid Kristen M. Vogelhuber,†,‡ Ryan S. Booth,†,‡ and Christopher J. Annesley*,† †
Space Vehicles Directorate, Air Force Research Laboratory, Kirtland AFB, New Mexico 87117, United States Institute for Scientific Research, Boston College, Chestnut Hill, Massachusetts 02467, United States
‡
S Supporting Information *
ABSTRACT: There is a need to replace current hydrazine fuels with safer propellants, and dicyanamide (DCA−)-based systems have emerged as promising alternatives because they autoignite when mixed with some oxidizers. Previous studies of the hypergolic reaction mechanism have focused on the reaction between DCA− and the oxidizer HNO3; here, we compare the calculated pathway of DCA− + HNO3 with the reaction coordinate of the ion pair sodium dicyanamide with nitric acid, Na[DCA] + HNO3. Enthalpies and free energies are calculated in the gas phase and in solution using a quantum mechanical continuum solvation model, SMD-GIL. The barriers to the Na[DCA] + HNO3 reaction are dramatically lowered relative to those of the reaction with the bare anion, and an exothermic exit channel to produce NaNO3 and the reactive intermediate HDCA appears. These results suggest that Na[DCA] may accelerate the ignition reaction.
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INTRODUCTION Hydrazine and its derivatives are typically used in today’s spacecraft propulsion systems, but their reliability and efficiency come at the expense of difficult and hazardous handling and storage.1 The discovery that some energetic salts and ionic liquids (ILs) based on the dicyanamide anion (N(CN)2−, DCA−) undergo a hypergolic reaction (autoignite) when they come into contact with the oxidizer nitric acid (HNO3)1 prompted research into these safer, low-vapor-pressure alternatives2 to hydrazine. Although promising, the ignition delay, or the time delay between contact and ignition, of current DCA−-based systems is too long.3 To reduce ignition delays and tailor the system to meet propulsion delivery needs, it is necessary to better understand the hypergolic reaction mechanism so that accurate and predictive models can be developed. Over the past decade, the hypergolic reactions of nitric acid with DCA−-based salts and ILs have been studied in the condensed phase, in aerosols, and in the gas phase. Studies of HNO3 dropped into bulk liquid ILs have shown that ILs comprising imidazolium cations paired with DCA− anions are particularly promising; 4 for example, 1-propargyl-3methylimidazolium[DCA] exhibited a 15-ms ignition delay time,1 approaching the desired 5-ms delay necessary for thruster applications. The pure solid salt sodium dicyanamide (Na[DCA]) exhibits hypergolic behavior but ignites after longer delay times.4 Studies of the reaction of IL nanodroplets of 1-butyl-3-methylimidazolium[DCA] with nitric acid reveal rapid reactions near the surface of the IL aerosol.5 Using a different method to study this reactivity, isolated electrosprayed anions in a selected ion flow tube at 298 K showed that the reaction of gas-phase bare DCA− with HNO3 results in the formation of an unreactive adduct.6 © XXXX American Chemical Society
Because experiments have indicated that the reaction takes place primarily on the anion,4 most previous theoretical studies of the hypergolic reaction have focused on the reaction between the DCA− anion and HNO3.4,6−9 In 2008, Chambreau and coworkers proposed a generalized mechanism4 for the reaction of DCA− + HNO3 that was intended to imply fully solvated DCA−.5 The mechanism begins with the protonation of DCA− at the terminal N atom4,6 to form HDCA, followed by NO3− attack of the electrophilic C atom. The shift of NO2 to the terminal N yields the low-energy, mononitro intermediate HN4C2O3− that has been proposed to either react with a second HNO3 molecule to form dinitrobiuret,4 which decomposes into the products Chambreau and co-workers observed using FTIR,4 or decompose10 directly to the observed preignition products.11 The above DCA− + HNO3 reaction does not offer a complete picture, however. The calculated barriers5−7 to this proposed mechanism are relatively high for such a fast reaction, and this result was validated by experiments in which gas-phase bare DCA− + HNO3 did not react hypergolically.6 Previous studies have indicated that the hypergolic ignition takes place in the vapor above the IL,12 and ILs vaporize as ion pairs, although their vapor pressures are very low.13 Furthermore, the reactivity of ILs has been shown to inversely correlate with electron density of the cation,14 implying there may be a cation effect. More recent computational studies have begun to look outside of the fundamental DCA− + HNO3 reaction. Reactions of HNO3 with the intermediate HDCA have been calculated,5,7 as it is formed during the initial step in the hypergolic reaction Received: November 27, 2017 Revised: January 12, 2018 Published: January 31, 2018 A
DOI: 10.1021/acs.jpca.7b11661 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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Figure 1. Calculated gas-phase reaction coordinate of Na[DCA] + HNO3. Stationary points were calculated using M06-2X/6-311++G(d,p); zeropoint corrected energies (ΔH298K) are given in kcal/mol. Dashes denote transition states.
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sequence,4 and proton transfer from HNO3 to DCA− is favored at equilibrium in the condensed phase.13 Chambreau and coworkers showed that in the condensed phase, the reaction of HDCA + HNO3 is calculated to have lower free energy barriers, but also substantially less free energy release, than the bare DCA− + HNO3 reaction.5 In the gas phase, Schmidt and Gordon calculate the effective NO2 shift barrier to be lower for the reaction of HDCA + HNO3 than for DCA− + HNO3, although the earlier barriers are higher.7 Most recently, the effect of anionic and neutral boron clusters,7 which have been shown to reduce ignition delay,15−18 and the relationship between ionicity of the IL ion pair and ignition delay19 have been examined. However, the explicit calculation of the reaction coordinate of a DCA−-based ion pair plus HNO3 is lacking. It is therefore necessary to investigate the role, if any, of the cation in the energetics of these ignition reactions. In an effort to examine the effect of cations on the hypergolic reaction energetics, we have undertaken a theoretical study of the reactions of HNO3 with various DCA−-based IL ion pairs and clusters to complement future spectroscopic experiments. Germane to ignition delay, we focus on the energetics of the initial steps of the reaction mechanism to produce the lowenergy, mononitro intermediate HN4C2O3−. On the basis of the previous experimental work, three situations have been implicated: gas-phase anions, gas-phase ion pairs, and solvated anions. Here, we present the first theoretical studies of explicit cations in the gas phase as well as explicit cations solvated in IL. We found that the Na+ cation has a dramatic effect on the calculated reaction coordinate of DCA− + HNO3. Here, we report the calculated reaction coordinate of Na[DCA] + HNO3 in the context of DCA− + HNO3 and 1,3-dimethylimidazolium dicyanamide ([MMIM][DCA]) + HNO3 to show that this result is unique to the Na[DCA] system and is not a general cation effect. [MMIM][DCA] has been chosen for comparison because it serves as a representative of the imidazolium-based ILs at a reduced computational cost. In a forthcoming paper, we will present a more thorough discussion of the reaction of [MMIM][DCA] + HNO3, along with the reaction energetics and illustrated reaction coordinates of HNO3 with a series of dicyanamide-based IL ion pairs and clusters with imidazolium cations, including [EMIM][DCA].
THEORETICAL METHODS
Optimized geometries, energies, and vibrational frequencies were calculated using the Gaussian 0920 and Gaussian 1621 electronic structure calculation program hosted by the Department of Defense High Performance Computing Modernization Program. We use the M06-2X/6-311++G(d,p) functional and basis set to define the set of functions used to approximate molecular orbitals. We have chosen the M06-2X functional22 because good agreement has been demonstrated between MP2 calculations and the less computationally expensive M06-2X for ILs.23,24 We conservatively estimate error in the reported energetics to be approximately 2 kcal/ mol; we expect this to be an upper limit to the error because values reported here are relative to reactants. We performed a thorough search of conformations of Na[DCA] and found three minima; these conformers and their relative energies are given in Figure S1. The lowest energy conformer of these is used in this work. Experimental25 and recent theoretical4,6,7 studies agree that protonation of the terminal nitrile is preferred to protonation of the central N atom; thus, all calculations in this work assume protonation of the terminal nitrile. Previous calculations of the DCA− + HNO3 reaction coordinate6,7 serve as points of departure for our own calculations of reactions with nitric acid. State designations were chosen to preserve this framework. TSs were found through a combination of QST3 optimizations and relaxed potential energy scans along the appropriate internal coordinate. All TSs possess a single imaginary vibrational frequency corresponding to motion along the internal coordinate of interest. TSs 2/2.5, 2.5/3, 2/3.5, and 3.5/4 were confirmed via intrinsic reaction coordinate (IRC) analysis, and TS 3/3.5 was confirmed by relaxed potential energy scans. Displacement vectors of the imaginary frequencies are shown in Figure S2. IRC results are shown in Figure S3. Natural Bond Orbital (NBO) analysis was executed using the Gaussian 16 software package21 to provide more detailed information about bonding interactions than is available through visual inspection. NBO calculations were performed on geometries optimized at the M06-2X/6-311++g(d,p) level B
DOI: 10.1021/acs.jpca.7b11661 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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HNO3 calculated at the same level of theory is provided in Figure S4.) In all three systems, the reactants first associate to form a proton-bound complex, Intermediate (Int) 2. From here, the DCA− + HNO3 and [MMIM][DCA] + HNO3 reactions follow a similar path, with the MMIM+ cation providing moderate enthalpic (5.7 kcal/mol) destabilization of Int 2 and modest enthalpic (3.5 kcal/mol for TS 2/3 and 2.0 kcal/mol for TS 3.5/4) stabilization of the subsequent barriers (Figure 2). Following association, however, the reaction of Na[DCA] + HNO3 is qualitatively different from that of DCA− + HNO3 and [MMIM][DCA] + HNO3. In the reactions of DCA− and [MMIM][DCA] with HNO3, the proton is transferred and a C−O bond is formed in a concerted Transition State (TS) 2/3; however, in the reaction of Na[DCA] + HNO3, Int 2 passes through a nearly barrierless TS 2/2.5 to transfer the acidic proton to DCA−, forming the complex Int 2.5. Int 2.5 may then follow a path similar to that of the bare anion and [MMIM][DCA], involving a series of TSs to form a C−O bond (TS 2.5/3), rotate NO2 (TS3/3.5), and shift NO2 (TS 3.5/4) to form Int 4 (gray trace, Figure 1). While MMIM+ modestly lowers each of the barriers to the formation of Int 4 by a few kcal/mol of enthalpy, Na+ substantially lowers the C−O bond formation barrier by 14.2 kcal/mol and the NO2 shift barrier by 6.9 kcal/mol relative to the bare DCA− reaction, such that only the final barrier to the NO2 shift in the Na[DCA] + HNO3 system lies above the energy of the reactants (ΔH298 K(TS 3.5/4) = 6.1 kcal/mol). Thus, the presence of Na+ increases the likelihood that this reaction will proceed and create the first step in the implicated production of dinitrobiuret.4 Most striking, however, is the fact that in the reaction of Na[DCA] + HNO3, Int 2.5 may dissociate to HDCA + NaNO3 in a net exothermic reaction from the separated reactants, Int 1 (black trace, Figure 1). In the gas phase, the dissociation channel releases 4.6 kcal/mol of heat (ΔH298K), and all barriers to dissociation are submerged below the energy of the reactants (Figure 2a). The entropic increase provided by the dissociation makes the exit channel (black) even more favorable relative to the alternate (gray) pathway (Figure 2b); the exit channel has a net negative ΔG298K, while the pathway to Int 4 involves barriers above the energy of the reactants. This low-lying, kinetically favorable exit channel exists in the Na[DCA] system because Int 2.5 appears to be a complex of the products HDCA and NaNO3. To confirm this assertion, Natural Bond Orbital (NBO) analysis was performed on Int 2.5 in an effort to quantify the electrostatic interactions between the Na+, NO3−, and HDCA fragments; NBO provides the atomic charges as well as the extent of bonding interactions present in the molecular complex. Examination of the NBO bonds and charge distribution (Figure 3) of Int 2.5 confirms that it is a complex of NaNO3 + HDCA without significant bonding interaction between NO3− and the central π system of HDCA, indicating direct correlation with the separated products. There is strong interaction between Na+ and NO3− due to substantial donation from the NO3− group to Na+, as one finds in NaNO3 alone. Meanwhile, the overall charge of the HDCA unit is nearly neutral, showing that there is no significant charge delocalization onto this subunit that would provide significant bonding. The strong binding of this complex is due to an ion−dipole interaction between Na+ and NC, as well as weak O−H−N interactions at the opposite end of the complex, rather than interaction between NO3− and HDCA.
and visualized using GaussView 6. Charges reported throughout this Article represent the absolute NBO atomic charges. Energetics of the condensed phase reaction coordinates were calculated using the quantum mechanical continuum solvation model for ILs, SMD-GIL,26 at the M06-2X/6-311++G(d,p) level of theory in the solvent [EMIM][DCA]. We have chosen [EMIM][DCA] as the solvent due to alignment with the previously referenced experiments as well as availability of solvent parameters. The following SMD-GIL parameters were used for [EMIM][DCA]: ε = 11.00, n = 1.5329, γ = 66.07, α = 0.229, β = 0.265, ϕ = 0.231, and ψ = 0.000.26
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RESULTS AND DISCUSSION Gas-Phase Reactivity. The reaction coordinate of Na[DCA] + HNO3, calculated using M06-2X/6-311++G(d,p), is shown in Figure 1. The reaction path is based on the hypergolic reaction pathway proposed by Chambreau and coworkers4 and calculated by Nichols et al.6 and Schmidt et al.;7 the numbering scheme is based on that of Nichols et al.6 and has been modified as necessary to add newly discovered stationary points. The Na[DCA] + HNO3 reaction energetics (black/gray lines) are summarized and compared to those of bare DCA− + HNO3 (red line) and [MMIM][DCA] + HNO3 (green dots) in Figure 2. (The reaction coordinate of DCA− +
Figure 2. Energetics of the Na[DCA] + HNO3 gas-phase reaction (black and gray) as compared to those of bare DCA− + HNO3 (red and brown) and [MMIM][DCA] + HNO3 (green dots). (a) Zeropoint corrected energies (ΔH298K) as well as (b) free energies (ΔG298K) are calculated using M06-2X/6-311++G(d,p) and are given in kcal/mol. C
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Figure 3. Visualizations of the NBO bonds and charge distributions of the proton-transferred complex Int 2.5 in the Na[DCA] + HNO3 reaction, as well as the NBO bonds and charge distribution of Int 3 of the DCA− + HNO3 reaction.
The same dissociation channel to create HDCA is not as favorable in the bare DCA− reaction. In the bare DCA− reaction, we do not find the analogous proton-transferred Int 2.5 to facilitate the formation of NO3− + HDCA. In the absence of a cation, the proton is transferred to form HDCA at the same time that a bond is formed between C of DCA− and O of HNO3 (TS 2/3) to yield the proton-transferred complex Int 3 (Figure 2, Table S1). The NBO bonds and charge distributions of the proton-transferred intermediate (Int 3) of the DCA− reaction are shown in Figure 3. In the DCA− system, where there is no cation to which NO3− can bond, the NO3− group attacks the electrophilic C atom and forms a bond between the NO3− group and HDCA. As noted by Chambreau et al.,5 the dissociation DCA− + HNO3 → NO3− + HDCA could potentially take place in a barrierless reaction originating from Int 2. However, as shown in Figure 2, dissociation of DCA− + HNO3 (brown traces) is predicted to be much less thermodynamically favorable in the absence of Na+. Specifically, the dissociation DCA− + HNO3 → NO3− + HDCA is predicted to be 11.3 kcal/mol endothermic and 10.7 kcal/mol endoergic. Thus, the low-lying dissociation channel is significantly more favorable in the Na[DCA] system than in the DCA− system, indicating that the presence of Na+ could enhance hypergolic reactivity. Liquid-Phase Reactivity. Because these hypergolic reactions are proposed to proceed rapidly in the liquid phase, the energetics of these pathways were also calculated in the solvent [EMIM][DCA]. To do so, a quantum mechanical continuum universal solvation model27 applied to ILs, known as SMD-GIL, was employed.26 Enthalpies (panel a) and free energies (panel b) of the stationary points of the complex solvated in [EMIM][DCA], the IL most relevant to this system with available solvent parameters,26 at 298 K are plotted in Figure 4. We find that the same trends that emerged in the gas-phase calculations hold true in the condensed phase: the barriers are significantly lowered in the Na[DCA] + HNO3 reaction relative to the DCA− + HNO3 reaction. Similarly, the barriers that were modestly lowered by the MMIM+ cation in the gas phase are again only modestly lowered in the condensed phase (green dots, Figure 4); each of the barriers is lowered by less than 4 kcal/mol of enthalpy (ΔH298K) and less than 3 kcal/mol of free energy (ΔG298K) with the MMIM+ cation, which will be discussed further in a forthcoming paper.
Figure 4. SMD-GIL condensed phase energetics of the Na[DCA] + HNO3 reaction (black and gray) as compared to those of the bare DCA− + HNO3 reaction (red and brown) and the [MMIM][DCA] + HNO3 reaction (green dots) solvated in [EMIM][DCA]. Zero-point corrected enthalpies (ΔH298K) and free energies (ΔG298K) are calculated using M06-2X/6-311++G(d,p) and are given in kcal/mol.
The thermodynamics of the dissociation channel have also been considered in the liquid phase. In solution the Na[DCA] + HNO3 exit channel to produce HDCA and NaNO3 becomes completely barrierless in terms of ΔG298K (black trace, Figure 4b) when solvated in [EMIM][DCA]. For the Na[DCA] system, this exit channel is 12.9 kcal/mol exoergic and 12.3 kcal/mol exothermic (ΔH298K), and the release of this heat to the system is expected to help overcome subsequent reaction barriers and drive the hypergolic reaction. Consistent with these theoretical results, water-soluble crystals attributed to NaNO3 were observed from the condensed-phase reaction of Na[DCA] with a dilute aqueous solution of HNO3;11 however, this observation does not necessarily implicate the dissociation channel, as NaNO3 can also be formed through aqueous ion exchange. This reaction is expected to proceed as ion pairs because the SMD-GIL model predicts that neither Na[DCA] nor NaNO3 will readily dissociate when solvated in [EMIM][DCA]. The dissociation Na[DCA] → Na+ + DCA− is calculated to be 14.4 kcal/mol endothermic and 7.1 kcal/mol endoergic, and the dissociation Na[DCA] + HNO3 → Na+ + NO3− + HDCA is calculated to be 15.7 kcal/mol endothermic and 7.7 kcal/mol endoergic (Table S1). As in the gas phase, the condensed-phase dissociation exit channel is less favorable in the absence of the Na+ cation (brown traces, Figure 4). Solvated in [EMIM][DCA], the D
DOI: 10.1021/acs.jpca.7b11661 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A dissociation reaction DCA− + HNO3 → NO3− + HDCA is endothermic (ΔH298K = 13.8 kcal/mol), and ΔG298K is slightly greater than zero (ΔG298K = 0.6 kcal/mol). Using M06/631+G(d,p), Chambreau et al. calculated this dissociation to be 2.7 kcal/mol exoergic when solvated in a generic IL;5 this difference highlights the sensitivity to the details of this calculation. When compared to the strongly exothermic and exoergic dissociation reaction of Na[DCA] + HNO3 (black traces, Figure 4), this result indicates that the Na[DCA] complex will react to form HDCA faster than DCA− will react to form HDCA. Because protonation of DCA− to form HDCA is the initial step in the proposed hypergolic reaction sequence,4 and because the reaction of HDCA with HNO3 is predicted to change the effective barrier height of the hypergolic reaction in both the condensed phase5 and in the gas phase,7 the presence of a low-lying exit channel to produce the HDCA intermediate may act to fuel the reaction and potentially enhance bipropellant performance.
ORCID
Kristen M. Vogelhuber: 0000-0002-8439-4013 Christopher J. Annesley: 0000-0002-5877-803X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We gratefully acknowledge funding from the U.S. Air Force Office of Scientific Research (LRIR #15RVCOR171) under the Molecular Dynamics Program. This work was supported in part by a grant of computer time from the Department of Defense High Performance Computing Modernization Program at the AFRL DSRC.
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CONCLUSIONS In this work, we have presented the calculated reaction coordinate of HNO3 with Na[DCA], with comparisons to the bare anion DCA− and the IL ion pair [MMIM][DCA]. While the addition of the MMIM+ cation makes only modest changes to the reaction energetics, we have shown that the addition of Na+ dramatically lowers the barriers to produce Int 4. For example, in the gas phase, Na+ lowers the enthalpy (ΔH298K) barrier to C−O bond formation (TS 2.5/3) by approximately 14 kcal/mol relative to bare DCA−; the corresponding free energy barrier (ΔG298K) is reduced by approximately 12 kcal/ mol. SMD-GIL calculations find similar results in the condensed phase, where Na+ lowers the enthalpy barrier of TS 2.5/3 by approximately 15 kcal/mol and lowers the free energy barrier by approximately 11 kcal/mol relative to bare DCA−. Further, we have found that in the Na[DCA] + HNO3 system there exists a low-lying, net-exothermic exit channel to directly produce the reactive intermediate HDCA. This exit channel becomes even more favorable in the solution phase, where SMD-GIL calculations predict that the reaction of Na[DCA] + HNO3 solvated in [EMIM][DCA] is increasingly negative at each stationary point with no free energy barriers, indicating that the dissociation reaction is spontaneous.
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b11661. Illustration of Na[DCA] conformers and their relative energies; illustration of displacement vectors for the imaginary frequencies of Na[DCA] + HNO3 transition states; IRC and relaxed potential energy scan results of transition states; the DCA− + HNO3 reaction coordinate; table of gas-phase ΔH298K and ΔG298K as well as ΔH298K and ΔG298K of stationary points solvated in [EMIM][DCA]; and Cartesian coordinates of stationary points along the reaction coordinate of [Na][DCA] + HNO3 (PDF)
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*Phone: (505) 846-1042. E-mail: afrl.rvborgmailbox@kirtland. af.mil. E
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DOI: 10.1021/acs.jpca.7b11661 J. Phys. Chem. A XXXX, XXX, XXX−XXX
